The bowling team at Lincoln High School must choose a president, vice president,
and secretary. If the team has 12 members, how many ways could the officers be
chosen?

Answer:

[tex]v = \frac{32\pi}{3}[/tex]

or

[tex]v=33.52[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 4x - x^2[/tex]

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

[tex][a,b] = [0,2][/tex]

Required

The volume of the solid formed

Rotating about the x-axis.

Using the washer method to calculate the volume, we have:

[tex]\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx[/tex]

Integrate

[tex]v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx[/tex]

[tex]v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx[/tex]

Substitute values for a, b, f(x) and g(x)

[tex]v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx[/tex]

Evaluate the exponents

[tex]v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx[/tex]

Simplify like terms

[tex]v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx[/tex]

Factor out 8

[tex]v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx[/tex]

Integrate

[tex]v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0[/tex]

[tex]v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0[/tex]

Substitute 2 and 0 for x, respectively

[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])[/tex]

[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])[/tex]

[tex]v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ][/tex]

[tex]v = 8\pi [ \frac{16}{3} - \frac{16}{4} ][/tex]

Take LCM

[tex]v = 8\pi [ \frac{16*4- 16 * 3}{12}][/tex]

[tex]v = 8\pi [ \frac{64- 48}{12}][/tex]

[tex]v = 8\pi * \frac{16}{12}[/tex]

Simplify

[tex]v = 8\pi * \frac{4}{3}[/tex]

[tex]v = \frac{32\pi}{3}[/tex]

or

[tex]v=\frac{32}{3} * \frac{22}{7}[/tex]

[tex]v=\frac{32*22}{3*7}[/tex]

[tex]v=\frac{704}{21}[/tex]

[tex]v=33.52[/tex]

Answer:

A i think

Step-by-step explanation:

Answer: 90 more tickets

Step-by-step explanation:

230 - 50 = 180

180 divided by 2 = 90 tickets

Answer:

  1.  shifts the graph right 2 units

  2. y = -2(x -3)² +7

Step-by-step explanation:

1) Replacing x with x-h in any function shifts the graph h units to the right. Here, you have replaced x with (x-2), so the graph will be shifted 2 units to the right.

__

3) The vertex form of the equation of a parabola is ...

  y = a(x -h)² +k . . . . . . . . for vertex (h, k) and vertical scale factor 'a'

Here, the vertex is (h, k) = (3, 7), and the parabola opens downward. This tells us the sign of 'a' is negative.

The graph is not so clear that it is easy to read the value of 'a' directly from it, but there are several clues.

The zeros of the above function are found at h±√(k/a). This graph shows the zeros to be located such that √(7/a) is slightly less than 2. This means the magnitude of 'a' will be slightly more than 7/2² = 1.75. The y-intercept of the function is 7-9a. It is less than -7, but probably more than -14. This puts bounds on 'a':

  -14 < 7-9a < -7

  -21/9 < -a < -14/9   ⇒   -2.33 < -a < -1.56

If we assume that 'a' is an integer value, we have bounded its magnitude as being between 1.75 and 2.33, so a=-2 is a reasonable choice.

The equation of the graph may be ...

  y = -2(x -3)² +7

Answer:

What type of line the picture represent

Answer:

cncjdkgkejgksjckwjnviekfkwkckkdk kdkf

Given:

The given phrase is 16 seconds faster than Aya’s time.

To find:

The algebraic expression for the given phrase.

Solution:

Let x be the Aya’s time.

16 seconds faster than Aya’s time. It means 16 seconds less than Aya’s time.

We know that a negative sign "-" is used for less than.

16 seconds less than Aya’s time = [tex]x-16[/tex]

16 seconds faster than Aya’s time = [tex]x-16[/tex]

Therefore, the required algebraic expression is [tex]x-16[/tex].

Answer:

The answer is A

Step-by-step explanation:

The given function is  [tex]\dfrac{x^2}{49}+\dfrac{(y+1)^2}{4}=1[/tex] Thus, the graph of the function will be elliptical.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

The given function is

[tex]\dfrac{x^2}{49}+\dfrac{(y+1)^2}{4}=1[/tex]

The given function represents the equation of an ellipse.

Thus, the graph of the function will be elliptical.

Learn more about finding the graphed function here:

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Answer: see below...

Step-by-step explanation:

Square units are when we are finding the surface area.

Since it is side x side, so ^2.

Cubic units are when we are finding the volume.

Since it is side x side x side, so ^3.

Answer:

87.3

Step-by-step explanation:

Answer:

85.3333333333

Step-by-step explanation:

add the number then divide them by the number u x them with

Answer:

12

Step-by-step explanation:

A = [tex]\frac{a+b}{2\\}[/tex] h

= [tex]\frac{3+5}{2}[/tex] · 3

= 12 ft

I hope this help

Answer:

9. B 10. A 11. B 12. A

Step-by-step explanation:

use slope intercept form

Answer:

the property that justifies the statement 17=17 is equality

Step-by-step explanation:

because it shows that it is equal

Answer:

34.48 maybe

Step-by-step explanation:

Answer:

Step-by-step explanation:

1450÷500%

1450÷5.0 = 290

Answer:

8727.30624 , this is the correct answer!

Answer: a=8727.30624

Step-by-step explanation:

Hope this helps :D

Answer: It’s B.

Step-by-step explanation: Got it on edge

Answer:

Answer: It’s B.

Got it on edge

Step-by-step explanation:

Got it right on edge

Answer:

145

Step-by-step explanation:

So lets recall what a supplementary angle is. A suppelemenatry angle is  two angles that make up 180 degrees.(half circle)

This is different from a complenenary angle with is two angles that make up 90 degrees(quarter circle)

Ok, so we can write the equation for the supplementary angle as:

35+b=180

Lets subtract the angle we knwo from both sides:

b=145

Now we know that B(second angle) must be equal to 145 degrees.

Hope this helps!

Answer:

The new point is (-3,-1)

Step-by-step explanation:

yessir

Answer:

C - 129

Step-by-step explanation:

180-51=129

Answer:

the answer is B.

Step-by-step explanation:

W= median is 58

R= median is 81

81-58=23

The median number of books checked out at Ryder is 23 more than the median number of books checked out at Williams.

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

Let the data of Williams be represented as W

Now , W = { 63 , 56 , 60 , 55 , 62 , 55 }

And , the data of Ryder be R

where R = { 80 , 75 , 82 , 84 , 82 , 79 }

And , the median of Williams = (56 + 60) / 2 = 58

And , the median of Ryder is = 81

So , the difference of medians = 81 - 58 = 23

Hence , median number of books checked out at Ryder is 23 more than Williams

To learn more about median click :

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Answer:

$6.22

Step-by-step explanation:

25.20

would be your answer!

Answer:

Option B ig

Step-by-step explanation:

hope it helps.. stay safe..✨

Answer:

Answer should be SAS( side angle side). According to me

Answer:

b, i think.

Step-by-step explanation:

Answer:

10+5x

Step-by-step explanation:

5(2+x)

Distribute the 5

so 10+5x

Answer:

The volume of the bookshelf is 180000 cm³.

Step-by-step explanation:

The dimensions of the bookshelf are 40 cm, 50 cm and 900 mm.

We know that,

1 mm = 0.1 cm

900 mm = 90 cm

Now the dimensions become 40 cm, 50 cm and 90 cm.

The volume of the bookshelf can be calculated as :

V = lbh

Substitute all the values,

V = 40 cm × 50 cm × 90 cm

V = 180000 cm³

So, the volume of the bookshelf is 180000 cm³.