A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election. How many of these voters actually voted in that election? Construct a 95% confidence interval for the proportion of registered voters who voted in the most recent school board election

Step-by-step explanation:

yes .. when you put x=2 y will be 3 .. you get it?

The equation to calculate the cost of her shoes without shipping included is: x = 55.25

Let x be the cost of Carly's shoes.

The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:

x + 5.50 = 60.75

To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:

x + 5.50 - 5.50 = 60.75 - 5.50

Simplifying:

x = 55.25

Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25

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The area of the rectangle is 27/70 square feet.

The area of a rectangle is given by the formula:

Area = base x height

Plugging in the given values, we get:

Area = (3/7) x (9/10)

Simplifying, we get:

Area = (27/70) square feet

Therefore, the area of the rectangle is 27/70 square feet.

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For pythagorean theorem  the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss

ANSWER 12

Answer:

To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.

To find out how many students this represents, we can set up a proportion:

40% = C/150

Where C is the number of votes received by Candidate C.

To solve for C, we can cross-multiply:

0.4 x 150 = C

C = 60

Therefore, 60 students voted for Candidate C.

Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.

Answer:

If the zeroes of a quadratic function are -1 and 6, then its factored form is:

(x + 1)(x - 6) = 0

Expanding the left side:

x^2 - 5x - 6 = 0

So the quadratic function in standard form is:

f(x) = x^2 - 5x - 6

Answer:

f(x) = x^2 - 5x - 6

Step-by-step explanation:

To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:

(x + 1)(x - 6) = 0

Expanding the factors, we get:

x^2 - 5x - 6 = 0

This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:

f(x) = x^2 - 5x - 6

This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.

The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.

Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.

P(B|A) is the conditional probability of B given A.

The Bayes theorem gives us:

P(B|A) is equal to P(A|B)*P(B)/P(A).

Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:

P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871

P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.

P(B) = (7C3 * 7C1) / (14C4) = 35/143

P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.

P(A) = 7/14 = 1/2

Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.

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The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The input and output variables for this problem are given as follows:

V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.

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The length of AB of the parallelogram is determined as 14.36 inches.

The length of AB of the parallelogram can be determined by applying cosine rule as shown below:

The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.

Length AB = Length AD = x

DB² = AB² + AD² - 2(AB x AD) cos (A)

22² = x² + x² - 2x²(cos 100)

484 = 2x² + 0.347x²

484 = 2.347x²

x² = 484/2.347

x² = 206.2

x = √206.2

x = 14.36 inches

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Answer: x = -11

Step-by-step explanation:

Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.

[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]

Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

What is the Pigeonhole Principle?

The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.

In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.

Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.

If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).

Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)

Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

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The equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

Explain the term equation

An equation is a mathematical statement that expresses the equality of two expressions or values. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and to solve problems in various fields, including mathematics, physics, and engineering.

According to the given information

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the two given points.

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

To find the slope of the line that passes through (4, 1) and (12, -3), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4, 1) and (x2, y2) = (12, -3)

m = (-3 - 1) / (12 - 4) = -4 / 8 = -1/2

Now that we have the slope of the line, we can use one of the two given points and the slope to find the equation of the line. Let's use the point (4, 1):

y - y1 = m(x - x1)

y - 1 = (-1/2)(x - 4)

Distributing the -1/2, we get:

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

Adding 1 to both sides, we get:

y = (-1/2)x + 3

Therefore, the equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.

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The ratio of the volume of both spheres is: 1/(24√3)

The formula for the volume of a sphere is expressed as:

V = ⁴/₃πr³

where:

r is radius

V is volume

We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:

Volume of sphere A/Volume of sphere B = (1:2√3)³

= 1/(24√3)

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The equation for the circle graphed in the coordinate axis is:

(x - 5)^2 + (y - 6)^2 = 16

Remember that the equation for a circle whose center is at (a, b) and has a radius R is.

(x - a)^2 + (y - b)^2 = R^2

On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:

(x - 5)^2 + (y - 6)^2 = 4^2

(x - 5)^2 + (y - 6)^2 = 16

That is the equation we wanted to find.

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The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325

Explain trigonometry.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.

According to the given information

We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).

Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.

Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.

Substituting these values into the identity for cos(A + B), we get:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

          = (-5/13)(-√7/25) - (12/13)(24/25)

          = (5√7)/(13*25) - (12*24)/(13*25)

          = (5√7 - 288)/(13*25)

          = (5√7 - 288)/325

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The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.

(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:

Sampling error = z*(standard deviation/square root of sample size)

Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.

Substituting the values, we get:

Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%

Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.

(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:

Confidence interval = point estimate ± (z*standard error)

Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.

Substituting the values, we get:

Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)

Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.

(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:

New sample mean = 0.96 * 550 = 528

The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.

To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:

Confidence interval = sample mean ± (t*standard error)

Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.

The standard error can be calculated as follows:

Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31

Substituting the values, we get:

Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)

Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

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Answer:

16.58. my answer needs to be more than 20 characters, soooo... how is your day going?

1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.

2. The range of the function is given as follows: The set of real numbers less than -5.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:

y = a(1/3)^x - 2.

When x = 0, y = -1, hence the parameter a is obtained as follows:

-1 = a - 2

a = 1.

Thus the function is:

g(x) = (1/3)^x - 2.

For item 2, we have that the function is:

Hence the range of the function is given as follows:

The set of real numbers less than -5.

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f(4) = 537. and f(-3) = 363.  To find f(-3), we replace x with -3 in the expression similarly for x=4.

what is expression  ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

To find f(-3), we replace x with -3 in the expression:

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

= 3(81) - 4(-27) + 3(9) + 15 - 3

= 243 + 108 + 15 - 3

= 363

Therefore, f(-3) = 363.

To find f(4), we replace x with 4 in the expression:

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

= 3(256) - 4(64) + 3(16) - 20 - 3

= 768 - 256 + 48 - 23

= 537

Therefore, f(4) = 537.

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Francine can type 38 words per minute at this rate.

To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.

Next, we can use the formula:

words per minute = total words / total minutes

where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).

Substituting these values into the formula, we get:

words per minute = 3,420 / 90 = 38

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Answer: A

Step-by-step explanation: cuz of the

pie chart

Answer:

Here

Step-by-step explanation:

The volume of a rectangular prism is found by multiplying the length, width, and height.

Volume = Length x Width x Height

Volume = 11 ft x 8 ft x 4 ft

Volume = 352 cubic feet

The surface area of a rectangular prism is found by adding up the areas of all six faces.

Surface area = 2lw + 2lh + 2wh

Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)

Surface area = 176 + 88 + 64

Surface area = 328 square feet

Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.

The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.

The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.

The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.

Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.

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The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

Linear function: y = 3x + 1

x y

3 10

5 16

7 22

9 28

The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.

The system of equations created by the two functions is:

y = -x^2 + 19

y = 3x + 1

By substituting y in the second equation with the first equation, we get:

-x^2 + 19 = 3x + 1

Solving for x, we get:

x = -2 or x = 5

Substituting these values of x back into either of the equations, we get the corresponding values of y:

(-2, 7) and (5, 16)

These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.

The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.

All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

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