SPEED VS. PRICE OF TICKET Speed (MPH) Price of Ticket ($) 25 65 Linear Regression Equation: y=4.671x-279.497 68 37 slope: 72 55 Y-intercept: 88 120 76 82 Predict the price of a ticket if you are driving 85 mph. 90 150 74 64​

Answer:

reason 1: Given

reason 2: Property of Cross Multiplication

reason 3: Vertical Angles are Congruent.

reason 4: SAS

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

A slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

The slope of a linear relationship represents the rate of change between two variables. In this case, a slope of b = 0.007 suggests a weak positive relationship between the variables. The positive sign indicates that as the independent variable increases, the dependent variable also tends to increase. However, the small value of 0.007 indicates that the increase in the dependent variable is relatively small for each unit increase in the independent variable.

To illustrate, let's consider an example where the independent variable represents time and the dependent variable represents the number of customers in a store. With a slope of 0.007, it means that for every unit increase in time (e.g., one hour), we can expect a small increase of 0.007 customers on average. This indicates a weak positive relationship, as the increase in customers is relatively modest for each unit increase in time.

In summary, a slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

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The difference in the medians is 1/3 times the IQR.

Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) for Speed Slide = Q₃ - Q₁

Interquartile range (IQR) for Speed Slide = 12 - 6

Interquartile range (IQR) for Speed Slide = 6.

For the interquartile range (IQR) for Wave Machine, we have:

Interquartile range (IQR) for Wave Machine = 14 - 8

Interquartile range (IQR) for Wave Machine = 6.

For the required expression, we have the following:

2 = 6x

x = 2/6

x = 1/3.

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Answer:

The difference in the medians is 1/3 times the IQR.

Step-by-step explanation:

hope this helps!

Answer:

  (c)  the converse of the original conditional statement

Step-by-step explanation:

If a conditional statement is described by p→q, you want to know what is represented by q→p.

For the conditional p→q, the variations are ...

As you can see from this list, ...

  the converse of the original conditional statement is represented by q→p, matching choice C.

__

Additional comment

If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.

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Answer:

  0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

  x^2 +y^2 = -xy

Factoring the expression of interest, we have ...

  x^3 -y^3 = (x -y)(x^2 +xy +y^2)

Substituting for xy using the first expression we found, this is ...

  x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0

The value of x^3 -y^3 is 0.

The probability that a student has a dog, given that they do not have a cat is 5/6.

The probability that a student has a dog given that they do not have a cat is :

P ( Has a dog | Does not have a cat ) = P ( Has a dog and does not have a cat) / P ( Does not have a cat )

Total number of students = 11 + 10 + 5 + 2 = 28

P ( Has a dog | Does not have a cat ):

= (10 / 28) / (12 / 28)

= 10 / 12

= 5 / 6

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The equation that represents d, the distance, in kilometers, that Clarissa has left to hike after stopping to rest is d = 7.36 - 1/4(7.36).

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario

From the information, Clarissa is hiking a trail that is 7.36 kilometers in length and she stops to rest after hiking a quarter of the total distance of the trail.

The equation to represent this will be:

d = Total distance - Distance hiked

d = Distance left

d = 7.36 - 1/4(7.36).

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As per the greedy algorithm, the change of the cent is three quarters, two dimes, and two pennies. (option c).

The greedy algorithm is a simple algorithm that always chooses the largest possible coin denomination to make change, until the amount owed is zero. Let's look at some examples:

To make change for 97 cents using the greedy algorithm, we start by choosing the largest coin denomination, which is a quarter. We can use three quarters, and we have 22 cents remaining.

Now, we use the largest coin denomination again, which is a penny. We can use two pennies to make up the remaining 2 cents. So, the answer is three quarters, two dimes, and two pennies.

Hence the correct option is (c).

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95% confidence interval : 30713 persons to 32433 persons.

The confidence interval is the mean of your estimate plus and minus the change in that estimate. This is the range of values ​​within which, with a certain level of confidence, you would expect your estimate to fall if you retest. In statistics, confidence levels are another way of describing probabilities.

According to the Question:

n = 100

x = 31,578

σ = 4413

class interval = 95% = 0.95

To construct a 95% confidence interval, we use the formula:

                          x ± z(σ/ √n)

α = 1 - CL = 1 - 0.95 =0.05

From the z score, Z(0.05) = Z (0.05/2) = Z 0.0025

Confidence Interval = X± 8 = X - 8= X+8

= (31578-865.34, 31578+ 865.34)

= (php 30713, php 32443)

Therefore, At 95% confidence interval There are 30713 person 32443 person.

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C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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Answer:

1/2

Step-by-step explanation:

In the given transformation, there is no change in the degree of angle, therefore degree measurement of angle c′ is 123°.

Any procedure that modifies a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation. The movement of two-dimensional figures about a plane or coordinate system is described by mathematical transformations.

A preimage, also known as an inverse image, is a two-dimensional shape that exists without any transformation. After transformation, the figure is shown in the image.

The transformations applied are:

I A four-unit horizontal shift to the right

ii) A two-unit vertical shift upward

We are aware that the translations do not change the angle.

Therefore, Angle C' degree measurement is 123°.

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Answer:

Cube with a side length of 2/5 cm: 8/125 cm^3

Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm, respectively: 36/125cm^3

Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3/5 cm, respectively: 6/125 cm^3.

Cube with a side length of 1/5 cm: 1/125 cm^3

Step-by-step explanation:

For the first one, cubes have equal sides, we would do 2/5*2/5*2/5, which is 8/125 cm^3.

Next we have a rectangular prism. For this, we will just multiply all of the sides with each other which is 3/5*4/5*3/5 which is 36/125 cm^3

Now we have another rectangular prism. Again, we will multiple all of the sides with one another: 1/5*2/5*3/5, which is 6/125 cm^3.

Lastly, there is a cube with a side length of 1/5 cm. We know that cubes have equal sides, so it would be 1/5*1/5*1/5, which is 1/125 cm^3.

I hope this helped.

The expression AB + AC is equal to:

[[ -2,  5, 29],

[-24, -18, 14],

[ 25, -17, -3]]

To compute the expression AB + AC, we need to perform matrix multiplication and then add the resulting matrices.

First, let's calculate AB:

AB = A * B

  = [[1, 3, 1], [-2, 1, 3], [4, -1, -1]] * [[4, -1, -1], [0, 2, 1], [-6, 2, 15]]

Multiplying these matrices, we get:

AB = [[1*4 + 3*0 + 1*(-6), 1*(-1) + 3*2 + 1*2, 1*(-1) + 3*1 + 1*15],

     [-2*4 + 1*0 + 3*(-6), -2*(-1) + 1*2 + 3*2, -2*(-1) + 1*1 + 3*15],

     [4*4 + (-1)*0 + (-1)*(-6), 4*(-1) + (-1)*2 + (-1)*2, 4*(-1) + (-1)*1 + (-1)*15]]

AB = [[-8, 7, 17],

     [-26, 10, 28],

     [26, -7, -23]]

To compute the expression AB + AC, we need to perform matrix multiplication and then add the resulting matrices.

First, let's calculate AB:

AB = A * B

  = [[1, 3, 1], [-2, 1, 3], [4, -1, -1]] * [[4, -1, -1], [0, 2, 1], [-6, 2, 15]]

Multiplying these matrices, we get:

AB = [[1*4 + 3*0 + 1*(-6), 1*(-1) + 3*2 + 1*2, 1*(-1) + 3*1 + 1*15],

     [-2*4 + 1*0 + 3*(-6), -2*(-1) + 1*2 + 3*2, -2*(-1) + 1*1 + 3*15],

     [4*4 + (-1)*0 + (-1)*(-6), 4*(-1) + (-1)*2 + (-1)*2, 4*(-1) + (-1)*1 + (-1)*15]]

AB = [[-8, 7, 17],

     [-26, 10, 28],

     [26, -7, -23]]

Next, let's calculate AC:

AC = A * C

  = [[1, 3, 1], [-2, 1, 3], [4, -1, -1]] * [[1, 4, 6], [4, 0, 2], [1, -6, 2]]

Multiplying these matrices, we get:

AB + AC = [[-8 + 6, 7 + (-2), 17 + 12],

          [-26 + 2, 10 + (-28), 28 + (-14)],

          [26 + (-1), -7 + (-10), -23 + 20]]

AB + AC = [[-2, 5, 29],

          [-24, -18, 14],

          [25, -17, -3]]

Now, let's add AB and AC:

AB + AC = [[-8 + 6, 7 + (-2), 17 + 12],

          [-26 + 2, 10 + (-28), 28 + (-14)],

          [26 + (-1), -7 + (-10), -23 + 20]]

AB + AC = [[-2, 5, 29],

          [-24, -18, 14],

          [25, -17, -3]]

Therefore, the expression AB + AC is equal to:

[[ -2,  5, 29],

[-24, -18, 14],

[ 25, -17, -3]]

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The inequality in a standard form that describes this situation is,

52000x + 84000y < 830000.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

From the given information, x = the number of junior programmers y = the number of senior programmers,

The inequality that represents the situation is,

52000x + 84000y < 830000.

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Answer:

\( \huge\boxed{d. \: 18a {b}^{3} \: and \: 16 {a}^{3} b}\)

is the unlike pair terms.

Answer:

For each birdhouse built, the cost increases by $3.50

Step-by-step explanation:

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:Three functions that are bounded above are y = x^2, y = x^3, y = e^x.

y = x^2 is a parabola that opens upward and has a vertex at the origin (0,0). As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.

y = x^3 is a cubic function that also opens upward. As x increases or decreases, y will always be positive and increases or decreases accordingly, so the function is bounded above by positive infinity.

y = e^x is the exponential function where e is Euler's number (approximately 2.718). As x increases, y will increase towards positive infinity, so the function is bounded above by positive infinity.

Step-by-step explanation:

Answer:

- 8

Step-by-step explanation:

To evaluate f(8) substitute x = 8 into f(x)

f(8) = - 2(8) + 9 = - 16 + 9 = - 7

Similarly for g(- 1)

g(- 1) = (- 1)² - 2 = 1 - 2 = - 1

Then

f(8) + g(- 1) = - 7 + (- 1) = - 7 - 1 = - 8

Answer:

A line that is perpendicular to y=2/5x-5 must have a slope of -5/2, but a line parallel to line y=5/2x+6 must have a slope of 5/2, and these slopes do not match up.

Explanation:

In order for a line to be parallel to another line, they must have the same slope. In order for a line to be perpendicular to another line, their slopes must be opposite reciprocals (meaning that when they are multiplied, the product is -1). From here you can find what slope the line must have to perpendicular or parallel to another line, and then you can see that the answers to not match up to be the same line!

Hope this helped :)

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Thus, there are 208 positive integers less than 1000 that are divisible by exactly one of 7 and 11. The rules used to find the number of positive integers less than 1000 that are divisible by exactly one of 7 and 11 are:

a. The principle of inclusion-exclusion for sets: This rule is used to count the number of integers that are divisible by both 7 and 11, and subtract them from the total number of integers that are divisible by either 7 or 11. This gives us the number of integers that are divisible by exactly one of 7 and 11.

b. The division rule: This rule is used to find the number of integers that are divisible by a certain number within a given range. For example, we can use the division rule to find the number of integers less than 1000 that are divisible by 7.

c. The product rule: This rule is used to find the number of ways two or more events can occur together. In this case, we can use the product rule to find the number of integers that are divisible by both 7 and 11.

d. The sum rule: This rule is used to find the total number of ways two or more events can occur separately. In this case, we can use the sum rule to find the total number of integers that are divisible by either 7 or 11.

By using these rules, we can find the number of positive integers less than 1000 that are divisible by exactly one of 7 and 11.

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The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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