Age (years) 10 20 30 40 50 60 Time (minutes) 13 16 11 16 14 22 —10. A group of six dentists were comparing how long they spend on initial examinations based on the age of their patients. The table shows the data points for the six dentists. Using technology, the equation of the best fit line was found to be û = 0.1257x + 10.93. Which calculation correctly determines the residual for the time spent on the initial examination of a 40-year-old patient? (A.) Ý40 = 0.1257 + 10.93(40) = 37.3257; 37.3257 – 40 = -2.6743 (B.) Ý40 = 0.1257 + 10.93(40) = 37.3257; 40 - 37.3257 = 2.6743 (C.) Ý40 = 0.1257(40) + 10.93 = 15.958; 16 - 15.958 = 0.042(D.) Ý40 = 0.1257(40) + 10.93 = 15.958; 15.958 - 16 = -0.042

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

  B - 1100 tickets

Step-by-step explanation:

Fixed costs appear to be ...

  $2,200 +1,500 = $3,700

The amount of cost that is not covered by concession income is ...

  $3,700 -1500 = $2,200 . . . . remaining cost

The contribution margin per ticket is apparently ...

  $5 -3 = $2

So, the number of tickets that must be sold to cover the remaining cost is ...

  $2200/($2/ticket) = 1100 tickets

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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Answer:

96

Step-by-step explanation:

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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N 11

Remember that

The law of sines

In this problem

Solve for x

sinX=(14.9*sin71)/25.5

Answer:

1/6

Step-by-step explanation:

out of the 6 sides of the die, you can roll a 6 1 time. The formula = favorable/possible.

Hope this helps!

Answer:

(b) 32

Step-by-step explanation:

From the information given :

sample mean of Philadelphia μ₁ = $1240

Sample size of Philadelphia n₁ = 15

Sample Standard deviation σ₁ = $270

sample mean of Paris μ₂ = $1,060

Sample size of Paris  n₂ = 19

Sample Standard deviation of Paris  σ₂ = $240

If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris;

the degrees of freedom for this hypothesis test can be calculated as;

degree of freedom df = n - 1

degree of freedom for both hypothesis test = (n₁ - 1 + n₂ -1)

degree of freedom for both hypothesis test  = (n₁ + n₂ - 2)

degree of freedom for both hypothesis test  = ( 15 + 19 - 2)

degree of freedom for both hypothesis test are   32  

The key features of this rational expression include the following:

Factor: f(x) = 2(x - 2)/(x + 2).

Domain: (-∞, -2) ∪ (-2, ∞) ∪ (1, ∞)

Holes: (1, -2/3).

Vertical asymptote: x = -2.

Horizontal asymptote​: y = 2.

In Mathematics, a rational expression simply refers to a type of expression which is expressed as a fraction. In this exercise, we would factorize the numerator and denominator for this rational expression as follows;

Numerator = 2x² - 6x + 4

Numerator = 2(x² - 3x + 2)

By using the sum-product pattern, we have the following:

Numerator = 2(x² - x - 2x + 2)

Numerator = 2(x - 2)(x - 1)

Denominator = x² + x - 2 = (x - 1)(x + 2).

f(x) = (2x² - 6x + 4)/(x² + x - 2) = [2(x - 2)(x - 1)]/[(x - 1)(x + 2)]

f(x) = 2(x - 2)/(x + 2)

Generally speaking, a hole is a point on the graph of a rational expression where the input value causes both its numerator and denominator to be equal to zero (0).

Holes = (1, -2/3).

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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‍‍‍Answer : -0.65

:)

Answer:

\(\huge\boxed{(-19)^{-8}=19^{-8}}\)

Step-by-step explanation:

Use

\(a^n\times a^m=a^{n+m}\)

\((-19)^{-12}\times(-19)^4=(-19)^{-12+4}=(-19)^{-8}\)

Answer:

They r correct lol

Step-by-step explanation:

Answer:

The first one-in green. 6x4=24, and there are four parts.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Give me a sec to work it out

The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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Hey there!

√144

= 12^2

= 12 * 12

= 144

Therefore, your answer should be: 12

Side note: There’s many ways to find the result of the square root but I just made it “easier” to solve and tackle future problems like this on your own.

Anyways

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The regression equation is Y = −12.201 + 2.195x.

In the given question,

A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

We have to find the regression equation.

Given that,

Coefficient of Intercept(a) = −12.201

Coefficient of Number of contacts(b) = 2.195

The regression equation is,

Y = a + bx

Y = −12.201 + 2.195x

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The right question is:

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

What is the regression equation?

The person that has the winning time is Alex.

From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.

It should be noted that in a race, the person that has the lowest time wins.

In this situation, the person with 8.625 seconds is the lowest.

Therefore, Alex wins.

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(a)

Given:

72 to be split into 1:3:5

Solution:

First divide the amount with the sum of the ratio given

72 / 1 + 3 + 5 = 72 / 9 = 8

Now multiply the answer with each value:-

8 × 1 = 8

8 × 3 = 24

8 × 5 = 40

∴ The ratio will be 8:24:40

{To check your answer add to get the exact value: 8 + 24 + 40 = 72}

(b)

Given:

150 to be split into 2:3

Solution:

First divide the amount with the sum of the ratio given

150 / 2 + 3 = 150 / 5 = 30

Now multiply the answer with each value:-

30 × 2 = 60

30 × 3 = 90

∴ The ratio will be 60:90

{Now check your answer in the same way above: 60 + 90 = 150}

The domain restrictions for (f/g)(x) are (c) x = 0, 6

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

That is a very Nice poem!

Answer:

1/1

Step-by-step explanation:

22/22 =1

Answer:

3.1in

hope it helps

Hey there!

Your answer is 2(n + 3)

"Double" represents multiplying by two. Also, "sum of a number and 3" represents the addition of 3 and a number, so we could put "n + 3". Since we are doubling the sum, it would be "2(n + 3)"

Have a terrificly amazing day! :D

Answer:

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

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

Answer:

43.6 has 3 significant figures.

Answer:

Solution: (3, 2)

Step-by-step explanation:

It's easier to graph when the equation of the lines are in their slope-intercept form, y = mx + b.

x - 3y = -3

-3y = -x - 3

Divide both sides by -3:

\(\frac{-3y}{-3} = \frac{-x - 3}{-3}\)

y = 1/3x + 1

where slope = 1/3

y-intercept = 1

x + y = 5

Subtract x from both sides to isolate y:

x - x + y = - x + 5

y = -x + 5

where slope = -1  

y-intercept, 5

I started by graphing the y-intercepts of each line. Then, I used the slope of each linear equation (rise over run) to plot the next points on the graph. In the attached screenshot of the graph, x - 3y = -3 is the blue line, while x + y = 5 is the green line. Their intersection occurs at point, (3, 2).

Therefore, the solution is (3, 2).

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