A state park changed an entrance fee besed on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20 and a van containing 8 people is charged $32 .If a bus is charged $122, how many people is contained?

if you wanted to visualize the change in the mean test score for the same exam over multiple semesters line chart will be used.

A line chart connects a number of data points with a continuous line to graphically depict the historical price movement of an item. The simplest sort of chart used in finance, it often merely shows the closing prices of a security over time.

A line chart, also known as a line graph or a line plot, uses a line to link a group of data points. This type of graph uses sequential values to show trends. The x-axis (horizontal axis) often shows a succession of numbers in consecutive order.

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a) The function will be C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)

b. The cost of 53 CDs will be $39.22

c. The cost of 201 CDs will be $143.69.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)

b) C(53) = 0.74 * min(53, 100) + 0.69 * max(53-100, 0)

= 0.74 * 53

= 39.22

c) C(201) = 0.74 * min(201, 100) + 0.69 * max(201-100, 0) = 0.74 * 100 + 0.69 * (201-100) = 74 + 0.69 * 101

= 74 + 69.69

= 143.69

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The combinations of items he can buy are:

1 popcorn balls and 1 candy stick.

2 candy sticks

Zeg has $9.20 left

First, calculate the price of items in his shopping basket:

2 giant lollipops = 2 * $1.75 = $3.5

3 popcorn balls = 3 * $0.5 = $1.5

1 candy bar = 1 * $0.99 = $0.99

5 candy sticks = 5 * $0.45 = $2.25

Total price =  $3.5 + $1.5 + $0.99 + $2.25 = $8.24

Amount left = $9.20 - $8.24 = $0.96

Since the price of 1 popcorn balls and 1 candy stick = $0.5  + $0.45 = $0.95

Also, 2 candy sticks = 2 * $0.45 = $0.90.

Notice that these two are still within $0.96 we have left

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Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.

A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.

The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).

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The value of the segment a for the similar triangles is equal to 6.

The triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle

and the length OY of the smaller triangle is similar to the length OM of the larger triangle

so;

a/(a + 18) = 4/(4 + 12)

16a = 4(a + 18) {cross multiplication}

16a = 4a + 72

16a - 4a = 72 {collect like terms}

12a = 72

a = 72/12 {divide through by 12}

a = 6.

Therefore, the value of the segment a for the similar triangles is equal to 6.

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The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

−2x + 3y = 15         ....1

x + y = 10

2x + 2y = 20           ...2

Add equations 1 and 2, then we have

5y = 35

y = 7

Then the value of the variable 'x' is given as,

x + 7 = 10

x = 3

The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

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The linear function that represents the relationship is given as follows:

y = 2x + 3.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 2, y increases by 4, hence the slope m is found as follows:

m = 4/2

m = 2.

Hence:

y = 2x + b

When x = 5, y = 13, hence the intercept b is obtained as follows:

13 = 2(5) + b

b = 3.

Meaning that the function is given as follows:

y = 2x + 3.

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Answer: The function f(x) = √x + 4 describes a radical function that maps a real number x to its square root, shifted to the right by 4 units. The graph of this function is an upward-opening parabola that intersects the x-axis at x = -4.

Here are four points on the graph of the function:

The leftmost point: (0, 4)

An additional point to the right of the leftmost point: (1, 4.5)

Another additional point: (2, 5)

The third additional point: (9, 5.5)

Note: The values of x used in these examples are arbitrary and can be any real numbers. These points are only intended to give you an idea of what the graph of the function might look like

Step-by-step explanation:

The function  [tex]f(x) = (x^2 - 9)^3[/tex]   is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function.

The function   [tex]f(x) = (x^2 - 9)^3[/tex]   is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function. A function is considered continuous at a point if the limit of the function as the input approaches the point exists and is equal to the function's value at that point. In this case, the function's domain is the entire real line, meaning that it is defined for all real values of x. The function is also a polynomial, which is a continuous function by definition. Thus, the function is continuous on the entire real number line.

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P(A) = 11/18

P(B) = 5/18

P(C) = 1/9

=====================================================

Explanation:

Check out the diagram below. I have marked your given diagram with fractions. The red fractions 1/3, 1/3, and 1/3 are probabilities that correspond to picking the left-most set of 3 branches. Each has 1/3 chance of randomly being selected. This assumes any of the branches are equally likely.

The blue fractions 1/2 and 1/3 are the probabilities for the next set of sub-branches. For instance, the upper pair of branches each have probability 1/2 of being randomly selected, since we have two of them.

The green fractions are the result of multiplying the red and blue fractions along a particular pathway. Eg: The upper-most pathway has (1/3)*(1/2) = 1/6

---------------

The diagram below shows that:

In summary

Side notes:

The functions for this problem are classified as follows:

a) q(x) is an odd function.

b) r(x) is an even function.

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The student council is selling t-shirts to increase awareness for the local animal shelter. For each t-shirt they sell, they will donate $5.00 to the shelter.

This means that the amount of money the student council will donate to the shelter will be directly proportional to the number of t-shirts they sell. The more t-shirts they sell, the more money they will donate to the shelter.

By selling t-shirts, they are taking a proactive step to help raise awareness and support for the local animal shelter.

Directly proportional: as one amount increases, another amount increases at the same rate. The symbol for "directly proportional" is ∝

(Do not confuse it with the symbol for infinity ∞)

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the proportionality ratio of the given Data is solved below.

the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given a figure where Two lines are intersecting three individual parallel lines.

Since Proportionality in Lengths is When quantities have the same relative size. In other words, they have the same ratio.

thus,

as we can observe the proportionality ratio for the given figures:

Therefore, the proportionality ratio of the given Data is solved above.

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Answer:

6.375 cubic inches

Step-by-step explanation:

To find the volume of a cube using the formula V = s^3, where s represents the length of one side, we simply need to raise s to the power of 3.

Given that the length of one side, s, is 2 1/4 inches, we need to first convert the fractional part to decimal form:

[tex]\sf:\implies{2 1/4 inches = 2 + 1/4 inches}[/tex]

[tex]\sf:\implies{= 2.25 inches}[/tex]

Now, we can use this value in the formula:

[tex]\sf:\implies{V = s^3 = 2.25^3}[/tex]

To raise a number to the power of 3, we simply multiply the number by itself three times:

V = 2.25 × 2.25 × 2.25 = 6.375 cubic inches

Therefore, the volume of the cube with sides of length 2 1/4 inches is 6.375 cubic inches.

The solutions to the equations -³/₄x + 2¹/₄ = (¹/₂)ˣ + 1 are; -1 and 1

The functions are given as:

f(x) = -³/₄x + 2¹/₄

g(x) = (¹/₂)ˣ + 1

The solution to these two simultaneous equations will be the point where they both intersect each other.

From attached graph, both functions intersect at at two coordinates that have their x-coordinates as x = -1 and x = 1

This means that- 1 and 1 represent the solutions to f(x) = g(x) or

-³/₄x + 2¹/₄ = (¹/₂)ˣ + 1

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The required complete table for the given function f(x) = 2x - 1 is given as,
  x =  1      0    -1     2
f(x) =  1     -1     -3    3

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Given function,
f(x) = 2x - 1

To complete the table,
Put x = 1
f(1) = 2(1) - 1
f(1) = 1

Similarly
f(0) = -1
f(-1) = -3
f(2) = 3

Thus, the required complete table for the given function f(x) = 2x - 1 is given as,
  x =  1      0    -1     2
f(x) =  1     -1     -3    3

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The probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points is 5.8%.

The distributed samples can be solved using the z-score formula:

We can set with mean  and standard deviation, the z-score of a measure X is given by:

[tex]Z=\frac{X-u}{sd}[/tex]

The Z-score defines how many standard deviations will be measured from the mean. After finding the Z-score, we should see the z-score table and find the p-value included with this z-score.

This p-value is the probability of the value measuring smaller than X, that is, the percentile of X. by Subtracting 1 from the p-value, we get the probability of the value of the measure is greater than X.

In this problem, we have that:

u=511 sd=120.

This is 1 subtracted by the value of Z when X = 700.

[tex]Z=\frac{X-u}{sd}\\\\Z=\frac{700-511}{120}[/tex]

Z=1.575.

Z=1.575 has a p-value of 0.942

1 - 0.942 = 0.058.

5.8% probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points.

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The dimensions of the rectangular region that will maximize the total area are 20ft x 50ft.

The goal is to find the dimensions of a rectangle that will maximize the total area when it is divided into 6 smaller rectangles.

Let the length of the rectangle be x and the width be y.

The total length of the fencing used to enclose the rectangle is 100 feet, so 2x + 2y = 100.

To divide the rectangle into 6 smaller rectangles, we need 5 partitions,

so we have x/6 = y, or y = x/6.

Substituting y = x/6 into 2x + 2y = 100 gives 2x + 2x/3 = 100, or x/3 = 50.

Solving for x, we find x = 150.

Then y = x/6 = 150/6 = 25.

The maximum area of the rectangle is 150 * 25 = 3750 square feet.

To maximize the area of the rectangular region, the width and length should be in the ratio of 1:2. This allows the rectangular region to be split into six smaller rectangles of equal area by placing five fences parallel to the width.

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The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].

The general antiderivative of a rate of change function is calculated by integrating the rate of change expression over the given interval. In this case, the rate of change of DVD orders is given by s(m) = 500m + 8 DVDs per month. We can calculate the general antiderivative of this expression by integrating it over the given interval from m = 0 (the beginning of the year) to some arbitrary value m. This gives us the following expression for the general antiderivative: [tex]S(m) = 250m^2/2 + 8m + C[/tex], where C is the constant of integration. To calculate the value of S(m) for any given value of m, we simply plug the value of m into the expression above and solve for S(m). For example, if m = 5, then [tex]S(5) = 250(5)^2/2 + 8(5) + C = 1250 + 40 + C = 1290 + C[/tex]

The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].

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The equation for a parabola that has x-intercepts (5,0) and (6,0) and y-intercept (0,1) is: [tex]y =[/tex] [tex]a(x + 0.5)^2 - 1[/tex]

The equation of a parabola can be found by using the vertex form of a parabolic equation, which is given by:[tex]y = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola. In this case, the x-intercepts (5, 0) and (-6, 0) can be used to find the value of h, which is the midpoint between the x-intercepts and is equal to (-6 + 5) / 2 = -0.5.

The y-intercept (0, -1) can be used to find the value of k. So, the equation is:[tex]y = a(x + 0.5)^2 - 1[/tex], where a is a constant that can be determined by substituting the vertex coordinates (h, k) into the equation.

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Let's call the event of flipping two tails in a row "success." The probability of success on any given flip is (1-p) ^2.

The number of flips required to get two tails in a row is a random variable, which we can calculate the expected value of. This expected value can be calculated as an infinite sum:

E = 1 * (1 - (1-p) ^2) + 2 * (1-p) ^2 * p + 3 * (1-p) ^2 * (p^2) + ...

This sum can be simplified using geometric series formula:

E = 1 / (1 - (1-p) ^2 * p)

So, the expected number of flips required to get two tails in a row with a biased coin with probability p of heads is given by the above formula.

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Yes, we would be more intrigued by looking so at mean, median, or mode for the below type of data set.

Choose the proper center measurement first, and then decide how to support your decision.

Correct center measurement

Justification:

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The correct question is-

For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning.

The price of cars on a car lot-

Answer:

The width of the walkway is 5ft long

Accordingly, x0 = 0, x1 = 3, x2 = 0, and x3 = 3 are the first three iterations of f ( x) = -2x + 3 when x0 = 0.

A loop is described as a section of code that runs repeatedly. The procedure in which a code fragment is run just once is referred to as iteration. One iteration is the single time a loop is run. A loop may run through numerous iterations.

x1 = f(x0) = f(0) = -2 * 0 + 3 = 3

x2 = f(x1) = f(3) = -2 * 3 + 3 = 0

x3 = f(x2) = f(0) = -2 * 0 + 3 = 3

So the first 3 iterates of the function f(x) = -2x + 3 when x0 = 0 are:

x0 = 0, x1 = 3, x2 = 0, x3 = 3

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The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

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At a significance threshold of 0.10, p-value(0.0005)< [tex]\alpha[/tex] =0.10, therefore we reject [tex]H_{0}[/tex].

Under the assumption of independence, the expected frequencies for contingency tables are

[tex]e_{ij} = \frac{(Row_{i}Total)(Column_{j} total)}{SampleSize}[/tex]

Using the formula for the number of freshmen without body art: (247*168)/490=84.69.

State the null and alternative hypotheses:

[tex]\alpha = 0.10[/tex]

[tex]H_{0}[/tex]: There is a connection between body art and class standing 

Ha: There is no connection between class standing  and rejection from body art. [tex]H_{0}[/tex] if the probability is less than 0.10.

the test statistic for independence is

[tex]X^2= \sum\limits_i \sum\limits_j\frac{(f_{ij}-e_{ij} )^2 }{e_{ij} }[/tex]

where fij = observed frequency for the contingency table category in rows i and j

eij = expected frequency for the contingency table category in rows i and j based on the assumption of independence

We only need to add up the values as they have already been obtained and are listed in the table to obtain the chi-square value.

Therefore,

[tex]X^2= 2.56+ 4.33+1.1+0.02+0.69+0.02+1.2+0+0.49+0.51+0.33+0.25+4.99+4.31+8.41+0.27[/tex]

[tex]X^{2} = 29.48[/tex]

Consequently, the probability of p-value=0.0005

Given DF=9.

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Answer:

The Panthers soccer team does not like to lose because they always try to be their best. One day, they were embarrassed when all their shirts were so loose they started to fall off during a game. Guess who did not win that day?