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The slope inteercept form of a line is , m=slope, and (0,b)=y-intercept.
y=1\2x-3. the slope is
, the slope, m=1/2
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find the area of the given trapezoid.
9 in across the top.3in inside vertical ,11in bottom.
The formula for finding the area of a trapezoid is:
, A=area, h=height, b1=base1 and b2=base2
b1=9 in
h=3 in
b2=11 in
Units for area in inches is in^2




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I hope you're allowed to use a TI-83 or 84 for this, otherwise, it's kind of a pain!
A statistics student needs a grade of at least 70 to pass an examination. The exam consists of 10 true/false questions. If he guesses at each question, what is the probability he will pass? and if the test was changed to 10 multiple-choice questions having 5 possible answers to choose from and he is still guessing what is the probability he will pass?
:
This is a binomial probability problem.
n=10 (The number of questions)
p=.5 (1/2 chance of getting a true-false question right)
q=1-.5=.5 (1/2 chance of getting it wrong)
x=7,8,9,10 (because he can pass with a 70,80,90, or 100)
:
The formula is:

P(x)=probability of x
n=number of trials
x=number of successes
p=probabillty of success
q=1-p=probabilty of failure
:
Add all the probability of x=7,8,9,10 together and the students has a probability of .171875 of passing. If you have a TI-83/84
1-binomialcdf(10,.5,6)=.171875
:
For the second one, everything is the same except:
p=1/5=.2 and q=4/5=.8
Add the probabilities of x=7,8,9,10 together and the student has a .0008643584 chance of passing.
1-binomialcdf(10,.2,6)=8.643584E-4=.0008643584
:
If I were the student, I'd study. Both probabilities are low, and the chance of passing a multiple choice test by guessing is almost 0!
That should be enough to help you solve it. If not, let me know.
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Frequency Table showing distribution of Exam scores
Exam scores # of students
90 & over 5
80-89 12
70-79 40
60-69 18
50-59 13
40-49 6
30-39 6
What is the probability that a student picked at random will have a score of at least 90? a score less than 90? a score of at least 60? and a score of more than 39 and less than 60?
There are a total of 5+12+40+18+13+6+6=100 students
P of at least 90 is 5/100=.05
P of less than 90 is (12+40+18+13+6+6)/100=.95
P of at least 60 is (5+12+40+18)/100=.75
P of more than 39 and less than 60 is (13+6+)/100=.19
:
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A water storage tank is shaped like a circular cylinder with half of a sphere at each end.Find the volume of the tank if the cylindrical section is 100cm long with a 40cm diameter.Use 3.14for pi.Round the final answer to two decimal places.
You have a sphere and a cylindar:
For a sphere the volume is
For a cylindar the volume is
d=40
pi=3.14
h=100
r=d/2=40/2=20
Units for volume: cm^3



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Please Help
Which of the following ordered pairs are solutions of 4x-3y=27? select all that apply.
A.(-5,3)
B.(3,6)
C.(12,15 3/4)
D.(-1,7 3/4)
E.(0,6 3/4)
F.(9 3/4, 0)
:
For A, let x=-5 and y=3, if the equation is equal, it is a solution.
4(-5)-3(3)=27
-20-9=27
-29=27 No, this one is not a solution.
:
For B, let x=3 and y=6
4(3)-3(6)=27
12-18=27
-6=27 No, this one is not a solution.
:
For C, let x=12 and y=15 3/4=63/4
4(-5)-3(63/4)=27
-20-189/4=27
-80/4-189/4=27
-269/4=27 No.
:
For D, let x=-1 and y=7 3/4=31/4
4(-1)-3(31/4)=27
-4-93/4=27
-16/4-93/4=27
-109/4=27 no.
:
For E, let x=0 and y=6 3/4=27/4
4(0)-3(27/4)=27
0-81/4=27
-81/4=27 no.
:
For F, let x=9 3/4=31/4 and y=0
4(31/4)-3(0)=27
31-0=27
31=27 no.
:
Are you sure you typed everything correctly, because something should have worked.
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Frequency Distribution:
Votes Number of Precincts
0-99 3
100-199 10
200-299 25
300-399 15
400-499 22
What is the probability that a randomly selected precinct will have had fewer than 100 votes? at least 300 votes? had at most 399 votes? and had no fewer than 100 votes?
Votes____________________Number of Precincts______frequency
0-99----------------------3-------------------------3/75=1/25=.04
100-199-------------------10------------------------10/75=2/15=.1333
200-299-------------------25------------------------25/75=1/3=.3333
300-399-------------------15------------------------15/75=1/5=.2
400-499-------------------22------------------------22/75=.29333
:
Fewer than 100 would be (0-99)---3/75=1/25=.04
At least 300 would be (300-499)---15/75+22/75=37/75=.49333
No fewer than 100 votes is (100-499)---10/75+25/75+15/75+22/75=72/75=24/25=.96
:
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In the equation P(x) = 2x^3 + 7x^2 + x + 3 how many variations of sign are there, in the sense of Descartes’ rule of signs? What is the number of positive real zeros of P(x)?
:
First note that a polynomial cannot have more real zeroes than its degree. The most zeros this polynomial can have is 3, because this is a third degree polynomial.
:
The Descartes' Rule of Signs States:
Let f denote a polynomial function written in standard form.
*The number of positive real zeroes of f either equals the number of variations in the sign of the nonzero coefficients of f(x) or else equals that number less an even integer.
*The number of negative real zeroes of f either equlas the number of variations in the sign of f(-x) or else equals that number less an even integer.
:
P(x) is always positive (++)(++)(++), the terms never change from + to - or - to +, therefore there are no positive zeros.
:
P(-x)=2(-x)^3+7(-x)^2+(-x)+3
P(-x)=-2x^3+7x^2-x+3
Has 3 variations of signs (-+),(+-),(-+), that means you can have 3 (or 3-2=1) negative zeroes.
:
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You need to provide more information. l*w is the area of a rectangle.
Sometimes they will tell you something like, the length is 5 more than the width.
The you would say:
let width be: x
Then length is: x+5
Then A=l*w is:
A=x(x+5)
A=x^2+5x
:
Hope that helps.
For the problem in your book,
let length be: 3x
Let width be:3x-3
A=l*w
A=3x(3x-3)
A=3x(x)+3x(-3)

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A water storage tank is shaped like a circular cylinder with half of a sphere at each end.Find the volume of the tank if the cylindrical section is 100cm long with a 40cm diameter.Use 3.14for pi.Round the final answer to two decimal places.
You have a sphere and a cylindar:
For a sphere the volume is
For a cylindar the volume is
d=40
pi=3.14
h=100
r=d/2=40/2=20
Units for volume: cm^3



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In 28 years, a country's population doubled. Write this equation exponentially









:

:
You can approximate k if your teacher would rather:

Round it off to whatever your teacher wants:

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In the equation P(x) = 2x^3 + 7x^2 + x + 3 how many variations of sign are there, in the sense of Descartes’ rule of signs? What is the number of positive real zeros of P(x)?
:
First note that a polynomial cannot have more real zeroes than its degree. The most zeros this polynomial can have is 3, because this is a third degree polynomial.
:
The Descartes' Rule of Signs States:
Let f denote a polynomial function written in standard form.
*The number of positive real zeroes of f either equals the number of variations in the sign of the nonzero coefficients of f(x) or else equals that number less an even integer.
*The number of negative real zeroes of f either equlas the number of variations in the sign of f(-x) or else equals that number less an even integer.
:
P(x) is always positive (++)(++)(++), the terms never change from + to - or - to +, therefore there are no positive zeros.
:
P(-x)=2(-x)^3+7(-x)^2+(-x)+3
P(-x)=-2x^3+7x^2-x+3
Has 3 variations of signs (-+),(+-),(-+), that means you can have 3 (or 3-2=1) negative zeroes.
:
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write it in standard form (Ax+By=C).
this is what i have done so far.
1.(-4,1);(-2,-1)
I can't follow what you've done, so I'm going to start from scratch. I assume that you have been given these two points and are being asked for the equation of the line in standard form.
In order to write the equation of a line, you need a point and a slope. So we need a slope.
To find the slope when given two points, we use the slope formula:, m=slope, (x1,y1) and (x2,y2) are the given points.
(x1,y1)=(-4,1) and (x2,y2)=(-2,-1)




Now we can use the point-slope formula to find the equation of the line:, m=slope and (x1,y1) is a given point.
m=-1 and (x1,y1)=(-4,1)

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I am assuming that you are supposed to factor.
6x-42+xy-7y Group the first two terms and last two terms.
(6x-42)+(xy-7y) Factor the GCF out of each.
6(x-7)+y(x-7) Factor the x-7 out
(6+y)(x-7)
(y+6)(x-7) is the same as above
:
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2a-6=-a
2a+a-6=-a+a
3a-6=0
3a-6+6=0+6
3a+0=6
3a=6
3a/3=6/3

:
Check, if a=2, do both sides of the equation =?
2(2)-6=-(2)
4-6=-2
-2=-2 Yes. We're right!!!
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What are the directions for this? I don't know what you need.

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4a + 7 = 2a = 19
You have a type-o. I'm going to change the second = into a +. Let me know if that's not what you meant and you still need help.
4a+7=2a+19
4a-2a+7=2a-2a+19
2a+7=19
2a+7-7=19-7
2a=12
2a/2=12/2
a=6
:
Check, if a=6, do both sides =?
4(6)+7=2(6)+19
24+7=12+19
31=31 Yes. We're right!!!
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0.4p-3.2=4.8p+4.2-0.7p
0.4p-3.2=4.1p+4.2
0.4p-0.4p-3.2=4.1p-0.4p+4.2
-3.2=3.7p+4.2
-3.2-4.2=3.7p+4.2-4.2
-7.4=3.7p
-7.4/3.7=3.7p/3.7
-2=p
:
Hint-If you really hate decimals, you can eliminate them by multiplying everything by 10.
10(0.4p-3.2)=10(4.8p+4.2-0.7p)
4p-32=48p+42-7p
4p-32=41p+42
4p-4p-32=41p-4p+42
-32=37p+42
-32-42=37p+42-42
-74=37p
-74/37=37p/37
-2=p
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Solve,


approximately.
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The formula for factoring the difference of cubes is:
Factor the difference of cubes on top, a=p and b=1.





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N IS 58% OF 955.0
One way to do it is to set up a proportion of part/whole=part/whole:



:
Another way to do it is to take 58% of 955.0.
The decimal form of 58%=58/100=.58


:
The advantageof the first way is that you set it up the same way everytime. You just need to pay attention to what is part and what is whole.
:
The advantage of the second way is that it's faster. The disadvatage is that with some problems you have to divide and others you have to multiply and you have to learn when to do what.
:
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How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=450e^.216t, where t is the time in years? Round your answer to the nearest hundredth year.
:
decay should have a negative k value, -.216. Otherwise, you're increasing instead of decreasing.
The original amount should be 450 if this is like most formulas.
1/2 that amount is 225
:











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Without the rest of the information, we can't help you with this one. Is there a picture or something that you're looking at. Is this an equilateral triangle? What are the other two vertices?

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y=2x^2-8x. Find the y-intercepts and any x-intercepts.
To find the y-intercept, let x=0 and solve for y.




The y-intercept is (0,0) This is where the graph would cross the y-axis.
:
To find the x intercepts, let y=0 and solve for x.
Factor the GCF, 2x out.
0=2x(x-4)
2x=0 and x-4=0
2x/2=0/2 and x-4+4=0+4
x=0 and x=4
The x-intercepts are (0,0) and (4,0)
Notice that the origin (0,0) is both an x-intercept and a y-intercept.
Here's what the graph looks like:

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Clear the parentheses on the left.
Combine like terms on the left.


Subtract 6x from both sides to get all your x's on the left.


Add 7 to both sides.


Divide both sides by 2


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Graph using the intercept method: 5x – y = 5.
To find the x intercept, let y=0 and solve for x.
5x-0=5
5x=5
5x/5=5/5
x=1
Put a point on (1,0) This is where the line will cross the x axis.
To find the y intercept, let x=0 and solve for y.
5(0)-y=5
0-y=5
-y=5
-1(-y)=-1(5)
y=-5
Put a point on (0,-5). This is the place where the line will cross the y-axis.
Connect the points and you should have a line that looks like this:

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Write the equation of the line with slope -1/2 and y-intercept (0, 3). Then graph the line.
The slope intercept form of a line is , m=slope, (0,b)=y-intercept.
For this problem, m=-1/2 and (0,b)=(0,3)

You plot the y-intercept by putting a point on 3 on the y axis.
From that point you use your slope to plot another point. . Our slope is m=-1/2, go down 1 (keep the sign with the rise, go up when it's positeve and down when it's negative) and right 2 (always run right) and plot another point at what should be (2,2).
Connect your points and you should have a line that looks tike this:

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Can somone help me solve this and show your work?






:
Check let x=36, do both sides equal?


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Find all real or imaginary solution to the equation.
6x=-(19x+25)/(x+1)
(6x)(x+1)=-19x-25
6x^2+6x+19x+25=-19x-25+19x+25
6x^2+25x+25=0
:
6x^2+10x+15x+25=0
(6x^2+10x)+(15x+25)=0
2x(3x+5)+5(3x+5)=0
(2x+5)(3x+5)=0
2x+5=0 and 3x+5=0
2x=-5 and 3x=-5
x=-5/2 and x=-5/3
You're right!!!
Keep up the good work!
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