taylor has enough money to buy either 90 granola bars or 78 pop tarts. After returning from the atore, taylor has no money, 75 granola bars and p pop tarts

If Riders have to climb a m staircase to board the ride at its lowest point.

a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).

b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).

c.  a sine function for Matthew is: h(t) = 30 sin(π/6 t).

(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.

The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:

h(t) = 60 sin(2π/12 t)

Simplifying this equation, we get:

h(t) = 60 sin(π/6 t)

(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:

h(t) = m + 60 cos(2π/12 t)

Simplifying this equation, we get:

h(t) = m + 60 cos(π/6 t)

where m is the height of the staircase that Eva has to climb to board the ride.

(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:

h(t) = 30 sin(2π/12 t)

Simplifying this equation, we get:

h(t) = 30 sin(π/6 t)

Therefore  sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).

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Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.

The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.

Given data:

surface area of pentagonal prism = 2* base area + 5*rectangle area

surface area of pentagonal prism = 2* B + 5*L*w

surface area of pentagonal prism = 2* 84.3 + 5*7*4

surface area of pentagonal prism = 168.6 + 140

surface area of pentagonal prism = 308.6 sq. ft

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

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Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)

The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,

                                     [tex]Area=length*width[/tex]

Now, Solving given problem,

The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft

Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft

The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft

Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft

To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:

(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft

So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft

The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft

Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft

The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft

Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft

Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:

Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft

So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft

Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.

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We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.

According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.

In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.

However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.

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Each side of Tavon's backyard is 7 meters long.This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters,

How to solve the problem?

To solve the problem, we can use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of one side of the square. Since we know that the fence around Tavon's backyard is 28 meters, we can set this equal to the perimeter of the square and solve for s:

28 = 4s

Dividing both sides by 4, we get:

s = 7

Therefore, each side of Tavon's backyard is 7 meters long.

This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters, we can divide that by 4 to find the length of each side. In this case, we get 7 meters, which is a reasonable length for a side of a backyard. Additionally, since the problem tells us that the backyard is shaped like a square, we know that each side must be the same length, so it makes sense that we would find a single value for s that satisfies the equation P = 4s.

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Your Complete question is :-14. The fence around Tavon's backyard is

28 meters. The backyard is shaped likea square. How long is each side of the backyard?

By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.

An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.

The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

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The perimeter of the figure is 37 m.

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is

12+12+7.75+2+3.25 = 37m

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The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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Answer: x2 - 4 = 0 and 4x2 = 16

Step-by-step explanation:

Answer:

18 5-dollar bills

10 20-dollar bills

the dimensions of the table runner are  [tex]20[/tex] inches in length and [tex]4[/tex] inches in width.

Let's denote the width of the table runner as "w" inches. Since the length is 5 times greater than the width, the length would be 5w inches.

The area of a rectangle is calculated by multiplying its length by its width. Given that the area of the table runner is 80 square inches, we can set up the following equation:

Length × Width = Area

[tex](5w) \imes w = 80[/tex]

Simplifying further:

[tex]5w^2 = 80[/tex]

Dividing both sides by 5:

[tex]w^2 = 16[/tex]

Taking the square root of both sides:

w = ±4

Since the width cannot be negative in this context, we discard the negative value. Therefore, the width (w) of the table runner is [tex]4[/tex] inches.

Substituting this value back into the equation for length:

Length   [tex]= 5w = 5 \times 4 = 20[/tex] inches

So, the dimensions of the table runner are  [tex]20[/tex] inches in length and 4 inches in width.

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We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

what is  vertex ?

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. It is a common term used in geometry, graph theory, and other areas of mathematics.

In the given question,

We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

To see why, suppose there exists a walk w of odd length starting and ending at v, and suppose w is the shortest such walk. If w does not repeat any vertices, then we have found an odd cycle that does not repeat any vertices, and we are done.

Suppose instead that w repeats some vertex v' (not equal to v). Then we can split w into two walks, w1 and w2, where w1 starts at v, goes to v', and then returns to v, and w2 is the rest of w starting and ending at v'. Since v' is not equal to v, both w1 and w2 are walks of odd length, and both are strictly shorter than w. By the minimality of w, both w1 and w2 must contain odd cycles that do not repeat any vertices. We can then combine these cycles to form an odd cycle that does not repeat any vertices in G, and we are done.

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Therefore, the perimeter of the rectangle is 42 centimeters.

The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.

Here,

To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.

We can use the formula for the area of a rectangle:

Area of rectangle = length x width

Plugging in the values we have:

108cm² = length x 9cm

Solving for the length, we can divide both sides by 9cm:

length = 108cm² / 9cm

length = 12cm

So, the length of the rectangle is 12 centimeters.

To find the perimeter of the rectangle, we can use the formula:

Perimeter of rectangle = 2 x (length + width)

Plugging in the values we have:

Perimeter of rectangle = 2 x (12cm + 9cm)

Perimeter of rectangle = 2 x 21cm

Perimeter of rectangle = 42cm

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Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.

Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).

Given data:

Principal P = $1500

Amount after interest A = $1600

Rate of simple interest R = 6.49%

Time  = T years

The formula for the simple interest:

SI = PRT/100

A = P + SI

A = P + PRT/100

PRT/100 = A - P

1500*6.49*T/100 = 1600 - 1500

1500*6.49*T = 100 *100

T = 10000 / 9735

T = 1.027 years

Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

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Answer:

14cm

Step-by-step explanation:

112÷8=14

base length=14cm

Answer:

To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:

Area = Length x Width

In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.

So, the equation for the area of the rectangle becomes:

112 = x * 8

To solve for "x", you can divide both sides of the equation by 8:

112 / 8 = x

x = 14

Therefore, the base length of the rectangle is 14 inches.

The exponential function of the population is P(x) = 15000 * 1.046^x

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

Initial, a = 15000

Rate, r = 4.6%

The equation of the function is represented as

P(x) = a * (1 + r)^x

Substitute the known values in the above equation, so, we have the following representation

P(x) = 15000 * (1 + 4.6%)^x

Evaluate

P(x) = 15000 * 1.046^x

Hence, the function is P(x) = 15000 * 1.046^x

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The sample variance ratio, denoted by [tex]$\frac{S_x^2}{S_y^2}$[/tex], which follows an F-distribution.

The sample variance for a random sample of size (m) from a normal distribution with mean [tex]$\mu_X$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{x} ^2 =\frac{1}{m-1}\sum_{i=1}^{m}($X_i$-$\overline{X}$)^2[/tex]

where [tex]$X_i$[/tex] are the individual observations from the sample, and [tex]$\overline{X}$[/tex] is the sample mean.

Similarly, the sample variance for a random sample of size (n) from a normal distribution with mean [tex]$\mu_{Y} _$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{y} ^2 =\frac{1}{n-1}\sum_{i=1}^{n}($Y_i$-$\overline{Y}$)^2[/tex]

where [tex]$Y_i$[/tex] are the individual observations from the sample, and [tex]$\overline{Y}$[/tex] is the sample mean.

Provided that both samples have normal distributions with the same variance [tex]$\sigma^2$[/tex], the ratio of sample variances [tex]\frac{Sx^2}{Sy^2}[/tex] follows an F-distribution with degrees of freedom [tex]m-1$ and $n-1$[/tex], respectively.

Thus,

[tex]\frac{S_x^2}{S_y^2} $\sim$ $F(m-1,n-1)$[/tex]

where [tex]$\sim$[/tex] denotes "follows the distribution of"

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Answer: Let the experienced one help you out! Read the explanation down below! Brainliest?

Step-by-step explanation:

The sample space for rolling a 4-sided die twice consists of all possible pairs of outcomes, where each outcome is a number from 1 to 4. To find which outcome is not part of the sample space, we can list all the possible outcomes and then look for a number pair that does not appear.

Possible outcomes:

(1,1), (1,2), (1,3), (1,4)

(2,1), (2,2), (2,3), (2,4)

(3,1), (3,2), (3,3), (3,4)

(4,1), (4,2), (4,3), (4,4)

There are 16 possible outcomes, so one of the numbers from 1 to 16 is not part of the sample space. The missing outcome is (3,4) or (4,3), depending on the order in which the dice are rolled.

if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.

It is a branch of mathematics that deals with the occurrence of a random event.

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space of rolling a 4-sided die twice can be represented by all possible ordered pairs of the outcomes, which can be listed as follows:

{(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}

Therefore,  if  4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.

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Answer: 3/2 or 1 1/2 or 1.5

Step-by-step explanation:

9/8 times 2 is 2.25 or 9/4

9/4-6/8= 3/2 or 1 1/2 or 1.5

Answer:

Let's start by writing the given statement as an equation.

Twice the sum of −4 and a number is the same as the number decreased by 5/2:

2(-4 + x) = x - 5/2

Where x represents the unknown number.

Now, let's simplify and solve for x:

-8 + 2x = x - 5/2

Adding 8 and 5/2 to both sides, we get:

2x + 8.5/2 = x + 1.5/2

Simplifying, we get:

2x + 17/2 = x + 3/2

Subtracting x and 3/2 from both sides, we get:

x + 17/2 = 3/2

Subtracting 17/2 from both sides, we get:

x = -7

Therefore, the number is -7.

To check our answer, we can substitute x = -7 into the original equation:

2(-4 + (-7)) = (-7) - 5/2

-2 = -2.5

The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.

The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]

The correct matches for the probability of falling below the z-score are:

-0.08: 0.4681

0.63: 0.7357

-2.7: 0.0035

1.95: 0.9744

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.

According to the given information

To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:

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subtract 3 from both sides to get

4x > 27

divide both sides by 4 to get

x > 27/4 or 6 3/4

Answer: The most appropriate design for this experiment is the third option:

- Number each item from 0000 to 1199.

- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.

This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.

Step-by-step explanation:

The variance of the population according to the given table is option B 41.

The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.

The variance is given by the formula:

variance = (sum of squared deviations from the mean) / (number of observations)

Using the table we have sum of squared deviations from the mean:

81 + 1 + 1 + 81 = 164

variance = 164 / 4 = 41

Hence, the variance of the population according to the given table is option B 41.

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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