Winona paid $115 for a lifetime membership to the zoo, so that she could gain admittance to the zoo for $1.95 per visit. Write Winona's average cost per visit C as a function of the number of visits when she has visited x times. What is her average cost per visit when she has visited the zoo 115 times? Graph the function for x> 0. What happens to her average cost per visit if she starts when she is young and visits the zoo every day? Find Winona's average cost per visit C as a function of the number of visits when she has visited x times C(x)- (Type an expression.) What is her average cost per visit when she has visited the zoo 115 times?

Each inch on the treasure map represents 20 feet in actuality.

Total distance on map

= 3 inches north + 2 inches west + 1. 5 inches north + 0. 25 inches east

= 3 inches + 2 inches + 1.5 inches + 0.25 inches

= 6.75 inches

\(\rm{ Each\ inch\ on\ the\ map=\dfrac{Actual\ distance\ of\ the\ entire\ route}{Total\ distance\ on\ map}\)

                                  \(=\dfrac{135\ feet}{6.75\ inches}\\\\= 20\ feet\)

hence, each inch on the treasure map represents 20 feet in actuality.

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Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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Answer:

4 1/5= 21/5

2 3/7= 17/7

21/5×17/7= 357/35

357/35= 10 1/5

Step-by-step explanation:

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Your friend is an antique coin collector and wants to predict the dollar-value of each of his coins. He has a long list of properties for each coin and a small dataset of coins with sales prize from prior purchases. So the option b "Logistic regression" best suited to predict the value of each coin,

Linear regression analysis is employed to predict the significance of one variable based on the values of some other variable. The variable you want to predict is known as the dependent variable. The variable you're using to predict the value of the other variable is known as the independent variable.

Based on a set of independent variables, logistic regression estimates the likelihood of an event occurring, such as voting or not voting. Because the outcome is a probability, the dependent variable is limited to values between 0 and 1.

Multinomial logistic regression is employed to predict classification placement in or the likelihood of categorization on a predictor variables based on multiple independent factors.

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The complete question is:

Your friend is an antique coin collector and wants to predict the dollar-value of each of his coins. He has a long list of properties for each coin (e.g. material, size, weight, ...) and a small dataset of coins with sales prize from prior purchases. Which model best suited to predict the value of each coin?

a. Linear regression

b. Logistic regression

c. Multinomial logistic regression

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

Answer:

9 is the most highest frequency and the third one is the answer

Answer:

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

6x+12+2x-4

6x+2x+12-4

8x+8

I am from grade 9 from which grade are you

Answer:

length= 9

width= 3

Step-by-step explanation:

x= width

length = x+6

x+6+x+6+x+x=24

4x+12=24

take 12 from both sides

4x= 12

x=3

Answer:

I'm gonna try to find the answers

Step-by-step explanation:

The variance of each random variable is given as follows:

a) Var(2x - y) = 10.4165.

b) Var(x + 3y - 5) = 20.833.

The number that occurs when each dice is thrown is represented by an uniform variable, with bounds a = 1 and b = 6, hence the variance of each variable is calculated as follows:

Var(x) = Var(y) = (6 - 1)²/12 = 2.0833.

When two variables are added, the variance is calculated as follows:

Var(aX + bY) = a²Var(X) + b²Var(Y)

Hence, for item a, the variance is calculated as follows:

Var(2x - y) = 2²Var(x) + (-1)²Var(y) = 4Var(x) + Var(y)

The variances were calculated before, which are both of 2.0833, hence:

4Var(x) + Var(y) = 4 x 2.0833 + 2.0833 = 10.4165.

For item b, the variance is calculated as follows:

Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5).

The variance of a constant is of zero, hence Var(-5) = 0, and then:

Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5) = 2.0833 + 9(2.0833) = 20.833.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

It should be -7/10

Answer:  The answer is -7/10 :)

Step-by-step explanation:

-1/2-1/5=-7/10

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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On the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

What is the linear equation in one variable?

A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.

In the given problem, the rental cost of a mid-sized car from Eliana's Rentals can be represented by the equation:

y = 60 + 6x (where y is the total cost and x is the number of days)

The rental cost of a mid-sized car from Arcadia Rent-a-Car can be represented by the equation:

y = 30 + 12x (where y is the total cost and x is the number of days)

At some point, renting from either one of the companies would cost the customer the same amount, so we can set both equations equal to each other and solve for x:

60 + 6x = 30 + 12x

Solving for x:

30 = 6x

x = 5

Hence, on the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.

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Answer:

Step-by-step explanation:

Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)

0.01p + 0.05n = 8.80

You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).

n = 2p

You can substitute this value of n into the first equation

0.01p + 0.05n = 8.80

0.01p + 0.05(2p) = 8.80

0.01p + 0.10p = 8.80 (multiplying out the brackets)

0.11p = 8.80 (collecting the p's)

p = 80

Putting this back into the second equation

n = 2p

n = 2(80) = 160

So there are 160 nickels and 80 pennies.

You can put this back into the first equation to check it.

0.01p + 0.05n = 8.80

0.01(80) + 0.05(160) = 0.80 + 8 =8.80

A 95% confidence interval with a 4% margin of error suggests that your statistic will be 95% of the time within 4 percentage points of the true population value.

A survey, may reveal that the 98% confidence interval is between 4.88 and 5.26. So, if the poll is repeated using the same methods, the true population parameter (parameter vs. statistic) will fall 98% of the time within the interval estimates (i.e. between 4.88 and 5.26).

The formal definition, on the other hand, includes a little more information. The margin of error in a confidence interval is defined as the range of values below and above the sample statistic. The confidence interval is a tool for demonstrating the level of uncertainty associated with a certain statistic (i.e. from a poll or survey).

In 2012, a Gallup poll (incorrectly) predicted that Romney would win the election, with Romney polling at 49% and Obama polling at 48%. The declared level of confidence was 95%, with a margin of error of 2. We can conclude that the results were computed to be 95% accurate within 2 percentage points.

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Answer:

the answer is b: (6,0) and (0,-9)

Answer:

X= -4

X=-2

Step-by-step explanation:

for

|a|=b

assume

a=b and a=-b

so

3-2|0.5x+1.5|=-2

minus 3 both sides

-2|0.5x+1.5|=-1

divide both sides by -2

|0.5x+1.5|=0.5

set negative and postivive

0.5x+1.5=0.5 and 0.5x+1.5=-0.5

solve each

0.5x+1.5=0.5

minus 1.5 both sides

0.5x=-1

times - 2 both sides

x=-2

other

0.5x+1.5=-0.5

minus 1.5 from oth sides

0.5x=-2

times 2 both sides

x=-4

the solutions are x=-2 and x=-4

Answer:

x=-4

Step-by-step explanation:

ok

Volume of a rectangular prism = 11 x 7 x 8

= 616 m^3

b. r(t) = (cos(t), sin(t)), for 0 <= t <= pi. c. Sphere of radius 1 centered at the origin: r(u, v) = (cos(u) * sin(v), sin(u) * sin(v), cos(v)), for 0 <= u <= 2pi and 0 <= v <= pi.

b) Here are the parameterizations for a line segment connecting two points of your choice and half of a circle centered at the origin:

Line segment from (0, 0) to (1, 2): r(t) = (1 - t) * (0, 0) + t * (1, 2) = (t, 2t), for 0 <= t <= 1.

Half of a circle of radius 1 centered at the origin: r(t) = (cos(t), sin(t)), for 0 <= t <= pi.

c) Here are the parameterizations for a plane and a sphere:

Plane passing through (1, 0, 0), (0, 1, 0), and (0, 0, 1): r(u, v) = u * (1, 0, 0) + v * (0, 1, 0) + (1 - u - v) * (0, 0, 1), for 0 <= u <= 1 and 0 <= v <= 1.

Sphere of radius 1 centered at the origin: r(u, v) = (cos(u) * sin(v), sin(u) * sin(v), cos(v)), for 0 <= u <= 2pi and 0 <= v <= pi.

Note that for the plane parameterization, we used the fact that a plane passing through three non-collinear points can be parameterized by a linear combination of the points, with the coefficients summing to 1. For the sphere parameterization, we used spherical coordinates to express the position of each point on the sphere in terms of two angles, u and v.

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Answer:

\(3)y = kx \\ 4)y = kx \\ 5)y = - kx\)

Answer:

5

Step-by-step explanation:

1.24 × 4 = 5

or it can be 1.24 ÷2 =0.265

The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

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

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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The value of k in this function is greater than zero. So, the correct answer is (c) k is greater than zero.

In order to analyze the graph and determine the value of k in the given radical function, we need to examine the characteristics of the graph.

Firstly, let's consider the general form of the radical function: f(x) = √(k - x). In this form, the variable k determines the horizontal shift of the graph. A negative value of k shifts the graph to the right, while a positive value of k shifts it to the left.

From the information given in the question, we can observe that the graph starts at the point (0, √k). This means that when x = 0, the function value is equal to √k.

By examining the graph, we see that it is decreasing as x increases. This implies that the value of k must be greater than zero. If k were less than zero, the graph would be increasing as x increases, which contradicts the graph's behavior.

Therefore, based on the given information and the characteristics of the graph, we can conclude that the value of k in this function is greater than zero. Thus, the correct answer is (c) k is greater than zero.

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The vectors t, n, and b at the given point (8, 0, 0) are as follows:

At the point (8, 0, 0) on the curve defined by r(t) = 8 cos t, 8 sin t, 8 ln cos t, the tangent vector (t) indicates the direction of the curve at that point. The normal vector (n) points towards the center of curvature, providing information about how the curve is bending. The binormal vector (b) is perpendicular to both t and n and completes the three-dimensional coordinate system, known as the Frenet-Serret frame. It is essential for understanding the curvature and torsion properties of the curve.

To find these vectors, we can differentiate the position vector r(t) with respect to t and evaluate it at t = 0 since the given point is (8, 0, 0). Taking the derivatives, we have:

r'(t) = -8 sin t, 8 cos t, -8 tan t sec t

Substituting t = 0, we get:

r'(0) = 0, 8, 0

This gives us the tangent vector t = (0, 8, 0) at the point (8, 0, 0).

Next, we compute the second derivative of r(t):

\(r''(t) = -8 cos t, -8 sin t, -8 sec^2 t\)

Substituting t = 0, we have:

r''(0) = -8, 0, -8

Normalizing this vector, we obtain the unit vector n = (-1/√2, 0, -1/√2).

Finally, we compute the cross product of t and n to find the binormal vector b:

b = t × n = (0, 8, 0) × (-1/√2, 0, -1/√2) = (0, 8/√2, 0)

Therefore, at the point (8, 0, 0), the vectors t, n, and b are (0, 8, 0), (-1/√2, 0, -1/√2), and (0, 8/√2, 0), respectively.

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The vectors t, n, and b at a given point for a curve are the tangent, normal, and binormal vectors respectively. These vectors need to be calculated via a series of steps involving calculus, however, the information provided does not explicitly give us what they are for your specific problem. It's recommended to review your given problem.

To answer your question regarding finding the vectors t, n, and b at a given point for r(t) = 8 cos t, 8 sin t, 8 ln cos t , at the point (8, 0, 0), we need to use the theory of curves and vectors in three-dimensional space. The vectors t, n, and b are respectively the tangent, normal, and binormal vectors of a curve at a point. However, your specific problem seems to involve calculus and an understanding of the theory of these vectors. Typically, we first find the velocity vector v(t) = r'(t), normalize it to get the unit tangent vector T(t) = v(t) / ||v(t)||. Afterwards, find the derivative of T(t) and normalize it too to get the normal vector N(t). Finally, the binormal vector B(t) is the cross product of T(t) and N(t). Unfortunately, as the information given does not allow to get these vectors precisely, you might want to check if the projectory r(t) or the point given is correct.

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