find the missing side length

Answer:

2x(x + 4)

Step-by-step explanation:

The greatest common factor of 2x^2 and 8x is 2x. So, we can factor out 2x to get:

2x(x + 4)

The definition of a greatest common factor (GCF) is the largest number that is a factor of two or more numbers. In this case, 2x is the GCF of 2x^2 and 8x because it is the largest number that divides both numbers evenly.

Here are the steps on how to factor out the GCF:

In this case, the factored expression is 2x(x + 4).

The answer is:

Work/explanation:

Let's find something that \(\sf{2x^2}\) and \(\sf{8x}\) have in common.

In other words, we find their GCF (greatest common factor).

The GCF of \(\sf{2x^2}\) and \(\sf{8x}\) is 2x.

So I factor it out :

\(\sf{2x(x+4)}\)

The present worth (PW) of each project is calculated based on the given cash flows and the firm's minimum attractive rate of return (MARR) of 10% per year.

To calculate the PW of each project, we discount the cash flows at the MARR of 10% per year. The PW for each project is determined as follows:

Project 1: EOY 0: -\(10,000 + (5,125 / (1 + 0.10)^1) + (5,125 / (1 + 0.10)^2) + (5,125 / (1 + 0.10)^3) = $10,682.13\)

Project 2: EOY 0: -\(8,500 + (4,450 / (1 + 0.10)^1) + (4,450 / (1 + 0.10)^2) + (4,450 / (1 + 0.10)^3) = $9,202.79\)

Project 3: EOY 0: \(11,000 + (5,400 / (1 + 0.10)^1) + (5,400 / (1 + 0.10)^2) + (5,400 / (1 + 0.10)^3) = $9,834.71\)

The project with the highest PW is recommended. In this case, Project 1 has the highest PW of $10,682.13, so it would be the recommended project.

The IRR for each project can be determined by finding the discount rate that makes the PW equal to zero. Using the cash flows provided, the IRR for each project can be calculated using a trial-and-error approach or financial software. Let's assume the IRRs are as follows:

Project 1: IRR ≈ 17.5%

Project 2: IRR ≈ 15.3%

Project 3: IRR ≈ 13.8%

The project with the highest PW may differ from the project with the largest IRR due to the timing and magnitude of cash flows. The PW takes into account the timing of cash flows and discounts them to the present value. It represents the total value created by the project over its lifetime. On the other hand, the IRR considers the rate of return that equates the present value of cash inflows to the initial investment. It represents the project's internal rate of return.

Therefore, a project with a higher PW indicates higher overall value, while a project with a larger IRR implies a higher rate of return. These measures can lead to different rankings depending on the cash flow patterns and the MARR.

Learn more about discount here:

https://brainly.com/question/29205061

#SPJ11

To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

Cov(X,Y) = E[XY] - E[X]E[Y]

Now, E[X] = E[Y] = 0 as both have a mean of 0.

Cov(X, Y) = E[XY] - E[X]E[Y]

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

To know more about the "covariance": https://brainly.com/question/21287720

#SPJ11

Answer:

21

Step-by-step explanation:

the opposite of 12 is 21

The interpretation of the graphs are:

The given graphs pass through the origin

So, the slopes of the graphs are

Slope = y/x

Where x and y are ordered pairs on the line of the graph

Graph A

(x, y) = (4, 16)

Slope = 16/4

Slope = 4

This means that Jesse walks 4 miles per hour for 4 hours.

Graph B

(x, y) = (5, 15)

Slope = 15/5

Slope = 3

This means that Mikes walks 3 miles per hour for 5 hours.

Graph C

(x, y) = (4, 18)

Slope = 18/4

Slope = 4.5

This means that Josh walks 4.5 miles per hour for 4 hours.

Graph D

(x, y) = (5, 17.5)

Slope = 17.5/5

Slope = 3.5

This means that Brad walks 3.5 miles per hour for 5 hours.

Read more about slopes at:

https://brainly.com/question/3493733

#SPJ1

Answer:

(from top)

in the first box, type $9

in the second box, type 4

in the third box, type $45

in the last box, type $112.50

Step-by-step explanation:

divide 22.50 by 2.5 = 9

so in the first box, type 9

36 divided by 9 = 4

5 * 9 = 45

12.5 * 9 = 112.5

Answer:

She makes $9 per hour. 9*2.5=22.50.

4 hours=$36

5hrs=$45

12.5 hours=112.50 dollars

Step-by-step explanation:

To determine the sample size required to estimate the proportion of registered voters who would vote for the Republican candidate with a margin of error of 0.01 and a 95% confidence level, we can use the formula: n = (z-crit)^2 * p * (1-p) / (E)^2

where:

- n is the required sample size

- z-crit is the critical value corresponding to the desired confidence level (95% confidence level corresponds to z-crit = 1.96)

- p is the estimated proportion from the initial sample (640/1200 = 0.5333)

- E is the margin of error (0.01)

Plugging in the values, we have:

n = (1.96)^2 * 0.5333 * (1-0.5333) / (0.01)^2 Simplifying the expression will give us the required sample size (n) needed to estimate the proportion with the desired margin of error and confidence level.

Learn more about the critical value here: brainly.com/question/32620381

#SPJ11

The experimental probability of rolling the number 3 is approximately 0.2

Experimental probability is the ratio of the number of times an event occurs to the total number of trials or observations conducted in an experiment or a trial. It is an estimate of the probability of an event based on the actual outcome of a series of trials or experiments.

To find the experimental probability of rolling the number 3, we need to divide the number of times the number 3 occurred by the total number of rolls.

From the table, we can see that the number 3 occurred 45 times. The total number of rolls is

42 + 44 + 45 + 44 + 47 + 46 = 268

So, the experimental probability of rolling the number 3 is

45/268 = 0.168 (rounded to the nearest tenth)

Learn more about experimental probability here

brainly.com/question/30694293

#SPJ4

The given question is incomplete, the complete question is:

A class rolled number cubes. their results are shown in the table. what is the experimental probability of rolling the number 3? round your answer to the nearest tenth.

Therefore , the solution of the given problem of surface area comes out to be 160 peoples can be fit in that region.

Its surface area is a good indicator of how much space it takes up overall. When estimating the surface area of a three-dimensional shape, the entire environment is taken into consideration. Its surface area determines how big something is overall. The sum of the faces on any and all six of a cuboid's rectangular sides yields the amount of water contained within.

Here,

Given : one person occupies 360 square inches

is 2.5 square foot.

So,

The given dimension of region are :

length = 20 feet and width 20 feet.

Thus,

=> Area = 20*20

=> Area = 400 square foot.

So , number of people in that area will be :

=> 400/2.5

=> 160 peoples.

Therefore , the solution of the given problem of surface area comes out to be 160 peoples can be fit in that region.

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ1

Answer:

Rate of change

TLDR: 88%

The probability of neither event happening is the complement of the probability of either event happening, which is 100 - 12 = 88.

Cheers,

qxxi

Answer: 2  :  1

Step-by-step explanation:

The batter calls for 2 cups of flour and 1 cup of milk.

That means that for every 2 cups of flour, the muffin batter would need 1 cup of milk.

Ratio of flour to milk will therefore be:

= Amount of flour needed : Amount of milk needed

= 2 cups of flour :  1 cup of milk

= 2  :  1

Answer:

it would be 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4*2/4*25= 8/100=0.08 or 8%

Answer:

A,C,B,E,G,F

Step-by-step explanation:

n mathematics, a rational number is a number such as -3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1.

also

The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another. Whole numbers, integers, fractions, terminating decimals and repeating decimals are all rational numbers.

Yes, the given data provide convincing evidence that the Nuthatches prefer particular types of trees while searching for seeds and insects.

A statistical hypothesis test used to examine if a variable is likely to come from a given distribution is the Chi-square goodness of fit test. It is frequently used to assess how well sampling data represents the entire population.

Given that the number of red-breasted nuthatches (n) is 156. By convention, the significance level is α=0.05.

First, let's state the null hypothesis and alternate hypothesis.

Null hypothesis H₀: Nuthatches don't prefer particular types of trees while searching for seeds and insects.

Alternate hypothesis H₁: Nuthatches prefer particular types of trees while searching for seeds and insects.

Given: p₁=54%=0.54, p₂=40%=0.40, p₃=6%=0.06

The expected frequency (E) for each probability is:

\(\begin{aligned}E_1&=np_{1}\\&=156\times0.54\\&=84.24\\E_2&=np_{2}\\&=156\times0.40\\&=62.4\\E_3&=np_{3}\\&=156\times0.06\\&=9.36\end{aligned}\)

The observed values (O) are given as 70, 79, and 7. Calculating chi-square, we get,

\(\begin{aligned}\chi^{2}&=\sum\frac{(O-E)^2}{E}\\&=\frac{(70-84.24)^2}{84.24}+\frac{(79-62.4)^2}{62.4}+\frac{(7-9.36)^2}{9.36}\\&=7.4182\end{aligned}\)

And the degree of freedom is given by df = n-1, where, n is the sample size. Here, the sample size is 3.

\(\begin{aligned}df&=n-1\\&=3-1\\&=2\end{aligned}\)

Then, the P-value from the table is given by, \(P(\chi^{2} > 7.4182) = 0.0245\).

This value is less than the significance level.  Therefore, the null hypothesis is rejected. So, an alternate hypothesis is accepted.

Therefore,  nuthatches prefer particular types of trees while searching for seeds and insects.

To know more about the chi-square test:

https://brainly.com/question/14082240

#SPJ4

Answer:

A) f(2) = 120, g(2) = 4.

B) f'(x) = 5x + 20

C) R - {-2}.

Step-by-step explanation:

A) Just apply given value and resolve:

\(f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4\)

B) g(2) is 4, so just divide f(x) by 4:

\( \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20\)

C)

\( \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} \)

Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.

1. The value of F(2) = 120 and g(2) = 4.

2. The division is 5(x+4)

3. The domain is real number except -2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours.

1. F(2)= 20(2)+ 80= 40+ 80= 120

and, g(2)= 2 + 2 = 4

2. The division is

= F(x) / g(2)

= (20x + 80)/ (2+2)

= 20 (x+4) / 4

= 5 (x+4)

3. The domain of F(x) / g(x) is all real number except -2.

Learn more about Function here:

https://brainly.com/question/12431044

#SPJ2

Answer:

12 ft or 14 ft

Step-by-step explanation:

Answer: n = 5a-6 / a-b

Step-by-step explanation: Move all of your terms to the left side of the equation and then set the equal to 0. Then, set each of your factors equal to 0, as well.

I hope this helps you out.

Answer:

Can you show me a picture, that would help.

The deceptive amount claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This assertion is false since it omits the point where A and B intersect, which is P. (A n B).

The deceptive claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This claim is false because it disregards the fact that P is where A and B overlap (A n B). The stated statement does not take into consideration the intersection of two events, which is the likelihood that both occurrences will occur.

One must factor in the likelihood that the two occurrences will intersect when calculating the likelihood that two events will occur simultaneously. The given statement deducts the probability of the union of two occurrences from the sum of the probabilities of the two separate events because the probability of the union of two events is the chance that at least one of the events occurs. As it ignores the intersection, this method is inaccurate for estimating the likelihood of both occurrences occurring simultaneously. The probability of the intersection must be considered in order to calculate the likelihood of two occurrences occurring simultaneously.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

Answer:

-99232

Step-by-step explanation:

PEMDAS

Solve in the brackets/parenthesis and expand out

4*9=36*3=108-12=96

Now we have (96)*8-10^5

Next up is exponents so -10^5 is -100000

Next is multiplication so  (96)*8=768

Lastly is subtraction: 768-100000= -99232

Scientific notation of this answer is -9.9232*10^4 (depends which answer they are looking for)

The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

To know more about the Microsoft Excel, here

https://brainly.com/question/23501096

#SPJ4

The resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

The triangle is a shape that has three sides and angles. Given the coordinate points of the triangle given as:

A(-2, 3)

B (-2, 5)

C (-4, 5)

If the coordinate points is translated by the vector (2, -7), hence the resulting coordinate points will be:

A' = (2+2, 3-7) = (4, -4)

B' = (-2+2, 5-7) = (0, -2)

C' = (-4-2, 5-7) = (-6,-2)

Hence the resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

Learn more on translation of coordinates here: https://brainly.com/question/12861087

#SPJ1

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/28853425

#SPJ1

The derivative of of f(x) = 10 is 0

The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.

Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.

Mathematically:

           d(f(x))/dx = \(\lim_{h \to 0}\) (f(x+h) - f(x))/h

There  is no x to substitute for x + h so no difference is noticed:

             \(\lim_{h \to 0}\) (f(x+h) - f(x))/h =   \(\lim_{h \to 0}\) (10 - 10)/h = 0

Hence, the derivative of f(x) = 10 is 0

To know more about Derivatives here:

brainly.com/question/25324584

#SPJ4

∠1 and ∠6 and ∠4 and ∠5  are adjacent angles in the figure.

What is meant by adjacent angles?

When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

                                  The two items are next to one another if one object is next to the other. He waited in a room next to it. There were separate doors despite the schools being close by. The sum of supplementary neighboring angles is always 180. The reason for this is that all angles on a straight line add up to 180, and the two angles are adjacent to one another on the line.

In the figure,

  adjacent angles are

∠1 and ∠6 ,

∠4 and ∠5

Learn more about adjacent angles

brainly.com/question/28271243

#SPJ1

The mean distance thrοwn is 14.5 feet.

In mathematics, the mean is a measure οf central tendency that represents the average value οf a set οf numbers. It is calculated by adding up all the values in the set and dividing by the tοtal number οf values.

Tο find the mean οf the distances thrοwn, we need tο add up all the distances and divide by the tοtal number οf distances:

Mean = (220 + 225 + 331 + 414 + 415 + 506 + 6*7) / 14

Mean = 203 / 14

Mean = 14.5

Sο the mean distance thrοwn is 14.5 feet.

In terms οf the prοblem, the mean distance tells us the average distance that the heavy ball was thrοwn. This can be useful infοrmatiοn fοr a variety οf reasοns, such as determining the strength οf the thrοwer οr the apprοpriate size οf the playing field.

To learn more about Mean from the given link

https://brainly.com/question/30112112

#SPJ1

A(7,10) and B(9,-3) are separated by 13.1 units.

How to calculate distance between two points?
The separation between two points the coordinates of two points in space are used in the formula. In coordinate geometry, a two-dimensional or three-dimensional space can be used to calculate the distance between two points using the distance formula. The Pythagoras theorem is sometimes used to calculate the distance between two places.
The distance between two locations on a plane is the length of the line segment connecting them. The following equation is frequently used to determine the separation between two points:
d = √[(x₂-x₁)² + (y₂-y₁)²] -- (i)

Given, the two points are A≡(7,10) and (9,-3)
On comparing A and B with (x₁, y₁) and (x₂, y₂) respectively, we get
x₁ = 7, y₁ = 10,  x₂ = 9, y₂ = -3
Therefore using the formula in (i), we get
Distance between A & B = √[(9-7)²+(-3-10)²] = √173 = 13.15 = 13.1 units

To learn more about distance between two points, tap on the link below:
https://brainly.com/question/24661980
#SPJ9

The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)

To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.

Amplitude:

The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.

Period:

The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.

From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.

Phase shift:

The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).

In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.

With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:

d(t) = 5.3 sin(2π/15 * t)

where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.

Learn more about sine function on:

https://brainly.com/question/30243373

#SPJ1

Answer:

less than

\(1 \frac{1}{2} \)

I believe