The mayor of a town has proposed a plan for the annexation of an adjoining bridge. A political study took a sample of 1500 voters in the town and found that 47% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 44%. Determine the P-value of the test statistic. Round your answer to four decimal places.

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

a. E(X) = 0.333 minutes

b. \(\mathbf{\sigma_x =0.333 \ minutes}\)

c.  0.9986

Step-by-step explanation:

a.

To find the mean time between counts

Let X be the random variable that illustrates the time between the successive log-ons, then X is exponential with the rate \(\lambda = 3\) log-ons per minute.

i.e.

\(E(X) = \dfrac{1}{\lambda}\)

\(E(X) = \dfrac{1}{3}\)

E(X) = 0.333 minutes

b. Since X is attributed to an exponential distribution, The standard deviation between counts is:

\(\sigma_x = \dfrac{1}{3}\)

\(\mathbf{\sigma_x =0.333 \ minutes}\)

c.

Given that;

The average number of count per minute = 3

The value of X such that P(X < x) = 0.95 can be calculated as;

\(\int \limits ^x_0 \lambda e^{-\lambda t}= 0.95\)

\(3\int \limits ^x_0 \lambda e^{3 t}= 0.95\)

\(\bigg [ -e^{3t}\bigg ]^x_0 = 0.95\)

\(e^{3t} = 1-0.95\)

-3x = ㏑ (0.05)

-3x = - 2.9957

x = -2.9957/ -3

x = 0.9986

The value of x = 0.9986

Answer:

a) 3

b)3

c) 8.9872

Step-by-step explanation:

a) According to the question, mean is 3.

b) Since it is an exponential distribution, standard deviation equals to mean. Therefore, the answer is 3.

c) P[x<X]=0.95

f(x)= λ*e^(-λ*x)

∫f(x)dx, 0 to x

mean = 1/λ =3. So, λ= 1/3.

∫(1/3)*e^(-x/3)dx= 1/3*e^(-x/3)/(-1/3)=-e^(-x/3) 0 to x

-e^(-x/3)+1 = 0.95

-e^(-x/3)=-0.05

x/3=ln(0.05)

x=ln(0.05)*3= 8.9872

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Answer:

12

Step-by-step explanation:

If their weight, in grams, is listed belοw. 88,97,90,93,82 The variance οf the data set is 25.2 (rοunded tο οne decimal place).

In statistics, the mean (alsο called the arithmetic mean οr average) is a measure οf central tendency οf a set οf numerical values, which is calculated as the sum οf all values divided by the tοtal number οf values.

Tο find the variance οf the data set, we need tο fοllοw these steps:

Find the mean οf the data set.

Subtract the mean frοm each data pοint tο find the deviatiοn.

Square each deviatiοn.

Find the mean οf the squared deviatiοns.

Let's fοllοw these steps:

Mean (average) οf the data set: (88 + 97 + 90 + 93 + 82) / 5 = 90

Deviatiοn οf each data pοint:

88 - 90 = -2

97 - 90 = 7

90 - 90 = 0

93 - 90 = 3

82 - 90 = -8

Square οf each deviatiοn:

\((-2)^2 = 4\)

\((7)^2 = 49\)

\((0)^2 = 0\)

\((3)^2 = 9\)

\((-8)^2 = 64\)

Therefοre, the variance οf the data set is 25.2 (rοunded tο οne decimal place).

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In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs , Option C is the right answer.

The complete question is

a. in a right triangle, the hypotenuse equals the sum of the squares of the legs.

b. in a right triangle, the square of the hypotenuse equals the sum of the legs.

c. in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

d. in a right triangle, the hypotenuse equals the sum of the legs.

According to the theorem for a right angled triangle , the square of the hypotenuse , the opposite side of the right angle is equal to the sum of the squares of the other two side.

By this definition , Option C is the right answer.

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Answer:

92

Step-by-step explanation:

The 10th term in a sequence whose general term is \(a_n = n^2 - 8\) will be 92. so option A is correct.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

We need to find the 10th term in a sequence whose general term is

\(a_n = n^2 - 8\).

So, the 10th term is (10)²- 8

= 100 - 8

= 92

Therefore, the 10th term in a sequence whose general term is

\(a_n = n^2 - 8\) will be 92. so option A is correct.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

from 10 to 15

Step-by-step explanation:

because when your finding the spread you take the highest and lowest number.

Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

Answer:between 5 and 5 1/2 inches

Step-by-step explanation:

Answer:

2 (+2)

Step-by-step explanation:

Answer:

1.5 cars/hour

Step-by-step explanation:

if you look at the graph and go up by hour it calculates to 1.5 cars/hour

hope it helps

Brainliest if right :)

Answer:

The average would be 5.25

Step-by-step explanation:

If you add up all of the points

1.5+3+4.5+6+7.5+9=31.5

Divide that by the number of points there are, which is 6

31.5/6

and you should get your answer of 5.25 cars Quick-E-Clean can detail in an hour.

The present value of an annuity that pays $500 per year from year 1 - 16 is $4711.24

An annuity can be defined as the payment of a specified amount of money for a stated period.

Present value is the value of the discounted cash flows at time zero

Present value is the sum of the discounted cash flows from year 1 to 16

Present value in year 0 = $500

Present value in year 1 =  $500 / (1.08) = 462.96

Present value in year 2 = $500 / (1.08^2) = 428.67

Present value in year 3 = $500 / (1.08^3) =396.92

Present value in year 4 = $500 / (1.08^4) = 367.51

Present value in year 5 = $500 / (1.08^5) =340.29

Present value in year 6= $500 / (1.08^6) = 315.08

Present value in year 7 = $500 / (1.08^7) =291.45

Present value in year 8 = $500 / (1.08^8) = 270.13

Present value in year 9 = $500 / (1.08^9) = 250.12

Present value in year 10 = $500 / (1.08^10) = 231.60

Present value in year 11 = 0

Present value in year 12 = $500 / (1.08^12) =198.56

Present value in year 13 = $500 / (1.08^13) =183.85

Present value in year 14 = $500 / (1.08^14) =170.23

Present value in year 15 = $500 / (1.08^15) =157.62

Present value in year 16 = $500 / (1.08^16) =145.95

Sum of present values is $4711.24

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Answer:

Step-by-step explanation:

x = 4

Substitute x and calculate:

Answer:

  262.5 gallons

Step-by-step explanation:

The amount used is the difference between the starting and ending amounts:

  350 -(1/4)(350) = 262.5 . . . . gallons used

We need to graph the equation

Let us put it in the form of y = mx + b

Add 7 to both sides

Now let us choose three values of x and find its corresponding values of y and use them to draw the graph

x = 0

The first point is (0, 1)

x = -1

The second point is (-1, -1)

x = 1

The third point is (1, 3)

Now we can draw the line which is the graph of the equation

The angle formed by the two hands have a measure less than 1/4 turn

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

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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Answer:

579>544

Step-by-step explanation:

579 is greater than 544

Answer:

544<579

Step-by-step explanation:

544 is less than 579. This is because 544 is not more than 579. 579 is the bigger number . < means less than .> means greater than .= means equal to

i dont know how this is even considered college math lol.

Answer:

A. (the vertical scale)

2nd part is the Bottom graph

Step-by-step explanation:

Answer:

A. The Vertical Scale

Step-by-step explanation:

the other one has more value than the other....And i got it right from

---------------------------------------E D G E N U I T Y 2 0 2 0--------------------------------------

hope this helps. :P

The value of c in the triangle is (b) 5 units

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

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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Answer:

3abc⁴ and 101abc⁴

A. 104abc  it A

B. 104abc⁴

C. 303abc⁴

D. 3abc⁸

7. Which is a like terms to 3a?

A. 20a  it D

B. a³

C. 3b

D. 3ab​

Answer:

3.75

Step-by-step explanation:

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Using properties of trapezium, x = 7° and y = 10°.

A quadrilateral with at least one set of parallel sides is known as a trapezium. A trapezium has the following characteristics:

Four vertices and four sides make up a trapezium.

The bases of a trapezium are its parallel sides. The legs are the non-parallel sides.

The distance that separates the bases of a trapezium perpendicularly is known as its height (or altitude). It need not be the same as the length of the legs.

The section that joins the midpoints of the legs is known as the mid-segment of a trapezium. It runs parallel to the bases and has the same length as the sum of the bases' lengths.

A trapezium's internal angles add up to 360 degrees.

A = 1/2 x (base1 + base2) x height, where base1 and base2 are the lengths of the two bases and height is the perpendicular distance between them, can be used to compute the area of a trapezium.

These are some of a trapezium's essential characteristics.

The given figure is trapezium,

As, two non - parallel sides are equal and they intersect a parallel line,

⇒ The angle at which they intersect will be equal,

⇒ 7x = 49

x = 7°

The sum of angles on adjacent sides of trapezium equals 180.

⇒ 13y + 1 + 7(7) = 180

⇒ 13 y + 50 = 180

⇒ y = 180 - 50 / 13

⇒ y = 10°

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Answer:

t=15.7

Step-by-step explanation:

The table that identifies the one-sided and two-sided limits of function f at x = 2 is table A.

It should be.noted that to graph this piecewise function, follow these steps:

Plot the two given points: open circle (2, 4) and closed circle (2, 1).

Draw a smooth curve that starts at the open circle (2, 4) and curves down toward the x-axis in quadrant 2. This is the curve part of the piecewise function.

Draw a straight line that starts at the closed circle (2, 1) and passes through the point (3, -2). This is the line part of the piecewise function.

The two parts of the piecewise function meet at the point (2, 0), which is where the curve intersects the x-axis. Mark this point with an open circle to indicate that it is not included in the function.

Shade in the region above the curve and to the left of the line, since those are the parts of the plane where the function is defined. The correct option is A.

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On the interval (1,b), f(x)=4x2-7 changes at an average rate of 8b-11. To determine this, divide the difference between the function at b and 1 (4b2-7-3) by the difference between the intervals (b-1).

The average rate of change of a function on an interval is a measure of the change in the output of the function over the given interval. It can be calculated by taking the difference of the output between the endpoints of the interval, and dividing by the difference between the endpoints of the interval. For the given function f(x)=4x²-7 on the interval (1,b), the average rate of change is 8b-11This is obtained by dividing the output difference between 1 and b (4b2-7-3) by the output difference between the intervals (b-1). Our average rate of change is given by this formula: (4b2-7-3) / (b-1) = 8b-11. This average rate of change provides us with a general understanding of the function's rate of change across the specified interval. The output of the function increases at a constant rate as the input increases in this situation because the rate of change grows linearly as b increases.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip