Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?

Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

According to the statement

we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.

So, we know that the

For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.

Looking at the two rectangles, the corresponding sides are pf the rectangles are:

4 m side corresponds to 8 m side in rectangle A

12m side corresponds to the 24 m side in rectangle B.

Then

The ratios of the both rectangles are:

In rectangle A is 8/4 = 2

In rectangle B is 24/12 = 2

From this it is clear that the ratios are equal.

Thus, the scale factor is 2

Since 8/4 = 24/12, we can rearrange to get;

12/4 = 24/8.

So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?

A. 12/3 = 24/12.

B. 12/2 = 27/8.

C. 11/4 = 23/8.

D. 12/4 = 24/8.

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The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

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Step-by-step explanation:

Reduce 13/100 to lowest terms

13

100

is already in the simplest form. It can be written as 0.13 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 13 and 100 is 1

Divide both the numerator and denominator by the GCD

13 ÷ 1

100 ÷ 1

Reduced fraction:

13

100

Therefore, 13/100 simplified to lowest terms is 13/100.

The mixed number [tex]7\dfrac{13}{100}[/tex] is [tex]\dfrac{713}{100}[/tex] on simplification.

A mixed number is a mathematical representation of a number that consists of a whole number and a fraction. It's called a "mixed number" because it combines both a whole number and a proper fraction. The whole number part represents a whole quantity, while the fractional proportion represents a proportion of a whole.

Mixed numbers are generally employed to represent measures that aren't whole numbers but are still greater than 1. They're particularly useful when dealing with magnitudes, such as lengths or quantities of things, that concern both whole units and fractional parts.

Given that

[tex]7\dfrac{13}{100}[/tex] [tex]= 7 + \dfrac{13}{100}[/tex]

       [tex]= \dfrac{700}{100}+ \dfrac{13}{100}\\= \dfrac{700+13}{100} \\= \dfrac{713}{100}[/tex]

Hence, The mixed number [tex]7\dfrac{13}{100}[/tex] can be simplified as [tex]\dfrac{713}{100}[/tex].

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The probability of rolling a sum of six or two even numbers.

is P = 1/3

Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:

6*6 = 36

Now, the outcomes that given a sum of 6 are:

dice 1    dice 2.

1              5

5              1

2              4

4              2

3             3

We have 5 outcomes there.

The outcomes where both numbers are even are:

dice 1    dice 2.

2             2

2             4

4             2

4             4

4            6

6             2

6             4

6             6

We have 8 outcomes here (such that 2 are in the ones we counted before).

Then the total number of outcomes that either add to 6 or have both even numbers are:

5 + 8 - 2 = 12

Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:

P = 12/36 = 1/3

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Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

First symmetrically cut the pentagon to get 5 pieces. (So that you will get the idea that this polygon is divided into 5 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} bh[/tex]

A = [tex]\frac{1}{2}[/tex] × 4 × 10

A = 20 m²

To find the area of the whole pentagon shape:

A = 20 × 5 = 100 m²

Hope it helps!

Based on the given parameters, the number of filet mignon the restaurant served is 14

From the question, the given parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

This means that the proportion of filet mignon is

filet mignon = 100%- Salmon filets

This gives

filet mignon = 100%- 80%

Evaluate the difference

filet mignon = 20%

The number of filet mignon is calculated as:

filet mignon = 20% * Dinner specials

Substitute the known values in the above equation

filet mignon = 20% * 70

Express 20% as decimal

filet mignon = 0.20 * 70

Evaluate the product

filet mignon = 14

Hence, the number of filet mignon the restaurant served is 14

So, the complete parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

filet mignon = 14

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Horizontal asymptote of c(x) is 450.

A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

Thus, the following formula represents the average cost to produce x refrigerators:

C(x) = (200000 + 450x)/x

Horizontal asymptote of c(x) would be

= 450x/x

= 450

Hence, Horizontal asymptote of c(x) is 450

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Answer:

True

Step-by-step explanation:

All faces of a cube are the same.

The mean in minutes of the length of time given= 9.1

The formula used for the determination of mean when a frequency table is given is

= total/n

Where total = frequency×midpoint

n = 42

To calculate the total, the mid point of each length of time is determined as follows;

1+4/2 = 2.5 × 4 = 10

4+7/2= 5.5 × 8 = 44

7+10/2 = 8.5 × 14= 119

10+13/2 = 11.5× 9 = 103.5

13+16/2= 14.5×5 = 72.5

16+19/2= 17.5× 2= 35

Total= 10+44+119+103.5+72.5+35 = 384

Therefore mean = 384/42= 9.1

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[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 -4ac}}{2a}[/tex]

There will be 60 residuals for simple bivariate regression's  60 observations.

According to the statement

We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.

So, For the solution of this problem,

We know that the

A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.

And we know that the it is always same for the number as the number of given observations.

That's why there is 60 residuals.

So, There will be 60 residuals for simple bivariate regression's  60 observations.

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Answer:

Akua now -- x

Ama now -- 4x

Akua in 10 years ---- x+10

Ama in 10 years ---- 4x+10

4x+10 = 2(x+10)

solve for x

let Ama's age be X and Akua's age be Y

X=4Y.......

X+10=(Y+10)2......

4Y+10=2Y+20

4Y-2Y=20-10

2Y=10 divide both side by 2

2Y/2=10/2

Y=5

X=4x5

X=20

therefore Ama =20years and Akua=5years

hope it helps..

Answer:67 wins, 26 losses

Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w =  2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.

Answer:

The file contains the solution to the question

Answer:

7.52 m^3

Step-by-step explanation:

This is like compound interest in a banking calculation

Future volume = 5 (1 + .06)^7 = 7.52 m^3

The value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The equation is given as

∝At + (1-∝) Ft

The value for Alpha = 0.7

1 - ∝ = 1 - 0.7

= 0.3

Forecast in match = 62

Ft = 51. 5

the difference = 62 - 51.5

= 10.5

The error = 10.5/62 * 100

= 16.94%

Hence the value of the  mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is  16.94%

The past demand data shown below can be regarded as stationary.

Month Demand

January

50

February

55

March

62

April

45

What is the mean absolute percentage error of the forecast for March found by the exponential smoothing method with a smoothing constant of 0.3?

O a. 14.68%

Ob. 16.94%

O c. 12.57%

Od. 11.33%

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Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )

m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

Answer:

-7

Step-by-step explanation:

[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]

Answer:

x = 7; y = 4 1/3

Step-by-step explanation:

The solution is the point of intersection of the lines.

Read the point of intersection.

You can also solve the system using algebra.

y = 1/3 x + 2

y = 4/3 x - 5

1/3 x + 2 = 4/3 x - 5

x + 6 = 4x - 15

-3x = -21

x = 7

y = 1/3 x + 2

y = 1/3 × 7 + 2

y = 2 1/3 + 2

y = 4 1/3

Answer: x = 7; y = 4 1/3

The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

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The y-intercept of the equation  g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation  g(x) = 3^x - 5 is y = -5

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The y-intercept is a point on the graph where the value of x is 0

This is represented by x= 0 or (0, y)

This means that we substitute 0 for x in the above equation

So, we have:

g(0) = 3^0 - 5

Evaluate the exponent 3^0

g(0) = 1 - 5

Evaluate the difference of 1 and 5

g(0)  = -4

Rewrite this point as

(0, -4)

This means that the y-intercept of the equation  g(x) = 3^x - 5 is (0, -4)

The equation of the function g(x) is given as:

g(x) = 3^x - 5

The asymptote is a point on the graph where that is parallel to the graph

In the above equation, we have:

g(x) = 3^x - 5

Express the radical as 0

y = 0 - 5

Evaluate the difference of 0 and 5

y  = -5

This means that the asymptote of the equation  g(x) = 3^x - 5 is y = -5

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Answer:

  0.33 ⋅ 10^−15

Step-by-step explanation:

Scientific notation requires exactly one non-zero digit to the left of the decimal point.

The number ...

  0.33 ⋅ 10^−15

has no non-zero digits to the left of the decimal point. It is not in "scientific notation."

__

Additional comment

Expressed in scientific notation, it would be ...

     3.3 ⋅ 10^−16

The price x which will maximize the company's revenue is 904

The price x which will maximize the company's revenue is 240

Let

Price of the good = x

Number of goods sold = 2712- 3x

The formula for revenue is given as;

Revenue = Price × Quantity

= x( 2712 - 3x)

Expand the bracket

2712x - 3x^2

Therefore, the price x which will maximize the company's revenue will be:

2712x - 3x^2 =0

Collect like terms

3x² = 2712x

3x =  2712

Divide both side by 3

3x/3 = 2712/3

x = 904

Hence, the price x which will maximize the company's revenue is 904

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