Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores.Use α=0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0 Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores. Use α = 0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0

Answer:

D

Step-by-step explanation:

f(x) = -3x^3 + x^2 – 3       f(2) means that wherever you see a x, put in a 2.

f(2)= -3(2)^3 + (2)^2 - 3

f(2) = -3*8 + 4 - 3

f(2) = - 24 + 1

f(2) = - 23

[tex]\\ \sf \longmapsto f(2)[/tex]

[tex]\\ \sf \longmapsto -3(2)^3+(2)^2-3[/tex]

[tex]\\ \sf \longmapsto -3(8)+4-3[/tex]

[tex]\\ \sf \longmapsto -24+1[/tex]

[tex]\\ \sf \longmapsto -23[/tex]

Answer:

The simplified answer of the given expression is 1.

Step-by-step explanation:

When you see (f + g)(x), then it means that you are going to add f(x) and g(x) together. So, we are going to add the terms together that are given in the problem. We are also given the value of x which is 1. So, we are going to combine this information together so we can simplify the expression.

(f + g)(1)

f(x) = x - 1

g(x) = x²

(f + g)(1) = (1 - 1) + (1²)

Simplify the terms in the parentheses.

(f + g)(1) = 0 + 1

Add 0 and 1.

(f + g)(1) = 1

So, (f + g)(1) will have a simplified answer of 1.

Answer:

7/6

Step-by-step explanation:

The LCD of these three fractions is 6; the denominators 3, 3 and 6 divide evenly into 6.

Therefore we have:

4/6 + 2/6 + 1/6 = 7/6

Answer:

The second graph is a function.

Step-by-step explanation:

This is the only one that passes the vertical line test.

(If there exits a vertical line which passes through more than one point, then the relation is NOT a function).

With a 10% profit the radio would be 2000 x 1.10 = 2,200

A 20 % discount means it would sell for 80% of the total price.

Divide the 2200 by 80% to get the fixed price:

2200/0.8 = 2750

Fixed price = 2750

Answer:

1260

Step-by-step explanation:

(7!)/ (2!times 2!)

7 factorial divided by 2factorial times 2 facotiral

The number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be calculated as;

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter of the word 'MILLION' is a total of 7 letters.

So, the number of possible arrangements will be

(7!)/ (2!times 2!)

= 1260

Therefore the number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

Learn more about permutations here -

brainly.com/question/4301655

#SPJ2

Answer:

Step-by-step explanation:

point est. 0.307824427

99% 2.58

Confidence Interval - "P" values  

(0.2914 , 0.3243 )  

Answer:

10,000

Step-by-step explanation:

There are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

A number system is defined as a system of writing to express numbers.

We need to find

positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

Let all 9 numbers ae

a+b+c+d+e+f+g+h+9=13

a+b+c+d+e+f+g+h=13-9

a+b+c+d+e+f+g+h=4

Then we use combinations

(n+k-1)Ck

¹¹C₄

11!/(11-4)!4!

11!/7!4!

330

Three hundred thirty times of nine is two thousand nine hundred seventy.

Now 330 ×9=2970

Hence there are 2970  positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ1

Answer:

x = 8

y = 2√3

Step-by-step explanation:

Since this is a right triangle

x^2 = (4√3)^2 + 4^2 ➡ x^2 = 64 and x = 8

Using Euclidean theorem

y^2 = (x-6)(x - x - 6) = 6x - 36

y^2 = 6×8 - 36

y^2 = 12

y = 2√3

Answer:

1 ) x = 8,

2 ) y = 2√3

Step-by-step explanation:

Take a look at the outermost triangle. I can tell that this is a 30 - 60 - 90 triangle, as if the leg opposite to the 30 degree angle was x, the other respective leg, opposite to the 60 degree angle, would be x√3. Here this " x " would be 4, but don't let that confuse you with the x we have to solve for.

As this outermost triangle is right, x is present as the hypotenuse and we can solve through Pythagorean Theorem,

( 4√3 )² + ( 4 )² = x²,

48 + 16 = x² = 64,

x = √64 = 8

And an inner triangle, present with y being a leg, has a respective leg length of x - 6, or 8 - 6 = 2. Let's solve for y using Pythagorean Theorem once more,

y² + 2² = 4²,

y² = 16 - 4 = 12,

y = √12 = √2 [tex]*[/tex] 2 [tex]*[/tex] 3 = 2√3

Answer:

Hey there!

We have tangent x=8/10

This simplifies to tangent x=0.8

Arctan=0.8, x=38.7 degrees.

Let me know if this helps :)

Answer:

38.7

Step-by-step explanation:

You are given the lengths of the legs of the triangle.

The trig ratio that relates the lengths of the legs is the tangent.

tan x = opp/adj

tan x = 8/10

tan x = 0.8

Use the inverse tangent function to find x.

tan^(-1) 0.8 = 38.7 deg

Answer: x = 38.7 deg

Answer:

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Step-by-step explanation:

The null and alternative hypotheses as

H0: μd=0    Ha: μd≠0

Significance level is set at ∝= 0.05

n= 6

degrees of freedom = df = 6-1 = 5

The critical region is t  ( base alpha by 2 with df=5) ≥ ± 2.571

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Sales                                      Difference

Person      After      Before   d = after - before      d²

1                   94          90                4                      16

2                  82          84               -2                       4

3                  90          84               6                       36

4                  76           70               6                       36

5                  79           80               -1                        1

6                  85          80                 5                       25  

∑                                                       18                   118

d`= ∑d/n= 18/6= 3

sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67

sd= 3.266

t= 3/ 3.266/ √6

t= 2.249

Since the calculated value of t= 2.249 does not  falls in the rejection region we therefore accept  the null hypothesis at 5 % significance level . On the basis of this we conclude that the  bonus plan has not  increased sales significantly.

Answer:

The critical value is 6.26.

Step-by-step explanation:

It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.

The critical value of F to test the significance of the model is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

Here,

k = number of independent variables

n = number of observations.

Then the critical value is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

                      [tex]=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26[/tex]

*Use a F-table.

Thus, the critical value is 6.26.

The correct answer is Hardware store

Explanation:

In this case, you need to determine the distance between the pet store and the locksmith to know if the distance is longer than the one from the pet store and the hardware (35 kilometers). Now this distance can be calculated by subtracting the distance from the locksmith to the garbage dump from the total distance between the pet store and the garbage dump. This is because the locksmith is between the pet store and the garbage, which means the distance between the pet store and the locksmith is a portion of the total distance, which is the distance from the pet store and the garbage dump. The process is shown below:

128.6 kilometers (distance from the garbage dump to the pet store) - 77.9 kilometers (distance from the garbage dump to the locksmith) = 50.7 (distance from the locksmith to the pet store

50.7 kilometers is greater than 35 kilometers, which means the  hardware store is closer to the pet store

17 is the answer

(Mark me brainliest)

Answer:

If something is guaranteed, it has a probability of 100%, or 1.

Step-by-step explanation:

A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)

Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.

What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.

So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled

The probability of getting a red card is 1.

No matter how you shuffle the cards, the no of cards will remain the same.

Therefore, it will not affect the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Learn more about probability here: https://brainly.com/question/251701

#SPJ2

Points: (-1,-7), (1,7)

Formula (y=mx+b):

y = 7x

Slope m: 7

Y-intercept b: 0

Parallel lines: 7x + any number

Must click thanks and mark brainliest

Answer:

3* 10 ^12

Step-by-step explanation:

(5x10^7)(6x10^4)

Multiply the numbers together

5*6 =30

Add the exponents

10^7 * 10 ^ 4 = 10 ^(7+4) = 10 ^11

30 * 10 ^11

But this is not scientific notation since 30 >10

Move the decimal one place to the left and add 1 to the exponent

3* 10 ^12

Answer:

3* 10 ^12

Step-by-step explanation:

Step-by-step explanation:

a.

[tex]y = k {r}^{2} [/tex]

[tex]7 = k {3}^{2} [/tex]

[tex]7 = 9k[/tex]

[tex]k \: = \frac{7}{9} [/tex]

[tex]y \: = \frac{7}{9} {r}^{2} [/tex]

b.

[tex]y \: = \frac{7}{9} \times {15}^{2} [/tex]

[tex]y = \frac{7}{9} \times 225[/tex]

y = 175

Subtracting a negative is the same as adding a positive. So 2-(-8) is really 2+8 = 10.

With something like 2-8, we start at 2 and move to the left 8 units to arrive at -6 on the number line. When we do 2-(-8), we start at 2 and move 8 units in the opposite direction since -8 is the opposite of 8.

In terms of money, you can think of a negative number as an IOU or it represents the amount of debt. Writing -8 means you are 8 dollars in debt. If we subtract away debt, then we have less of it and effectively its the same as adding dollars to your pocket. Subtracting away 8 dollars of debt is the same as adding 8 dollars to your pocket, which is one interpretation of how 2-(-8) is the same as 2+8.

Answer:

15.5846.>

Step-by-step explanation:

Answer:

6ft

Step-by-step explanation:

Answer:

6ft

Step-by-step explanation:

Answer: 44

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3

Step-by-step explanation:

The recursive formula for a geometric sequence is of the form

[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]

where r is the common ratio

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{0.9}{-0.3}[/tex] = - 3 , thus

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3

Answer:

[tex]\Large \boxed{\mathrm{D. \ 4}}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve the problem.

tan θ = opp/adj

tan 30 = y/(4√3)

y = 4√3 tan 30

y = 4

Answer:

Step-by-step explanation:

Temperature is a function of the time of day. There can be only one temperature at any particular time.

In contrast, a particular temperature can occur more than one time in a day, so time is not a function of temperature.

What we need to memorize when finding the slope is this formula:

[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

m here represents the slope. I hope this does not confuse you with line m.

The problem here is that we do not have any given points, but we have a way.

If we notice on the graph, the graph contains or passes through (2,-1) and (-2,1). We can use these points to find the slope. So let these be the following:

[tex] \displaystyle \large{(x_1,y_1) = (2 ,- 1)} \\ \displaystyle \large{(x_2,y_2) = ( - 2 ,1)} [/tex]

Then we substitute these points in the formula.

[tex] \displaystyle \large{m = \frac{ 1 - ( - 1)}{ - 2 - 2} }[/tex]

negative × negative = positive.

[tex] \displaystyle \large{m = \frac{ 1 + 1}{ - 2 - 2} } \\ \displaystyle \large{m = \frac{ 2}{ - 4} } \longrightarrow \boxed{m = - \frac{1}{2} }[/tex]

Since m represents the slope. Therefore, the slope of line m is -1/2

Answer:

Supplementary

Step-by-step explanation:

When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.

<AOB (40°) and <BOC (140°) are not equal angles.

<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.

<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.

<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.

Answer:

-5+3=-2

1/4 of 24 = 6

Step-by-step explanation:

Answer:

0.2207

Step-by-step explanation:

Here, we want to find the probability that the sample mean is greater than 25.

What we use here is the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question;

x = 65, mean = 63, SD = 13 and n = 25

Plugging these values in the z-score equation, we have

Z-score = (65-63)/13/√25 = 2/13/5 = 0.77

So the probability we want to calculate is ;

P(z > 0.77)

This can be obtained from the standard normal distribution table

Thus;

P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p