"An education researcher recorded the number of books students read over the last year and the number of vocabulary words that students defined correctly on a test of 100 vocabulary words. The resulting data were used to conduct a hypothesis test to investigate whether there is a positive linear relationship between the number of books read and the number of vocabulary words defined correctly. What are the correct hypotheses for the test?"

The question is incomplete. The complete question is :

The volume of a sphere is increasing at a rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4 pi / 3 cm^3. (Do not round your answer.)

Solution :

Volume of the sphere, [tex]$V=\frac{4}{3} \pi r^3$[/tex]

Given that [tex]$\frac{dV}{dt}= 7 \ cm^3/s $[/tex]

V = [tex]$\frac{4 \pi}{3} = \frac{4 \pi r^3}{3}$[/tex]

∴ r = 1

[tex]$\frac{dV}{dt} =\frac{4}{3} \pi .3.r^2 \ \frac{dr}{dt}$[/tex]

[tex]$7 = \frac{4}{3} ( \pi )(3) (1)^2 \frac{dr}{dt}$[/tex]

[tex]$\frac{dr}{dt}=\frac{7}{4 \pi}$[/tex]   cm/s

Surface area, [tex]$A = 4 \pi r^2$[/tex]

    [tex]$\frac{dA}{dt} = 8 \pi r \ \frac{dr}{dt}$[/tex]

[tex]$\frac{dA}{dt} = 8 \pi \times \frac{7}{4 \pi} \times 1$[/tex]

    [tex]$=14 \ cm^2/s $[/tex]

Answer:

2(8x+18)

multiply the values in the bracket with 2

2×8x=16x

2×18=36

16x + 36

Answer: 2(8x+18)   ,4(4x+9)

Step-by-step explanation:

16 x+36 =4(4x+9)=2(8x+18)

Answer:

7/24 is x and 24/25 is y :)

Step-by-step explanation:

hopefully that helped

Answer:

the mode is 12

Step-by-step explanation:

Arrange the numbers in order : 1 , 3, 6, 6, 9, 9, 12, 12, 12, 12, 12, 15, 15, 15, 15

Then count how many numbers that appears the most, so the number that appears the most is 12, therefore, the mode in the data set is 12 .

40° is your answer

Answer:

:

< ABC+<QRS=180

m<QRS=180-140=40°

Answer:

Michelle must get an 80 on her next test to keep her average score.

Step-by-step explanation:

Since Michelle got an average score of 80 on two tests, to determine what score she must get on the third test so that her average score for the three tests is the same as the average score for the first two tests, the following calculation must be performed:

X / 2 = 80

X = 80 x 2

X = 160

X x 3 = 80 x 3

X x 3 = 240

X = 240/3

x = 80

So, Michelle must get an 80 on her next test to keep her average score.

Answer:

16+3y=31

3y=31-16

3y=15

y=15/3

y=5

check.

16+3×5

=16+15

=31

Answer:x=18

Step-by-step explanation:

if she deposites 40 every week 40 times 18 is 720 so in 18 weeks she can have a t.V

Answer:

both of em

Step-by-step explanation:

Answer:

36043.305

Step-by-step explanation:

My brain is so tired I can't-

Multiply all the numbers with the information they gave you, then add them all.

I REALLY HOPE THIS HELPED MY BRAIN NEEDS A BREAK

Answer:

30% man this easy

Step-by-step explanation:

PLS GIMME BRAINLIEST PLS

Answer:

Apple costs $0.26

and orange costs $0.32

sorry i don't have time to explain but if u have doubts don't hesitate to ask

Answer:

Step-by-step explanation:

This is the proportional relationship:

We have x = 3, y = 24, then k is:

The table will look as:

Correct choice is C

Answer:

c

Step-by-step explanation:

Answer:

(x+3)(x-3)(x+1)(x-1)

Proof:https://www.symbolab.com/solver/step-by-step/x%5E%7B4%7D-10x%5E%7B2%7D%2B9

Answer:

1) 18 inches

Step-by-step explanation:

By the Midsegment Theorem: A midsegment connecting two sides of a triangle is parallel to the third side and is half as long the third side.

ans: 36/2 = 18

Step-by-step explanation:

1. K = 13 (13+5=18)

2. X= 36 (36-12=24)

3. Y = 14 (17=3+14)

4. Z= 24(22=24-2)

5. A=7 (divide both sides by 4)

6. H=12 (12/6=2)

7. B= 10 (100=10*10)

8. Y=42 (6=42/7)

I'm pretty sure that this is correct.

Answer:

4/3

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

[tex] { \frac{2}{3} }^{2} = \frac{4}{9} [/tex]

have a nice day

Answer:

Step-by-step explanation:

3/13

The probability of being dealt a picture card is 3/13

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the total number of cards in the deck be = 52 cards

Let the number of picture cards be = A

Now , the picture cards include 4 colors of Jacks , 4 colors of Queens and 4 colors of Kings

So , total number of picture cards = 4 + 4 + 4

                                                        = 12 picture cards

And the probability of drawing a picture cards is P =
number of picture cards / total number of cards in the deck

The probability of drawing a picture cards is P = 12 / 52

                                                                               = 3 / 13

Therefore , the value of P is 3/13

Hence , The probability of being dealt a picture card is 3/13

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ2

Answer:

< ABC+<QRS=180

m<QRS=180-140=40°

Answer:

Solution given:

<ABC+<QRS=180° {supplementary]

m<QRS=180°-140°=40° is your answer

Answer:

28yd²

Step-by-step explanation:

area of square = side *side

=6*6= 36²

area of rectangle (patio)= length* breadth

=4*2=8²

area of garden= area of square - area of rectangle

=36-8

=28 yd²

Answer:

Step-by-step explanation:

First Case:

Given,

Side of the big square = 6 yd

Therefore,

Area of the big square = side × side

= 6yd × 6yd

[tex] = 36 {yd}^{2} [/tex]

Second Case:

Length of the patio = 4 yd

Breadth of the patio = 2 yd

Therefore,

Area of the patio = Length × Breadth

= 4yd × 2yd

[tex] = 8 {yd}^{2} [/tex]

Last Case:

According to first and second cases,

Area of the garden

= Area of the big square - Area of the patio

[tex] = 36 {yd}^{2} - 8 {yd}^{2} [/tex]

[tex] = 28 {yd}^{2} [/tex]

Required area of the garden is 28 sq. yd (Ans)

Answer:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Step-by-step explanation:

We want to write the trignometric expression:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]

Take the secant of both sides:

[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]

By substitutition:

[tex]\displaystyle= \sin(2\theta)[/tex]

Using an double-angle identity:

[tex]=2\sin(\theta)\cos(\theta)[/tex]

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]

Simplify. Therefore:

[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]

Answer:

it would be 3 tons if I'm correct

Answer: 3 tons

Step-by-step explanation:

1 ton is equal to 2,000 pounds.

Divide 6,000 from 2,000 to find how many tons the animal weighs.

6,000/2,000=3.

Hope this helps!

Answer:

im pretty sure its A

Step-by-step explanation:

Answer:

1: 14z+2

2: 7z/4 + 5x

3: y²/3z

Answer:

4.33333333333 or 4 and 1/3

Step-by-step explanation:

Answer:

4 1/3

Step-by-step explanation:

1) Convert 5 3/4 to improper fraction.

2) Simplify 5x4 to 20.

3) Simplify 20+3 to 23.

4) Convert 1 5/12 to an improper fraction.

5) Simplify 1x12 to 12.

6) Simplify 12+5 to 17.

7) Find the least common denominator of 23/4 & 17/12.

8) Make the denominators the same.

9) Join the denominators.

10) Simplify 52/12 ( 4 1/3 )

Hope this helped!

​  

.

Answer:

Step-by-step explanation:

Center is 6, -2

Radius is 7

(x-6)^2 + (y + 4)^2 = 7^2

==============

Please give brainliest, I really want to rank up, thank you!

Answer:

5 i think

Step-by-step explanation: