you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. by the deadline, 1347 teachers return the questionnaire. the population is

The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Note that the general slope equation is:

y = mx + b

Where

m is the slope of the line and

b is the y-intercept.

In this specific instance, m is the change in the price of the ticket

b is the additional fee value that needs to be included for each ticket

Hence, the cost of the ticket (y) is given as:

y = (change rate of x) + added fee to every order

Where rate of change = 21; and

The fee added to each order is 10.25

Given the above, the general equation becomes:

y = 21x + 10.25

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Answer:

it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps

Step-by-step explanation:

The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.

Hypothesis:

H₀ : μ = 3000

H₁ : μ > 3000

The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.

The following information is provided:

s = 450

x = 3200

n = 14

Therefore, test statistics will be:

t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66

The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.

0.0601 is the p-value.

We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.

Since p =.0601, the director's assertion cannot be supported by the available data.

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Answer:

8.433 to the power of 4

Step-by-step explanation:

The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.

The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.

When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.

From standard normal tables,

P( -2.326 < Z < 2.326) = 0.98 here

The sample size required here is computed as:

n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12

Therefore, the required sample size, in this case, is 71.

To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.

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COMPLETE QUESTION:

An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)

The weight of the eggs in grams 95.38 grams.

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X ~ N(58,21)

where µ = 58 and σ = 21

The z score for this case is given by this formula:

z = x -  µ/σ

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

X =  µ+1.78σ

= 58 + 1.78×21

= 95.38

So, the corresponding weight for a z score of 1.78 is 95.38 grams.

Hence we get the required answer.

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The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The system of equation are

-3x + y = 3

-x + 2y = -4

Here we have to use the substitution method

-3x + y = 3

y = 3 + 3x

Substitute the value of y in the second equation

-x + 2(3 + 3x) = -4

-x + 6 + 6x = -4

-x + 6x = -4-6

5x = -10

x = -10/5

x = -2

Substitute the value of x in the first equation

-3x + y = 3

-3(-2) + y = 3

6 + y = 3

y = 3 - 6

y = -3

Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The complete question is:

Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?

a) On a coordinate plane, 2 lines intersect at (3, 0).

b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).

d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).

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Answer:

B

Step-by-step explanation:

both point intersect at ( -2, -3)

Answer:2380 minutes. By saying how many more minutes does an infant sleep than an adult in one week impies that you have to subtract how long an adult sleeps taken away from the amount of time an infinte sleeps. Once you get the answer you multiply it by seven.

Step-by-step explanation:

Answer:340 minutes

Step-by-step explanation:you subtract the amount an infant sleeps (820 minutes) by the amount an adult sleeps (480 minutes)

820-480=340

The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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the answer is 1 but it could be a I took the test

The required number is 94.

Let the digit on unit's place be 'x'

Digit on ten's place be 'y'

Therefore,

Original number = 10y + x

Given, the sum of the digits = 11

=> x + y = 11 →(I)

When the digits are reversed, new number = 10x + y

Therefore,

(10y + x) - (10x + y) = 63

10y + x - 10x - y = 63

9y - 9x = 63

=> y - x = 7 →(II)

Adding (I) and (II) we get

2y = 18

y = 9

Substituting the value of y in (I) we get

x + 9 = 11

x = 2

Therefore,

Original number = 10y + x = 10(9) + 4 = 94

The required number is 94.

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Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

The domain and the range of a function have the concepts given as follows:

The domain of a function or of a relation is the set that contains all possible input values. Hence, among possible representations, we have that:

The range of a function or of a relation is the set that contains all possible output values. Hence, among possible representations, we have that:

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Answer:

4/3x

Step-by-step explanation:

Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.

Given equation,

[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]

For values (-∞,-7)

equation stands true

For values (-7,5)

equation stands false

For values (5,12)

equation stands true

For values (12,∞)

equation stands false

Hence, x ∈ (-∞,-7)∪(5,12).

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The percent of the variation in the amount of money earned can be explained by differences in the number of hours worked 20.8%.

Given that, the correlation coefficient (r) between the number of hours worked x and the amount of money earned y is 0.456.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

The percent of the variation in the dependent variable that can be explained by the independent variable is called coefficient of determination, which is r².

In this case, r = 0.456. So r² = 0.456² = 0.208

That means 20.8% of the variation in the amount of money earned can be explained by differences in the number of hours worked.

Therefore, the percent of the variation in the amount of money earned can be explained by differences in the number of hours worked 20.8%.

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The solution to the inequality is y < -12 ( y less than negative 12).

Given inequality is;

y + 15 less-than 3

y+15<3

For solving the inequality, we will subtract 15 from both sides in order to find y.

Subtracting 15 from both sides of inequality

The solution to the inequality is y < -12 ( y less than negative 12).

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The domain of the given quadratic function is { -3 }

and range is { 1 }

A function's domain is the set of values that can be plugged into it. This set symbolizes the x values in a function like f. (x). Additionally, we can deduce that a function's range refers to the set of values it can accept. There are values in this set that the function returns when we enter an x value.

The domain of the given quadratic function is { -3 }

and range is { 1 }

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Answer:

7

Step-by-step explanation:

65x+9.45y=160.657 point 6 5 x plus 9 point 4 5 y is equal to 160 point 6 5

The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.

First, we will calculate the speed of the penguin. The speed is represented by the variable "s".

s = 1,760/8

s = 220 feet per minute

The location of the penguin after 2 minutes is calculated below.

d = 2×s

d = 2×220

d = 440

Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

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Answer:

Step-by-step explanation:

Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample​ proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.

Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.

50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.

It will be demonstrated by:

1 - p = 1 - 10% = 1 - 0.10 = 0.90

np = 50 × 0.1 = 5. This suggests the number of victories.

Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.

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The question is -

For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?

The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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The total quantity of diesel fuel is 15.75 gallons.

The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.

1 quart = 0.25 gallon

For first container, 3 quarts = 0.25 × 3

3 quarts = 0.75 gallon

For second container, 2 quarts = 0.25 × 2

2 quarts = 0.5 gallon

For third container, it has 0.25 gallon

1 pint = 0.125 gallon

For first and third container, it has 0.125 gallon

So, amount of diesel fuel in first container = 3 + 0.75 + 0.125

Amount of diesel fuel in first container = 3.875 gallons

Amount of diesel in second container = 5 + 0.5

Amount of diesel in second container = 5.5 gallons

Amount of diesel in third container = 6 + 0.25 + 0.125

Amount of diesel in third container = 6.375 gallons

So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375

The total quantity of diesel fuel = 15.75 gallons

Hence, the total quantity is 15.75 gallons.

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a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².

b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².

Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:

df / dx = (df / du) · (du / dx)

a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:

F'(x) = [2 · g(x) + 6] · g'(x)

F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²

b) Now we proceed to expand the polynomial in its standard form:

F'(x) = [(2 / 3) · x³ + 7] · x²

F'(x) = (2 / 3) · x⁵ + 7 · x²

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The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

[tex]\pi[/tex] ± z[tex]\sqrt{\frac{\pi \p(1-\pi )}{n} }[/tex]

z is the z-score that has a pvalue of [tex]1-\frac{\alpha }{2}[/tex]

Since, the coin is fair, so [tex]\pi =0.5[/tex].

The margin of error is:

[tex]M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}[/tex]

99% confidence level:

So [tex]\alpha =0.01[/tex] ,z is the value of Z that has a p value of 1-[tex]\frac{0.01}{2}[/tex]=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=[tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

[tex]0.18=2.575\sqrt{\frac{0.5*0.5}{n} }[/tex]

[tex]0.18\sqrt{n} =2.575*0.5[/tex]

[tex]\sqrt{n}=\frac{2.575*0.5}{0.18}[/tex]

[tex]\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}[/tex]

n = 51.16

Thus, we have to flip the coin at least 52 times.

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The rate of change here represents the time in seconds it takes her to perform a certain number of skills task

The rate of change is defined as the rate at which one quantity is changing with respect to another quantity. Mathematically:

rate of change = change in y /  change in x

Given that: The x-coordinate is the skills task number and the y-coordinate is the time in seconds

Thus, rate of change = time in seconds / skills task number  

Therefore, the rate of change in this context represents the time in seconds it takes  to perform a certain number of skills task

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The slope is m = 5.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

We have to find the slope of the points given.

First to find the change between each y - value.

16 - 11 = 5

21 - 16 = 5

26 - 21 = 5

31 - 26 = 5

So the change between each y - value is 5.

Now, to find the slope of the points.

Since,

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

[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]

Hence, the slope of the given points is 5.

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Answer:

The answer is 5

Step-by-step explanation:

Though there is also a bottom number, just put a 1 in the bottom number

Answer:

No solution (0 = 1)

Step-by-step explanation:

Given equation,

→ 5 + 2x = 2x + 6

Then the value of x will be,

→ 5 + 2x = 2x + 6

→ 2x = 2x + 6 - 5

→ 2x - 2x = 1

→ 0 = 1

Hence, there is no solution.

[tex]\boxed{\begin{array}r \large{ \tt solution \: : } \: \: \: \: \: \\ \\ { \longrightarrow5 + 2x = 2x + 6}  \\ \\ \\ ( \sf 2x \: \: present \: \: on \sf\: \: both \: \: \\ \sf sides \: \: of \: \: equality \: \: \: \\ \sf \: \: gets \: \: \sf canceled\: \: out) \\ \\ \sf \longrightarrow5 \neq6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \: \: therefore \: \: there \: \: is \\ \tt no \: \:solution \: \: for \: \: x \: \: \\ \\ \tt that \: \: is \: \: no \: \: value \: \: \: \: \\ \tt \: of \: \: x \: \: that \: \: satisfies \\ \tt the \: \: given \: \: equation\end{array} }[/tex]