A school administrator believes that the mean class GPAs for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05, and checks a randomly chosen sample of 50 classes. Create a histogram, and calculate x¯, the t-statistic, and the p-value.Here is the data for the class GPAS:3.092.732.582.682.842.682.642.622.352.722.632.772.723.032.712.962.743.012.882.682.833.022.832.712.672.792.652.562.782.892.402.382.412.832.863.012.802.842.952.752.932.482.342.972.852.742.843.102.622.77The questions to answer:From the histogram, can normality be assumed? Yes/NoX =T=P=Since the P-value is (greater/less than) than the significance level of 0.05, than the null hypothesis (fails to be rejected/is rejected). (sufficient/insufficient) evidences exists that the new mean GPA is greater than 2.75

The question according to the equation will be a board that is 1/4 yard long cut into 2 equal pieces. Hence, option A is correct.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The given equation in the question is,

1/4 ÷ 2 = 1/8

It can be clearly seen that 1/4 divided by 2 is mentioned in the question and the product obtained is 1/8.

It means that 1/4 is divided into 2 equal pieces and the length of each piece is 1/8.

So, the question will be a board that is 1/4 yard long cut into 2 equal pieces. How long is each piece?

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The score that Alaina will have to get to tie the Winning teams score is 4.4.

Given that the long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m.

Also, Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m.

Therefore, Alaina's score to beat the other team will be:

= 25.6 - (5.46m + 4.84 + 4.92 + 5.98m)

= 25.6 - 21.2

= 4.4

Therefore, she must get 4.4 to tie.

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Answer:The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.

Step-by-step explanation:

The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.

Answer:

You can write it like 25.20 x -2 = -50.40

Step-by-step explanation:

Answer:

37 is LeBron 41 years old is kobe

The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

The definition of an exponential function is given by the equation

y = aeᵇˣ, where a and b are constants.

The given function is f(x) = 87000(0.9)ˣ.

Given that x = 0 represents the year 2010.

Therefore, x= 5 represents the year 2015.

Substitute x = 5 into the given function:

f(5) = 87000(0.9)⁵

     ≈ 51373

Hence, the population of Orange country is about 51373 in 2015.

Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.

The population of Greene city after 5 years is given by:

78000(1-8%)⁵

= 78000(1 - 0.08)⁵

= 78000(0.92)⁵

= 51408

Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

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The first four terms of the given sequence A(n)=4n^3+2 is 6, 34, 110, 258.

In the given question, the nth term of a sequence is given.

We have to write the first four terms of the sequence and we also have to express the terms in simplified form when applicable.

The given sequence is:

A(n)=4n^3+2

We find the four terms of the given sequence by putting n=1,2,3,4 in the given sequence.

Now putting n=1 in the given sequence

A(1)=4(1)^3+2

A(1)=4*1+2

A(1)=4+2

A(1)=6

Now putting n=2 in the given sequence

A(2)=4(2)^3+2

A(2)=4*8+2

A(2)=32+2

A(2)=34

Now putting n=1 in the given sequence

A(3)=4(3)^3+2

A(3)=4*27+2

A(3)=108+2

A(3)=110

Now putting n=1 in the given sequence

A(4)=4(4)^3+2

A(4)=4*64+2

A(4)=256+2

A(4)=258

Now the first four terms of the given sequence is 6, 34, 110, 258.

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The right question is:

The nth term of a sequence is given. Write the first four terms of the sequence. Express the terms in simplified form when applicable.

A(n)=4n^3+2

Phil's final debt after 20 years will be around $320,679.

To purchase a home, Phil borrowed $150,000 from a bank at a 3.5% annual interest rate.

The annual compounding of interest causes the amount of interest for each year to rise in proportion to the debt. Phil will be required to pay the initial sum plus interest after the first year, which comes to

$150,000 + 3.5% of $150,000 = $155,250.

Since interest is charged on the new amount owed for the second year, Phil will owe

$155,250 + 3.5% of $155,250, which

= $160,551.75.

For the next 20 years, this procedure is repeated, with the amount owed rising yearly by the sum of the year before plus interest. Phil's debt after 20 years will be around $320,679.

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The square of the hypotenuse equals the square of the sum of the other two sides is 13.89ft

Definition Of Pythagoras Theorem :

The Pythagorean theorem states that the total of the squares on a right triangle's legs equals the square on the hypotenuse (the side opposite the right angle)—or, in popular algebraic form, a2 + b2 = c2.

Given:

Height of the Tent Pole = 6ft.

Base of the Pole of the Tent = 12ft.

Now we will use Pythagoras theorem to find how long the rope is.

Use of Pythagoras theorem

Hence, the length of the rope is 13.89ft.

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After solving the expression, the number is 5.

In the given question we have to answer twice the sum of five times a number increased by one is twelve.

We have to determine the number by solving the given statement.

To solve the question we have to read the statement carefully. Then write the expression according to the statement. Then solve the statement according the rules.

In the given statement given that five time a number.

Let the number be x. So the expression should be 5x.

Again says that five times a number increased by one. So the expression 5x+1.

Then says that twice the sum of five times a number increased by one. Now the expression should be 2(5x+1).

Then says that twice the sum of five times a number increased by one is twelve. Now the statement is 2(5x+1)=12

Now solving the expression.

Divide by 2 on both side, we get

5x+1=6

Subtract 1 on both side, we get

5x=5

Divide by 5 on both side, we get

x=1

Now the number is 5.

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Answer:

Step-by-step explanation:

Pros: Lower rates: Insurance rates are reduced for most consumers. ✓ Rates match risk: Higher-risk policyholders may pay a higher rate that accurately reflects their higher risk of loss – so lower-risk policyholders don't have to subsidize the cost of insurance for higher-risk policyholders.

Cons: HIGHER rates.

Insurance companies justify the use of insurance scores by citing studies showing a positive correlation between credit scores and insurance claims

A higher credit score decreases your insurance rate, often significantly, with almost every company and in most states. Getting a quote, however, does not affect your credit. Your credit score is a key part of determining the rate you pay for insurance.

Answer:

x - 16 = -3

Step-by-step explanation:

x - 16 = -3  Add 16 to both sides of the equation

x = 13

It was 13 degrees at noon

for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, p value will be pchisq(8.4345,5)

To test a hypothesis' validity against actual data, a statistical calculation called a p-value is used. The probability of experiencing the results that were observed is calculated using a p-value, assuming that the null hypothesis is true. The p-value can be calculated by looking up the 8.4345 value in the Chi-Square distribution table with 5 degrees of freedom (6-1=5). The resulting p-value will depend on the significance level you choose.

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The number of pounds of strawberries sold and the number of pounds of blueberries sold are 50 and 23 respectively.

As in the question Keilantra runs a farm stand that sells strawberries and blueberries. Each pound of strawberries sells for $2.25 and each pound of blueberries sells for $4. Keilantra made $204.50 from selling a total of 73 pounds of strawberries and blueberries.

Let x be a number of strawberries and y is that of blueberries.

2.25x + 4y = 204.5-----------------------(1)

And

x + y = 73--------------------------------------(2)

On solving equation (1) and (2), we get,

x = 50 and y = 23

So, there are 50 pound strawberries and 23 pound  blueberries are sold.

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The graph the system of linear equations on a coordinate plane is added as an attachment and the solution is (2, 2)

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y=-1/2x+3 and y=2x-2

Rewrite the equations in the system of equations as follows:

So, we have the following representation

y = -1/2x + 3

y = 2x - 2

Next, we plot the graph of the system of equations

See attachment for the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (2, 2)

This means that the solution to the system of equations is (2, 2)

Recall that

y = -1/2x + 3

y = 2x - 2

Solution = (2, 2)

So, we have

2 = -1/2 x 2 + 3 = 2 --- true

2 = 2 x 2 - 2 = 2 --- true

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Answer:

A. y=6x

Step-by-step explanation:

A. y=6x that's all I know

Answer: A. y=6x

Step-by-step explanation:

Answer:

A. is the answer

Step-by-step explanation:

y as a function of x meaning:

Every x has a y, but the x value cannot repeat and every x has it's own y.

Example:

x: 1 2 3 4 5

y: 2 4 6 8 10

This is y as a function of x because the x values do not repeat and they each have a y value.

Example 2:

x:3 4 5 3 6

y: 1 2 3 4 5

This wrong because the 3 in the x value repeats twice which cause y not to be a function of x.

The reason why it wouldn't be B is because of -1

The reason why it wouldn't be C is because the y values repeat

The reason why it wouldn't be D is because all the x values are -7

Hope this helped!

Answer:

Step-by-step explanation:

70 mph

Answer:

Step-by-step explanation:

hi

Answer: -3x2

Step-by-step explanation:

Answer:

in five hours you will travel 153.75 miles

Hello!

What does this problem want:

==> how far will the car have traveled in 5 hours

What we must find ==> how many miles does the car travel in an hour

  [tex]\text{Rate}=\frac{61.5 \text{ miles}}{2 \text{ hours}} =30.75\text{ miles per hour}[/tex]

Therefore: the car will travel in 5 hours

   5 * 30.75 = 153.75 miles

Hope that helps!

Answer:

-3 is the answer.

Step-by-step explanation:

Given

(-12)3 + (24+9)----------^

= -12*3 + 33 ---------

= -36 + 33

= -3

If the model's p-value is less than 0.05, we rule out the null hypothesis and declare it to be significant.

Using the R software.

R codes : d=read.table('data.csv',header=T,sep=',')

head(d)

attach(d)

fit=lm(Heart.Rate~Age+Weight+Height)

summary(fit)

fit2=lm(Heart.Rate~Age+Weight)

summary(fit2)

R outputs:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

Heart Rate Age Weight Height

1         85  60    201     67

2        102  48    263     59

3         67  58    167     69

4         58  58    109     60

5         75  40    135     62

6         70  27    144     64

> attach(d)

> fit= lm(Heart.Rate~Age+Weight+Height)

> summary(fit)

Call:

lm(formula = Heart.Rate ~ Age + Weight + Height)

Residuals:

   Min       1Q   Median       3Q      Max

-21.1662  -7.9919   0.3377  10.3521  25.4165

Coefficients:

          Estimate Std. Error t value Pr(>|t|)

(Intercept) -2.86211   36.23799  -0.079   0.9377

Age          0.45993    0.21595   2.130   0.0428 *

Weight       0.12192    0.04841   2.519   0.0183 *

Height       0.59428    0.50119   1.186   0.2464

Significant codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.15 on 26 degrees of freedom

Multiple R-squared:  0.2841, Adjusted R-squared:  0.2015

F-statistic: 3.439 on 3 and 26 DF,  p-value: 0.03137

> fit2=lm(Heart.Rate~Age+Weight)

> summary(fit2)

Call:

lm(formula = Heart.Rate ~ Age + Weight)

Residuals:

  Min      1Q  Median      3Q     Max

-26.126  -9.851   1.049  10.328  22.284

Coefficients:

          Estimate Std. Error t value Pr(>|t|)

(Intercept) 36.63974   14.36802   2.550   0.0168 *

Age          0.45122    0.21744   2.075   0.0476 *

Weight       0.12065    0.04876   2.474   0.0199 *

Significant codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.25 on 27 degrees of freedom

Multiple R-squared:  0.2454, Adjusted R-squared:  0.1895

F-statistic:  4.39 on 2 and 27 DF,  p-value: 0.02235

a) Multiple linear regression equation :

y hat =  -2.862    +   0.460 X1  +    0.122 x2    +   0.594 x3

b) F =   3.439 on 3 and 26 DF,

p-value: 0.03137

We reject the null hypothesis and determine that the model is significant because the p-value is less than 0.05.

c) Heart rate is highly linked with the variable whose p-value is less than that variable. Heart rate and fluctuating weight are strongly connected in this instance.

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The graph of the new function compared to the first one will be shifted down.

Vertical translation describes the movement of a function graph upward or below. The function's form is preserved in this case. The graph moving or shifting along the y-axis is another name for it. Each point on the graph moves k units vertically during vertical translation, and the graph is said to have translated k units.

The two functions are

f(x) = x + 2

g(x) = x - 1

You can see that all you need to do to transform f into g is just take 3 off of it.

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

= x + 2 - 3

= x - 1

= g(x)

Every transformation, such as f(x) f(x) + k, now produces a vertical translation, which is translated upward if k > 0 and downward if k 0. The correct response is C since the function is translated three units down in our situation where k = -3.

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The complete question is:

"If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?

A. It would be shifted up.

B. It would be shifted left.

C. It would be shifted down.

D. It would be less steep."

In the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.

What is a polynomial?

'poly' means many and 'nominal' means term. A polynomial is a type of algebraic expression with many terms having variables and coefficients.

Given polynomial is,

[tex] {(x + y)}^{6} [/tex]

Expanding the given sixth-degree polynomial using binomial expansion we get the expression of the picture given.

Solving all expressions we get,

[tex] {(x + y)}^{6} = {x}^{6} + 6 {x}^{5} y +15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6x {y}^{5} + {y}^{6} [/tex]

The middle term is

[tex]20 {x}^{3} {y}^{3} [/tex]

The coefficient of the term is 20

The sum of all coefficients is 1+6+15+20+15+6+1= 64

Hence, in the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.

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As asked in the question the value of xz and y will be even ,

xz is even and y is also even

given

X = factor of Y

Y = factor of Z

Therefore,

z= mnz = mnx  , xz = even

because

either z even, so the answer is directly yes or x is even (or both) but if x is even and as then  z= mnz = mnx must be even too (one of the multiples of z is even, so z is even too).

(2) y=  even

because

as z=ny then as one of the multiples of z even then only  z  will be even

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.

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Answer:

69.29 deg

Step-by-step explanation:

Recall that tan(x) = opposite/adjacent. This is helpful because we know the opposite and adjacent leg from the angle x! This gives us tan(x) = 43/18, so we can solve for x by taking tan^-1 of both sides, giving x = tan^-1(43/18), or 67.29 degrees.

The probability of bike can travel more than 50 miles without refueling is 0.1151, according to the question.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

According to data in the given question,

We have the given information:

Mean = 44

deviation = 5

Let X be the random variable that represents the population's average number of motorcycle kilometers; in this instance, we know the distribution for X is provided by:

X ~ N(44.5)

Where μ=44 and σ=5,

We are interested on this probability,

P(X>50)

We can also apply the z score formula from:

z=x-μ/σ

Using this formula, we obtained:

P(X>50) = P(X-μ/σ > 50-μ/σ) = P(Z > 50-44/5) = P(z > 1.2)

Using the normal standard distribution and the complement rule, we can determine this probability, giving us:

P (z > 1.2) = 1 - P(z > 1.2) = 1 - 0.8849 = 0.1151

Therefore, the probability is 0.1151.

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A parametric test would be more suitable because it provides a more appropriate answer.