Find the length of an arc on a circle whose radius is 10 cm and whose central angle subtends a central angle of 20º

the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.

a) The chi-square test statistic is 15.95 and is significant at the 0.005 level. This indicates that the population proportions of students who drove while drinking are not the same in the two calendar years.

b) The behavior of college students regarding driving while drinking changed between 2013 and 2017.

c) The test based on the normal approximation to the binomial distribution also yields a significant result (p-value = 0.0045), indicating that the population proportions of students who drove while drinking are not the same in the two calendar years.

d) The 95% confidence interval for the true difference in population proportions is [-0.072, -0.023].

e) Yes, the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.

Chi-square test statistic:

X2 = 15.95

Normal approximation test statistic:

P-value = 0.0045

95% confidence interval:

[-0.072, -0.023]

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1. The first step is to determine the sample size. In this case, the sample size is 9 response times.

2. Next, the dispatcher should collect the response times from the log books.

3. After collecting the response times, the dispatcher should calculate the mean or average of the sample. This is known as the sample mean and is represented by the x-bar.

4. To calculate the sample mean, the dispatcher should add together the values of all the response times and divide this sum by the sample size (9). The result of this calculation is the sample mean or x-bar.

5. Finally, the dispatcher can use the value of the x-bar to calculate the standard deviation of the response times. This is done by taking the square root of the sum of the squares of the differences between each response time and the mean, divided by the total number of response times (in this case, 9). This will give us the standard deviation of the response times.

Question: Suppose dispatcher a takes a random sample of 9 response times from the log books in march. dispatcher a calculates x-bar

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The sum of the interior angles of a triangle is sometimes, but not always, 180º is false.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

There are three angles in a triangle.

The sum is always 180 degrees.

Thus,

The sum of the interior angles of a triangle is always 180°.

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Answer:

A

Step-by-step explanation:

5.7(3) can be expressed as a fraction

(573 -57)/90

516/90

AS per the given confidence interval, the z score is 0.54

The term confidence interval refers a parameter will fall between a pair of values around the mean.

Here we have given that if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent

And we need to find the z value.

While we looking into the given situation, we have identified the following values,

Confidence interval = 95%

Interval = 34 - 50

Mean = 10

Through the given interval we have identified the that sample size was calculated as,

=> 50 - 34

=> 16

Then the z score is

=> z = 10/√16

=> z = 10/4

=> z = 2.5

Then according to the confidence interval, the value from the z table is obtained as.

=> z = 1.96

Then the difference is

=> 2.5 - 1.96

=> 0.54

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Out of the given choices, we choose 'not enough information given to answer this question' and concluded that  the true slope for the population is equal to zero.

Since, we are given a p-value associated with a test of the slope coefficient equal to 0.028 which leads to 3% level of significance, it means that there is 3% chance of finding difference which is larger than the one given in our study given that the null hypothesis is true. Since, it is less than 5% level of significance, the null hypothesis is rejected and accept an alternative hypothesis. As this hypothesis is not given, we conclude that there is not enough information to give an answer to the question.

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a) The Keynesian cross graphs an economy's planned expenditure function,

[tex]$\mathrm{E}=\mathrm{C}(\mathrm{Y}-\mathrm{T})+\mathrm{I}+\mathrm{G}$[/tex],

and the equilibrium condition that actual expenditure equals planned expenditure.

How do you find the expenditure function?

To derive the expenditure function we can either (i) invert V(·) and solve for M, or (ii) set up the dual of the consumer's choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.

The amount by which[tex]$\mathrm{Y}$[/tex]falls is given by the product of the tax multiplier and the increase in taxes

[tex]: $\Delta \mathrm{Y}=[-\mathrm{MPC} /(1-\mathrm{MPC})] \Delta \mathrm{T}$.[/tex]

c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b :

[tex]\Delta \mathrm{Y}=\left[(1 /(1-\mathrm{MPC}))^* \Delta \mathrm{G}\right]-[(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{T}[/tex]

Because government purchases and taxes increase by the same amount, we know that [tex]\Delta \mathrm{G}=\Delta \mathrm{T}$. Therefore we can rewrite the equation as:$$\Delta \mathrm{Y}=[(1 /(1-\mathrm{MPC}))-(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{G}=\Delta \mathrm{G}[/tex]

This expression tells us that an equal increase in government purchases and taxes increases [tex]$\mathrm{Y}$[/tex] by the amount that [tex]$\mathrm{G}$[/tex] increases. That is, the balanced-budget multiplier is exactly 1 .

Complete question: Consider the Keynesian model with a change in the way that taxes are incorporated: (1) PAE = C + IP + G + NX Definition of Planned Aggregate Expenditure (2) C = C+ mpc (1-1) .y Consumption Function (3) PAE = Y Short-run Equilibrium Condition In this case, taxes paid are proportional to income, i.e. taxes paid are t - Y, where t is the tax rate and 0<t< 1. Disposable income is the part of income after taxes, i.e., (1-t). Y. Solve for the PAE spending line with PAE as a function of Y. What is the slope?

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The interval is [4, 6], and the compound inequality equals 4 ≤ x < 6 as indicated on the number line.

Given,

The number line;

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Here,

The blue line runs from 1 to 4 and then to 6.

The solid dot at position 4 denotes inclusion, whereas the hollow dot at position 6 denotes exclusion.

Then,

x  ≥ 4 and x < 6

Combindlly  4 ≤ x < 6

Hence "The interval is [4, 6], and the compound inequality on the number line is 4 ≤ x < 6 ."

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0.0405 is the number that contains the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

based on data gathered from the sources

Suppose the information as shown by

How many eight-digit numbers have more 5s than 3s and contain the digits 2 exactly once, 3 exactly twice, and 4 precisely three times

Let there be more 5s than 3s and more 8-digit numbers with the digits 2 once, 3 twice, 4 three times, and 5s than 3.

2,3,3,4,4,4

after that:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now, 0.405, followed by a digit 2 and 3 make up the eight-digit number.

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On solving, the given system reduces to x1 = 12, & x2 = —7 which is the required solution.

Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.

Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are

T he augmented matrix of the given system is B =

[tex][AB] = \left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right] \\on solving we get \\ [AB] = \left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right] \\[/tex]

Hence the given system reduces to x1 = 12   x2 = -7

Hence the given system reduces to

x1 = 12, & x2 = —7

which is the required solution.

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As a result, if (0,0) is a solution to the system of inequalities above, the connection between a and b is a>b in the xy-plane.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.

Here,

Given, y<−x+a and y>x+b

As given, (0,0) is a solution to the above inequalities.

0<0+a and 0>0+b

a>0 and b<0

Thus, we can conclude from the above inequalities that a is a positive number and b is a negative quantity.

Therefore, it can be surely said that a>b.

Hence, the relationship between a and b is a>b in the xy-plane, if (0,0) is a solution to the system of inequalities above.

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The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its centroid located at (5 , 3).

Centroid of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.

Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.

First, try to graph and visualize the triangle formed by the three vertices. (see photo)

From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.

One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.

To get the circumcenter, find the midpoint of the line BC.

midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]

M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]

M(xm ,ym) = (5 , 3)

Hence, the centroid is located at (5 , 3).

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The least among all 4 integers such that they sum up to 100 will be 22.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Suppose the first integer is x.

The next three digits will be, x + 2, x + 4, and x + 6 correspondings.

Sum x + x + 2 + x + 4 + x + 6 = 100

(x + x + x + x) + (2 + 4 + 6) = 100

4x + 12 = 100

4x = 88

x = 22

Hence"The smallest of the four integers that add up to 100 is 22".

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Answer:

Step-by-step explanation:

Since the domain of the function h is -3 ≤ x ≤ 11 and the range is 1 ≤ h(x) ≤ 25, the possible values of h(x) for a given value of x in the domain will be within the range of 1 to 25. Additionally, we are given that h(8) = 19 and h(-2) = 2, so for the values x = 8 and x = -2, the corresponding values of h(x) are 19 and 2, respectively.

Given this information, the statement that could be true for the function h is: "For every value of x in the domain of h, the corresponding value of h(x) is within the range of 1 to 25." This statement is true because the domain and range of h are such that the possible values of h(x) for any value of x in the domain will be within the range of 1 to 25.

To express the set of real numbers x that satisfies the inequality -2 ≤ x < 5, we used the Interval notation method and got the solution set as [-2,5).

Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers. We can use this notation to express inequalities.

Generally, we read about the three types of intervals :

We have given an inequality as -2 ≤ x < 5

We have to express the set of real numbers x that satisfies the given inequality.

Let's started, The first thing we'll want to ask ourselves is if we're going to use parentheses or brackets when we write this.

y = { x | -2 ≤ x < 5 }

We see that the lower value of x is -2 or greater than -2 and higher value of x is less than 5. We're just going to write it down. Using the interval notation, the lower side x is greater than and equal to -2 so, we use closed bracket here and the upper side x is less than 5 that is we use parentheses or open bracket here.

Thus, in interval notation y = x , x∈[-2, 5)

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Answer:

One

Step-by-step explanation:

The equation 9x+7=8x+7 has only one solution. This can be seen by setting the two sides of the equation equal to each other and then solving for x.

First, we set the two sides equal to each other by canceling out the 7 on the right side of the equation:

9x+7 = 8x+7

Then, we move all of the terms that have an x on the same side of the equation, and all of the constant terms on the other side:

9x - 8x = 7 - 7

Next, we combine like terms on the left side of the equation:

x = 0

Finally, we solve for x to find the value of x that makes the equation true:

x = 0

Therefore, the only solution to the equation 9x+7=8x+7 is x=0.

If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function

The reciprocal function of a linear function is given by the formula:

f(x) = 1/x

If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.

To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.

In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.

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The number of welcome packets that you will be able to fully complete in the time allotted would be = 14

The time allotted for the refilling of the whole welcome packets = 3 hours

To convert to mins = 3 × 60 = 180 mins.

To run each packet will take the following time:

5 minutes to print,

2 minutes to organize, and

5 minutes to proofread which is a total of 12mins

But for every 5 packets = 5×12+3 = 63 mins.

Therefore X packets = 180 mins.

Make X packets the subject of formula;

X packets = 5 × 180/63

= 900/63

= 14.2

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We will see that the linear function h(x) is:

h(x) = -21x - 15

The slope is -21, and the y-intercept is -15.

Remember that a general linear function is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we start with the linear function:

f(x) = -7x + 9

First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:

g(x) =f(x + 2)

Replacing the actual function we will get:

g(x) = -7*(x + 2) + 9

Now we multiply the output of function g by 3 to get h(x), then:

h(x) = 3*g(x)

We will get:

h(x) = 3*[-7*(x + 2) + 9]

h(x) = -21*(x + 2) + 27

h(x) = -21x - 42 + 27

h(x) = -21x - 15

So we can see that the slope of function h(x) is -21, while the y-intercept is -15.

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Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the confidence interval for the mean speed (mu) of all cars on this section of the highway, we can use the following formula:

Confidence interval for mu = sample mean +/- z * standard error of the mean

Where:

sample mean is the average speed of the 81 cars in the sample, which is 60 mph

z is the z-score corresponding to the desired confidence level. In this case, the desired confidence level is 86.9%, which corresponds to a z-score of 1.96.

standard error of the mean is the standard deviation of the sampling distribution of the mean, which is calculated as the standard deviation of the population divided by the square root of the sample size.

In this case, the standard error of the mean is 13.5 / sqrt(81) = 2.26 mph.

Plugging these values into the formula, we get:

Confidence interval for mu = 60 +/- 1.96 * 2.26 = 59.131 to 60.869

Therefore, at a confidence level of 86.9%, we can be confident that the interval between 59.131 and 60.869 mph includes the true mean speed of all cars on this section of the highway.

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The skier's distance to the east of the center of the ski trail is

x = 1.25cosθ

The skier's distance to the north of the center of the ski trail is

y = 1.25sinθ

When radius 'r' and the angle θ are given, the coordinates (x,y) as shown

x = east direction

y = north direction

In this case we get,

x = r cosθ

y = r sinθ

Given r = 1.25 km

We get,

x = 1.25 cosθ in east direction

y = 1.25 sinθ in north direction

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Only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.

In the given question we have to name a point on ∠MNO.

As we know that;

Evaluating the number of points in the curve of the triangle's vertices that are close to the location in question is the easiest method for determining whether a point is inside a triangle. The point on the curve is inside the triangle if it has three points; if it has four, it is outside the triangle.

When we check in the graph then only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.

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Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

As given in the question,

Let 'x' represents the number of people

And 'y' represents the total cost

Linear relationship between number of people and total cost is:

y = mx + b

Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)

Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)

              = (58 - 52)/ (9 -6)

              = 6 / 3

              = 2

y = 2x + b

Now for, (x. y) = ( 12,64)

64 = 2(12) +b

⇒b = 64 - 24

⇒b = 40

Hence, required function is :

y = 2x + 40

a. Independent variable is the number of people.

Here it is x which represents the number of people.

True.

b. Initial value for the picnic is $40

y- intercept when x =0 ⇒ y = $40

True.

c. Rate of change is $8.67 per person.

No, rate of change is $2 per person.

d. Number of people increases as total cost of picnic increases

True .

e. If x = 4

⇒y = 2(4) + 40

     = 48 ≠46

False.

Therefore, function y = 2x + 40 represents that following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

The above question is incomplete, the complete question :

The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. a. The independent variable is the number of people.

b. The initial value (initial fee) for the picnic is $40.

c.  The rate of change is $8.67 per person.

d. As the number of people increases, the total cost of the picnic increases.

e.  If 4 people attended the picnic, the total cost would be $46.

Number of people               Total cost ($)

6                                                 52

9                                                 58

12                                               64

15                                               70

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The option a is giving the same value according the table. So the option a is correct answer.

In the given question, the table represents some points on the graph of linear function f.

We have to find which function represents f.

(a) f(x)= 32(3x-1)

(b) f(x)= -32(x-3)

(c) f(x)= -2(32x-3)

(d) f(x)= 16(2x-1)

We find the pattern we firstly observe the given table closely.

So from the given table;

f(-2) = -224, f(1) = 64, f(5) = 448, f(10) = 928

To check which option is giving the value of f(x) right according to table, we put the value in each option.

Firstly taking the option a.

f(x)= 32(3x-1)

Now checking the option 1.

Putting x=-2, if the value of f(-2) = -224, then the option is correct.

f(-2)= 32(3(-2)-1)

f(-2)= 32(-6-1)

f(-2)= 32*(-7)

f(-2)= -224 (True)

Now putting x=1 in the same option to cross check, if the value of f(1) = 64, then the option is correct.

f(1)= 32(3(1)-1)

f(1)= 32(3-1)

f(1)= 32(2)

f(1)= 64

Now the option a is giving the same value according the table. So the option a is correct answer.

We find the right answer so we don't check the further option. To check next option you can use the same way.

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If  there are 40 school days in a 2-month period. The number of times can a boy be expected to take attendance is: B. 20.

Given data:

Number of school days = 40

Number of month = 2

Now let find the number of attendance times

Number of attendance times =  Number of school days/ Number of month

Number of attendance times = 40/2

Number of attendance times = 20

Therefore the correct option is B.

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Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Surface S = √21

A surface integral in mathematics is a generalization of multiple integrals to integration over surfaces, particularly in multivariable calculus. It can be viewed as the line integral's double integral equivalent. One can integrate a vector field or a scalar field across a given surface.

Equation of surface (S) is,

x/1 - y/2 + z/4 = 1

From here we get,

z = 4 - 4x + 2y

∫∫(S)xdS = ∫∫ (D)x(1 + (∂z/∂x)² + (∂z/∂y)²)^1/2 dxdy

Here (D) is projection of (S) on xy coordinate plane

so, (D) is triangle with vertices (1, 0, 0), (0, - 2, 0) and  (0,0,0).

∂z/∂x = - 4, ∂z/∂y = 2.

In (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Now we have,

∫∫(S)xdS = ∫∫(D)x(1 + (- 4)² + 2²)^1/2 dxdy

= √21∫₋₂⁰dy ∫₀¹xdx

= √21y₋₂⁰x²/2₀¹

= √21

Hence, Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0 and Surface S = √21

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Answer:

Step-by-step explanation:

40

Answer:

The number is:

321/7

Step-by-step explanation:

a + a/6  + 7 = 121/2

6a/6 + a/6 + 42/6 = 363/6

6a + a + 42 = 363

7a = 363 - 42

7a = 321

a = 321/7

Check:

321/7 + (321/7)/6 + 7 = 121/2

321/7 + 321/42 + 7 = 121/2

1926/42 + 321/42 + 294/42 = 2541/42

1926 + 321 + 294 = 2541

The expression of the statement 40 divided by m is 40/m

From the question, we have the following parameters that can be used in our computation:

40 divided by m

The above statement is a mathematical statement

The mathematical statement can be expressed as an expression

Recall that, we have

40 divided by m

The term "divided by" means a quotient expression

To divide is represented as / i.e. quotient

So, the expression that represents 40 divided by m is 40/m

Hence, the complete expression is 40/m

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