if n is an integer for which the greatest common factor of n and 18 is 6 and the least common multiple of n and 9 is 126, what is the value of n?'

q = 40 is the value of q in quadratic equation.

What is quadratic equation explain?

The equation x ax2+bx+c=0 is a quadratic equation, which is a second-order polynomial equation in a single variable. with a ≠ 0 .

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial equation. The answer could be simple or complicated.

the roots of a quadratic expression

             ax² + bx + c = 0

Since x' and x'' are the roots of this equation, then we can write the Vieta's formula

                 x' + x'' = -b/a

               x' * x'' = c/a

let's replace the 2nd equation of the Vieta's formula by that and make it a Linear System.

                  x' + x'' =  14/1

                 x' * x'' = 6

after solve the equations

               x' = 10

Solving the  equations

       10 + x''=14

           x'' = 4

Since we have a=1

   x^2-14x + q = 0

      Then we can make q as the parameter c.

    q = x' * x'' = 4 * 10 ⇒ 40      

x2−14x+ 40 = 0

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The complete question is -

The difference between the roots of the quadratic equation x2−14x+q=0 is 6. Find q.

[tex]\dfrac{z}{10} =5[/tex]

Multiply both sides by 10:

[tex](\dfrac{z}{10} )\times10=(5)\times10[/tex]

[tex]\fbox{z = 50}[/tex]

z/10 = 5

Multiply both sides by 10:

z/10 * 10 = 5 * 10

z = 50

The work required to stretch the spring is 91.6 Ibs-inch

What is work?

Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.

Δx : displacement from equilibrium position

f = k Δ x (force due to spring = -kΔx)

where, k is the spring constant

Given,

f = 20ibs

Δx = 24 -18 Inches = 6 inches

∴ k = 20/6 ibs/inch

Now, PE stored in spring = 1/2 k (Δx)²

Δx : displacement from equilibrium position

Work done = change in PE

= 1/2K (Δx₂)² -1/2k (Δx₁)²

given,

Δx₁ = 21-18 inches = 3 inches

Δx₂ = 26-18 inches = 8 inches

∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches

=10/6 *5*11

work done = 91.6 ibs-inch

The spring must be stretched with 91.6 Ibs-inch of force.

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Step-by-step explanation:

In the figure ,angle DEF=Angle DHG=50.prove that

The amount of flour that the cake recipe call for would be equal to 3.5 cups.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

Let's write the equation according to the statement,

x = 7 × 1/2

x = 3.5 cups or,

x = 3 & 1/2 cups.

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In the given diagram, the measure of diagonal EG is 80

From the question, we are to determine the measure of diagonal EG

From the given diagram,

We have a parallelogram.

Since the diagonals of a parallelogram bisect each other, we can write that

EJ = JG

Thus,

4w + 4 = 2w + 22

Solve for w

4w - 2w = 22 - 4

2w = 18

w = 18/2

w = 9

But

EG = EJ + JG

EG = 4w + 4 + 2w + 22

Substitute the value of w

EG = 4(9) + 4 + 2(9) + 22

EG = 36 + 4 + 18 + 22

EG = 80

Hence, the measure of EG is 80

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The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

On data that is dispersed normally, the Z test is a parametric process that is applied. The z-test can be applied to proportions, two samples, or one sample to test hypotheses. When the population variance is known, it is possible to determine whether the means of two significant groups differ.

The second is one-way analysis of variance (ANOVA), which checks if three or more samples originate from populations with the same mean using the F-distribution.

The test statistic should be compared to the crucial value. If the test statistic is more extreme in favor of the alternative than the crucial value, the alternative hypothesis should be considered instead of the null hypothesis. If the test statistic is not as extreme as the crucial value, the null hypothesis should not be disregarded.

Therefore,

The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

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Corresponding angles are two angles that are formed by two coplanar lines and a transversal and they occupy the same relative positions.

There are numerous pairs of angles that are created when a transversal cuts any two parallel lines. These angles include consecutive interior angles, alternate interior and exterior angles, and comparable angles.

Each set of comparable angles are equal when a transversal cuts two parallel lines.

The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles. The matching angles are equivalent when the lines are parallel.

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a) California has the lowest premium and Pennsylvania has the highest premium.

b) Pennsylvania has the highest median premium.

c) Texas has the smallest range of premium. California has the smallest interquartile range.

Insurance Premium:

A premium is the amount an individual or business pays for an insurance policy. Premiums are paid for policies that cover health insurance, auto insurance, home insurance, and life insurance. When the premium is paid, it becomes income for the insurance company. It also constitutes liability, as the insurer must pay for claims arising from the policy. Failure to pay individual or corporate premiums may result in the cancellation of the policy.

The insurance company actuary is responsible for determining premium payments using statistics and calculations. Determine the likelihood of encountering an event or accident requiring insurance coverage. We will also be charged for any costs associated with the coverage.

Using the above factors to determine the premium, the actuary determines the price charged by the insurance company so that the amount the actuary receives is greater than the amount the company has to pay for the claim. increase.

Information gathered by actuaries is entered into tables called actuarial tables and passed on to insurance companies who set premium prices.

From the above discussion, we get:

a) California has the lowest premium and Pennsylvania has the highest premium.

b) Pennsylvania has the highest median premium.

c) Texas has the smallest range of premium. California has the smallest interquartile range.

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Answer:

60

Step-by-step explanation:

both triangles are 30 60 90, angle G is made up of 2 30 degree angles

30 plus 30 is 60

If you have to maintain the same average as in the first quarter of the year, you will have to spend $183 in the month of June.

Given is that your average monthly expenditure for gasoline during the first quarter was $167.70. You spent $147.20 in April and $172.90 in May.

Assume that you can spend $x in the month of June. So, we can write -

(147.2 + 172.9 + x)/3 = 167.7

147.2 + 172.9 + x =503.1

x = 183

Therefore, you can spend $183 in the month of June to have the same average.

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Answer:

A D F

Step-by-step explanation:

The parent functions with a domain of all real values of x are the linear function, the absolute value function, the square root function, and the cube root function.

The linear function is defined by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The domain of this function is all real values of x.

The absolute value function is defined by the equation y = |x|, where |x| is the absolute value of x. The domain of this function is all real values of x.

The square root function is defined by the equation y = √x, where √x is the square root of x. The domain of this function is all nonnegative real values of x.

The cube root function is defined by the equation y = ∛x, where ∛x is the cube root of x. The domain of this function is all nonnegative real values of x.

Therefore, the correct answers are A, D, and F. The reciprocal function, the cubic function, and the quadratic function do not have a domain of all real values of x.

A correlational research design investigates relationship between variables without the researches controlling or manipulation any of them.

Correlational analysis is statistical method that is used to discover if there is a relationship between two variables/dataset, and how strong that relationship may be.

A correlation reflects the strength and direction of the relationship between two variables. The direction of a correlation can be either positive or negative.

Correlational research is ideal gathering data quickly from natural settings. They helps you generalize your findings to real-life situations in an externally valid way.

Correlation is also used to establish the reliability and validity of measurements. A positive correlation is a relationship between two variable s in which bothe variables move in the same direction. A negative correlation is a relationship between two variables in which as increase in one variable is associated with a decrease in the other. A zero correlation exist when there is no relationship between two variables.

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Answer:

See below.

Step-by-step explanation:

(a) y=x²-5  NO - the x term is squared.

(b) y=x³     NO - the x term is cubed

(c) y=-9x    YES

(d) y=-x+3  YES

See attached graph.

Answer:

A = NO

B = NO

C = YES

D = YES

Step-by-step explanation:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables.

For A: The degree of variable y is 1 and the degree of variable x is 2.

So it is not linear.

For C: The degree of variable y is 1 and the degree of variable x is 1.

So it is linear.

Therefore , the slope of the ski slope is 39.197°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Here ,

Given:

She begins her skiing at an elevation of 1.8 miles above sea level, 1.2 miles east of the ski lodge. At an altitude of 1.2 miles above sea level, she comes to an end 0.3 miles to the east of the ski lodge.

a = 1.2 miles

b =  1.8 miles

x = 1.2 miles

y= a-b = 1.8-1.2 = 0.6 miles

=>y tan A = A1

=> arctan(-) = arctan( 0.6 )

=> 0.68413 radian

A = A1 → degree= 0.68413 * 180 /π = 39.197°

Therefore, the slope of the ski slope is 39.197°.

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If the expression AXB is defined, and A is a 3X5 matrix, then the dimension of B could be 5XN.

“N” could be the any number as in order to do any multiplication, the number of columns of first matrix and the number of rows of second matrix should be same in order to perform the multiplication between those matrices.

A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. If the matrix has m rows and n columns, it is referred to as a "m by n" matrix, abbreviated "mXn."

A matrix A multiplied by a matrix B yields a matrix C only when the number of columns in the first matrix A equals the number of rows in the second matrix B. To find the element cij, which is in the product's ith row and jth column, multiply the first element in the ith row of A by the first element in the jth column of B, the second element in the row by the second element in the column, and so on until the last element in the row is multiplied by the last element in the column; the sum of all these products yields the element cij.

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The total area of the two lawns is 30000m²

james mows two lawns

.the first lawn is 1000 meters long and 100 meters wide

Area of a rectangular lawn is calculated by the formula

area = l x w

Where l stands for the length of the lawn and w stands for the width of the lawn

Here, length is 1000m and width is 100m

area = 1000 x 100 = 100000

the second lawn is thee same length, and a width that is 2 times as much as the first one.

Area = l x w

Here Here, length is 1000m and width is 2 x 100m = 200

area = 1000 x 200 = 200000

The total area of the two lawns is equal to summatiom of area of 1st lawn and 2nd lawn

total area = 100000 + 200000 = 30000m²

Therefore,  the total area of the two lawns that is of area of 1st lawn and 2nd lawn is 30000m²

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This city's data had the higher median monthly apartment cost of the two cities by $155.

The city of austin's data had the higher interquartile range of the two cities by $87.

The city of austin had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

The given data for the cost of renting a one-bedroom apartment in Dallas in ascending order is as follows;

$994, $1,322, $1,075, $1,189, $1,172, $1,465, $1,215, $930, $1,090, $1,288

$930, $994, $1,075, $1,090, $1,172, $1,189, $1,215, $1,288, $1,322, and $ 1,465

Analyzing the above using Microsoft Excel, we see that;

Dallas Mean = $1180.5

Dallas Interquartile range = $213

Standard Deviation = $159.9597

The given data for the cost of renting a one-bedroom apartment in Austin in ascending order using is;

$900, $950, $1,100, $1,250, $1,296, $1,375, $1,389, $1,400, $1,450, $1,495

Analyzing the above using Microsoft Excel, we see that;

The mean = $1335.5

The interquartile range = $300

The standard deviation of the sample = $209.0945

The difference in the median cost of the two cities is $1,335.5 - $1,180.5 = $155

Therefore, the Austin's city data has the higher median monthly apartment cost of the two cities by $155

The difference in the sample standard deviation of the two cities is $209.0945 - $159.9597 = $49.13476

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The number of units x that produces a maximum revenue is approximately 1890.56 units.

To find the number of units x that produces a maximum revenue R, you need to find the value of x that maximizes the function R = [tex]171x^2 - 0.06x^3.[/tex]

To do this, you can take the derivative of the function with respect to x and set it equal to 0. The derivative of a function gives us the slope of the function at a particular point, so setting the derivative equal to 0 will give us the points where the function is at a relative maximum or minimum.

The derivative of R with respect to x is:

R' = [tex]342x - 0.18x^2[/tex]

To find the value of x that maximizes R, we set R' equal to 0 and solve for x:

[tex]0 =[/tex] [tex]342x - 0.18x^2[/tex]

[tex]0.18x^2 = 342x[/tex]

[tex]x = \frac{342}{0.18}[/tex]

[tex]x = 1890.56[/tex]

Therefore, the number of units x that produces a maximum revenue is approximately 1890.56 units. Keep in mind that this is only a local maximum, and there may be other values of x that produce a higher revenue. To find the absolute maximum or minimum of the function, you would need to examine the behavior of the function over its entire domain.

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y=3 is the equation of a horizontal line that passes through the point (9, 3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If a line passes through a point (x₁, y₁) and has a slope of m, then the

equation of the line is given by (y-y₁) = m(x-x₁).  

Because the question states the line is horizontal, the slope is zero, or m=0.

Plugging the information into the slope equation gives:

(y-(3)) = 0(x-(9)).

y-3= 0

y= 3.

Hence, y=3 is the equation of a horizontal line that passes through the point (9, 3).

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As per the volume of cylinder, the value of k is 3.06 centimeters.

Volume of cylinder:

According to geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.

Given,

Here the glass pictured to the left can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.

Here we need to find the value of k, in centimeters.

While we looking into the given question we have identified that the value of the following,

Volume of the glass = 473 cubic centimeter

Height of the glass = 16 fluid ounces.

Radius of the glass = k

Then the value of k is calculated by using the volume of cylinder formula,

=> V = πr²h

Here we have to apply the values on the formula, then we get,

=> 473 = π x k² x 16

Apply the value of π = 3.14,

=> 473 = 3.14 x k² x 16

=> k² = 9.41

=> k = 3.06

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Answer:

$7800

Step-by-step explanation:

1 year = 10%

3 years = 30%

30% = 0.3

6000 times 0.3 = $1800

6000 + 1800 = $7800

So, they will pay $7800

To be able to make predictions for future outcomes based on present data, a statistical technique called regression analysis is used .
It helps in developing prediction models.
Regression analysis is basically a tool to show a relationship between two or more variables.  Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

It is a quantative method wherein the basic form of regression models includes unknown parameters (β), independent variables (X), and the dependent variable (Y). Regression allows researchers to predict or explain the variation in one variable (called the dependent variable) based on another variable( known as the independent variable).
The most common and simple form of regression is the Linear Regression model.
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Because domain restrictions apply to this rational expression, x cannot be equal to {-2, 2}.

Domain restrictions are any points in the domain where the function will not have a value. This basically means that there is a point in the function where x will not work.

For the numerator, any value of x will suffice. We can have a value of 0 in the numerator, or a positive, negative, or decimal number.

However, the denominator cannot be equal to zero. This is due to the fact that a fraction bar represents division, and we cannot divide by zero.

Here,

x²-4=0

Add 4 to both sides:

x²-4+4 = 0+4

x² = 4

Take the square root of both sides:

√x² = √4

x = 2 or x = -2

The x cannot be equal to {-2, 2} as domain restrictions apply to this rational expression.

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32% of students does not plan to go to graduate school.

We have given that,

total number of college seniors is 400.

The percentage of a value of x from N total is given as,

percentage of x = [tex]\frac{x}{N}[/tex] × 100%

Therefore

percentage of students does not go to graduate level = [tex]\frac{128}{400}[/tex] × 100%

                                                                                           = 32%

Hence the percentage of the students does not plan to go to graduate school is 32%.

Survey is defined as the act of examining a process or questioning a selected sample of individuals to obtain data about a service, protect, or process. Data collection surveys collect information from a targeted group of people about their opinions, behavior or knowledge. A survey is a method of gathering information using relevant questions from a sample of people with the aim of understanding populations as a whole.

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The scale factor required for the dilation of the living room is 1/3.

A scale factor is a multiplicative fraction that can be used to either increase or decrease (i.e resize) the shape of a given object. It is given by the expression:

scale factor = [tex]\frac{length on the drawing}{length of the original object}[/tex]

Dilation is type of transformation that can be used to resize the dimensions of a given object. So that an image of the object is formed.

Therefore, the required scale factor is;

scale factor = [tex]\frac{length on the drawing}{length of the original object}[/tex]

                   = 7/21 or 9/27

                   = 1/3

scale factor = 1/3

The scale factor of the dilation as required in the question is 1/3.

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