A statistics teacher conducted an experiment to test whether the use of a new review booklet will improve her students' semester grades. The teacher randomly selected 20 students from her class and assigned the new review booklet to 10 of the students. The remaining 10 students did not use any review material.

At the end of the semester, the teacher reviewed the students' semester grades. The semester grades of the students who used the new review booklet were the same as the semester grades of the students who did not.

What can be concluded from the teacher's observations?

A. It can be concluded that the new review booklet does not improve students' semester grades.

B. It can be concluded that the new review booklet reduces students' semester grades.

C. There is not enough information to make any conclusions regarding the new review booklet.

D. It can be concluded that the new review booklet improves students' semester grades.

The answer you are looking for is 9/11.

When dividing fractions, you multiply the first value by the inverse of the second value. The inverse is found by simply flipping the numbers of the last fraction. So, the inverse is 9/4. Then, multiply 4/11 and 9/4 to get 36/44. 36/44 simplified (divided by 4/4) is 9/11. Thus making 9/11 the answer.

I hope this helps.

Answer:

9/11

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

Write out the equation

5n-8=n-48

move like terms to the same side

4n=-40

divide 4n and 4 by 4 to get n by itself.

n=-10

The number is -10.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given,

Eight less than 5 times a number is 48 less than the number

Let the number be x

then statement can be written as

5x - 8 = x - 48

5x - x = - 48 + 8

4x = -40

x = 40/4

x = -10

Hence, -10 is the number.

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Answer:

3/4

Step-by-step explanation:

- He ate 1/4

- 4-1=3

- 3/4 of the pizza is left

Final answer:

The fraction representing the remaining pizza after Jason ate 1/4 of it is 3/4. We calculate this by subtracting the portion Jason ate (1/4) from the whole (4/4).

Explanation:

If Jason ate 1/4 of the whole pizza for dinner, we can easily calculate the fraction that represents the amount of pizza remaining. To find out the remaining portion of the pizza, we subtract the portion Jason ate from the whole. Since the whole is considered to be 1 (or 4/4 in this case, as there are four quarters in a whole), we subtract 1/4 from 4/4:

Remaining pizza = Whole pizza - Portion eaten by Jason

Remaining pizza = 4/4 - 1/4

Remaining pizza = (4 - 1)/4

Remaining pizza = 3/4

Therefore, the fraction that represents the remaining pizza after Jason has eaten is 3/4.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (1, 3) and (3, 1). Substitute:

[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]

Answer:

$22.30

Step-by-step explanation:

To determine how much money Chapman saved from purchasing a gift for his mother, calculate 2/5 of $55.75, which equals $22.30.

To find how much money Chapman saved:

Calculate 2/5 of $55.75: (2/5) x $55.75 = $22.30

Therefore, Chapman saved $22.30

Answer:

1/12 of the watermelon in each piece

Step-by-step explanation:

The final answer is 1/12.

I hope this helped!

Answer:

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Caleb has [tex]\frac{1}{3}[/tex] of a watermelon. To know what fraction each portion of watermelon represents after cutting it into 4 equal parts, just divide the portion that Caleb owns ([tex]\frac{1}{3}[/tex]) by the amount of sliced ​​portions (4):

[tex]\frac{\frac{1}{3} }{4}[/tex]

Given that 4 can also be represented by the fraction [tex]\frac{4}{1}[/tex], then:

[tex]\frac{\frac{1}{3} }{\frac{4}{1} }[/tex]

To divide two fractions, the SECOND FRACTION must be reversed, that is, change the denominator to the numerator and change the numerator to the denominator. Then, the two fractions are multiplied.

[tex]\frac{\frac{1}{3} }{\frac{4}{1} } =\frac{1}{3} *\frac{1}{4} =\frac{1}{12}[/tex]

The fraction of the watermelon that corresponds to each piece is [tex]\frac{1}{12}[/tex]

The volume of a larger cone:

[tex]V_l=\dfrac{1}{3}\pi\cdot4.5^2\cdot(3+6)=\dfrac{1}{\not3_1}\pi\cdot20.25\cdot\not9^3=(20.25)(3)\pi=60.25\pi\ cm^3[/tex]

The volume of a smaller cone:

[tex]V_s=\dfrac{1}{3}\pi\cdot3^2\cdot6=\dfrac{1}{\not3_1}\pi\cdot\not3^1\cdot3\cdot6=18\pi\ cm^3[/tex]

The volume of the frustum:

[tex]V=V_l-V_s\\\\V=60.25\pi-18\pi=42.75\pi\ cm^3[/tex]

Answer:

72 is 8 times as many as 9

Step-by-step explanation:

72 is the product of 8 groups of nine

72 is 9 times as many as 8 is the answer that completes the statement.

To solve the equation 72 = q × 8, we need to find the value of q.

By dividing both sides by 8, we get:

72/8 = q × 8/8

q = 72/8

q = 9.

This means that 72 is 9 times greater than 8 and to correctly complete the statement, we write: 72 is 9 times as many as 8.

Answer:

Total charge per month = $ 16 + (0.08) * x

equation for having same charge

0.08 x - 0.12 y = 8

Step-by-step explanation:

Part 1:

Monthly fee = $ 16

Per check fee = $ 0.08

Checks signed in month = x

Total Charge monthly = Monthly fee + Checks fee

Putting the values

Total charge per month = 16 + (0.08) * x             ...........(i)

Part 2: Let she signs y checks for account B

Monthly fee of B = $ 14

per check fee = @ 0.12

Total Charge = monthly fee + checks fee

                     =  $ 14 + y *(0.12)                         ..................(ii)

For having same value in the bank then equation (i) and  (ii) shuld be equal to each other

i.e.

16 + 0.08x = 24 + 0.12y

0.08 x - 0.12 y = 24-16

0.08 x - 0.12 y = 8

this will be the equation

Answer:

First, you have to get all of the variables on one side of the equation.

x15 on both sides

8 + a = 15+15a/6

x6 on both sides

48 + 6a=15+15a

Subtract 15 on both sides and Subtract 6a on both sides

33=11a

a=3

Step-by-step explanation:

Answer: Let x=length of the longest side of the smaller triangle.

x/20=3/12

x=60/12

x=5

Final answer:

To find the longest side of the similar triangle, multiply the longest side of the original triangle (20) by the scale factor, which is the ratio of the shortest sides (3/12 = 0.25). This results in a longest side of 5 units for the similar triangle.

Explanation:

The question pertains to finding the longest side of a similar triangle given that the shortest side is 3 and the original triangle has sides 12, 15, and 20. To find the answer, we need to calculate the scale factor between the similar triangles. The scale factor is obtained by dividing the shortest side of the new triangle (3) by the shortest side of the original triangle (12), which is ¼ or 0.25.

We then multiply the longest side of the original triangle (20) by the scale factor (0.25) to get the longest side of the similar triangle. Calculating, 20 * 0.25 = 5. Therefore, the longest side of the triangle with the shortest side 3 is 5 units long.

Answer:

A = 2/5

Step-by-step explanation:

r = sqrt(v) / (pi*h)

10 = sqrt(v) /(pi * h)

Solve for the volume by multiplying by pi * h on each side

10 * pi * h = sqrt(v)

Now square each side

(10*pi* h) ^2 = v

Now we have a second cylinder with a height that is 25 times the height of the other cylinder  but the same volume.  Solving for volume, we will multiply by

r = sqrt(v) / (pi*h)

r = sqrt(v) /(pi *25h)

r* pi * 25h = sqrt(v)

Now square each side

(r*pi*25h) ^2 = (sqrtv) ^2

(r*pi*25h)^2 = v

The problem states the the 2 cylinders have the same volume

(10 * pi * h) ^2 =  ( r * pi * 25h) ^2

Take the square root of each side

10*pi*h = r*pi * 25h

Divide each side by pi and h

10 = 25r

Divide by 25

10/25 =r

2/5 =r

Answer:

f(x) = -8 x + 34

Step-by-step explanation:

First, normalize the equation 8y = x-16 into y = ... form (divide by 8):

y = 1/8 x - 2

So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b

Now all we have to do is find b such that f(x) goes through (5,-6).

So f(5) = -8*5 + b = -6, and solve it for b:

-40 + b = -6 =>

b = 34.

So f(x) = -8x + 34

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]

[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]

To find out how much longer the record alligator is than the one Taylor saw, we subtract the length of the alligator Taylor saw from the record length. The record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

To find out how much longer the record alligator is than the one Taylor saw, we need to subtract the length of the alligator Taylor saw from the record length.

To do this, we need to convert the mixed numbers to improper fractions. 12 11/12 is equal to 155/12 and 19 1/6 is equal to 115/6.

Subtracting 155/12 from 115/6 gives us (115/6) - (155/12) = (230/12) - (155/12) = 75/12 = 6 3/4.

Therefore, the record alligator is 6 feet and 3/4 feet longer than the alligator Taylor saw.

Answer:

We will need 27/31 of an ounce of red

Step-by-step explanation:

3 /10 red + 11 /15 blue  makes 1 1/30 purple

Get a common denominator of 30

3/10 * 3/3 = 9/30  red

11/15 *2/2 = 22/ 30  blue

1  1/30 = 31/30   purple

So the ratio of red to purple is

9/30

--------  =   9/ 31

31/30

Keeping this ratio, we want 3 ounces purple

9 red                      x red

--------           =  --------------

31 purple             3   purple

Using cross products,

9*3 = 31 *x

27 = 31x

Divide each side by 31

27/31 = x

We will need 27/31 of an ounce of red

Answer:2x−3y=6

Step-by-step explanation:Standard form: Ax + By = C

Just take 2/3x to the other side.

So the answer would be

−23x+y=−2

In standard form

x

can't be negative and A, B and C need to be an integers (whole numbers)

(I multiplied the whole equation by -3)

2x−3y=6

So the final answer would be: 2x−3y=6

Answer:

Option B.

Step-by-step explanation:

Dr. Peterson works about 178 hours each month.

There are 12 months in one year.

So Dr. Peterson works in a year = 178 × 12 = 2,136 hours

We will go through all the options to find which is the closest to the answer.

Option A : 200 × 20 = 4,000 hours

Option B : 180 × 10 = 1,800 hours

Option C : 100 × 12 = 1,200 hours

Option D : 100 × 10 = 1,000 hours

Therefore, Option B is the best estimate of the number of the hours she works in a year.

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]

Answer:

The pole is 6 ft tall

Step-by-step explanation:

We can solve this using ratio's

4ft tall Mary        x ft tall  pole

-----------        =     -------------------

10 ft shadow      15 ft shadow

Using cross products

4 * 15 = 10 x

60 = 10x

Divide by 10

60/10 = 10x/10

6 =x

The pole is 6 ft tall

Answer:

it is 6 feet

Step-by-step explanation:

i dont have much of an explaination except that you have to draw a diagram inorder not tom get confused.

hope it helps.

Answer:

SA = 201 in^2

Step-by-step explanation:

The formula for surface area of a sphere is

SA = 4pi r^2

We know that the diameter is 8

To find the radius we cut the diameter in half.

r = d/2

r = 8/2 =4

Substitute in what we know.

SA = 4 *pi *4^2

    = 4*pi*16

   = 64*pi

Letting pi = 3.14

  = 200.96 in^2

We want to round to the nearest whole number

SA = 201 in^2

Answer:

Solutions are  (3, -8) and (5, -10)

Step-by-step explanation:

From the equation x + y + 5 = 0 :-

x = -y - 5

Substitute for x in the other equation:

y = (-y - 5)^2 - 9(-y-5) + 10

y = (y^2 + 10y + 25) + 9y + 45 + 10

y^2 +  18y + 80 = 0

( y + 8)(y + 10) = 0

y  = -8, -10

Substitute these values of y in the equation x + y + 5 = 0:-

x = -8:-

x - 8 + 5 = 0 so x = 8-5 giving.x = 3

x = -10:-

x - 10 + 5 = 0 sox = 10-5 giving x = 5

Answer:

angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.

Step-by-step explanation:

a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))

The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.

In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.

Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.

The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.

Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.

So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.

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Answer:

9/25

Step-by-step explanation:

The answer is 9/25

Answer:

System has only one solution. x= 4 and y = 2.

Step-by-step explanation:

We have given two equations :

2x + y = 10    ----------(1)

x - 3y = -2   ----------(2)

From equation (2), we can write:

x - 3y = -2

or x = -2 + 3y  , substitute this in equation (1).

We get,  2x + y = 10

2*(-2 + 3y) + y = 10

-4 + 6y + y = 10

7y = 10 + 4

y = 14/7 = 2

And x = -2 + 3*2 = -2 + 6 = 4

Hence we get x= 4 and y = 2. System has only one solution

The system of equations 2x+y=10 and x-3y=-2 has one solution, which is found by solving for y in terms of x using the first equation, substituting into the second equation, and solving for x, then solving for y. The solution is (4, 2).

To solve the system by substitution, we can express one variable in terms of the other using one of the equations and then substitute this into the second equation. Starting with the system:

2x + y = 10

x - 3y = -2

We can solve the first equation for y:

y = 10 - 2x

Next, we substitute this expression for y into the second equation:

x - 3(10 - 2x) = -2

Solving this equation for x:

x - 30 + 6x = -2

7x = 28

x = 4

Now we substitute x = 4 back into the equation y = 10 - 2x to find y:

y = 10 - 2(4)

y = 2

So the one solution to the system is (4, 2).

Since we found a unique solution, the system of equations has exactly one solution and is therefore consistent and independent.

Answer:

n=2

Step-by-step explanation:

I am assuming that you want to solve this algebraic equation

4n+3 =11

Subtract 3 from both sides

4n+3-3=11-3

4n =8

Divide each side by 4

4n/4 = 8/4

n =2

Answer:

[tex]\frac{19}{12}[/tex] feet

Step-by-step explanation:

First, we need to find the height after one year:

2.25 + 1 1/6 = [tex]\frac{41}{12}[/tex]

Now to find the amount in the second year, we can subtract the above amount from 5:

5 - [tex]\frac{41}{12}[/tex] = [tex]\frac{19}{12}[/tex]

So in the second year it grew [tex]\frac{19}{12}[/tex] feet