Click to show whether each function is linear or non-linear.

Work Shown:

x = length

x-2 = width

area = length*width

area = x(x-2)

x(x-2) = 168

x^2-2x = 168

x^2-2x-168 = 0

Plug a = 1, b = -2, c = -168 into the quadratic formula.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-168)}}{2(1)}\\\\x = \frac{2\pm\sqrt{676}}{2}\\\\x = \frac{2\pm26}{2}\\\\x = \frac{2+26}{2} \ \text{ or } \ x = \frac{2-26}{2}\\\\x = \frac{28}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 14 \ \text{ or } \ x = -12\\\\[/tex]

Ignore x = -12 since we cannot have a negative length.

The only practical solution is x = 14.

If x = 14, then x-2 = 14-2 = 12

The rectangular mirror is 14 inches by 12 inches

Check: area = length*width = 14*12 = 168

The answers are confirmed.

True

A square matrix called a permutation matrix is one in which every row and column has exactly one element equal to 1 and every other element is equal to 0. A matrix's rows or columns can be permuted by using permutation matrices.

The resultant matrix will also include exactly one 1 in each row and column and all other elements will be 0. This is because two permutation matrices are multiplied together. This is thus because a permutation matrix created by multiplying two other matrices represents the composition of the permutations represented by the individual matrices.

Similarly, By switching the rows and columns in a permutation matrix, it is possible to create the inverse of that matrix. For example, to get the inverse of a permutation matrix P, swap its rows and columns so that the 1s now occupy the locations where the row and column indices were original. Because each row and column still contain exactly one element that is equal to 1 and all other elements are equal to 0, this matrix is also a permutation matrix.

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The p-value he obtains and the general conclusion that can be made at a 99% significance level is 0.01

A p-value is a measure of the evidence against a null hypothesis. In this case, the null hypothesis is that the coin is fair and equally likely to turn up heads or tails.

The coach carries out a significance test to determine if the number of tails in his trial of 100 flips is significantly different from what would be expected if the coin were fair.

The p-value is calculated by comparing the observed number of tails (35) to the expected number of tails (50, if the coin were fair) using a binomial distribution.

This involves finding the probability of observing 35 or fewer tails in 100 flips, assuming the null hypothesis is true. If this probability is low (i.e. if the p-value is small), then it suggests that the coin is not fair and that the observed difference is unlikely to have occurred by chance.

At a 99% significance level, a common threshold used in statistical tests, the p-value needs to be less than 0.01 to reject the null hypothesis and conclude that the coin is not fair.

If the p-value obtained is less than 0.01, then we can conclude with 99% confidence that the coin is biased towards heads. On the other hand, if the p-value is greater than 0.01, then we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the coin is unfair.

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Answer:

Evaluate the function for x = 10 , that is substitute 10 into any x in the function.

f(10) = 102+8=5+8=13

Step-by-step explanation:

I hope it helps you

The value of function f(x) at x= 10 is 13.

The correct option is C.

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.

We have,

f(x) = x/2 + 8

Now, we have to find the value of function at x= 10.

So, put the value x= 10 the f(x) we get

f(10)= 10/2+ 8

f(10) = 5 + 8

f(10) = 13

Thus, the required value is 13.

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The distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane is, 10.63 units

The distance between two points in the coordinate plane can be calculated using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

The given points

J=(-4, 0) and E = (4, 7),

we have:

x₁ = -4, y₁ = 0

x₂ = 4, y₂ = 7

Plugging in these values into the distance formula, we get:

d = √((4-(-4))² + (7-0)²)

  = √(8² + 7²)

  = √(64 + 49)

  = √113

  = 10.63 (rounded to the nearest hundredth)

So, the distance between points J and E is approximately 10.63 units.

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Answer:

The width of the television is 23 in.

What is rectangle?

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.

Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches

Perimeter of a rectangle = 2(length+width)

According to question,

l = 3+2w

Therefore,

Perimeter = 2(w + 3+2w) = 144

3w + 3 = 72

3w = 69

w = 23

Hence, The width of the television is 23 in.

Answer:

The width of the television is 23 in.What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inchesPerimeter of a rectangle = 2(length+width)According to question,l = 3+2wTherefore,Perimeter = 2(w + 3+2w) = 1443w + 3 = 723w = 69w = 23

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Find the factors (numbers that the given number can be divided by to make a whole number) of each number:

9: 1,3,9

18: 1,2,3,6,9,18

It's quite easy here because the numbers are small but if you get bigger numbers, it might be helpful to draw out a prime factorization tree. And then multiply together all the common prime numbers. (I haven't explained this in great detail but if you want to know leave a comment :))

If the current selling price, variable costs, and fixed costs are the same as last year, the expected net income in the current year is $162,105.

Net income can be computes as follows:

Net income = total revenue - total cost

Total cost consists of two costs, fixed cost and total variable cost.

Total cost = fixed cost + total variable cost

Fixed cost does not depend on the produced quantity, while total variable cost is a function of produced quantity.

Let q = produced quantity, then:

Total variable cost = variable cost per unit x q.

Let's assume that the sold quantity = produced quantity. Hence,

Total revenue = selling price x q

Information from last year:

Total revenue = $475,000

475,000 = selling price x q

Here, q = the product quantity sold last year.

Let r = the product quantity sold in the current year. Since the selling price is the same, we have:

500,000 = selling price x r

Comparing with last year, we have:

selling price = 475,000/q = 500,000/r

Hence,

r = (500,000/475,000) q

r = (20/19) q

Hence, the quantity sold this year is 20/19 higher than last year.

Total variable cost this year = variable cost per unit x r.

Substitute r = (20/19) q:

Total variable cost this year = variable cost per unit x (20/19) q

Total variable cost this year = (20/19) x variable cost per unit x q

Total variable cost this year = (20/19) x Total variable cost last year

Total variable cost this year = (20/19) x 150,000 = 157,895

Therefore,

Net income this year = total revenue - fixed cost - total variable cost

                                   = 500,000 - 180,000 - 157,895

                                   = 162,105

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Answer:

Step-by-step explanation:

A 1 standard deviation increase means that a data point has increased by one unit of standard deviation from the mean of a dataset. In a normal distribution, the standard deviation is a measure of the spread of the data around the mean. Approximately 68% of the data falls within 1 standard deviation of the mean, so a 1 standard deviation increase means that the data point has moved farther away from the mean, but still falls within the range of the typical values.

For example, if the mean of a dataset is 100 and the standard deviation is 10, a data point with a value of 110 would be 1 standard deviation above the mean. This means that it is one standard deviation unit away from the mean, in the direction of higher values. Similarly, a data point with a value of 90 would be 1 standard deviation below the mean, meaning it is one standard deviation unit away from the mean in the direction of lower values.

It's worth noting that standard deviation is a relative measure, so a 1 standard deviation increase or decrease in one dataset may have a different absolute effect than in another dataset with a different mean and standard deviation.

Answer:

The given equation is:

√(x+10) - 9 = -7

Adding 9 to both sides of the equation, we get:

√(x+10) = 2

Squaring both sides of the equation, we get:

x + 10 = 4

Subtracting 10 from both sides, we get:

x = -6

Therefore, the solution of the equation √(x+10) - 9 = -7 is x = -6.

Answer:

Write both linear equations in slope intercept form.

The length of the fishing pole is approximately 2.40 meters.

the equation is

The equation that relates the length of the fishing pole, the distance from the base of the pole to the wall, and the angle of elevation is:

cos (angle of elevation) = adjacent / hypotenuse

In this case, the hypotenuse side is the length of the fishing pole, x, and the adjacent side is the distance from the base of the pole to the wall, 0.5 meters. The angle of elevation is 78 degrees. Therefore:

cos (78) = 0.5 / x

x = 0.5 / cos (78)

x ≈ 2.40 meters

Therefore, the length of the fishing pole is approximately 2.40 meters.

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Answer: A Parameter is a value that represents a property of a population. This could be the population mean.A statistic is a value that represents a property of a sample. This could be the sample mean.In the given scenario, the population is the entire 14 teams.

Step-by-step explanation: I hope this helps^^

The water spills out from the two spills in 1 hour is [tex]9.72*10^{8}[/tex] cubic feet.

Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.

In Hoover Dam, for every second the water is passes through the 2 spills.

Amount of water spills in 1 second in the two spills = 270,000 cubic feet.

We have to estimate the number of cubic feet of water that pass through both spills in 1 hour.

Water spills in one minute = 60*270000

                                           = 1,620,000cubic feet.

Water spills in hour, i.e., 60 minutes = 60*1620000

                                                             = 9,72,000,000 cubic feet.

It can be rewrite as [tex]9.72*10^{8}[/tex]

Hence, the water spills out from the two spills in 1 hour is[tex]9.72*10^{8}[/tex] cubic feet.

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The amount of interest in 7 years will be $126.

To calculate the interest earned by Buddy after 7 years, we can use the formula for simple interest, which is given by:

I = Prt

Where I is the interest earned, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time period in years.

We are given that Buddy invests $600 in a savings account that pays 3% interest, which means that the annual interest rate r is 0.03. Therefore, we can plug these values into the formula and solve for I:

I = 600 x  0.03 x 7

I = $126

Therefore, Buddy will earn $126 in interest after 7 years.

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The cruise ship traveled 78 miles.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

A cruise ship traveled at a constant rate of 16 mph for 3 hours.

Then it traveled for 2 hours at a constant rate of 15 mph.

The total traveled distance,

= distance at the rate of 16 mph for 3 hours + distance of 15 mph for 2 hours.

= 16 x 3 + 15 x 2

= 48 + 30

= 78 miles.

Therefore, the total distance is 78 miles.

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Answer:

Step-by-step explanation:

Objective: Solve distance problems by creating and solving a linear

equation.

An application of linear equations can be found in distance problems. When

solving distance problems we will use the relationship rt = d or rate (speed) times

time equals distance. For example, if a person were to travel 30 mph for 4 hours.

To find the total distance we would multiply rate times time or (30)(4) = 120.

This person travel a distance of 120 miles. The problems we will be solving here

will be a few more steps than described above. So to keep the information in the

problem organized we will use a table. An example of the basic structure of the

table is blow:

Rate Time Distance

Person 1

Person 2

Table 1. Structure of Distance Problem

The third column, distance, will always be filled in by multiplying the rate and

time columns together. If we are given a total distance of both persons or trips we

will put this information below the distance column. We will now use this table to

set up and solve the following example

1

Example 1.

Two joggers start from opposite ends of an 8 mile course running towards each

other. One jogger is running at a rate of 4 mph, and the other is running at a

rate of 6 mph. After how long will the joggers meet?

Rate Time Distance

Jogger 1

Jogger 2

The basic table for the joggers, one and two

Rate Time Distance

Jogger 1 4

Jogger 2 6

We are given the rates for each jogger.

These are added to the table

Rate Time Distance

Jogger 1 4 t

Jogger 2 6 t

We only know they both start and end at the

same time. We use the variable tfor both times

Rate Time Distance

Jogger 1 4 t 4t

Jogger 2 6 t 6t

The distance column is filled in by multiplying

rate by time

8 We have total distance, 8 miles, under distance

4t + 6t = 8 The distance column gives equation by adding

10t = 8 Combine like terms, 4t + 6t

10 10 Divide both sides by 10

t =

4

5

Our solution fort, 4

5

hour(48 minutes)

As the example illustrates, once the table is filled in, the equation to solve is very

easy to find. This same process can be seen in the following example

Example 2.

Bob and Fred start from the same point and walk in opposite directions. Bob

walks 2 miles per hour faster than Fred. After 3 hours they are 30 miles apart.

How fast did each walk?

Rate Time Distance

Bob 3

Fred 3

The basic table with given times filled in

Both traveled 3 hours

2

Rate Time Distance

Bob r + 2 3

Fred r 3

Bob walks 2 mph faster than Fred

We know nothing about Fred,so use r for his rate

Bob is r + 2,showing 2 mph faster

Rate Time Distance

Bob r + 2 3 3r + 6

Fred r 3 3r

Distance column is filled in by multiplying rate by

Time.Be sure to distribute the 3(r +2)for Bob.

30 Total distance is put under distance

3r + 6+ 3r = 30 The distance columns is our equation, by adding

6r +6 = 30 Combine like terms 3r + 3r

− 6 − 6 Subtract 6 from both sides

6r = 24 The variable is multiplied by 6

6 6 Divide both sides by 6

r =4 Our solution for r

Rate

Bob 4+2 =6

Fred 4

To answer the question completely we plug 4 in for

r in the table.Bob traveled 6 miles per hour and

Fred traveled 4 mph

Some problems will require us to do a bit of work before we can just fill in the

cells. One example of this is if we are given a total time, rather than the individual times like we had in the previous example. If we are given total time we

will write this above the time column, use t for the first person’s time, and make

a subtraction problem, Total − t, for the second person’s time. This is shown in

the next example

Example 3.

Two campers left their campsite by canoe and paddled downstream at an average

speed of 12 mph. They turned around and paddled back upstream at an average

rate of 4 mph. The total trip took 1 hour. After how much time did the campers

turn around downstream?

Rate Time Distance

Down 12

Up 4

Basic table for down and upstream

Given rates are filled in

1 Total time is put above time column

Rate Time Distance

Down 12 t

Up 4 1 − t

As we have the total time, in the first time we have

t,the second time becomes the subtraction,

total − t

3

Rate Time Distance

Down 12 t 12t

Up 4 1 − t 4 − 4t

=

Distance column is found by multiplying rate

by time.Be sure to distribute 4(1 − t)for

upstream. As they cover the same distance,

= is put after the down distance

12t = 4 − 4t With equal sign, distance colum is equation

+ 4t + 4t Add4tto both sides so variableis onlyon one side

16t =4 Variable is multiplied by 16

16 16 Divide both sides by 16

t =

1

4

Our solution,turn around after 1

4

hr(15 min )

Another type of a distance problem where we do some work is when one person

catches up with another. Here a slower person has a head start and the faster

person is trying to catch up with him or her and we want to know how long it

will take the fast person to do this. Our startegy for this problem will be to use t

for the faster person’s time, and add amount of time the head start was to get the

slower person’s time. This is shown in the next example.

Answer:

29.5735296 cc = 1 oz

Answer:

use the formula: mEq = (mg x valence) / atomic or molecular weight

Step-by-step explanation:

Area of the scale drawing is 10 square inches. Area of the actual deck would be 160 square feet.

Area of the actual deck would be 16 times the area of the scale drawing.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given scale drawing can be made into two squares.

One with a side length of 1 inch and other with side length of 3 inches.

Area of a square with side length 'a' = a²

Area of the given scale drawing = (1 inch)² + (3 inches)²

                                                     = 1 inch² + 9 inches²

                                                     = 10 inches²

If the scale is 1 inch = 4 feet,

Area of the actual deck = (1 × 4 feet)² + (3 × 4 feet)²

                                       = 4² [(1 feet)² + (3 feet)²]

                                       = 4² (10)

                                       = 160 feet²

Area of the actual deck = 160 feet²

                                        = 16 (Area of the scale drawing)

If the scale is 1 inch = k feet,

Area of the actual deck = k² ( Area of scale drawing)

                                        = 10 k² square feet

Hence the area of the actual deck would be 10k² if the scale is 1 inch = k feet.

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Answer:

13.6

Step-by-step explanation:

To find the mean number of movies that the students saw, we add up all the reported numbers of movies and then divide by the total number of students (which is 8 in this case).

Adding up the reported numbers of movies:

4 + 17 + 17 + 20 + 13 + 4 + 16 + 18 = 109

Dividing by the number of students:

109/8 = 13.625

Rounding to the nearest tenth:

Mean number of movies seen = 13.6

Therefore, the mean number of movies that the students saw, rounded to the nearest tenth, is 13.6.

Answer: 13.6

Step-by-step explanation:

Your basically finding the average:

(4+17+17+20+13+4+16+18)/8 = 13.6

Yes, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3

Proportionality are relationships between two variables where their ratios are equivalent.

Given that, are two arrangements of flowers done by Cara and Hector,

We need to find whether the Cara’s arrangements proportional or not, and an equation relating the number of flowers,

The numbers of white flowers =  3, 6, 9, 12, 15

The numbers of yellow flowers = 5, 10, 15, 20, 25

A proportional relation given by =

y = kx

Put x = 5, and y = 3

3 = 5x

x = 3/5

Put x = 10, y = 6

6 = 10x

x = 3/5

Therefore, the relation is proportional, and the equation will be y = 5w/3

Hence, the numbers of white and yellow flowers in Cara’s arrangements are proportional, the equation relates the number of white flowers, w, to the number of yellow flowers, y is y = 5w/3

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Two membership options are available at a water park: unlimited use for $70 per month or $10 per month plus $5 per visit. 12 visits are the preferred schedule.

AQUAPARK THE BIGGEST IN THE NETHERLANDS! An incredible sight to behold a floating playground island that is 2,000 square meters in size and made up of various floating playsets. For anyone who like climbing, sliding, and jumping, this is a veritable wonderland. Malta's waters received a 96.6% outstanding rating in the assessment and are renowned for their clear waters and undeveloped coasts. Look no farther if you're searching for one of Europe's cleanest open-water locations. Siam Park is the place to go if you want a rush of adrenaline and fast-moving water rapids. While travelling with children, Aqualand is a great option if you're seeking for more family-friendly rides.

The cost of a $10 monthly charge plus $5 for each visit can be calculated as follows:

Cost = 10 + 5*v

where v denotes the monthly visits.

If both membership levels have the same price, then:

[tex]10 + 5*v = 70[/tex]

[tex]5*v = 70 - 10[/tex]

[tex]v = 60/5v = 12[/tex]

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The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
It can be seen from the equation p = 17s, where p is the profit and s is the number of sweaters. The constant 17 represents the profit per sweater. So, The constant of proportionality from the number of sweaters to the total profit is 17 dollars and cents.

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[tex]A = B^-1 * BC[/tex]

Since B is invertible, it can be used to solve the equation.

1. Calculate the inverse of B, [tex]B^-1[/tex].

2. Multiply[tex]B^-1[/tex] with BC, to obtain A.

Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, [tex]B^-1[/tex]. The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying [tex]B^-1[/tex] with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.

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The measure of asymmetry, also known as skewness, is a statistical measure that describes the degree of asymmetry in a distribution of data.

It provides information on the shape of the distribution and the deviation of the data from a normal distribution. In a symmetrical distribution, the mean, median, and mode are all equal, and the distribution is said to have zero skewness. A distribution that is skewed to the right, or positively skewed, has a tail that extends to the right, and the mean is larger than the median. A distribution that is skewed to the left, or negatively skewed, has a tail that extends to the left, and the mean is smaller than the median.

Skewness is calculated by taking the third standardized moment of the distribution, which is the average cubed deviation from the mean, and dividing it by the cube of the standard deviation. This gives a measure of the degree of asymmetry of the distribution.

Skewness is an important measure in many fields, including finance, economics, and biology, as it can indicate whether a distribution is likely to produce extreme values, and can help identify outliers in the data. It is also important in hypothesis testing, as many tests assume that the data are normally distributed, and skewed data can affect the validity of the results.

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You should multiply the top equation by 3 to be able to add the equations and eliminate the x-values in this system.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

2x + 5y = 5                .........equation 1.

-6x + 7y = -37                .........equation 2.

By multiplying equation 1 by 3, we have:

3(2x + 5y = 5) = 6x + 15y = 15    ......equation 3

By adding equation 2 to equation 3, we have:

6x + 15y = 15

-6x + 7y = -37

22y = -22

y = -22/22

y = -1.

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The measure of the missing side b is 12 unit.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The triangle is right angled so we have;

opposite = side opposite the angle 42° = 20

adjacent = b

hypotenuse = 20

b^2 + 16^2 = 20^2

b^2 = 400 - 256

b^2 = 144

b = 12 unit

Approximately to the nearest whole number, b = 12

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The approximate volume of the sphere is 904.32 cm³

The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant.

From the figure, r = 6cm and we are to use π = 3.14. Thus:

V = (4/3)πr³

V = (4/3) * 3.14 * 6³

V =  904.32 cm³

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