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What is the smallest integer value of k such that (1/2)to the power of k < 0.001?







9.965784 < k

k > 9.965784

Since k > 9.965784, then the smallest integer value of k, is

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make up a set of 4 numbers with a mean of 8 a median of six and 1 half and a mode of 6 help pleaseeeeee

The 4 numbers are:

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Simplify (u^3/-3w^4)^2

------ -----

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Jack has $10,000 to invest in three accounts. He invests part of the money at 7% annual interest and twice that amount in an account paying 5.5% annual interest. The remaining money is invested at 4% annual interest. How much was invested in Each account if the total annual income from the three investments was $490?
I tried the question and got it wrong. I did:
.07x+5.5(2x)=490
.07x+11x=490
11.07x=490
x=44.26
4y=10000
y=2500
$44.26=7%
$88.52=5.5%
$2500=4%

Sorry to say but you're way off!!

Let amount invested in the 7% and 4% interest-accounts be S, and F, respectively
Amount he invested in account paying 5.5% = 2S
Therefore, S + F + 2S = 10,000 ---- 3S + F = 10,000 ----- eq (i)
Also, .07S + .055(2S) + .04(F) = 490 --- .07S + .11S + .04F = 490 --- .18S + .04F = 490 --- eq (ii)
- .12S - .04F = - 400 ------ Multiplying eq (i) by - .04
.06S = 90 ---- Adding eqs (ii) & (i)
S, or amount invested in the % interest-account = , or $

Amount invested in the % interest-account = 2(1,500), or $

3(1,500) + F = 10,000 ------ Substituting 1,500 for S in eq (i)
4,500 + F = 10,000
F, or amount invested in the % interest-account = 10,000 – 4,500, or $

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The side of one square is 3 cm longer than the side of another square. If the sum of the area of the 2 squares is 65 centimetres squared find the lengths of each square.
Can you please help me? thanks in advance

Let one side of smaller square be S

Then one side of larger square = S + 3

Area of smaller square = S(S), or

Area of larger square = (S + 3)(S + 3), or , or

Since sum of areas of the 2 squares = 65, then:









(S + 7)(S - 4) = 0

S = - 7 (ignore)

S, or length of ones side of smaller square =

Length of one side of larger square = 4 + 3, or

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The altitude of a triangle is 2 metres longer than its base what are the dimensions of the altitude and the base if the area of the triangle is 40 metres squared.

Formula for area of a right-triangle: , where A is the area of the triangle, H is the height (altitude) and B, the base

Since H (altitude) is 2 metres longer than B (base), then it can be said that B = H - 2. As A or area = 40 becomes:

-----

---- Cross-multiplying



(H + 8)(H - 10) = 0

H = - 8 (ignore as ray/segment/line CANNOT be negative)

H, or height = metres

Base = 10 - 2, or metres

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Hello I had a question regarding arithmetic sequences.
Here we have 1+3+5+...+915.
How would I find the sum using a formula?
Thank You all for your time to help and teach.

This problem can be solved by using the number of numbers formula: , first, to determine the number of numbers, or "n," with being the first term, and = 1, and being the last term, and = 915.

----- ----- -----


The formula for sum of an arithmetic sequence, or A.P. is: , with , 1st term, or = 1; n, or amount of terms to be summed = 458, and d, or common difference = 2

Therefore, becomes:







, or sum of the 458 terms in the series =

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Please help me solve this problem.
( )/6 + ( )/4 =2/3 Missing Denominators?

FYI: The NUMERATORS are missing, not the denominators!!

(?)/6 + (?)/4 = 2/3

The following can be the numerators:

; --------

; --------

; -----

; -----

; -----

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a train leaves a station and travels north at a speed of 75mph. four hours later, a second train leaves on a parallel track and travels north at 175mph. how far from the station will they meet.

Let distance from station be D
Time taken by 1st train to travel to "meeting" point, equals time taken by 2nd train to travel to "meeting" point, plus 4, OR


7D = 3D + 2,100 ------ Multiplying by LCD, 525
7D – 3D = 2,100
4D = 2,100
D, or distance from station = , or miles

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You have just been given a new job in sales. You have to salary options. You can receive a straight salary of $500 per week(no commission option) or you can receive a salary of $200 per week plus 5% of your weekly sales (commission option). What dollar amount of product must you sell each week in order for the commission option to be the better deal?

Let weekly sales be S
Then: 200 + .05S > 500
.05S > 300
S, or weekly sales > , or > $ (greater than $6,000, meaning $6,000.01, or more)

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a function is defined by the equation y=1/2x-3/2 which equation defines the inverse of this function?
(1)y=2x+3 (3)y=2x+3/2
(2)y=2x-3 (4)y=2x-3/2
hi there so this is the question i will be asking the most important thing is that i know how to do this question so if you would please give instructions on how you arrived to your answer that would be Aweosome and also thank you in advance



To find the inverse, just interchange variables, and then solve for y, as follows:





---- Multiplying by LCD, 2

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Find the three solutions to x^3=8
I've already factored it using the difference of cubes and found one solution, 2, but when i get to the quadratic formula I'm confused.

-----

---- Applying difference of cube factorization

The discriminant () for the quadratic equation: signifies roots that are imaginary (< 0), so the only solution is

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the sum of the digits is 7. when the digits are interchanged, and the resulting number is subtracted from the original one, the difference is 45. what are the digits?

Let the tens and units digits be T and U, respectively

Then: T + U = 7 ----- eq (i)

Original number = 10T + U, and interchanged number = 10U + T

Therefore, 10T + U - (10U + T) = 45 ---- 10T + U - 10U - T = 45 --- 9T - 9U = 45 ---- 9(T - U) = 9(5) ---- T - U = 5 ---- eq (ii)


T + U = 7 ----- eq (i)
T - U = 5 ----- eq (ii)
2T = 12 ----- Adding eqs (ii) & (i)
T, or tens digit = , or

6 + U = 7 ------ Substituting 6 for T in eq (i)
U, or units digit = 7 - 6, or

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9^(1/2)=3
Complete the equivalent logarithmic equation.
Log_9(enter here)=(enter here)



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Would you please help me identify the equation for the following problem:
"Together we are 98 years old. I am twice as old as you were when I was as old as you are now."
I understand A+B=98, but cannot figure the second statement.
Thank you,
Caroline

Let my age be M, and yours, Y

Then the 1st equation is: M + Y = 98

The 2nd equation which you asked for is:

When solved, M, or my age, is 56 and yours, or Y, is 42

You should realize from the problem that I am older than you are.

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Tom is 3 years older than Mary and Jane is 5 years older than Tom. What is the average age?

Let Mary's age be M
Then Tom's is: M + 3, and Jane's is: M + 3 + 5, or M + 8

Sum of their ages = M + M + 3 + M + 8, or 3M + 11

Average age = , or

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mark has twice as many quarters as nickles and 3 more dimes than nickles, he has $4.20 in all, how many of each does he have. we need formula to figure this out, my daughter is having horrible time with this, and it has been to long for me to remember.

Let amount of nickels, quarters and dimes he has, be N, Q, and D, respectively

Based on the given information, Q = 2N, and D = N + 3

From this, the following coin-value equation can be formed:
.05N + .25(2N) + .1(N + 3) = 4.2

.05N + .5N + .1N + .3 = 4.2

.65N + .3 = 4.2

.65N = 4.2 - .3

.65N = 3.9

N, or amount of nickels = , or

Amount of quarters = 2(6), or

Amount of dimes = 6 + 3, or

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Could a friendly soul please assist with this problem: Bless your heart. I need to understand work process and how answer was gotten. Thankyou.
Solve: 1/x-1 + 2/x = x/x-1
Rational Equation



** Note that , or , since these values would render fractions in the equation as UNDEFINED.

------ Multiplying by LCD, x(x - 1)







(x - 1)(x - 2) = 0

x = 1 = 0, or x = 1

As explained above, , so

x - 2 = 0, or

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An arithmetic series has a third term of 0. The sum of the first 15 terms is – 300. What is the first term?

Formula for d, or the common difference in a series: , with = = 0, and n = 3

Therefore, becomes: ------ ------ eq (i)

Formula for sum of a series of numbers, or : , with = = - 300 ; and n = 15

Therefore, becomes: --- --- --- eq (ii)

------ Substituting for d in eq (ii)







, or 1st term = , or

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Driving from Tulsa to Detroit, Dean's average speed was 50 mph. If he had averaged 60 mph instead, this would have decreased the drive time by 3hr. How many miles was the drive from Tulsa to Detroit?
note: let x = the distance from Tulsa to Detroit, do not use other variables. Answer part a and b.
a) Fill in chart:
R ----- T ----- D
50
60
b) Write and solve a correct equation that could be used to solve for x.

What I've tried:

Chart:
r: 50 t: x/50 d: x
r: 60 t: x/60 - 3 d: x
my equation:
x/50 = x/60 -3
(lcd = 300)
300(x/50)=300(x/60)- 300(3)
6x = 5x - 900
x = -900
my answer: x =-900
I don't think it's right due to the negative answer but it's the best I can come up with.

D (distance): x ; Rate (r) = 50 ; t (time) =
D (distance): x ; Rate (r) = 60 ; t (time) =



5x = 6x – 900 ------ Multiplying by LCD, 300
5x – 6x = - 900
- x = - 900

x, or distance = , or miles

You were correct right up until you tried to create the equation. You have to realize that the time traveled at 60 mph will BE LESS THAN the time traveled at 50 mph, or that the time traveled at 50 mph will be greater than the time taken to travel at 60 mph, by 3 hours, hence the equation: . This is where you went wrong. Furthermore, a negative distance could never be correct, as you have surmised.

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Peter purchased 450 apples for $375 and sold it at the rate of $13 per dozen. What is the percent of profit or loss that he makes?

He sold them for more than he purchased them for so he made a profit

Sale price = ---- 37.5 * 13, or $487.50

Profit = 487.5 - 375, or $112.50

Profit percent = , OR

Profit percent = , or %

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Factor: 2x^2-11x+15



----- Replacing - 11x with factors, - 6x and - 5x

2x(x - 3) - 5(x - 3)



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-8 ≤ 8m + 28
My son says the answer should be a whole number. can not figure it out.

The solution is NOT AN INTEGER. It's 4.5, or the range of values greater than 4.5, as seen below.







----- Switch expressions, changing signs in the process

, or , or

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How many ounces of a 30% saline solution must be added to 60 ounces of a 20% saline solution to make a 25% saline solution? Can you please show me the steps?

Let amount of 30% saline solution to be added be T
Then: .3(T) + .2(60) = .25(T + 60)
.3T + 12 = .25T + 15
.3T - .25T = 15 – 12
.05T = 3

T, or amount of 30% saline solution to be added = , or oz
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Please help me in this inequality problem.
David has $15.000 to invest. He invests $10.000 in a mutual fund that pays 12% annual simple interest. If he wants to make at least $2200 in yearly interest , at what minimum rate does the remainder of the money need to be invested?

Let rate that $5,000 ($15,000 – 10,000) need to be invested at, be r
Then: .12(10,000) + r(5,000) ≥ 2,200
1,200 + 5,000r ≥ 2,200
5,000r ≥ 2,200 – 1,200
5,000r ≥ 1,000

r, or rate to invest $5,000 ≥ , or %
OR

$5,000 need to be invested at a certain rate in order to make $1,000 ($2,200 - 1,200). This is then written as: r(5,000) ≥ 1,000. Solve for r and the rate is found.

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Can I please get help on this question? Lin paid 42 cents for a pencil and two erasers. Kim paid 91 cents for five pencils and three erasers? What were the prices of pencils and erasers?

Let price of each pencil and each eraser be P, and E. respectively

Then: P + 2E = 42 ----- P = 42 - 2E ----- eq (i)
Also, 5P + 3E = 91 ------ eq (ii)

5(42 - 2E) + 3E = 91 ----- Substituting 42 - 2E for P in eq (ii)

210 - 10E + 3E = 91

-10E + 3E = 91 - 210

- 7E = - 119

E, or price of each eraser = , or cents

P = 42 - 2(17) ----- Substituting 17 for E in eq (i)

P = 42 - 34

P, or price of each pencil = cents

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Five decreased by eleven times a number greater than 71. evaluate this problem situation for values of the number.

Let number be N

Then: 5 - 11N > 71

- 11N > 71 - 5

- 11N > 66

, or

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Solve the Equation.
(x^3)(9^x) - 9^x =0







----

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Could you please give me some direction in solving a complex expression involving polynomials with negative exponents? I've placed the specific expression below, and I've been asked to present an answer in which all exponents need to be positive. I've multiplied the factors involved in both the numerator and denominator, adding and subtracting exponents as needed. I know it's very lengthy, but--in general, I think I followed the rules correctly. I ended up with "i^-46" in the numerator, so I flipped it into the denominator. Here's the expression:
(16g^-7h^8i^-21j^0k^9)(h^-5j^-6)^-12(7g^5h^11i^-1k^20)^3/(5g^-7h^14i^-30j^1k^9)(4h^1i^2j^-5k^-4)^-4
Here is my best answer: 878080000g^15h^91j^51k^76/i^46
Am I even in the neighborhood with my answer?
Thank you so much for your time.



















---- -----

, or

This is what I came up with. I don't believe that there are any errors, but you need to check every line of calculation.

THIS WAS AN EXTREMELY EXCRUCIATING AND EXTENSIVE SIMPLIFICATION PROBLEM. After working this problem I was too tired to check it, so you can check it to see if I'm correct or you are.

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Solve the equation and express the solution in exact form...
log9(x-4)+log9(x-4)=1

This is what I have done...
9=(x-4)(x-4)
9=(x^2-4x-4x+16)
-9 -9
0=(x^2-8x+7)
(x-7)(x-1)
x=7, x=1

not sure what Iam doing wrong.... Thanks!













(x - 1)(x - 7) = 0

x = 1 (ignore as this value will result in a NEGATIVE log value)



Your answers are CORRECT. However, you need to do the check, which as you'll see will eliminate as a solution, thus leaving the only solution as (see above).

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I need help with this problem: Chris bikes a steady speed of 9 feet/second. Mark bikes a steady speed of 12 feet/second. If Chris gets a 75 second head start, how many feet will Mark have to bike until he catches up to Chris? Type your answer as a decimal rounded to the nearest hundredth. --- I know how to start it with the equation chris: 9(timechris)= distance and mark: 12 (time mark)= d and then I get lost. Not sure if someone can help me or not, but I sure hope so!Thanks in advance!

Let the distance that Mark has to travel to catch up to Chris be D
As Chris’ speed is slower than Mark’s, then Chris will take 75 seconds more than Mark to get to the “catch up” point
Chris’ time taken to travel to “catch-up” point equals Mark’s time to travel to the “catch-up” point, plus 75 seconds, OR


4D = 3D + 2,700 ----- Multiplying by LCD, 36

4D – 3D = 2,700

D, or distance traveled by Mark to catch up to Chris = feet

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