A real estate agent working in a large city believes that, for three-bedroom houses, the selling price of the house decreases by approximately $2,000 for every mile increase in the distance of the house from the city center. To investigate the belief, the agent obtained a random sample of 20 three-bedroom houses that sold in the last year. The selling price, in thousands of dollars, and the distance from the city center, in miles, for each of the 20 houses are shown in the scatterplot. The table shows computer output from a regression analysis of the data.


(a) Describe the relationship between distance from city center and selling price.


(b) Find the linear regression equation. Interpret the slope and y-intercept in context.


) One house that was 11 miles from city center had a residual of -2.962. What was the actual selling price of the home?

The probability of selecting a lemon-filled donut followed by a jelly-filled donut is  [tex]\frac{5}{138}[/tex]

Probability is the potential for something to happen. In this area of mathematics, random events are studied. The range from 0 to 1 is used to express the value. To forecast the possibility of events, probability has been included into mathematics. The degree of likelihood that something will happen is basically how probability is defined. This fundamental theory of probability, which also applies to the probability distribution, can be used to estimate the likelihood of results in a random experiment.

The distribution of donuts is given as:

jelly = 2

lemon = 10

custard = 12

Total = 24

Eating a chosen donut without replacing it is an example of a selection.

So, the probability of selecting one lemon-filled donuts and one jelly filled donut is:

P = [tex]\frac{lemon}{Total}[/tex]×[tex]\frac{jelly}{total - 1}[/tex]

Substitute known values

P = [tex]\frac{10}{24}[/tex]×[tex]\frac{2}{23}[/tex]

Simplify

P = [tex]\frac{5}{138}[/tex]

Hence, the probability is  [tex]\frac{5}{138}[/tex]

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Explanation:

Imagine a rectangle that is 12 by 26. Multiplying the length and width will get us the area.

We can break the 12 into 10+2

Also, break the 26 into 20+6

Check out the diagram below. We have 4 smaller rectangles. Finding the product of those sub-areas will then get us the partial products needed.

In the bottom right corner we have a 2 by 6 rectangle, so it has area 2*6 = 12 square units. This is one of the four partial products. The other partial products are found the same way.

Once you determine the four partial products, we then add them up

12+60+40+200 = 12+100+200 = 12+300 = 312

Therefore, 12*26 = 312 which we can use a calculator to confirm.

The inequality is |4x-2|+1>7. By solving inequality we got x>-1 and x>2.

Given that,

The inequality is |4x-2|+1>7

We have to solve the inequality.

|4x-2|+1>7

Take +1 and right hand side we get -1

|4x-2|>7-1

Subtracting 7-1

|4x-2|>6

Now, it is modulus so we get + or -

1st we take +

4x-2>6

Take -2 and right hand side we get +2

4x>6+2

Adding 6+2

4x>8

Taking 4 to right hand side we get in the division.

x>8/4

x>2

Now, take -

-(4x-2)>6

Multiplying -1 on both sides

4x-2>-6

Take -2 and right hand side we get +2

4x>-6+2

Subtracting -6 and 2

4x>-4

Taking 4 to right hand side we get in the division.

x>-4/4

x>-1

Therefore, by solving inequality we got x>-1 and x>2.

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For all the given functions, the range lies between  {y ∈ R |-∞ < y < ∞} as non of the function has imaginary number.

For all the given functions;

For any value of x ∈ R (real number), the value of y of f(x) will lie in the given range.

Thus, all the given function have the range of  {y ∈ R |-∞ < y < ∞}.

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Answer:

Slower

Step-by-step explanation

The scooter travels 60 feet in 4 seconds, so it is going faster than the skateboard, which travels 55 feet in 4 seconds. A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?

The number line 5 ≤ 8-3x  shows the solution to the inequality as x cannot be more than 1.

A inequality compares two values and indicates whether one is smaller, larger, or simply not equal to the other.

a  ≠ b is the information that a and b are not equal.

If a  > b, a is greater than b. (these two are defined as strict inequality)

a ≤ b proves that a is less than or equal to b

a ≥ b proves that a is greater than or equal to b

The number line 5 ≤ 8-3x  shows the solution to the inequality as x cannot be more than 1.

If x is more than 1, lets say 2

Then the inequality as follows

5 ≤ 8-3(2) ≤ 14

5 ≤ 8-6 ≤ 14

5 ≤ 2 ≤ 14  this statement becomes false

Therefore x, must be lower than 1

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To identify the data corresponding to the points in the plane:

In x you count the units of distance from 0 to the point: from left (negative x) or right (positive x).

In y you count the units of distance from 0 to the point: down (negative y) or upwards (positive y)

Then, in coordinates (x,y) you have the next:

Corresponding to the table:

An artist can cut the metallic paper and pink glittery paper of the largest size of 12 inches without any waste.

The length of the metallic paper is 24 inches.

The length of the pink glittery paper is 36 inches.

To find the largest size, find the HCF of both number.

First find the factors using prime factorisation;

24 = 2×2×2×3

36 = 2×2×3×3

Find the common term,

HCF (24, 36) = 2×2×3

HCF (24, 36) = 12

Thus, an artist can cut the metallic paper and pink glittery paper of the largest size of 12 inches without any waste.

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The diameter is 3.75 cm

The value of the expression will be equal to 55.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that 6 is added to the product of 7 and a number 7. The expression will be written as,

E = 7 x 7 + 6

E = 49 + 6

E = 55

Therefore, the value of the expression will be equal to 55.

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Answer:

8

Step-by-step explanation:

56 shirts were sold, and including Mandy, 7 people sold them.

7 * x = 56

(7x)/7=56/7 (canceling out the 7 to get x alone)

x=8

So basically just 56 divided by 7

The solution to the given equation (2(-2) - 4 = 12) is -20 and its graphical solution is shown in the image attached below.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Next, we would solve the given equation as follows:

2(-2) - 4 = 12

Let us introduce a variable x into the equation as follows:

x = 2(-2) - 4 - 12

x = -4 - 4 - 12

x = -20

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Total students in sixth grade 200students

What is  Percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no associated unit of measurement.

Given,

No. of students using Tablet = 164

No. of students using book = 18%

The students in sixth grade either use book or tablet

When 164 student use tablet then remaining use tablet, that is 18%

Then, the remaining percent would be the students using tablet:

100% - 18% = 82%

converting 82% into decimal we get,

82 /100

i.e, 0.82

Number of students in sixth grade = 164/0.82

                                                          = 200 students

Hence, 200 students are in sixth grade

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The percentage of increase in her score is 6.82%

Here we will define her first score, 88, as the 100%.

So we can write the relation:

88 = 100%.

Her next score is 94, this will be a percentage X, then we can write:

94 = X

Taking the quotient between the two equations:

94/88 = X/100%

Solving this for X we get:

(94/88)*100% = X = 106.82%

The difference between the percentages gives the increase:

106.82% - 100% = 6.82%

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Answer:

7/9

Hope this helps!

Have a good day :)

Answer:

7/9

Step-by-step explanation:

I took the quiz

Answer:

y= vw/ux

Step-by-step explanation:

hope this help

If to find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. The height of  the tree is 72 feet.

Given data;

6 ft

2 ft 24 ft

Hence,

Angle of incidence = Angle of reflection

Hence,

m ∠ ACD = m ∠ ECD

Two triangle will only be the same if their corresponding angles are congruent
So,

Sine m ∠ ACD = m ∠ ECD

m Δ ABC  = Δ EDC

The corresponding of similar triangles are proportional

Hence,

BC / DC = AB / ED

= 2 / 24 = 6 / ED

2ED = 24 × 6

2ED = 144

Divide both side by 2

ED = 144 / 2

ED = 72 feet

Therefore we can conclude that the tree height is measure at 72 feet.

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3x + 2y = 10

3x is adding on the left, then it will subtract on the right:

2y = 10 - 3x

or

2y = -3x + 10

2 is multiplying on the left, then it will divide on the right:

The correct option is option C

Answer:

$0.91

Step-by-step explanation:

Given:

If one pound of Parmesan cheese costs $14.60, to find the cost of a one-ounce portion, simply divide the cost of one pound by 16:

[tex]\implies \textsf{1 ounce portion}=\dfrac{\$14.60}{16}=\$0.9125=\$0.91\;\sf (nearest \; cent)[/tex]

Therefore, the standard portion cost for a one-ounce portion of Parmesan cheese is $0.91 (nearest cent).

Answer:

798

Step-by-step explanation:

11. v = l x w x h

19 x 12 x 3.5 = 798

20. 3+x=10

The highest common factor of the given number is 35.

The biggest positive number that divides each integer in a set of two or more is known as the greatest common divisor in mathematics. The GCD of two integers x, and y is the greatest common divisor of x and y. A group of numbers' largest factor that they all share is known as the group's greatest common factor (GCF). Components 2 and 4 are shared by the numbers 12, 20, and 24, for instance. We claim the GCF of 12, 20, and 24 equals 4 since 4 is the largest. The greatest integer that may divide two or more numbers is known as the highest common factor (HCF), sometimes known as the GCF. The definition of highest is the highest or largest number. Any two or more numbers that share a common meaning.

Factors of 70

= 7 ,2 ,5 , 1 , 10 , 35 , 14

Factors of 385

= 1 , 5 , 7 , 11 , 35 , 55

HCF

= 35

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In order to convert a percent to a decimal number we need to move the decimal point two units to the left

The value of x is 10.

A mathematical expression consists of a statement, at least one arithmetic operation, and at least two integers or variables. With this mathematical operation, you can multiply, divide, add, or subtract.

Given:

E is between D and F.

DE = 3x + 2

EF = 18

DF = 5x

We need to determine the value of x which is a variable, whose value is unknown to us and can take any value.

So, DF = DE + EF

Substituting the given values, we get

5x = 3x + 2 + 18

5x - 3x = 20

2x = 20

x = 20/2

x = 10

Therefore, the value of x is 10.

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Polynomials are algebraic expressions that consist of the variables and coefficients. Six complex number system, polynomial 3x6x³-4x²+3x+52 = 0 have.

Polynomials are algebraic expressions that consist of the variables and coefficients. Variables are also sometimes called the indeterminates. We can perform the arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

We have following polynomial for this situation.

We observe that polynomial graph only intersects the vertical axis once.

There are no additional x-axis cutoff points in graph.

As a result, polynomial:

6 difficult solutions

No actual solution

So, we can 6 difficult solutions.

We have following polynomial for this situation.

We observe that polynomial graph only intersects the vertical axis once.

There are no additional x-axis cutoff points in graph.

As a result, polynomial:

6 difficult solutions

No actual solution

So, 6 complex solutions can be said to exist.

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We need to find which expression represents the situation given, in this case we have two values a distance (80 ft) and the elapsed time (40 s). The time is the input of the equation, it will be placed on the "x" variable and the distance is the output of the equation, it will be placed on the "y" variable. We need to find the expression that outputs "80" when we input 40. Let's check them one by one:

A.

This outputs 20 ft when we input 40 s, therefore it is not this one.

B.

This one outputs 160 ft when we input 40 s, therefore it is not this one.

C.

This one outputs 80 ft when we input 40 s, therefore this is the correct expression.

We now need to use this expression to calculate the distance the person will travel in 10 seconds, so we will make x equal to 10 s.

The person will walk 20 ft.

The correct option is "C".

In the PEMDAS method of solving , it goes to the five basic operations

1.Parenthesis 2. Exponents 3. Multiplication 4. Addition 5.Substraction

In this exercise there are NOT parenthesis, so then the first operation is Exponentiation and 2nd operation is Multiplication

So the answer is Multiply, the first option.