SOLUTION: A certain airplane can maintain a speed, without the presence of wind, of 210 mi/h and goes in the direction N 30° E. A wind is blowing west at 30 mi/h. Determine the final bearin

Question 1168000: A certain airplane can maintain a speed, without the presence of wind, of 210 mi/h and goes in the direction N 30° E. A wind is blowing west at 30 mi/h. Determine the final bearing of the plane and its ground speed. Calculate the speed in mi/h and the bearing in degrees.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
Alright, let's break down this problem step by step to find the final bearing and ground speed of the airplane.
**1. Represent the Velocities as Vectors:**
* **Airplane's Velocity (relative to air, $\mathbf{v}_a$):**
* Magnitude: 210 mi/h
* Direction: N 30° E. This means 30° east of the north direction. In terms of a standard Cartesian coordinate system (where the positive x-axis is East and the positive y-axis is North), the angle with respect to the positive x-axis is $90^\circ - 30^\circ = 60^\circ$.
* Vector form:
$$\mathbf{v}_a = \langle 210 \cos(60^\circ), 210 \sin(60^\circ) \rangle = \langle 210 \cdot \frac{1}{2}, 210 \cdot \frac{\sqrt{3}}{2} \rangle = \langle 105, 105\sqrt{3} \rangle$$
* **Wind's Velocity ($\mathbf{v}_w$):**
* Magnitude: 30 mi/h
* Direction: West. This means it's along the negative x-axis.
* Vector form:
$$\mathbf{v}_w = \langle -30, 0 \rangle$$
**2. Determine the Ground Velocity ($\mathbf{v}_g$):**
The ground velocity of the airplane is the vector sum of its velocity relative to the air and the velocity of the wind:
$$\mathbf{v}_g = \mathbf{v}_a + \mathbf{v}_w = \langle 105, 105\sqrt{3} \rangle + \langle -30, 0 \rangle = \langle 105 - 30, 105\sqrt{3} + 0 \rangle = \langle 75, 105\sqrt{3} \rangle$$
**3. Calculate the Ground Speed (Magnitude of $\mathbf{v}_g$):**
The ground speed is the magnitude of the ground velocity vector:
$$|\mathbf{v}_g| = \sqrt{(75)^2 + (105\sqrt{3})^2} = \sqrt{5625 + 105^2 \cdot 3} = \sqrt{5625 + 11025 \cdot 3} = \sqrt{5625 + 33075} = \sqrt{38700}$$
$$|\mathbf{v}_g| \approx 196.72 \, \text{mi/h}$$
**4. Determine the Final Bearing (Direction of $\mathbf{v}_g$):**
The direction of the ground velocity vector can be found by calculating the angle it makes with the positive x-axis (East). Let this angle be $\alpha$.
$$\tan(\alpha) = \frac{\text{y-component}}{\text{x-component}} = \frac{105\sqrt{3}}{75} = \frac{7\sqrt{3}}{5} \approx 2.4249$$
$$\alpha = \arctan\left(\frac{7\sqrt{3}}{5}\right) \approx 67.65^\circ$$
This angle is measured counterclockwise from the positive x-axis (East). To express this as a bearing (relative to North or South), we need to convert it:
* Since the x-component (East) is positive and the y-component (North) is positive, the direction is in the Northeast quadrant.
* The angle with respect to the North direction is $90^\circ - \alpha$:
$$90^\circ - 67.65^\circ \approx 22.35^\circ$$
Since the angle is east of North, the final bearing of the plane is approximately N $22.35^\circ$ E.
**Summary of Results:**
* **Ground Speed:** Approximately $196.72$ mi/h
* **Final Bearing:** Approximately N $22.35^\circ$ E
Let me know if you'd like any part of this calculation explained in more detail!
Answer by ikleyn(52769)   (Show Source): You can put this solution on YOUR website!
.

In January, February, March and April of 2025, @CPhill (which is the synonym of the Google AI)
posted 1941 solved problems to this forum.

He posted them at the rate of 25-30 solved problems per day.
Some of them (many of them) were solved incorrectly.

During these months, I tried to check the incoming problems, but, surely, been a human, not a
computer tool, I was not able to check all of them at the same rate.

Therefore, starting from the end of April 2025, and during May and June 2025, I checked
the remaining problems- those of them where I was competent to check.

I did not check the advanced Statistics problems, since I am not an expert in this field.
I also did not check advanced Finance problems, where I am not an expert.

But I checked a lot of other problems.
So, this file below contains the list of problems that (in my opinion) are solved incorrectly by @CPhill.
This list contains 151 incorrectly solved problems, so far.

For most of them, I placed my correct solutions.

Now some statistical counts.

As I said, the full number of solutions posted by @CPhill was 1941.

Of them, a huge portion were advanced statistics problems, which I did not check.
Their number was 2/3 or 3/4 of all problems - I did not count them.

Also, I did not check advanced Finance problems.

I think (I estimate approximately) that I checked from 500 to 600 problems,
As I said, so far the number of incorrect solutions is 151.

This number 151 does not cover all erroneous solutions by @CPhill - the number
of his erroneous solutions is more: I could miss some of them.

But this ratio "wrong to checked" = "151 to 500 or to 600" is HUGE.
It characterizes the level of this modern/contemporary version of this AI.

        ********************************************

            Surely, it is unacceptable level for an AI.

        ********************************************

I am not an enemy to AI. But I want we all have right/correct understanding of what is the AI now
in solving school Math problems.

So, I hope that this my huge work on checking this AI is useful both for visitors of this site,
as well as for the developers of this AI.

Probably, in the future I will return to this checking, and then this list of erroneously solved problems will become greater.

ikleyn
June 29, 2025

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

            The list of problems solved incorrectly by @CPhill
      =====================================================

1208643
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1208643.html
We call a number cozy if every digit in the number is either a $3$ or next to a $3.$ For example, the numbers $333,$ $83,$ $303,$ and $3773$ are all cozy,
but the numbers $32423,$ $786,$ $340,$ and $3999$ are not cozy.
How many positive $10$-digit numbers are cozy?

1209502
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209502.html
Let be three positive numbers such that:
x^2 + y^2 + z^2 = 2(xy + xz + yz).
x + y + z + \frac{1}{xyz} > 4.

1209450
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209450.html
A triangle ABC, where |AB| = |AC|, a line CD is drawn from angle C and intersects side AB at D, such that |AD| = |CD| = |BC|.
Find the measure of angle A in degrees.

1193410
https://www.algebra.com/algebra/homework/playground/test.faq.question.1193410.html
Julita owes Jose the following am
a. 55,000 at the end of 4 years,
b. 48,000 at the end of 5 years, and
c. 75,000 due in 3 years from today at 9% converted quarterly.
What single payment at the end of 2 years will settle Julita’s
obligations if money is worth 15% converted monthly?

1193440
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1193440.html
A shipment of 10 items has two defective and eight non defective units. In the inspection of the shipment , a sample of units will be selected and tested.
If a defective unit is found , the shipment of 10 units will be rejected.
If a sample of four is selected , what is the probability that the shipment will be rejected?

1192630
https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1192630.html
the semiannual withdrawals possible over 4.5 years from an account earning 5.25% compounded semiannually
and starting with $11,000. (Round your answer to the nearest cent.)

1192634
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192634.html
In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance.
IQ test scores are normally distributed with mean 100 and standard deviation 16
a. What percentage of people would qualify for admittance to the school.
b. If the public school wishes 95 percent of all children to qualify for admittance,
what minimum IQ test score should be required for admittance?

1209484
https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1209484.html
Trapezoid ABCD has diagonals that cross at E. The area of triangle EDC is n².
If AB has length m and DC has length n, find the area of trapezoid ABCD in terms of m and n.
Diagram: https://ibb.co/svwxc0w

1192431
https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1192431.html
you are given 20 true false questions and required to find probability of almost 4 are correct?

1192508 (10)
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192508.html
A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood.
The device is not totally reliable: 7 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser
as being above the legal limit, while 10 % of drivers who are above the legal limit will give a reading below that level.
Suppose that in fact 14 % of drivers are above the legal alcohol limit, and the police stop a driver at random.
Give answers to the following to four decimal places.
Part a)
What is the probability that the driver is incorrectly classified as being over the limit?
Part b)
What is the probability that the driver is correctly classified as being over the limit?
Part c)
Find the probability that the driver gives a breathalyser test reading that is over the limit.
Part d)
Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.

1192522
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192522.html
It is estimated that approximately 8.37% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes
will correctly diagnose 98% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3% of all adults over 40
without diabetes as having the disease.
a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as having diabetes
(such diagnoses are called "false positives").
b) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes.
c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes
(such diagnoses are called "false negatives").
(Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)

1209504
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209504.html
Jamie spent 3/4 of her money on 3 books of the same price. Grace spent 5/9 of her money on 2 diaries.
They were each left with an equal amount of money. One book cost $3.30 more than one diary.
How much money did they have altogether.

1192298
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1192298.html%20algebra.com
Find the number of permutations of 10 numbers in a spinner.

1192052
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1192052.html
Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk.
The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed
is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school
and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour.
a) On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture,
so Nikita and Peter walk the rest of the way home. How far from school is Peeta when the cyclists arrive home?
b) On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back
towards school to collect Nikita. How far from school is Nikita when Reeta reaches her?
c) On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta hops off and walks the rest of the way,
while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike?
d) On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home. Meanwhile he returns to pick up Reeta
and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off and pick-up points?

Part (d) is interpreted and solved INCORRECTLY by @CPhill.

1209514
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209514.html
There were 220 chickens, ducks and goats on a farm. The ratio of chickens to ducks and goats is 3 to 2. The ratio of goats to ducks and chickens
is 1 to 3. What is the ratio of chickens to ducks to goats. If a goat is sold at $98 each, Find the amount if all the goats are sold.

1209515
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209515.html
There were some oranges in baskets A B and C. The ratio of A to B and C is 1 to 4.
The ratio of C to A and B is 3 to 4.
How many oranges were in C if there were 54 more oranges in B than in A.

1209520
https://www.algebra.com/algebra/homework/Polygons/Polygons.faq.question.1209520.html
Square SQUR has sides of length x. If triangle SQE is equilateral, find the area of triangle QAU.
Link to diagram: https://ibb.co/C58rZ09R

1192249
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192249.html
Hotel A and B offers 2 types of packages that include lodging only or lodging with
breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only
and 120 tourists choose Hotel B for lodging with breakfast.
Altogether 110 tourists choose to stay in Hotel A.
A tourist is selected randomly.
(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?
(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?
(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?
(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?

1192250
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1192250.html
Hotel A and B offers 2 types of packages that include lodging only or lodging with
breakfast. From a group of 300 tourists, 30 tourist choose Hotel A for lodging only
and 120 tourists choose Hotel B for lodging with breakfast.
Altogether 110 tourists choose to stay in Hotel A.
A tourist is selected randomly.
(a) What is the probability that the tourist chooses Hotel A or tourists chooses lodging only?
(b) What is the probability that the tourist to choose Hotel B for lodging with breakfast, if he chose Hotel B?
(c) What is the probability that the tourist to choose Hotel A, if he chose lodging without breakfast?
(d) What is the probability that the tourist chose Hotel A without breakfast or choose Hotel B with breakfast?

1209524 (20)
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1209524.html
Sector ABC is 1/12 of a circle with diameter 24k. Line segment AD is perpendicular to segment BC.
Find the area of the shaded region.
Link to diagram: https://ibb.co/5gNwX0K6

1191371
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1191371.html
Suppose you want to have $600,000 for retirement in 30 years. Your account earns 10% interest.
How much would you need to deposit in the account each month?

1190652
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190654.html
What is the present value of an ordinary annuity having semi-annual payments
of 8, 000 pesos for 12 years with an interest rate of 12% compounded annually?

1209532
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1209532.html
Point R is chosen on the circumference of a circle and arc PQ is drawn with R as its center.
If P and Q are joined, the line segment formed is a diameter of the circle with length 2r cm.
Find the area of the shaded region in terms of r, in square centimeters.
Link to diagram: https://ibb.co/GQFdy2SV

1186907
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1186907.html
The world production of gold from 1970 to 1990 can be modelled by G = 5.2t 2 - 76t + 1492, where G is the
number of tonnes of gold and t is the number of years since 1970, t = 1 for 1971 and so on.
a. What was the most amount of gold mined in one year?
b. How much gold was mined in 1978?

1186928
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1186928.html
For each of the following statements, explain why it is true for all functions f and g or give
an example of specific functions f and g showing that it is false.
a. All elements in the domain of g must be in the domain of f o g (fog)
b. All elements in the range of f must be in the range of f o g

1187156
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1187156.html
During the scholarship examination of a certain scholarship grant taken by 10,000 applicants,
Donnabelle's score was 350 greater than the scores of 8995 applicants who took the examination.
What is the percentile of Donnabelle's score?

1209553
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209553.html
If x + (24)^(⅓) = (16)^(⅓) + (36)^(⅓)
find (10³/x⁶) - (x³/10³) - (30/x³)

1186854
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1186854.html
Two vertices of a regular quadrilateral are A(0,4) and B(0,24). Which of the following could be the other two vertices?
a. C(4,4) and D(4,24)
b. C(24,4) and D(24,24)
c. C(8,24) and D(8,4)
d. C(0,8) and D(0,28)

1186205
https://www.algebra.com/algebra/college/linear/Linear_Algebra.faq.question.1186205.html
The Intellectual Company produces a chemical solution used for cleaning carpets.
This chemical is made from a mixture of two other chemicals which contain cleaning agent X and cleaning agent Y.
Their product must contain 175 units of agent X and 150 units of agent Y and weigh at least 100 pounds.
Chemical A costs ₱ 8 per pound, while chemical B costs ₱ 6 per pound.
Chemical A contains one unit of agent X and three units of agent Y.
Chemical B contains seven units of agent X and one unit of agent Y.
a. Set up the following:
i. Variables
ii. Constraints
iii. Objective Function
b. Find the minimum cost
c. Determine the best combination of the ingredients to minimize the cost.

1186248 (30)
https://www.algebra.com/algebra/college/linear/Linear_Algebra.faq.question.1186248.html
The Intellectual Company produces a chemical solution used for cleaning carpets.
This chemical is made from a mixture of two other chemicals which contain cleaning agent X and cleaning agent Y.
Their product must contain 175 units of agent X and 150 units of agent Y and weigh at least 100 pounds.
Chemical A costs ₱ 8 per pound, while chemical B costs ₱ 6 per pound.
Chemical A contains one unit of agent X and three units of agent Y.
Chemical B contains seven units of agent X and one unit of agent Y.
a. Set up the following:
i. Variables
ii. Constraints
iii. Objective Function
b. Find the minimum cost
c. Determine the best combination of the ingredients to minimize the cost.

1186455
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1186455.amp
On her recent birthday, April 22, 2001, Nicole was given by her mother a certain sum of money as birthday present.
She decided to invest the said amount on 20% exact simple interest. If the account will mature
on Christmas day at an amount of P 10,000.00, How much did Nicole receive from her mother on her birthday

1186235
beginning at the origin a spiral is constructed from three semmi-circles with centres at (1,0), (0,0) and (2,0)
the area of the shaded region in u^2 is?
https://drive.google.com/file/d/1OLUZW44XSyKqEXVuIhuwpkMDvT8E14xU/view?usp=sharing

1186272
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1186272.html
On a wall, 60 1/2 cm wide, Oscar is going to hang three pictures beside each other, each measuring 9 1/3 cm wide.
He will leave 3 1/2 cm in between each pair of adjacent pictures. He plans to use two nails to hang each picture,
and will centre these nails leaving 4 cm between each pair. How far, in cm, from the end of the wall(on either side)
will the first nail be placed?

1209558 <<<---=== solution for (a) is incorrect. solution for (c) is incorrect.
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209558.html
a) If 7^sin²x - 7^cos²x = 8
find the value of x.
b) Let m be a given real number, Find all complex numbers x such that,
([x/(x+1)]² + [x/(x-1)]² = m² + m
c) ab = ½, bc = ⅓, ac = 1/6,
find (1/a²) + (1/b²) + (1/c²)
d) 2^x - 3^y = 5
2^(x+2) + 3^(y+2) = 59.
find xy
e) find m,
9^4^m = 4^9^m
f) (7^log₈x)×(x^log₉x) = 3969,
find x.

1186068
Suppose events A and B are independent and
P(A) = 1/4

P(B) = 1/5
Find the probability. (Enter the probability as a fraction.)
_____
P(A ∩ B) the line is above a and b only

1186121
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1186121.html
Tickets for a raffle cost $12. There were 713 tickets sold. One ticket will be randomly selected as the winner,
and that person wins $1800 and also the person is given back the cost of the ticket.
For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?

1185780
https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1185780.html
The director of MIS Center At a large company wants to do stuff consulting station with two shifting teams:
Team A will compromise of 3 senior programmers and 3 system analyst and
team B will consist 2 senior programmers and 5 system analysts.
the director wants to use no more than 42 individuals.
There will be at least 48 hours to be filed during the week, with team A serving for 4 hours and the team B shift servings for 3 hours.
The cost of team A is 3200 per hour and 2800 per hour for team B shift.
Determine the number of shifts each team has to render in order to minimize the cost.
•What is the Test ratio for table 2?
•What is the pivotal/al column in Tableu 1?
•What is the result in the last row of Tableu 4?
•Show the proper representation of Tableu

1209595
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1209595.html
limit x (1 - 2 cos ((pi x)/(3 x - sqrt3))) as x \[LongRightArrow] + \[Infinity]

1209654
https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209654.html
Find the unique pair of real numbers (x,y) satisfying
(6x^2 - 18x + 17) + (3y^2 + 6y + 11) = 28
and x + y = 20.

1209644 (40)
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209644.html
Find all complex solutions to the equation z^8 + 144 = 25z^4 + 10z^6 + 10z^2.

1209645
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209645.html
Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.

1209660 <<<---=== the problem is posed incorrectly, and the answer by @CPhill is incorrect
https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1209660.html
Find the conic section represented by the equation
x^2 - 4x + y^2 = y^2 + 8x + 20

1209701
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209701.html
Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - i \sqrt[3]{3}$.
Give your answer in expanded form.

1209688 <<<---=== Fake problem and wrong solution/answer by @CPhill
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209688.html
The polynomial
f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66
has one integer root. What is it?

1184157
https://www.algebra.com/algebra/homework/Distributive-associative-commutative-properties/Distributive-associative-commutative-properties.faq.question.1184157.html
Construct two examples of bijective function from ZxZ to Q where Z is set of all integers and Q is set
of rational numbers.

1184450
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1184450.html
A certain class has 11 students, 2 of whom are sisters. The class needs to be split across three rooms
for a socially distanced exam, where room A can seat 2 students, room B 3 students, and room C 6 students.
How many ways can the students be divided across the rooms, if the 2 sisters are not allowed to be in
the same room (say, for academic integrity) ?

1184115
https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1184115.html
Berlin and Cheryl had a total of 6750 stamps. At first, Andy have 50%
of his stamps to Berlin. Berlin then gave 1/3 of her stamps to Cheryl.
Finally, Cheryl gave 1/6 of her stamps to Andy. In the end, the ratio of the
number of Andy’s stamps to the number of Berlin’s stamps became 4:5.
Cheryl had twice the total number of stamps that Andy and Berlin had.
How many stamps did Berlin and Cheryl have in total at first?

1174471
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1174471.html
To save for retirement, Karla Harby put $500 each month into an ordinary annuity for 10 years.
Interest was compounded monthly. At the end of the 10 years, the annuity was worth $84,608.
What annual interest rate did she receive?
The interest rate she received was approximately ___%

1174826
https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1174826.html
find the equation of parabola which has contact of third order with the conic ax^2 +2hxy + by^2 +2gx +2fy +c =0 at origin.

1209808 (50)
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209808.html
Find the value of θ,
sin(20°)*sin(θ) + sin(100°)*sin(20 - θ)° = 0

1209677
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209677.html
When g(x) is divided by x^2 - x - 6, the remainder is 2x + 7. What is the value
of g(8)?

1209710
https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1209710.html
4^(1/√x) + 16^(1/√x) = 64^(1/√x)

1209712
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209712.html
If (x√x)^(1/x) = 2, find x.

1181712
https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1181712.html
A rocket is being launched vertically over a point 𝐴 on the ground with
a velocity of 550 𝑚𝑖Τℎ𝑟. Twenty five miles away from point 𝐴 on the
ground, there is a photographer video-taping the launch. At what rate
is the angle of elevation of the camera changing when the rocket
achieves an altitude of 25 miles?

1181729
https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181729.html
The diameter of a sphere coincides with the axis of a right circular cone, and the surface of the cone intersects the surface of the sphere in in a great circle. Find
(a) the vertical angle of the cone:
(b) the volume of the cone;
(c) the volume common to the two solids:
(d) the volume of that portion of the cone which lies outside the sphere:
(e) the volume of that portion of the sphere which lies outside the cone. Denote radius of sphere by R.
Solve Problem if (a) R=2: (b) R=3.72.

1181730
https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181730.html
The center of each of three spheres of radius R lies in the surfaces of the other two.
Pass a plane containing the centers of the spheres.
Find the area common to the three great circles cut from the spheres by this plane.

1181731
https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1181731.html
A sphere is inscribed in a right circular cone of altitude h and radius of base r.
Write a formula in terms of r and h for the volume of the sphere.

1181618
https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1181618.html
Modern oil tankers weigh more than a 1/2 million tons and have lengths up to one - fourth mile. Such massive ships require a distance of 5.0 km about (3.0 mi)
and a time of 20 minutes to come to a stop from top speed of 30 km/h.what is the magnitude of such ship's average acceleration in m/s squared in coming to a stop?
B. What is the magnitude of the ship's average velocity in m/s

1209741
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209741.html
If 1/9^(1/x) + 1/3^(1/x) = 30,
find x.

1209729 (60)
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209729.html
Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.

1209740
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209740.html
Factor x^2 - 2x - y^2 + 2yz + 5z^2 as the product of two polynomials of degree 1.

1209728
Let r, s, and t be solutions of the equation 3x^3 - 4x^2 - 2x + 12 = 0.
Compute (rs)/t^2 + (rt)/s^2 + (st)/r^2.

1209735
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209735.html
69% of all Americans are home owners. If 37 Americans are randomly selected, find the probability that
a. Exactly 27 of them are are home owners.
b. At most 27 of them are are home owners.
c. At least 23 of them are home owners.
d. Between 23 and 28 (including 23 and 28) of them are home owners.

1209737
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1209737.html
The dots on the opposite faces of a die have a sum of 7.
How many different sum of dots on three adjacent faces are there on a die?

1209731
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209731.html
Let r, s, and t be solutions of the equation x^3 + 2x^2 - 5x + 15 = 0. Compute
1/(r - 2s - 2t) + 1/(s - 2r - 2t) + 1/(t - 2r - 2s)

1180634
https://www.algebra.com/algebra/homework/equations/Equations.faq.question.1180634.html
This pandemic, Abheedette learned to bake while on home quarantine.
She also realized that she will be able to make P60.00 profit per tray of banana muffins
and P120.00 profit per tray of blueberry muffins.
She needs 2 cups of milk and 3 cups of flour to bake a tray of banana muffins.
And, baking a tray of blueberry muffins takes 4 cups of milk and 3 cups of flour.
She has 16 cups of milk and 15 cups of flour.
How many trays of each flavor must be baked to maximize the profit?
a. Define the variable used:
b. LP Model:
c. Identify the feasible region:
d. Corner Points and the objective functions:
e. Optimal Solution (final answer):

1209745
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209745.html
in the blanks, to complete the factorization:
(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)

1180382
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1180382.html
a particle jumps between three positions A, B, and C. If it starts at A, it stays at A with probability 44%,
and it goes to B with probability 18% and to C with probability 26%. If, however, it starts at C, it goes to A with probability 51%
and to B with probability 16%.
Find the transition matrix.
If the particle stays at A, what is the probability that it stays at A after three jumps?

1179711
Determine the periodic payments on the given loan or mortgage.
$5,000,000 borrowed at 7% for 30 years, with quarterly payments

1179768 (70)
The problem on pendulum
https://gyazo.com/78c37f667cf2af63efadea4314e5642c

1179791
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1179791.html
If the area (in square units) of the region under the curve of the function f(x) = 3x − 1 on t he interval [a, 4],
where a < 4, is 12 square units, identify all the possible values of a.
what values are correct?
a. -3
b. 0
c. -16/5
d. 8/3
e. -2
f. 7/2

1179819
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1179819.html
Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly.

1179653 - about a pendulum, horizontal displacement.
https://gyazo.com/848645a235363970dae8196a58a2bbdc

1179602
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1179602.html
If 35% of the people in a community use the emergency room at a hospital one year.
Find these probabilities for a sample of 12 people
A) exactly 4 used the emergency room
B) At most 4 used the emergency room
C) At least 10 used the emergency room

1209768 <<<---=== incomplete solution: one solution is found; other solution is missed
https://www.algebra.com/algebra/homework/playground/lessons/test.faq.question.1209768.html
If a = sin50(1 + 2cos170°),
b = sin170°(1 + 2cos140°),
c = sin140°(1 + 2cos50°),
then (3 - 2A)ˣ = (x + 1)²,
find x

1209770 <<<---=== Total, global and fatal deceiving of a reader
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209770.html
Find all (real or nonreal) x satisfying
(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).

1179081 <<<---=== The problem is non-sensical. The solution by @CPhill is non-sensical, too.
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1179081.html
Nick has been depositing $190 in a savings account every three months for the past three years. This account paid 3 % convertible quarterly.
Nick has just made the last deposit. Nick is buying a car for $ 14000. He is taking out a car loan. He will use the accumulated value of his savings account
as the downpayment on the car. The loan is at 3 % convertible semiannually and has a term of 4 years. Find the size of Nick's monthly car loan payment.

1209773
https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.1209773.html
If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + a_1 = 17,
a_{18} + a_{19} + a_1 + a_2 = 18,
a_{19} + a_1 + a_2 + a_3 = 19,
what is the value of a_19?

1178715
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1178715.html
Solve each problem.
1. Your monthly electric bill has a mean of ₱120.00. what is the percentage that you will pay an amount between ₱1,380 and ₱1,740?
2. Suppose the scores in the mathematics exam are normally distributed. If the exam has a mean score of 25 and a standard deviation of 5,what is the probability that if you take th

1178377 (80)
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1178377.html
Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90,
and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2.
A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2.
A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2.
Formulate this as an LP problem to minimize the cost of the dog food. How many
pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?

1209775 <<<---=== AI produced the same wrong solution, kind of gibberish, and I reported to AI
https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209775.html
Let a, b, c, and d be distinct real numbers such that
a = sqrt(4 + sqrt(5 + a)),
b = sqrt(4 - sqrt(7 + b)),
c = sqrt(4 + sqrt(9 - c)),
d = sqrt(4 - sqrt(11 - d)).
Compute abcd.

1209776 <<<---=== the "solution" by @CPhill is unreadable gibberish
https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209776.html
Suppose the real numbers $a$, $b$, $x$, and $y$ satisfy the equations
ax + by = 3,
ax^2 + by^2 = 5,
ax^3 + by^3 = 17,
ax^4 + by^4 = 23.
Evaluate ax^5 + by^5.
See the solution at AoPS under this link
https://artofproblemsolving.com/wiki/index.php/1990_AIME_Problems/Problem_15?srsltid=AfmBOoq3eeok8NtsAuOBNtICcVv9fxgXqq0z4Tix5v0NoDfFL11W2Z72

1209790
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209790.html
If x^x = 5, find x^x^(x+1).

1177476 <<<---=== part (a) was solved INCORRECTLY by @CPhill
https://www.algebra.com/algebra/homework/playground/test.faq.question.1177476.html
There are 150 people at an International Medical Conference.
40 are Africans, 70 are women and 110 are doctors.
12 of the women are Africans, 46 of the doctors are women and 31 of the Africans are doctors.
If 5 of the African men are not doctors:
(a) how many of the African women are doctors ?
(b) how many of the men are neither African nor doctors?

1177187
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1177187.html
Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses
to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds.
Determine the equation of a sinusoidal function that would model this situation, assuming
Owen reaches his first maximum at 6 seconds.

1176885
https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1176885.html
If a simple, connected, graph has 20 vertices, what is the maximum number of edges it can have?
(Recall that a simple graph does not have loops and does not have multiple / parallel edges)

1176989
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1176989.html
EVOL is a cyclic quadrilateral, inscribed in a circle with center S. Given that the radius of this circle
is 25 in. and angle VEL is 55 degrees, explain your work to find the following measurements.
a) Length of Major Arc VL
b) Angle measure of Minor Arc VL
c) Angle VOL
d) Length of Chord VL

1177001
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1177001.html
EVOL is a cyclic quadrilateral, inscribed in a circle with center S. Given that the radius of this circle
is 25 in. and angle VEL is 55 degrees, explain your work to find the following measurements.
a) Length of Major Arc VL
b) Angle measure of Minor Arc VL
c) Angle VOL
d) Length of Chord VL

1176067 <<<---=== Inaccurate/icorrect calculations
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1176067.html
state lotto has a prize that pays $1,700 each week for 40 years.
Find the total value of the prize.
If the state can earn 3% interest on investments, how much money will they need to put
into an account now to cover the weekly prize payments?

1209804 (90)
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209804.html
If sinx + sin²x + sin³x = 1,
find cos⁶x - 4cos⁴x + 8cos²x

1176479
https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1176479.html
Given seven equal circles on a hexagonal grid, how many permutations are possible where circles are always adjacent
(repetitions such as inversions and reflections excluded)?

1209808
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209808.html
Find the value of θ,
sin(20°)*sin(θ) + sin(100°*sin(20 - θ)° = 0

1209794
(x+4)^2/9+(y+3)^2 /4 =1

1177711
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1177711.html
Roll a die once. Then roll it as many times as the outcome from the first roll.
Getting the special number "3" on any roll means a win.
What is the expected number of wins from this experiment?

1177712
A box has 3 red and 4 black balls. You randomly take one ball at a time without putting it back in.
Stop as soon as all the black balls are drawn out of the box. How many red balls do you expect to be left in the box?
(Hint: find the expected value of the properly defined random variable)

1209827
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209827.html
Find a closed form for S_n = 1!*(1^2 + 1) + 2!*(2^2 + 2) + . . . + n!*(n^2 + n)
for any integer n >= 1.

1209826
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209826.html
S_k = 1*(1^2) + 2!*(2^2)*3 + . . . + k*k!*(k + 1).
Find a closed form for S_k.

1173952
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1173952.html
A spheroid (or oblate spheroid) is a surface obtained by rotating an ellipse around its minor axis the ball
in figure 1.41 is in the shape of the lower half of a spheroid that is its horizontal cross-section as circles
well its vertical cross-section that pass through the center a semi-ellipse s if this bowl is 10 inch wide
at the opening and square root 10 in deep at the center how deep does a circular cover with diameter 9 in go into the bowl

1174226 <<<---=== what is presented by @CPhill as "the solution", is a complete gibberish.
https://www.algebra.com/algebra/homework/Average/Average.faq.question.1174226.html
A ladder 4m long at a construction site is resting against a wall. The bottom of the ladder is slipping away from the wall.
Find the estimate of the instantaneous rate of change of the Height H of the top of the ladder with respect to the Distance D
of the bottom of the ladder from the wall when the bottom of the ladder is 2.5m away from the wall.
Use h = 0.01 as the central interval.

1209832 (100)
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1209832.html
A body of weight 500N rests on a plane inclined at 20o to the horizontal. The coefficient of friction
is 0.4, determine a force F at an angle of 15o to the plane required to
(a) Pull the body upwards
(b) Push the body downwards
(c) Pull the body downwards
(d) Push the body upwards

1173392
In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject,
and the rest are optional. How many arrangements of the subjects are available for the students?

1172965
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1172965.html
A certain household would like to buy a washing machine set payable for 6 months starting at the end of the month.
How much is the cost of the washing machine if the monthly payment amounts to $3000 and interest is 9% compounded semi-annually?

1172947
The Whittier Company needs to produce 40 units of Product A tomorrow. They can produce on either machine X or machine Y or both.
Each unit of Product A when pro cessed on machine X takes 30 minutes of time, while a unit processed on machine Y takes 25 minutes.
It costs the company $2 per minute and $3 per minute respectively to operate machines X and Y.
Tomorrow, machine X has only 10 hours available to produce Product A, while machine Y can be operated as long as desired.
Use the graphical method to deter mine how many hours to schedule on each machine to minimize production costs.
Draw the isocost lines corresponding to production costs of $2,500, $2,700, $3,000, and $3,500.
Which of the isocost lines result in a feasible but suboptimal solution: Which line is both feasible and optimal? Which is not feasible?

117902
In a class of 50 students 24 like football 21 basketball and cricket six like football and basketball 3 like basketball only,
five like all three games, and 14 did not like any of the three games.
1.illustrate this information of Venn diagram
2. Find the number of students who like
A. Football and cricket
B. Exactly one of the game
C. Exactly two of the game.

1172981
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1172981.html
The Truth in Lending Law requires all lending institutions to fully disclose interest rates on all loans.
$5000 is loaned for 36 months with monthly payments of $162.50. Determine annual interest rate.

1171791
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1171791.html
a predator requires 21 units of food A 12 units of food B, and 21 units of food C as its average daily consumption.
these requirements are satisfied by feeling on two prey species.
one prey of species A, provides 6,2 and 3 units of food of A,B, and C, respectively.
to capture and digest a prey of species B provides 3,3 and 5 units of A, B and C, respectively.
to capture and digest a prey of species A requires 7 units of energy, on the average.
the corresponding energy.
How many preys of each should the predator capture to meet its food requirement with minimum expenditure?
find the objective function, constraints and max/min value.

1171394
27 % adults favor the use of unmanned drones by police agencies.
Twelve U.S. adults are randomly selected. Find the probability
that the number of U.S. adults who favor the use of unmanned drones by police agencies is
(a) exactly three,
(b) at least four,
(c) less than eight.
(a) P(3)=

1209876
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209876.html
Polynomials-and-rational-expressions/1209876: Find the largest value of x where the plots of
f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}

1209874
https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1209874.html
Let (x,y,z) be the real solution to the system of equations
x + y = \sqrt{4z + 3}
y + z = \sqrt{4x - 1}
z + x = \sqrt{4y + 5}
Find x + y + z.

1171432 (110)
https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1171432.html
#1. Log2(3x-7)+log2(x+2)=log2(x+1) <<<---=== the solution is incorrect.
#2. Log2(3x+1)-log2(2-4x)>log2(5x-2)

1209929
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1209929.amp
The Pireras are planning to go to Europe 4 years from now and have agreed to set aside $180/month for their trip.
If they deposit this money at the en each month into a savings account paying interest at the rate of 3%/year
compounded monthly, how much money will be in their ‘travel fund at the end of the fourth year?
(Round your answer to the nearest cent.)

1209924
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209924.html
Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

1209908
Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2,
then what is the maximum value of wxyz?

1170818
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1170818.html
A company claims to have invented a device that can measure the momentum of objects inside it with extreme
accuracy. The device fits within a matchbox, and the claimed precision with which it can measure momentum is
δp = ±10^−26kg ms^−1
Explain why the claimed performance cannot possibly be accurate, and estimate the smallest possible size of a
device with such momentum precision, according to laws of quantum physics.

1209937 <<<---=== the problem itself is SELF-CONTRADICTORY non-sensical gibberish
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209937.html
Let f be a function such that
f(xy) + x = xf(y) + f(x) + xy^2
for all real numbers x and y. If f(-1) = 3, then compute f(100).

1209938
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209938.html
Let f be a function such that
f(x) + f(2x + y) + 5xy = f(4x - y) - x^2 + 5xy - 8x + 17y + 1
for all real numbers x and y. Find f(10).

1209952
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209952.html
The function f(n) is defined for all integers n, such that
f(x) + f(y) = f(x + y) - 4xy - 1 + f(x^2) + f(y^2)
for all integers x and y, and f(1) = 1. Find f(n).

1209950
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209950.html
The function f(n) takes the integers to the real numbers such that
f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn
for all integers m and n, and f(1) = 2. Find f(n).

1209949
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209949.html
The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
f(x)*f(y) - f(xy) = -2x - 6y + 10
for all x, y \in \mathbb{R}. Find f(x).

1209964 (120)
https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1209964.html
ACDF is a Parallelogram. DEF is a sector. ABC is a right triangle. Solve for the area of the composite figure.
https://ibb.co/MyW8MZ2P

1209959
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209959.html
A club buys tickets for 15 seats in a row for a local production and then sends the tickets randomly
to the 15 people who ordered seats. Of these 15 people, 9 are actors and 6 are backstage workers.
Find the probability that:
(a) An actor and backstage worker will receive tickets sitting together.
(b) The actors will be seated together, and the backstage workers will be seated together.

1209960
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209960.html
55% of all shark attacks are not fatal. Let r be the number of nonfatal attacks out of a random sample of five shark attacks.
(a) What is the probability all five shark attacks are nonfatal?
(b) What is the probability that three or more of the five shark attacks are nonfatal?
(c) What is the expected number of nonfatal shark attacks out of the five?
(d) What is the standard deviation of the r-probability distribution?

1210228
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210228.html
Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5.
(Note that for the empty subset, we take the sum of the elements as 0.)

1169789
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1169789.html
Given a right pyramid ABCDE, on a square base ABCD, with AB = 8 cm, and height EO = 5 cm,
what are the values of the following:
(a) angle EAB
(b) angle β between a slant edge and the plane on the base.
(c) angle θ between a slant face and the plane on the base.

1210155
https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.1210155.html
ABCE is a Parallelogram. ADEF is a Rhombus. Find the area of the composite figure.
https://ibb.co/Jj2jKPD3

1210151
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1210151.html
In many ways can the letters of "lyltalqdr" be arranged such that no letter remains in its original position?

1168949
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1168949.html
A quilt is made up of strips of cloth, starting with an inner square
surrounded by rectangles to form successively larger squares.
The inner square and all rectangles have a width of 1 foot.
Write an expression using summation notation that gives the sum of
the areas of all the strips of cloth used to make the quilt shown.
Then evaluate the expression.

1168977
https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.1168977.html
Conjugate axis along the y-axis, ome vertex at (0,7), asymptotes are 6x-5y+30=0 and 6x+5y-30=0.
Need help finding the Equation of this hyperbola. How?

1169051
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1169051.html
The sample of work produced by lathe is 10000.
a. If the machine doubled this production every 20 minutes, how much will it produce
in one hour?
b. How long will it take the machine to produce 8 million?

1210173 (130)
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1210173.html
Let P be a point chosen uniformly at random inside triangle ABC. Extend ray BP to hit side AC at D.
What is the probability that BD < 4 ?
The sides of triangle ABC are 3, 5, and 7.

1210172
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210172.html
Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals
intersect at an endpoint? Consider rotations and reflections distinct.

1210184
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210184.html
I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next
three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.
How many seven-digit telephone numbers can I remember?
(For this problem, a telephone number cannot start with a 0.)

1210183
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210183.html
In how many ways can we seat 3 pairs of siblings in a row of 10 chairs, so that nobody sits next to their sibling?
(Two chairs will be left empty, of course.)

1168409
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1168409.html
73% of all Americans live in cities with population greater than 100,000 people.
If 35 Americans are randomly selected, find the probability that
a. Exactly 26 of them live in cities with population greater than 100,000 people.
b. At most 26 of them live in cities with population greater than 100,000 people.
c. At least 25 of them live in cities with population greater than 100,000 people.
d. Between 21 and 25 (including 21 and 25) of them live in cities with population greater than 100,000 people.

1210201
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1210201.html
Let ABCD be a square with side length 1. A laser is located at vertex A, which fires a laser beam at point X on side BC,
such that BX = 2/3. The beam reflects off the sides of the square, until it ends up at another vertex; at this point,
the beam will stop. Find the length of the total path of the laser beam. The diagram is linked below
https://artofproblemsolving.com/texer/zqcbfanp

1210212
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210212.html
How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit,
and the sum of the digits is 6?

1210211
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210211.html
How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit,
and the sum of the digits is 6?

1210210
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210210.html
How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

1210204
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210204.html
Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other,
no two Cs are next to each other, and no two Ds are next to each other.

1209733 (140)
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1209733.html
60% of all violent felons in the prison system are repeat offenders.
If 45 violent felons are randomly selected, find the probability that
a. Exactly 26 of them are repeat offenders.
b. At most 29 of them are repeat offenders.
c. At least 29 of them are repeat offenders.
d. Between 25 and 33 (including 25 and 33) of them are repeat offenders.

1168408
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1168408.html
64% of all violent felons in the prison system are repeat offenders.
If 48 violent felons are randomly selected, find the probability that
a. Exactly 28 of them are repeat offenders.
b. At most 30 of them are repeat offenders.
c. At least 32 of them are repeat offenders.
d. Between 28 and 34 (including 28 and 34) of them are repeat offenders.

1168513
https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1168513.html
Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month
for 3 1/2 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?

1210228
https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1210228.html
Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)

1209711
https://www.algebra.com/algebra/homework/playground/test.faq.question.1209711.html
[x-(1/x)]^(1/x) + [1-(1/x)] ^(1/x) = x

1209827
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209827.html
Find a closed form for
S_n = 1! \cdot (1^2 + 1) + 2! \cdot (2^2 + 2) + \dots + n! \cdot (n^2 + n).\]
for any integer n \ge 1. Your response should have a factorial.

1209826
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1209826.html
For a positive integer k, let
S_k = 1 \cdot 1! \cdot 2 + 2 \cdot 2! \cdot 3 + \dots + k \cdot k! \cdot (k + 1).
Find a closed form for S_k.

1179819
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1179819.html
Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly

1209870
https://www.algebra.com/algebra/homework/Functions/Functions.faq.question.1209870.html
Fill in the blanks.
(a) If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.
(b) If f(x) is an odd function and g(x) is an odd function and h(x) is an even function, then f(x)*g(x) + h(x) is an ___ function.
(c) If f(x) is an even function and g(x) is an odd function and h(x) is an odd function, then f(x)*(g(x) + h(x)) is an ___ function.
(d) If f(x) is an odd function and g(x) is an even function and h(x) is an odd function, then f(x)*g(x)*h(x) is an ___ function.
The answer to (d) in the post by @CPhill is incorrect.

1209715
https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.1209715.html
P(x) be a polynomial of the form
P(x) = 2x^3 + ax^2 - 23x + c,
such that 12 and 7 are roots of P(x). What is the third root?
For the polynomial in part (a), compute the ordered pair (a,c).

1190651 (150)
https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html
What is the future value of an ordinary annuity having daily payments of 50 pesos for 30 days with an rate of 20% compounded daily?

1209897
https://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.1209897.html
Let x and y be real numbers satisfying
\frac{x^2y^2 - 1}{2y - 1} = 4x + y.
Find the largest possible value of x.

ikleyn
June 29, 2025

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