10. The data set below shows the mileage and selling prices of eight used cars of the same model. Mileage Price 21,000 $16,000 34,000 $11,000 41,000 $13,000 43,000 $14,000 65,000 $10,000 72,000 $12,000 76,000 $7,000 84,000 $7,000 (a) Calculate r , the correlation coefficient between these two variables. r = (b) Interpret the value of r : the association is positive or negative and (strong or moderate or weak or negligible) (c) Compute the regression line for predicting price from mileage. ˆ y = x + (d) Predict the price of a car with 30,000 miles. $ (e) Does the student with 43,000 miles on it have a higher or lower price than the one predicted by the regression line? Higher Lower

Answer:120 dollars

Step-by-step explanation:

If Katerina completes a 15-mile run in 2 1/2 hours. She will complete a mile in an average of five minutes. Option B is correct.

It is described as a single number that indicates either the closed value for each entry in the set of data or the mean value for the entire set of data.

It is given that, In 2 1/2 hours, Katerina completes a 15-mile run.

We have to find the average number of minutes it takes her to run 1 mile.

15 miles = 2 1/2 hours

15 miles=5/2 hours

The unitary approach allows us to calculate the value of a single unit and then use that value to calculate the value of the required number of units.

1 miles= 5 /30 hours

1 miles = 1/6 hours

As we know that 1 hour consists of 60 minutes.

1 hours = 60 minute

1 mile = 60 / 6 minutes

1 miles = 10 minute

Thus, the average number of minutes it takes her to run 1 mile will be 10 minutes. Option B is correct.

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Answer:

x+1/3

Step-by-step explanation:

Add the terms together (3x+1), then divide by how many terms there are (3), to get the average of the expressions

We are given a set of coordinates which are;

And the slope which is;

The equation of a line in slope-intercept form is;

Note that in this equation, the variable m is the slope (that is, the coefficient of x). we can now substitute for x, y and m into the equation above and we'll have;

We now have the values of the slope and the y-intercept as

The equation now can be written as;

ANSWER:

The error term, which refers to the sum of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

Y=αX+βρ+ϵ

where:

α,β=Constant parameters

X,ρ=Independent variables

ϵ=Error term

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A. Addition

Explanation

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete

Step 1

so, firts calculate the parenthesis

the operation in parenthesis is an addition

i hope this helps you

Answer:

the value of pi is 3.14159

The highest cut-off interest rate is 2.66%

Given that,

Standard deviation (sigma) = 0.37

Mean percentage (Mu) = 2.28 %

P(Z > 1.04) = 0.15

z = 1.04

Using the z-score formula,

x = (z × sigma) + mu

x =  (1.04 × 0.37 )+ 2.28 = 2.66 %

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The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:

i⁰ = 1 (any number with the exponent 0 equals 1)

i¹ = i (any number with the exponent 1 is the number itself)

i² = -1 (this follows from the definition of the imaginary number, the square root of -1)

i³ = i² * i = -1 * i = -i

Now, the results start to repeat from 1 to -i:

i⁴= i² * i² = (-1) * (-1) = 1

i⁵ = i⁴ * i = 1 * i = i

i⁶ = i * i⁵ = i * i = i² = -1

i⁷ = i⁶ * i = -1 * i = -i

From that, we can follow the steps below to find the value of a power of i:

• divide the exponent by 4;

• if the rest of the division is 0, then the power equals ,i⁰ = 1,;

• if the rest of the division is 1, then the power equals ,i¹ = i,;

• if the rest of the division is 2, then the power equals ,i² = -1,;

• if the rest of the division is 3, then the power equals ,i³ = -i,.

So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:

• 649/4, has a quotient of 162 and the, rest 1,. Therefore:

i⁶⁴⁹ = i¹ = i

Thus, i⁶⁴⁹ equals i.

The Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the Cost of the small greeting card = is $1.25 .

The Cost of the large greeting card =$4.50.

We need to determine the Total cost of 5 small and 4 large greeting cards and the total cost of x small and y large greeting cards.

The Cost of 5 small greeting cards = 6.25

The Cost of 4 large greeting cards = 18

Then the Total cost = $6.25+ $18 =$24.25

Therefore, the Total cost of 5 small and 4 large greeting cards is; $24.25.

Now, the total cost of x small and y large greeting cards will be;

Cost of x small greeting cards = 1.25x

Cost of y large greeting cards = 4.50y

Total cost = 1.25x + 4.50y

Therefore, the Total cost of x small and y large greeting cards is; 1.25x + 4.50y.

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Answer:

slope = -1/9

Step-by-step explanation:

Hope this helps!!!

The most appropriate choice for perimeter of a shape will be given by-

UT = 19 ft

ST = 19 ft

RS = 19 ft

UR = 19 ft

What is perimeter of a shape?

Perimeter of a shape is the length of the boundary of the shape.

It is obtained by taking the sum of all the length of the boundary.

Here,

UT = (25 - x) ft

ST = (3x + 1) ft

RS = (13 + x) ft

UR = (4x - 5) ft

Perimeter = UT + ST + RS + UR

                = (25 - x + 3x + 1  + 13 + x +4x -5) ft

                = (7x + 34) ft

By the problem,

[tex]7x +34 =76\\7x = 76 -34\\7x = 42\\x = \frac{42}{7}\\x =6[/tex]

UT = [tex]25 - 6[/tex] = [tex]19[/tex] ft

ST = [tex]3 \times 6 + 1[/tex] = [tex]19[/tex] ft

RS = [tex]13 + 6 = 19[/tex] ft

UR = [tex]4\times 6 - 5[/tex] = 19 ft

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Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

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

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

Always that we have an integer, let's say 2, we can rewrite it like:

This will help us when multiplying fractions. To multiply two fractions, we simply multiply the numerator with the numerator and denominator with denominator. In this case:

And then solve:

Now we can further simplify this fraction, because 14 and 4 are divisible by 2, then:

14 = 2 x 7

4 = 2 x 2

Then the final answer is:

Answer:

994

Step-by-step explanation:

work inside the parenthesis first. 8+2 = 10 then raise 10 to the power of 3 which is 1000. subtract 6 from 1000 & you get 994

Answer:

994

Step-by-step explanation:

PEDMAS

Do the math inside the parentheses first

8+2 = 10         Now do the exponent    10^3 = 1000   Now subtract 6  = 994

The graph of the equation y = –12x – 6 is attached in the solution.

We can find the x and y intercept of the line to find make the graph.

Putting x = 0 in the given equation, we get:-

y = -12(0) - 6 = 0 - 6 = -6

Hence, the x -intercept is (0,-6).

Putting y = 0 in the given equation, we get:-

0 = -12x - 6

6 = -12x

x = 6/(-12)

x = -1/2

Hence, the y -intercept is (-1/2,0).

We can find another point on the line.

Putting x = -1 in the given equation, we get:-

y = -12(-1) - 6

y = 12 - 6 = 6

y = 6

Hence, another point on the line is (-1,6).  

Plotting these points we can graph the equation of the line.

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There is sufficient evidence at the 0.10 level of significance that the percentage is not 33%.

According to the newsletter publisher that 33% of their readers own a Rolls Royce.

The testing firm says that this is an inaccurate issue and performs a test to dispute the publisher's claim, after performing the test at the 0.10 level of significance the results are as follows,

Null hypothesis:

H₀ : p = 0.33

Alternative hypothesis:

H₁ : p ≠ 0.33

We reject H₀ at the 0.10 level of significance.

Therefore, There is sufficient evidence at the 0.10 level of significance  that the percentage is not 33%.

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Answer:

-29.8

Step-by-step explanation:

4 (-1.2-4-4.75) +1+(-3)²

4 (-1.2-4-4.75) +1+(-3)²

4 (-9.95) +1+9

4 (-9.95) +1+9

-39.8 +1+9 = -29.8

The reminder of 2 to the 100th power divided by 5 is 1

2 to the 100th power is:

[tex]2^{100}[/tex]  = 1,267,650,600,228,229,401,496,703,205,376

Then dividing 2 to the 100th power by 5:

1,267,650,600,228,229,401,496,703,205,376 / 5 = 253,530,120,045,645,880,299,340,641,075  (without considering the decimal value)

This tells us how many times 5 can divide 2 to the 100th power.

Next, we need to multiply the answer obtained from the division by 5 (since we used 5 to divide):

253,530,120,045,645,880,299,340,641,075 x 5 = 1,267,650,600,228,229,401,496,703,205,375

Lastly, subtracting our last answer from the value of 2 to the 100th power will give us the reminder:

1,267,650,600,228,229,401,496,703,205,376 - 1,267,650,600,228,229,401,496,703,205,375 = 1

Therefore, the reminder when 2 raised to the power of 100 is divided by 5 is  1.

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Answer:

9 inches

Step-by-step explanation:

Set it up like a fraction ratio and solve for x.  as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.

[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]

13*36 = 468

468/52 = 9

Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.

To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)

This is:

Thus, the final answer is 34.9.

2.

Explanation

To answer the question, we have to understand the different parts of an algebraic expression

An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

We are given the algebraic expression:

For the given question

The difference means the result of subtracting one number from another or How much one number differs from another, so we have

Then

The coefficient is is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial, so we have

Also

A quotient is a number resulting from the division of one number by another, so we have

Finally,

A product is the result of multiplication or an expression that identifies factors to be multiplied.

Thus, we have

The chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings are very low.

In radio transmission, a radio transmitter's antenna couples electromagnetic energy into the atmosphere or other open space. Electromagnetic radio waves are caught by a receiving antenna during radio reception and coupled into a receiver for detection.

Radio waves have a low frequency, which limits their ability to deliver large amounts of data at once.

There are extremely slim odds that radio signals from Earth or messages placed on far-off space probes will ever be received by living things, it is acceptable to the state. Remember that some scientists have held this belief about the existence of extraterrestrial life for years without any convincing evidence.

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Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

approximately 7 years old

Step-by-step explanation:

The values are given as;

1. - 2a - 9 = 6a + 15,  a = -3

2. 14 + 3n = 5n - 6, n = 10

An algebraic expression can simply be described as a mathematical expression that composed of arithmetic operations, such as;

They are also known to be made up of terms, variables, constants, factors and coefficients.

Given the algebraic expression;

- 2a - 9 = 6a + 15

Let's take the following steps;

collect like terms

- 2a - 6a = 15 + 9

add or subtract like terms

-8a = 24

Make 'a' the subject

a = 24/-8

Find the quotient

a = -3

14 + 3n = 5n - 6

collect like terms

3n - 5n = -6 - 14

-2n = -20

Make 'n' the subject of formula

n = 10

Hence, the values are -3 and 10

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Answer:

G

Step-by-step explanation:

the domain is the interval or set of all valid x values.

we see x starts at -3 and goes up to +1.

but x = 1 has the be excluded (the hollow point tells us that, a filled point says "include").

therefore, the -3 <= x < 1 answer is correct