PLEASE HELP!! ITS DUE SOON

Loretta simplified the expression below as shown. Explain Loretta’s error and correct her works

(16m^2n^20)^1/2=8mn^10

The equation which shows the cost of the admission tickets with tax inclusive is 4x + 25  = 175.

The cost is therefore $ 37.50.

As each admission ticket is the same price, the total cost of 4 tickets can be written as 4x.

Given that the price of parking and four entry tickets is $175.00, we can write:

4x + $25.00 = $175.00

We may find x by simplifying the problem as follows:

4x = $175.00 - $25.00

4x = $150.00

x = $37.50

Therefore, the cost, in dollars, of each admission ticket, including tax, is $37.50.

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A simultaneous equation is a system of two or more equations that are to be solved together to find the values of the unknown variables.

The unknown variables in each equation are related to each other and their values must satisfy all the equations in the system.

Given that;

x + y = 50

3x + 5y = 174

x = 50 - y

Substitute (3) into (2)

3(50 - y) + 5y = 174

150 - 3y + 5y = 174

150 + 2y = 174

2y = 174 - 150

y = 24/2

y = 12

Thus;

x + 12 = 50

x = 50 - 12

x = 38

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The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.  

To graph, the line that represents the relationship between the time Jermaine rides his bicycle and the distance he travels use the slope-intercept form of a linear equation.

This form of the equation is used to represent a straight line on a graph, where the slope represents the rate of change of the dependent variable with respect to the independent variable, and the y-intercept represents the initial value of the dependent variable when the independent variable is 0.

Here we have

Jermaine decides to travel at a constant speed and travels 50 miles in 5 hours.

To graph the line that represents the relationship between the time and the distance he travels, we can use the formula for the slope-intercept form of a linear equation:

    y = mx + b

We know that Jermaine travels 50 miles in 5 hours

Slope (m) = (change in y) / (change in x) = (50 - 0) / (5 - 0) = 10

This tells us that for every 1 hour that Jermaine rides his bicycle, he travels 10 miles.

Hence, the equation of the line y = 10x + b

Take x = 0 and y = 0   [ Since the line passes through (0, 0)

=> 0 = 10(0) + b

=> b = 0

This tells us that the y-intercept of the line is 0.

Hence, the equation of the line, y = 10x

Now draw the graph of y = 10x as shown below

Therefore,

The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.  

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A sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

We may use the formula to determine the minimal sample size n required to estimate the mean weight of mice with a 95% confidence interval and a margin of error of 0.4 grams:

[tex]n = (\frac{ z * 6}{E} )^{2}[/tex]

where z is the required degree of confidence (in this case, 95% equates to a z-score of 1.96), б is the standard deviation (3 grams), and E is the maximum permissible error (0.4 grams).

When we enter the given values into the formula, we get:

[tex]n = [(1.96*3)/0.4]^2\\n = 274.576...[/tex]

We round up to the nearest integer because we can't have a fraction of a mouse and get:

n = 275 (rounded near to 100th)

As a result, a sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

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The time periods that satisfy the requirement include:

(B) f(x)<=0 over the interval [0,2]

(D) f(x)>0 over the interval (-2,0)

(E) f(x)>=0 over the interval [2,∞)

In the given situation:

The table containing values for x and f(x)

Let's examine the table and determine whether each choice satisfies f(x) or not.

Look at the values of x between -3 and 3, there are both positive and negative values for f(x).

Then, f(x)>0 is false over the interval (-∞,3)

The values of f(x) are 0 and negative between 0 and 2.

Then, f(x)<=0 over the interval [0,2]

F(x) values are both positive and negative over the range (-1, 1).

f(x)<0 is false over the interval (-1,1)

In the interval (-2,0), the f(x)  is positive.

f(x)>0 over the interval (-2,0)

When divided by [2, ∞], f(x) is positive.

f(x)>=0 over the interval [2,∞)

Therefore, the time periods that satisfy the requirement include:

(B) f(x)<=0 over the interval [0,2]

(D) f(x)>0 over the interval (-2,0)

(E) f(x)>=0 over the interval [2,∞)

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The value of the vehicle 13 years after purchase is $13,695.24.

What is exponential decay?

Exponential decay is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decay also decreases.

We can use the formula for exponential decay to find the approximate value of the vehicle 13 years after the purchase:

[tex]$V = V_0 e^{-rt}$[/tex]

where V0 is the initial value of the vehicle, r is the annual depreciation rate (as a decimal), t is the number of years since purchase, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

[tex]$V \approx 29800 e^{-0.06*13}$[/tex]

[tex]$V \approx 29800 e^{-0.78}$[/tex]

V ≈ 29800 x 0.4593

V ≈ 13695.24

Therefore, the approximate value of the vehicle 13 years after purchase is $13,695.24.

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Answer:

In absolute terms, you have grown 9 inches (69 - 60).

In relative terms, your growth can be expressed as a percentage increase. To calculate this, we can use the formula:

(relative increase) = (absolute increase / original value) x 100%

Using the values given in the problem, we can plug in and solve:

(relative increase) = (9 / 60) x 100%

(relative increase) = 0.15 x 100%

(relative increase) = 15%

So in relative terms, you have grown 15% since you were 60 inches tall three years ago.

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The most appropriate conclusion is: A) This is convincing evidence of an association between longer hand and longer foot.

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It is used to compare observed frequencies of data to the expected frequencies to determine if they differ significantly. The test is based on the principle of comparing the difference between the observed frequencies and the expected frequencies, and then determining if this difference is statistically significant.

Here,

At the 0.05 significance level, with a chi-square statistic of 11.942 and 4 degrees of freedom, the P-value is 0.018.

Since the P-value is less than the significance level, we reject the null hypothesis of no association and conclude that there is evidence of an association between longer hand and longer foot.

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Complete question:

Imani was curious if there was a relationship between one hand being longer than the other and one foot being longer than the other for 100 randomly selected students. Here is a summary of the data and the results from a chi-square test:

part a .

the probability of winning the lottery when the order of the five numbers does not matter is 1

part b.

the probability of winning the lottery when the order of the five numbers does matter is 1

(a) When the order of the five numbers does not matter, we are dealing with combinations.

The probability of winning can be found as shown:

Number of ways to select 5 numbers out of 20 = 20 C 5 = (20!)/(5!15!) = 15,504

Total number of possible combinations of 5 numbers out of 20 = 20 C 5 = 15,504

So, the probability of winning is:

P = Number of ways to win / Total number of possible combinations

P = 15,504 / 15,504

P = 1/1

P = 1

(b) When the order of the five numbers does matter, we are dealing with permutations.

The probability of winning is:

Number of ways to select and order 5 numbers out of 20 = 20 P 5 = 20! / (20-5)! = 3,584,000

Total number of possible permutations of 5 numbers out of 20 = 20 P 5 = 20! / (20-5)! = 3,584,000

The probability of winning is:

P = Number of ways to win / Total number of possible permutations

P = 3,584,000 / 3,584,000

P = 1/1

P = 1

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The t statistic: Stays the same

A switch from using a one-tailed test to a two-tailed test: Increases

An increase in the sample standard deviation (s): Decreases

A decrease in the significance level (such as using α = .01 instead of α = .05): Increases

A decrease in the sample size (n): Decreases

The t statistic: Stays the same

The t statistic itself is calculated based on the sample mean, the population mean, and the sample standard deviation.

Therefore, changing the study design or results in ways that do not affect these values will not change the t statistic.

A switch from using a one-tailed test to a two-tailed test: Increases.

An increase in the sample standard deviation (s): Decreases

A decrease in the significance level (such as using α = .01 instead of α = .05): Increases

A decrease in the sample size (n): Decreases

As the sample size decreases, the standard error of the mean increases, meaning that there is more variability in the sample means. Therefore, the t statistic will be smaller, making it less likely to reject the null hypothesis.

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The form p = -n/250 + 34 is a linear equation that gives the price (p) they can charge for n shirts.

An algebraic equation of the form y=mx+b is a linear equation. m is the slant and b is the y-capture. A "linear equation in two variables" with y and x as variables is sometimes referred to as the one above. A linear equation is one in which a variable is raised to its first power. One example of a one variable is ax+b = 0. x is a variable and an and b are genuine numbers.

Given that the relationship is linear and the equation has the form: Let n be the number of shirts and p be the price of a shirt. p = mn + b

Consequently we will view as m first. Let us express the two values of p and two of n as cartesian coordinates: 1000, 30) (3000 , 22)

(p₂ - p₁) = m(n₂ - n₁)

(22 - 30) = m(3000 - 1000)

m = 22 - 30/3000 - 1000

m = -8/2000

= -1/250

So the equation becomes:

p = -n/250 + b

Now to find b, :

30 = -1000/250 + b

b = - 4 = 30

b = 34

Now the equation becomes:

p = -n/250 + 34

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we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards.

How to solve the question ?

To construct the confidence interval for the mean difference in yardage between the two types of footballs, we first need to calculate the pooled standard deviation and the standard error of the mean difference. Since the sample sizes are large and the populations are assumed to be normal with equal variances, we can use the following formulas:

Pooled standard deviation:

s_p = √[((n1-1)*s₁² + (n2-1)*s₁²)/(n₁+n₂-2)]

s_p = √[((14-1)*3² + (12-1)*4²)/(14+12-2)]

s_p = 3.517

Standard error of the mean difference:

SE = s_p√(1/n₁ + 1/n₂)

SE = 3.517√(1/14 + 1/12)

SE = 1.416

Next, we can calculate the margin of error by multiplying the standard error by the t-value for the 80% confidence level with degrees of freedom equal to n1+n2-2=24. Using a t-table or calculator, we find that the t-value is 1.329.

Margin of error:

ME = tSE

ME = 1.3291.416

ME = 1.776

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the sample mean difference in yardage.

Confidence interval:

(281-233) +/- ME

48 +/- 1.776

(46.224, 49.776)

Therefore, we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards. This means that, on average, the football filled with helium travels 46.224 to 49.776 yards farther than the football filled with air.

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Answer:

3x + 3

Step-by-step explanation:

The given expression is 24x - 27 - 15 + 18 - 21x + 27.

To simplify this expression, we can combine like terms. Like terms are terms that have the same variable(s) and exponent(s). In this expression, we have two terms that have x: 24x and -21x. These terms can be combined by subtracting 21x from 24x to get 3x.

The other terms without any variables are -27, -15, 18, and 27. We can combine these terms by adding them together to get 3.

Therefore, the simplified expression is 3x + 3.

Answer:

3x+3

Step-by-stepStep-by-step explanation:

Combine like terms:

(24x+(−21x))+(−27+(−15)+18+27)

3x+3

The expression can be condensed to a single logarithm as: In(6x^9) - In(x^2) = In(6x^7)

We can use the quotient rule of logarithms, which states that:

log(base a)(b) - log(base a)(c) = log(base a)(b/c)

Using this rule, we can simplify the expression as:

In(6x^9) - In(x^2) = In(6x^9/x^2)

Now, we can simplify the expression inside the logarithm by dividing 6x^9 by x^2:

In(6x^9/x^2) = In(6x^7)

Therefore, the expression can be condensed to a single logarithm as: In(6x^9) - In(x^2) = In(6x^7)

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Answer:

Step-by-step explanation:

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

a) There are 5 grades within one standard deviation of the mean.

b) All of the grades fall within two standard deviations of the mean.

c) There are 4 grades with a z-score less than 0.3.

The standard deviation is the square root of the variance.

We need to first calculate the mean and standard deviation of the grades.

Step 1: Calculate the mean

Mean = (60 + 64 + 75 + 77 + 83 + 86 + 91 + 95 + 98 + 100) / 10

= 811 / 10

= 81.1

Step 2: Calculate the standard deviation

s = √ {Σ(xi - x)²} / (N - 1)

where xi is the individual grade, x is the mean, and N is the total number of grades.

SD = √ {(60 - 81.1)² + (64 - 81.1)² + ... + (100 - 81.1)²} / 9

SD = √ [9746.9] / 9

SD = 10.78

Step 3: Use the mean and standard deviation to answer the questions.

A) One standard deviation from the mean in either direction would be:

81.1 - 10.78 = 70.32

81.1 + 10.78 = 91.88

So, the grades that fall within one standard deviation of the mean are:

(75, 77, 83, 86, 91)

There are 5 grades within one standard deviation of the mean.

B) Two standard deviations from the mean in either direction would be:

81.1 - 2(10.78) = 59.54

81.1 + 2(10.78) = 102.66

So, the grades that fall within two standard deviations of the mean are:

(60, 64, 75, 77, 83, 86, 91, 95, 98, 100)

All of the grades fall within two standard deviations of the mean.

C) To calculate the z-score for each grade, we use the formula:

z = (x - μ) / σ   ; where x is the individual grade, μ is the mean, and σ is the standard deviation.

For a z-score to be less than 0.3, we need to find the grades that satisfy:

(x - μ) / σ < 0.3

Rearranging this inequality, we get:

x < μ + 0.3σ

Substituting the values for μ and σ, we get:

x < 84.86

So, the grades that have a z-score less than 0.3 are (60, 64, 75, 77)

There are 4 grades with a z-score less than 0.3.

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Answer:

1) x = 4.721559618

2) x = 38.69059499

3) x = 56.44269024

4) x = 13.50132272

Step-by-step explanation:

We have to use the term SOHCAHTOA which stands for:

sin(Ø) = opposite / hypotenuse

cos(Ø) = adjacent / hypotenuse

tan(Ø) = opposite/adjacent.

Key:

Ø = angle

1. we use tan because we know the adjacent side length and we need to work out the opposite side length

so we do tan(34) = x/7

now we need to get x on its own. so we do tan(34)*7 = x

type into the calculator tan(34)*7

= 4.721559618

2. we use cos because we know the adjacent side length and we need to work out the hypotenuse length.

so we have to do cos(17) = 37/x

now we get x on its own. we do x*cos(17) = 37

then x = 37 / cos(17)

x = 38.69059499

3. we use sin because we know the hypotenuse length and opposite length.

sin(x) = 10/12

get x on its own.

x = sin^-1(10/12)

x = 56.44269024

4. we use cos because we know the adjacent side length and we need to work out the hypotenuse length.

cos (61) = 8/x

get x on its own.

x*cos(61) = 8

x = 8/cos(61)

x = 16.50132272

a) The scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet. b) The scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.

A ratio is a comparison between two quantities, often expressed as a fraction. It represents the relative size of two or more values, and can be used to compare, scale, or measure different quantities.

a. To find the scale of the drawing, we can use the ratio of the length in the drawing to the actual length.

The length in the drawing is 6 inches and the actual length is 18 feet, which is equivalent to 216 inches (since 1 foot = 12 inches).

So the scale of the drawing is:

1 inch in the drawing = 216 inches in reality

Therefore, the scale is:

1 inch : 216 inches

Simplifying this ratio, we get:

1 : 216

Therefore, the scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet.

b. In the new scale drawing, the length of the room is 4 inches. We need to find the scale of this new drawing.

Let x be the scale of the new drawing, such that:

1 inch in the new drawing = x feet in reality

We can set up the proportion:

6 inches in the old drawing : 18 feet in reality = 4 inches in the new drawing : y feet in reality

Simplifying this proportion, we get:

6 : 18 = 4 : y/x

Dividing both sides by 2, we get:

3 : 9 = 2 : y/x

Cross-multiplying, we get:

3x = 18

Dividing both sides by 3, we get:

x = 6

Therefore, the scale of the new drawing is:

1 inch in the new drawing = 6 feet in reality

Simplifying this ratio, we get:

1 : 72

Therefore, the scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.

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the volume of the square pyramid is 50 cubic units. The volume of a square pyramid can be calculated using the formula:

Volume = (1/3) x Base Area x Height

what is  square pyramid ?

A square pyramid is a three-dimensional geometric shape that has a square as its base and four triangular faces that meet at a common point called the apex. The triangular faces of the pyramid slope upwards and meet at the apex, which is directly above the center of the square base.

In the given question,

The volume of a square pyramid can be calculated using the formula:

Volume = (1/3) x Base Area x Height

where the base area is the area of the square at the base of the pyramid.

In this case, the side of the square base is given as 5, and the height of the pyramid is given as 6. To find the base area, we can use the formula for the area of a square:

Base Area = side²

Base Area = 5²

Base Area = 25

Now, we can plug in the given values into the formula for volume and simplify:

Volume = (1/3) x Base Area x Height

Volume = (1/3) x 25 x 6

Volume = (1/3) x 150

Volume = 50

Therefore, the volume of the square pyramid is 50 cubic units.

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No,  a continuous function  function f(x) exits in (0 , 2 ) .

What does continuous function mean?

In mathematics, a continuous function is a function without discontinuities, i.e. without unexpected changes in value.

                        A function is continuous if it can be guaranteed for arbitrarily small changes by limiting the changes in the input to be small enough. 

A function f(x) such that

        f(0) = 10,   f(2) = 2

f'(x) ≤ 1   ∀  in (0,2)

If f'(x) ≤ 0

then f(x) decreasing on (0, 2 )

But her  f'(x) ≤ 1

So,  f(x) is not continuous  (0, 2 )

So, No continuous function f(x) exits in (0 , 2 ) .

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Answer: D

Step-by-step explanation:                                                                        

Note that when rewritten, the sum using sigma notation becomes Option B.

The rewritten sum using sigma notation with k as the index variable:

∑[k/(k+2)(k+1)], from k=1 to infinity

where ∑ denotes the sum from k=1 to infinity, and k represents the index of the summation.

In other words, the kth term of the series is k/(k+2)(k+1), and we are adding up all the terms of the series starting with k=1 and going to infinity.

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a. The arc measure of mAC is approximately 0.936 radians.

b. The arc measure of mAE is approximately 0.446 radians.

c. The arc measure of mGDH is approximately 0.936 radians.

d. The arc measure of mBHC is approximately 1.566 radians.

In mathematics and geometry, an arc is a segment of a curve or a portion of the circumference of a circle. More specifically, an arc is defined as the set of points on a curve that are located between two endpoints, which adrive-thru re typically referred to as the arc's "start point" and "end point".

For example, consider a circle with center O and radius r. An arc on this circle could be defined as the set of points on the circle that lie between two points A and B, where A and B are two distinct points on the circle. The arc would be denoted as "arc AB" or "arc BA", and it would be measured in units of length or degrees, depending on the context.

Arcs are commonly used in geometry and trigonometry to calculate angles, distances, and areas. They are also used in many other fields, including physics, engineering, and computer graphics.

Arc Length = (Angle Measure / 360) x (2πr)

where r is the radius of the circle. Since the circle graph does not provide the value of the radius, we can assume it to be 1 unit.

a. mAC represents the arc measure of the Developed category. According to the graph, the percentage of land used for developed purposes is 14.9%. To find the arc measure, we can use the formula:

Arc Length = (Angle Measure / 360) x (2πr)

Arc Length for Developed = (14.9 / 100) x (2π x 1)

Arc Length for Developed = 0.149 x 2π

Arc Length for Developed ≈ 0.936 radians

Therefore, the arc measure of ArC is approximately 0.936 radians.

b. mAE represents the arc measure of the Cropland category. According to the graph, the percentage of land used for cropland purposes is 7.1%. To find the arc measure, we can use the same formula:

Arc Length for Cropland = (7.1 / 100) x (2π x 1)

Arc Length for Cropland = 0.071 x 2π

Arc Length for Cropland ≈ 0.446 radians

Therefore, the arc measure of mAE is approximately 0.446 radians.

c. mGDH represents the arc measure of the Water and Federal categories combined. According to the graph, the percentage of land used for water purposes is 8.5%, and the percentage of land used for federal purposes is 10.4%. Therefore, the combined percentage is:

Combined Percentage = 8.5 + 10.4 = 18.9%

To find the arc measure, we can again use the same formula:

Arc Length for Water and Federal = (18.9 / 100) x (2π x 1)

Arc Length for Water and Federal = 0.189 x 2π

Arc Length for Water and Federal ≈ 1.187 radians

Therefore, the arc measure of mGDH is approximately 1.187 radians.

d. mBHC represents the arc measure of the Other Rural, Pasture, and Range categories combined. According to the graph, the percentages of land used for these categories are:

Other Rural: 7.2%

Pasture: 10.1%

Range: 6.6%

Therefore, the combined percentage is:

Combined Percentage = 7.2 + 10.1 + 6.6 = 24.9%

To find the arc measure, we can once again use the same formula:

Arc Length for Other Rural, Pasture, and Range = (24.9 / 100) x (2π x 1)

Arc Length for Other Rural, Pasture, and Range = 0.249 x 2π

Arc Length for Other Rural, Pasture, and Range ≈ 1.566 radians

Therefore, the arc measure of mBHC is approximately 1.566 radians.

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The arithmetic or geometric sequences, common difference (d) or the common ratio (r) include:

A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed number, which is called the common ratio (r). In other words, a geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by the same number.

For example, the sequence 2, 4, 8, 16, 32 is a geometric sequence with a common ratio of 2. To get each term in the sequence, you multiply the preceding term by 2. So, 2 x 2 = 4, 4 x 2 = 8, and so on.

The explicit formula for a geometric sequence is: an = a1 × r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

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Image transcribed:

For the following problems:

Determine whether the sequence is arithmetic or geometric. ⚫ Find the common difference (d) or the common ratio (r).

Write the explicit formula for the sequence.

Find the next 3 terms of the sequence.

1) 2,4,6,...

Arithmetic or Geometric

OR r =

an=

Terms:

2) 8,4,2

Arithmetic or Geometric

d=

OR r =

1

e

an=

Terms:

3) 7,8.5, 10, 11.5

4) 5, 20, 80, 320,

Arithmetic or Geometric

Arithmetic or Geometric

d=

d =

OR r =

an

Terms:

OR r=

an=

Terms:

The acres of land that will be pollinated by 18 beehives is 48 acres of land.

The table shows the ratio of the number of beehives to the number of acres of the orchard.

The bees pollinate the plant at a constant rate. Let's find the acres of land that will be pollinated by 18 beehives.

Therefore, using the constant rate,

y = kx

where

Therefore,

8 = 3k

k = 8 / 3

Therefore, let's find the acres of land for 18 beehives

y = 8 / 3 × 18

y = 144 / 3

y  = 48 acres.

Therefore,

number of acres pollinated by 18 beehives = 48 acres

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The median age of the 120 people seated in the first five rows of the concert was 31.

Value is an important concept in economics and business. It is the worth of goods, services, or assets that is determined by the market or by an individual. It can be measured in terms of money, time, or effort. Value is also used to describe a person’s sense of worth or importance. Values can be seen as the principles, standards, or goals that guide an individual’s actions and decisions. Ultimately, value is subjective and is held by each person and can change over time.

The box and whisker plot provided by the sponsor shows the ages of the 120 people seated in the first five rows of the concert. The box and whisker plot shows a minimum value of 18, a maximum value of 45, a median of 31, a first quartile of 24, and a third quartile of 37. This indicates that 50% of the 120 people in the first five rows had an age of 31 or below, and 50% of the 120 people had an age of 37 or above. The median age of the 120 people seated in the first five rows of the concert was 31.

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The correct equations are for:

[tex]x^{2}[/tex] – 4 = 0

4[tex]x^{2}[/tex] = 16

An equation is a mathematical statement that indicates that two expressions are equal. An equation consists of two sides: the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can be made up of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Mathematical operations are procedures or actions that are used to manipulate or calculate numbers, variables, or other mathematical entities. These operations are the basic building blocks of mathematics and are used in a wide range of mathematical applications.

The equations that are true for x = –2 and x = 2 are:

1) [tex]x^{2}[/tex] – 4 = 0 (when x = -2, this equation becomes ([tex]-2^{2})[/tex] - 4 = 0, which is true; when x = 2, this equation becomes [tex]2^{2}[/tex] - 4 = 0, which is also true)

2) 4[tex]x^{2}[/tex]= 16 (when x = -2, this equation becomes 4[tex]-2^{2}[/tex] = 16, which is true; when x = 2, this equation becomes 4[tex](2^{2})[/tex] = 16, which is also true)

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