a professor wants to determine the average age of all students enrolled in statistics courses at state university. she obtains data from 167 currently enrolled students. in this context, the variable of interest would be .

The distance between the two points can be calculated from the absolute value equation if the points are on the same vertical or horizontal line

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance be represented as D

Let the two points lie on the same vertical line

So , let the two points be P ( x , y₁ ) and Q ( x , y₂ )

The x coordinate of the two points remains the same

So , the difference between the y coordinate will give us the distance between the two points on the vertical line

So , | y₂ - y₂ | = distance D

The absolute value will always gives the result as a positive value and distance is always positive

Now , Let the two points lie on the same horizontal line

So , let the two points be R ( x₁ , y ) and S ( x₂ , y )

The y coordinate of the two points remains the same

So , the difference between the x coordinate will give us the distance between the two points on the horizontal line

And , | x₂ - x₁ | = distance D

The absolute value will always gives the result as a positive value and distance is always positive

Hence , the absolute value equation is used to calculate the distance if the two points are on the same line

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(30,38) is an approximate extrapolation for x = 30 from the line of best fit.

The equation of the Linear Regression line is

y=1.14 x + 3.805

Q asking 4 an approximate for x=30

So (23,30) and (44,30) are out.

From the line of best fit:

x=0, y=4

x=16, y=22

x increases by 16 and y increases by 22-4=18

so at x=32, y=22+18 ⇒y=40

at x=30, the nearest best answer is (30,38).

Therefore, (30,38) is an approximate extrapolation for x = 30 from the line of best fit.

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From the descriptive statistics, we can see that the mean score for the sample is 22.25, with a standard deviation of 2.49.

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The cost of hiring the car in pounds Nina hired is  £210.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nina hired a car in the United States. The cost of hiring the car was $294.

Now, To covert the dollar into pounds, we have to multiply the total amount in dollars by the unit conversion rate which is, £1 = $1.4 ⇒ $1 = £(1/1.4),

Therefore,

$294 is equal to £(294/1.4) = £210.

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2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

[tex](Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}[/tex]

                        [tex](2.5)^{2}+(6)^{2}=(6.5)^{2}[/tex]

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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The required average increase in the number of students enrolled per hour are 120 students.

A function of time is anything that can be described by a mathematical equation that varies reliably over time. Over time, a moving object's position changes. The location is said to be a function of time if it fluctuates in a way that can be mathematically predicted.

The function appears to be f(x) = 4. (x - 1).

You can find out how many pupils are registered at hours 2 and 4 using that function.

At hour two, there are f students enrolled (2),

f(2) = 4^ (2 - 1) = 4

At hour four, there are f students enrolled (4),

f(4) = 4^(4 - 1) = 4^3 = 64

The average growth is therefore [64 - 4] students / [4 - 2] hours = 60

students / 2 hours = 30 pupils every hour.

The numbers are as follows if the function is f(x) = 4(x - 1) rather than f(x) = 4x - 1.

f(2) = 4^2 - 1 = 16 - 1 = 15

f(4) = 4^4 - 1 = 256 - 1 = 255

The average growth rate is (255 - 15) / (4 - 2) = 240 / 2 = 120 pupils per hour.

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Complete Question:

The number of students enrolled in a new course as a function of time can be represented by the function. f(x)=(4)^x−1 What is the average increase in the number of students enrolled per hour between hours 2 and 4?

Answer:

Parallel: y= -(7x/3)-20

Perpendicular: y= 3x/7 - 24/7

Step-by-step explanation:

Slope of parallel line: -7/3

So the equation is y=-7x/3+a

Solve for A:

−6=(−7/3)⋅(−6)+a

So A is -20 and the equation is y=-7x/3=20

Slope of perpendicular line: 7/3

So the equation is y=3x/7 + a

Solve for A:

-6=(3/7)*(-6)+a

Therefore, a= -24/7

So the equation is y= 3x/7 - 24/7

Answer:

Equation of the parallel line: [tex]y = -\frac{7}{3}x - 20[/tex]

Equation of the perpendicular line: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Step-by-step explanation:

To find the equation of a parallel line, we already know that the slope is the same as the original line, so let's find the equation of our original line. We are given:

-7x - 3y = 5

So, we will add 7x to both sides to leave y on a side by itself:

-3y = 7x + 5 (This is the slope-intercept form which is what we will be using)

Then, divide by -3 to isolate y, giving us:

[tex]y= -\frac{7}{3} x - \frac{5}{3}[/tex]

Since it is a parallel line, our slope is the same, giving us:

[tex]y = -\frac{7}{3}x + b[/tex]

Now, the slope of a line is [tex]\frac{rise}{run}[/tex]. Rise is the gain in y, and run is the gain in x. So, since we want to find the y-intercept, we need x to be 0, so let's say for every 3 we gain on the x-axis, we lose 7 on the y-axis (because we need one of the two values to have a negative so that our overall fraction is negative). Now, since we have the point (-6, -6) We need to gain 6 on the x-axis. Meaning, we need to use our slope twice. This means that we will need to also multiply our -7 by 2. So we have:

(-6 + 6, -6 - 14)

Giving us:

(0, -20)

Which is our y-intercept. So our equation for the parallel line is:

[tex]y = -\frac{7}{3}x - 20[/tex]

Now, for the perpendicular line, we need to get the negative reciprocal of the slope of our original line. Our original line's slope was [tex]-\frac{7}{3}[/tex]. So, the negative reciprocal of that is [tex]\frac{3}{7}[/tex]. So, our equation is:

[tex]y = \frac{3}{7}x + b[/tex]

Now, we will find the y-intercept. Since we need to gain 6 on the x-axis, but we have a normal gain of 7, we will need to multiply both our run and rise (3 and 7 respectively) by [tex]\frac{6}{7}[/tex]. Giving us that our x coordinate is:

[tex](-6 + 7 * \frac{6}{7} , -6 + 3 * \frac{6}{7} )[/tex]

Simplifying gives us:

[tex](-6 + 6 , -6 + \frac{18}{7} )[/tex]

Adding the x coordinates gives us:

[tex](0, -6 + \frac{18}{7})[/tex]

Now, to make this simple, we will put -6 over 7. To achieve this, we will need to multiply -6 by 7, giving us -42. So, we have:

[tex](0, -\frac{42}{7} + \frac{18}{7})[/tex]

42 - 18 = 24. So, we get:

[tex](0, -\frac{24}{7})[/tex]

So, the slope of the perpendicular line is:

[tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

So, these are the two equations of the parallel and perpendicular lines respectively:

Parallel: [tex]y = -\frac{7}{3}x - 20[/tex]

Perpendicular: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Hope this helped!

Answer:

4.2 units

Step-by-step explanation:

To find the length of the arc, we can use the relationship between the length of an arc, the radius of the circle and the measure of the angle in radians. This relationship is:

arc length = (angle in radians) * (radius)

In this case, the radius is 2 and the angle in radians is 2.1. So we can substitute these values into the equation:

arc length = (2.1) * (2)

arc length = 4.2

So the length of the arc is 4.2 units to the nearest 10th

The probability of getting a total value of $50 is 1/6.

There are three possible outcomes for Ben's prize: $5, $10, or $20.

There are two possible outcomes for Jamie's prize: $30 or $40.

Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.

To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.

The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.

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Answer: 43

Step-by-step explanation:

x+x+10 = 96

2x = 86

x = 43

The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS

The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.

The specified information are;

The bisector of ∠ACB = [tex]\overline{DC}[/tex]

Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

Required; to prove that ΔACD ≅ ΔBCD

The two-column method can be used to prove the congruency of the triangles as follows;

Step     [tex]{}[/tex]             Statement            [tex]{}[/tex]        Reasons

1.  [tex]{}[/tex]                    [tex]\overline{DC}[/tex] bisects ∠ACB          Given

                 [tex]{}[/tex]      [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

2.  [tex]{}[/tex]                  ∠ACD ≅ ∠BCD              Definition of bisected angles

3.                [tex]{}[/tex]    [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex]                       Reflexive property of congruency

4. [tex]{}[/tex]                   ΔACD ≅ ΔBCD               SAS congruency rule

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$32,250 must be paid back at the end of the 5-year period if the loan is paid in full.

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

A = P * (1 + rt)

Where A is the amount to be paid back, P is the principal amount borrowed (28,000), r is the interest rate (3.25%), t is the number of years (5), and t is the time period in years.

So, plugging in the values, we have:

A = 28,000 * (1 + 0.0325 * 5) = 28,000 * (1 + 0.1625) = 28,000 * 1.1625 = 32,250

So, $32,250 must be paid back at the end of the 5-year period if the loan is paid in full.

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On solving the provided question, we can say that probability P(B)(1–0.6)=0.3 =>P(B)=3/4= 0.75

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

If two events A and B are independent then,

[tex]P(A n B)= P(A).P(B)\\P(A u B)= P(A)+P(B)-P(A n B)[/tex]

Since A and B are independent, so

[tex]P(A u B)= P(A)+P(B)-P(A).P(B)\\0.9=0.6+P(B)-(0.6 * P(B))\\P(B)(1–0.6)=0.3\\P(B)=3/4= 0.75[/tex]

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A)  The 95% confidence interval is:

     0.58 ± 0.062

B) At the 0.01 probability value, there is neither substantial evidence of a home-field  advantage in professional football (they won and over half of the games).

Now, According to the question:

A) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]

Where:

z = The z score corresponds to the amount of confidence.

p = sample proportion.

q = probability of failure

q = 1 - p

p = x/n

Where

n = the number of samples

x = the number of success

From the information given,

n = 240

x = 138

p = 138/240 = 0.58

q = 1 - 0.58 = 0.42

To determine the z score,  The confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Thus,

1 - 0.025 = 0.975

The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.

As a result, the 95% confidence interval becomes

0.58 ± 1.96√(0.58)(0.42)/240

Confidence interval is

0.58 ± 0.062

B) Earning more than half of the games equates to winning 120 games or more.

p = 120/240 = 0.5

The hypothesis test will be

For the null hypothesis,

P ≥ 0.5

For the alternative hypothesis,

P < 0.5

Probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 138

n = number of samples = 240

P = 138/240 = 0.58

We need to find the values of  the test statistic which will be the z score

z = (P - p)/√pq/n

z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48

Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.

P value will be = 1 - 0.9934 = 0.0066

Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.

The given question is incomplete, The complete question is this:

__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__

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Answer:

To find the percent of change, we can use the following formula:

(New Value - Old Value) / Old Value x 100

In this case, the new value is $315,000 and the old value is $180,000.

So the percent of change is:

($315,000 - $180,000) / $180,000 * 100

This evaluates to:

$135,000 / $180,000 * 100 = 0.75 * 100 = 75%.

Therefore, the percent of change is 75%.

well, the change or difference was 315000 - 180000 = 135000.

if we take $180,000 (origin amount) to be the 100%, what's 135,000 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 180000 & 100\\ 135000& x \end{array} \implies \cfrac{180000}{135000}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 4 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 4x=300\implies x=\cfrac{300}{4}\implies x=75[/tex]

Answer: The answer would be 745.5 yd.

Each lap is 250 yd, and Jasmine plans on running 3 laps, so 3*250 = 750 yd.

The answer is 745.5 yd, which is the closest to 750 yd.

Step-by-step explanation:

Step-by-step explanation:

a) 2x - 7

because "seven less than twice a number". if it says "seven less twice a number" it would be 7 - 2x.

b) x/2 + 4

c) (x - 6)y

the comma after "six" is important. without it it should be x - 6y

d) x + 2/3

the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Answer: -8

Hope this helps :)

Step-by-step explanation:

Adding two negative integers is just like adding two regular numbers

Answer:

negative 8

Step-by-step explanation:

calculator

The student has 1024 number of possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

4*4*4*4*4 = 1024

The student has 4 number of possible answer choices for each question. This means that for each question the student has 4 possible choices.

For the 5 multiple choice questions, the student has 4 possible choices for each question. This means that the student has 4^5 = 4*4*4*4*4 = 1024 possible ways to answer the five questions.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

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One example of a search problem I encounter in everyday life is finding a specific item in a grocery store.

An algorithm is a set of instructions designed to perform a specific task. Algorithms are a key component of computer programming, used to create programs that can solve problems and perform tasks. Algorithms are typically used to solve complex problems and can be thought of as a set of steps that must be followed in order to achieve a desired goal. Algorithms can range from simple, such as a basic sorting algorithm, to complex, such as an artificial intelligence algorithm.

This search problem generally uses a sequential search algorithm, where I must search through the aisles of the store in order to locate the item. This is a linear search, where I may have to search each aisle until I find the item. This type of search is effective for larger stores with many items, as it is relatively simple and efficient.

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Answer: 6w - 7 = 8

Step-by-step explanation:

        We will write an equation using w for the unknown number using the mathematical vocabulary used in the sentence.

seven less than ➜ - 7

product of 6 and a number ➜ 6w

equals 8 ➜ = 8

                          6w - 7 = 8

The first player will eventually win, when the second player runs out of free slots.

On the first move place the coin on the center of the table.

Then player B will place his coin anywhere on the table.

Now, you put your coin on the line of diameter passing through the coin placed by player B, at the same distance away from the boundary of the circle ( mimic his placement on the opposite side of the table).

If player A has space to place a coin, so will player B. Player B will run out of place before player A.

The first player will eventually win, when the second player runs out of free slots.

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We have,

nth term = 4n+1

Putting n = 3, we have the 3rd term, i.e.,

4(3) + 1 = 12 + 1 = 13

Answer:

13

Answer:

Step-by-step explanation:

(a) To work out the value of 64 - 1/2, we first need to understand that -1/2 is the same as raising the number to the power of -1/2. So, 64 -1/2 can be written as 64^(-1/2)

The value of 64^(-1/2) is equal to 1/√(64) = 1/8

(b) To work out the value of 81 - 1/2, we can write it as 81^(-1/2)

The value of 81^(-1/2) is equal to 1/√(81) = 1/9

(c) To work out the value of 64 - 1/3, we can write it as 64^(-1/3)

The value of 64^(-1/3) is equal to 1/∛(64) = 1/4

(d) To work out the value of 125 - 1/3, we can write it as 125^(-1/3)

The value of 125^(-1/3) is equal to 1/∛(125) = 1/5

Note: √ represents square root and ∛ represents cube root

The possible solution would be 10 bags of popcorn and 3 pretzels.

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.

Given, 'x' represents the number of bags of popcorn purchased and 'y' represents the number of bags of pretzels purchased.

Therefore,

x + y ≥ 13 and 7x + 5y ≤ 85.

The possible solution to these inequalities is where the graph of two intersects which is at (10, 3).

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Answer: A

Step-by-step explanation:

1/5k-2/3j=-2/3j+1/5k

15% of that number is 39.

What is a percentage?

A percentage is a way to express a number as a fraction of 100. It is commonly used to represent a proportion or ratio of a number to a whole. For example, 10% of a number means 10/100 or 1/10 of that number, 25% means 25/100 or 1/4 of that number, and 15% means 15/100 or 3/20 of that number.

To find 15% of a number, if we know that 10% of it is 26, and 25% of it is 65, we can use algebra:

Let X be the number we're trying to find

10% of X = 0.10X = 26

25% of X = 0.25X = 65

We know that 15% is between 10% and 25% so we can use the proportionality between them:

15% of X = 0.15X = (15/10)*26 = 39

Hence, 15% of that number is 39.

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Answer:

20,000

Step-by-step explanation:

1,000/ 5% = 20,000