A principle at a certain high school claims that the students in her school are above average in SAT. She collects a random sample of 50 students and given an SAT test that provided with a mean score of 541. Is there sufficient evidence statistically to support the principal’s claim? The mean population SAT score is 500 with a standard deviation of 100. SAT scores are normally distributed. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.  

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.  

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.  

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].  

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.  

(b) Explain why one rate of change is greater than the other.  

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

rate of change or slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]

y = mx + b

"b" is y-intercept

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Answer:

the first one and the last one

Step-by-step explanation:

Hope it will helps you ❤️❤️❤️

Please mark me as a brainliest

Answer:

The numbers are 11,12,13

The smallest number is 11

Step-by-step explanation:

Let the first number be x

The next number is x+1

The third number is x+2

x+x+1+x+2 = 36

Combine like terms

3x+3 = 36

Subtract 3 from each side

3x+3-3 = 36-3

3x=33

Divide each side by 3

3x/3 = 33/3

x=11

The numbers are 11,12,13

The smallest number is 11

[tex]\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail h(4)[/tex]

[tex]\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 1/5(16-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 10/5-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 2-8[/tex]

[tex]\\ \tt\bull\rightarrowtail -6[/tex]

Answer: -1 3/4

Step-by-step explanation

just add the fractions together :)

(between the -2 and -1 1/2)

Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.

The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing

I’m not sure but I need points so please mark this as answer :)

Answer:

Step-by-step explanation:

As they are similar triangles

24/AB = 24/2AD = 12/AD = (x + 2)/AD

12 = x + 2

x = 10

(y + 6) + (x - 3) / 24 = (y + 6)/(x + 2)

(y + 6) + (10 - 3) / 24 = (y + 6)/(10 + 2)

             (y + 13) / 24 = (y + 6)/12

                 12(y + 13) = 24(y + 6)

                12y + 156 = 24y + 144

                          12y = 12

                             y = 1

AC = (y + 6) + (x - 3)

AC = (1 + 6) + (10 - 3)

AC = 14

Answer:

x=32

Step-by-step explanation:

answer

TRUE

HOPE IT WILL HELP YOU

Answer:

32

Step-by-step explanation:

180 - 148 = 32

I hope this helps!

Answer:

110

Step-by-step explanation:

Know the angle for BCD which is 130.

Subtract 180 from 130 and you get angle c for the triangle which is 50

Already knowing B and C, add them both which comes up to 70

All triangle angles equal 180 so subtract 70 for 180 and you get 110

Answer:

1/15

Step-by-step explanation:

2/3 x 1/10 = 2/30 or 1/15

Answer:

1/15

Step-by-step explanation:

Answer:

y=-x+9

Step-by-step explanation:

The answer above is written in slope-intercept form because it is the easiest form to graph (in my opinion); slope-intercept form is y=mx+b, where m is slope and b is the y-intercept. However, to get the answer, you must first use slope-point. Slope-point is [tex]y-y_{1}=m(x-x_{1})[/tex]. So, plug in the point and slope into the formula. This gives the equation, y-6=-1(x-3). Then, solve the equation for the answer of y=-x+9.

On a graph, the y-intercept will be 9. So, the line will cross the y-axis at a value of 9. Additionally, the slope is -1. So, y will increase by one and x will decrease by one. This means that the line will look like it decrease left to right.

Answer:

Step-by-step explanation:

The share of stock is $88.33 worth now which is the value of a share of stock on the stock market decreased by 14%.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

The value of a share of stock on the stock market decreased by 14%. If it used to be worth $102.64 which is given in the question.

We have to determine the evaluation of 15% of 60.

⇒ 14% of $102.64

15%  is expressed as 15/100 in fractional form

⇒ (14/100)(102.64)

15/100  is expressed as 0.15 in decimal form

⇒ (0.14)(102.64)

Apply the multiplication operation, and we get

⇒ 14.31

Therefore, 14% of $102.64 would be $14.31.

The share of stock is worth now: $102.64 - $14.31 = $88.33.

Learn more about the percentages here:

brainly.com/question/24159063

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Answer:

Yes

Explanation:

1.3/7.8 = 0.167

3/18 = 0.167

An equivalent fraction is a fraction that is the same as another fraction with a different denominator.

I hope it helps.

Answer:

10 tomatoes (bottom fruit) - 9 kiwis (top fruit) = 1 tomato

10-9=1

Step-by-step explanation:

Step-by-step explanation:

Ok, so we know the bank loaned part of the $17,500 at a 4% interest rate. Lets call this loan amount x. Then the rest of the 17,500 was loaned at a 9% interest rate. Whatever this amount was, we can define it as 17,500 - x. We also know that the total interest earned was $1,100. With this information, we can form the following equation:

.04(x) + .09(17500 - x) = 1100

Multiply the .09 times the inside of the parentheses:

.04x + 1575 - .09x = 1100

Simplify:

-.05x + 1575 = 1100

-.05x = -475

x = 9500

Since x is originally the amount loaned at the 4% interest rate, we know that $9,500 was loaned at a 4% interest rate.

To figure out the other amount loaned at 9%, simply subtract 9,500 from 17,500 -- this gets us 8,000. So $8,000 was loaned at a 9% interest rate.

I hope this helps!

Answer:

x=7

Step-by-step explanation:

1/2(x-6)=1/2

(1/2)(x)+(1/2)(−6)=1/2

1/2x+−3=1/2

1/2x−3=1/2

1/2x−3+3=1/2+3

1/2x=7/2

2*(1/2x)=2*(7/2)

x=7

tada!

Answer:

Part A: 8 ribbons

Part B: see below

Step-by-step explanation:

first 5 1/3 = 16/3

[tex] \frac{16}{3} \div \frac{2}{3} \\ = \frac{16}{3} \times \frac{3}{2} \\ = \frac{48}{6} = 8[/tex]

the answer is 8 dude!

Answer:

its not sixes theres 4 sixes equal 24 so there is no answer

Step-by-step explanation:

can i have brainliest pls

Answer:

9

Step-by-step explanation:

Double 27 is 54. 6 times 9 is 54

3xyz = P

xyz = P/3

xy = P/3z

x = P/3yz

Answer is not there in the options.....but it's correct.

____

Hope it helps ⚜

Answer:

25%

Step-by-step explanation:

8-6=2

2/8=0.25

0.25×100=25%

Answer:

I am stuck on the same question please comment if someone answers

Answer:

3

Step-by-step explanation:

Okay so 18 chairs were used more for 6 more rows so each row has 3 length.

x = 3

Now this makes no sense, because I don't know why you would leave 6 chairs if you only have 3 chairs for each row but....(Hue is weird so let's not question him)

Anyways mathematically

first arrangement = 2x + 6

second arrangement = 8x - 12

2x + 6 = 8x - 12

6x = 18

x = 3

Answer:

936

Step-by-step explanation:

Therefore you multiply 6 by 18 = 6×18= 108

1,044 - 108 = 936

So therefore the total is 936

From the power rules, the power [tex]3^{-2}[/tex] is equal to the fraction [tex](\frac{1}{3})^{-2}[/tex].

There are different power rules one of them is the negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]5^{-3}=(\frac{1}{5})^3=\frac{1}{125} \\ \\ \\ {\frac{4}{6} }^{-2}={\frac{6}{4} }^2=\frac{36}{16}[/tex]

Then, the question gives:

[tex]3^{-2}=({\frac{1}{3}})^2[/tex]

Read more about power rules here:

https://brainly.com/question/12140519

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Answer:

y+1=3(x+8)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(-6-(-8))

m=(5+1)/(-6+8)

m=6/2

m=3

y-y1=m(x-x1)

y-(-1)=3(x-(-8))

y+1=3(x+8)