There are 80 students in a school. Every student is taking either algebra or pre-calculus, and some students are taking both. There are 60 students in the algebra class. If 15 students are taking both algebra and pre-calculus, what is the probability that a randomly selected student is taking pre-calculus but not algebra?

Answer:

85.4

Step-by-step explanation:

first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

A.) Chord CD must not only bisect but must also be perpendicular to diameter AB.

Step-by-step explanation:

The error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.

Geometric construction is method todraw any sketch lines, angles, and other geometric forms and figures only using a compass and a straightedge. It generally is done without employing precise measurements of length, angle, etc.

Now the steps taken by Makayle are,

→draw diameter AB

→use a compass and a straightedge to find chord CD that bisects diameter AB.

→use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.

Now here the error she is making is that the required chords will be AB, BC, CD, and DA, not AC, AD, BC, and BD.

Hence,the error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.

To learn more about Geometry:

https://brainly.com/question/7558603

#SPJ2

Answer:

36pi

Step-by-step explanation:

Answer:

36pi

Step-by-step explanation:

i got it right on my test

Answer:

56.52 in

Step-by-step explanation:

Circumference Formula: C = 2πr

Since we are given radius r = 9, simply plug it into the formula:

C = 2π(9)

C = 18π

C = 56.5487

Answer:

56.5

Step-by-step explanation:

The circumference is the product of the diameter and PI

P = (9+9)*π = 18*3.14=56.52

Answer: 0.8284 units²

Step-by-step explanation:

To find the area between curves, we need to use the integral. We can see that both sides of the shaded region are equal to each other. Therefore, we can find the area of one shaded part and multiply it by 2 for the 2 shaded regions. For the integral, we can find the area of the shaded region on the left side, on the interval from 0 to π/4.

Now that we know the integral, we can figure out the function. We do this by subtracting the top curve by the bottom curve. The top curve on the left shaded region, is y=cosx. The bottom curve on the shaded region is y=sinx. Therefore, we will subtract cosx-sinx.

[tex]2\int\limits^\frac{\pi }{4} _0 {cosx-sinx} \, dx[/tex]

Now that we have the integral, we can solve by splitting the integral into 2 separate integrals by the Sum Rule. Let's disregard the multiply by 2 for now, but we will make sure to multiply by 2 at the end.

[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx -\int\limits^\frac{\pi }{4} _0 {sinx} \, dx[/tex]

Now, we can solve each integral separately.

[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx =sinx]^\pi^ /^40[/tex]

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

[tex]sin(\frac{\pi }{4} )-sin(0)=\frac{\sqrt{2} }{2} -0=\frac{\sqrt{2} }{2}[/tex]

Now, we can find the integral of sinx.

[tex]\int\limits^\frac{\pi }{4} _0 {sinx} \, dx=-cos]^\pi ^/^40[/tex]

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

[tex]-cos(\frac{\pi }{4} )-(-cos(0))=-\frac{\sqrt{2} }{2} -(-1)=-\frac{\sqrt{2} }{2} +1[/tex]

Now that we have the integral of each integral, we can subtract them, and multiply by 2.

[tex]\frac{\sqrt{2} }{2} -(-\frac{\sqrt{2} }{2} +1)=\sqrt{2}+1[/tex]

[tex]2(\sqrt{2} +1)=0.8284 units^2[/tex]

Answer:

Step-by-step explanation:

There are 9 possible outcomes for (Bill, Ben)'s cards:

  (4, 4) total 8; (4, 5) total 9; (4, 6) total 10;

  (5, 4) total 9; (5, 5) total 10; (5, 6) total 11;

  (6, 4) total 10; (6, 5) total 11; (6, 6) total 12.

Of these 9 outcomes, 4 have an odd total; 6 are less than 11.

 P(odd) = 4/9

  P(sum < 11) = 2/3

Answer:

b)A cube with side lengths of 4 feet has a volume of 64cubic feet

Step-by-step explanation:

volume=length×width×height

=4×4×4

=64feet³

Answer:

[tex]3{x}^{3} + 2x + 5[/tex]

Step-by-step explanation:

Sorry if my notes weren't very clear.

Answer:B

Step-by-step explanation: got it right

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

Answer:

g(x) = (x + 3)^2

Step-by-step explanation:

When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.

If we have a quadratic function

[tex]f(x)=x^2[/tex]

and the graph is shifted 3 units to the left, then we can think of a new unit u that is:

[tex]g(x)=u^2[/tex]

The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.

Then, the relation between u and x is:

[tex]u-x=0-(-3)=3\\\\u=x+3[/tex]

We can use this relation in the new graph and replace u as:

[tex]g(x)=(x+3)^2[/tex]

Answer:

g(x) = (x + 3)^2

Step-by-step explanation:

I took the practice test as well.

Answer:

i think is e or b

Step-by-step explanation:

[tex]7(b-2)[/tex]  Can be interpreted as letter E.

Answer:

[tex]6 \pm 2.861(0.3354)[/tex]

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.861.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.861\frac{1.5}{\sqrt{20}} = 2.861(0.3354)[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The format of the confidence interval is:

[tex]S_{M} \pm M[/tex]

In which [tex]S_{M}[/tex] is the sample mean

So

[tex]6 \pm 2.861(0.3354)[/tex]

Explanation:

The identity we'll use is cos(-x) = cos(x) for any value of x.

So cos(-150) = cos(150).

Then locate the angle 150 on the unit circle. The terminal point is [tex]\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]

The x coordinate of this terminal point is the value of cos(150).

Answer:

Cos(-150°)=-√3/2

Step-by-step explanation:

-150° is found at the third quadrant so the cost value at third quadrant is negative

Cos(-150°)= -cos(30)=-cos(210)

Cos(-150°)=- (√3/2)

Cos(-150°)=-√3/2

Hope it helps

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

a

Step-by-step explanation:

Maybe: the SRS condition is OK but we need to look at the data to check Normality.

The normality inference is important in that the null compares the difference in the sample means to the difference that one would expect by random variation, or by chance, alone meaning that the sample is assumed to have being from a normal distribution with a mean and standards deviation.

Answer:

h = A ÷ ½(a - b)

Step-by-step explanation:

A = ½ah - ½bh

A = ½h( a - b)

Divide both sides by the coefficients of h

A ÷ ½(a - b) = h

Answer:

After 25 years, Minneapolis will have 154,062 more residents than Anoka.

Step-by-step explanation:

First, let's write a function for each case.

For Anoka, the initial population is 18,000. The population grows 5.2% or 0.052 each year. Thus:

[tex]A(x)=18000(1.052)^x[/tex], where x represents the amount of years after 1994.

Inversely, for Minneapolis, the population decreases by 2.3% or 0.023. Another way to write this is that it in changes by 1-0.023 or .977 or 97.7%. Thus:

[tex]M(x)=390000(0.977)^x[/tex].

To find how many more people are living in Minneapolis than Anoka after 25 years, simply plug 25 into the functions and then subtract.

In Anoka, after 25 years, there will be:

[tex]A(25)=18000(1.052)^{25}\approx 63924[/tex] residents.

In Minneapolis, after 25 years, there will be:

[tex]M(25)=390000(.977)^{25}\approx217986[/tex] residents.

217986-63924=154,062 residents.

Answer:

AB = 3π

Step-by-step explanation:

See attachment for correct format of question.

Given

From the attachment, we have that

θ = 20°

Radius, r = 27

Required

Find length of AB

AB is an arc and it's length can be calculated using arc length formula.

[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]

Substitute 20 for θ and 27 for r

[tex]Length = \frac{20}{360} * 2\pi *27[/tex]

[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]

[tex]Length = \frac{1080 \pi}{360}[/tex]

[tex]Length = 3\pi[/tex]

Hence, the length of arc AB is terms of π is 3π

Answer:

729

Step-by-step explanation:

Replace x with 9. [tex]9^{2}[/tex] which is 9*9=81 than [tex]9^{1}[/tex] which is 9*1=9. Simplify 81*9=729.

Answer:

A. BA + 2πrh

C. 2πr² + 2πrh

Step-by-step explanation:

height of cylinder = h

Radius of cylinder = r

=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)

L.A of a cylinder = 2πrh

=>Base area = BA (this is the area of both circular bases of the cylinder)

Area of circle = πr²

Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²

=>Surface area of a right cylinder = B.A + L.A

= 2πr² + 2πrh

The formulas that can be used to find surface area of a right cylinder from the given options are:

A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)

C. 2πr² + 2πrh

Answer:

x-6+x

2x-6=14

2x=20

x=10

Answer:

x-6+x

2x-6=14

2x=20

x=10

Step-by-step explanation:

I tried hard... I really hope this helps!

Answer:

C. (x + 3)(x − 8)

Step-by-step explanation:

We need two numbers that add to -5 and multiply to -24.

They are -8 and 3 since -8 + 3 = -5, and -8 * 3 = -24.

x^2 - 5x - 24 = (x - 8)(x + 3)

Answer:

3rd option

Step-by-step explanation:

-5 is smaller than -2.

-2 is smaller than 1

1 is smaller than 3

Answer:

the 3 one

Step-by-step explanation:

the larger the negative number,the higher up the number line it goes

so -5 is the greatest negative number,-2 the next, the 1 and 3

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:

1222 billion dollars.

Step-by-step explanation:

To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:

In the period 1960-1970, we have x = 1, and the growth is:

[tex]y(1) = 43e(1/2) = 70.895[/tex]

In the period 1970-1980, we have x = 2, and the growth is:

[tex]y(2) = 43e(2/2) = 116.8861[/tex]

The growth in the following 3 periods are:

[tex]y(3) = 43e(3/2) =192.7126[/tex]

[tex]y(4) = 43e(4/2) = 317.7294[/tex]

[tex]y(5) = 43e(5/2) =523.8472[/tex]

So the total growth in the period 1960 - 2010 is:

[tex]Total = y(1) + y(2) + y(3) + y(4) + y(5)[/tex]

[tex]Total = 70.895 + 116.8861+192.726+317.7294+523.8472[/tex]

[tex]Total = 1222.08\ billion\ dollars[/tex]

Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.

Answer:

m∠1 = 91°

Step-by-step explanation:

Since ∠2 and ∠3 are Supplementary Angles, to find x:

5x + 14 + 7x - 14 = 180

12x = 180

x = 15

Now we plug in x as 15 in to find m∠2:

m∠2 = 5(15) + 14

m∠2 = 75 + 14

m∠2 = 89

Since ∠1 and ∠2 are also supplementary, to find m∠1, we simply subtract 180°:

m∠1 = 180 - m∠2

m∠1 = 180 - 89

m∠1 = 91°

Answer:

D.

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]

Step-by-step explanation:

hello

we need to compute the following

[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]

hope this helps