a triangle has two sides of length 18.9 and 2.9. what compound inequality describes the possible lengths for the third side, x?

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

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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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 half of the mentioned number after performing multiplication with 1/2 is 0.9375.

The half of 1.875 can be calculated by multiplying with (1/2). Half refers to two parts of one thing and hence it represented as the fraction 1/2. So, to find the half, we will multiply the mentioned number with 1/2.

Half value = 1.875 × 1/2

Now performing division and multiplication on Right Hand Side of the equation

Half value = 1.875/2

Half value = 0.9375

Thus, based on the division, the half of 1.875 is 0.9375.

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The probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

Given that,

A survey of middle school students asked what is your favorite winter sport so they have given the result in the table we can see.

Below is a summary of the findings. A participant from this study is chosen at random from among these 545 students, who serve as the sample space.

We have to find what is the probability that the chosen student, a grade 8 student, likes skiing over ice skating.

The total 8th grade are 180

The skiing are 171

The ice skating are 163

Probability = 180/(171+163) = 0.5389 = 53.89%

Therefore, the probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

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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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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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[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 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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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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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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Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

In mathematics, an equation is a logical statement with two algebraic expressions on either side of the equals (=) sign. In relation to one another, the expressions on the left and right are equal. Every mathematical equation begins with the expression LHS = RHS (left hand side = right hand side). The value of a variable or quantity can be found by solving an equation. Unless the statement contains the "equal to" sign, it is not an equation.

Here,

The company charges a monthly fee of $31 to deliver a box of pet supplies each month

x be the number of subscribers and y be the price.

equation used is

Since , company currently has 290,000 subscribers. For each $1 increase in price ,the company loses 10,000 subscribers

Therefore to  to maximize monthly revenue

he has to increase the price by $2

Therefore he will loose 20,000 subscribers

and the maximum revenue he will generate is

=> 270,000 * 33

=>8,910000

Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

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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.

Step-by-step explanation:

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

It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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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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Summarizing a number of survey questions into a single concept could be achieved with which type of analysis?

a. factor analysis

b. multiple discriminant analysis

c. multiple regression analysis

d. cluster analysis

Factor Analysis

The correct option is (a)

Now, According to the question:

Let's know:

What is factor analysis?

Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. This technique extracts maximum common variance from all variables and puts them into a common score. As an index of all variables, we can use this score for further analysis.

Factor Analysis

The correct option is (a)

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The question is like this:

Summarizing a number of survey questions into a single concept could be achieved with which type of analysis?

a. factor analysis

b. multiple discriminant analysis

c. multiple regression analysis

d. cluster analysis

Answer: -5

Step-by-step explanation:

[tex]-2.5y + 8y - 10.5[/tex]

[tex]= 5.5y - 10.5y[/tex]

[tex]= -5y[/tex]

Hence, the answer is [tex]-5[/tex].

Answer:

---------------------------------------------

All terms have same variable of y.

Collect all terms and simplify by adding up the coefficient:

The coefficient of the variable is -5.

Answer:

27.21 to nearest hundredth

Step-by-step explanation:

You find the lengths of the 4 sides and add them.

AB = 4 - (-2) = 6

BC = 4 - (--1) = 9

CD = √(-1-(-5)^2 + (-2-4)^2)

     = √(16 + 36)

     = √52

AD = 5

So, the perimeter

= 6 + 9 + 5 + √52

= 20 + √52

= 27.21 to nearest hundredth.

Answer:

3x-9

Step-by-step explanation:

Just add the two together. (x-2) + (2x-7)= 3x-9

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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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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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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Answer: 3 ft per second

Step-by-step explanation: 40/4 120/4
10/10 30/10

1 second = 3 ft

OR

120/40=3

Answer:

a. $1240

b. $2020

c. 8.3 years

d. 16.7 years

Step-by-step explanation:

Using the simple interest formula, I = Prt, we solve as follows.

a.

I = 1000 × 0.06 × 4 = 240

1000 + 240 = 1240

Answer: a. $1240

b.

I = 1000 × 0.06 × 17 = 1020

1000 + 1020 = 2020

Answer: b. $2020

c.

$1500 - $1000 = $500

Interest is $500

500 = 1000 × 0.06 × t

t = 8.3

Answer: c. 8.3 years

d.

$2000 - $1000 = $1000

Interest is $1000

1000 = 1000 × 0.06 × t

t = 16.7

Answer: d. 16.7 years

Answer:

Please note I have assumed the interest is compounded annually.

a)  $1,262.48

b)  $2,692.77

c)  7 years

d)  12 years

Step-by-step explanation:

Assuming the interest is compounded annually.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula to create an equation for A in terms of t:

[tex]\implies A=1000(1+0.06)^t[/tex]

[tex]\implies A=1000(1.06)^t[/tex]

To calculate how much will be in the account after 4 years, substitute t = 4 into the equation:

[tex]\implies A=1000(1.06)^4[/tex]

[tex]\implies A=1000(1.2624769...)[/tex]

[tex]\implies A=1262.4769...[/tex]

Therefore, there will be $1,262.48 in the account after 4 years.

To calculate how much will be in the account after 17 years, substitute t = 17 into the equation:

[tex]\implies A=1000(1.06)^{17}[/tex]

[tex]\implies A=1000(2.69277278...)[/tex]

[tex]\implies A=2692.77278...[/tex]

Therefore, there will be $2,692.77 in the account after 17 years.

To calculate how many years it will take for the account to contain $1,500, substitute A = 1500 into the equation and solve for t:

[tex]\implies 1500=1000(1.06)^t[/tex]

[tex]\implies 1.5=(1.06)^t[/tex]

[tex]\implies \ln 1.5=\ln (1.06)^t[/tex]

[tex]\implies \ln 1.5=t \ln (1.06)[/tex]

[tex]\implies t=6.95851563...[/tex]

Therefore, it would take 7 years for the account to contain $1,500.

To calculate how many years it will take for the account to contain $2,000, substitute A = 2000 into the equation and solve for t:

[tex]\implies 2000=1000(1.06)^t[/tex]

[tex]\implies 2=(1.06)^t[/tex]

[tex]\implies \ln 2=\ln (1.06)^t[/tex]

[tex]\implies \ln 2=t \ln (1.06)[/tex]

[tex]\implies t=11.8956610...[/tex]

Therefore, it would take 12 years for the account to contain $2,000.

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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