How do I solve this? (with work)

Answer:

  See attached

Step-by-step explanation:

Given trapezoids with midlines, you want to find various values in the figures shown.

The length of a midline of a figure is the average of the parallel edges. That means ...

These relations are used in solving the figures shown. Work and results are given in the attachment.

The two numbers are 30 and 15.

An equation is a statement that asserts the equality of two mathematical expressions. It typically consists of two sides separated by an equal sign (=), where each side contains one or more variables and mathematical operations.

Let's call the two numbers "x" and "y".

From the problem statement, we know:

[tex]x + y = 45[/tex] (equation 1)

[tex]x - y = 15[/tex] (equation 2)

We can solve this system of equations by adding equation 1 and equation 2:

[tex](x + y) + (x - y) = 45 + 15[/tex]

Simplifying the left side of the equation:

[tex]2x = 60[/tex]

Dividing both sides by 2:

[tex]x = 30[/tex]

Now that we know x, we can use equation 1 to solve for y:

[tex]30 + y = 45[/tex]

Subtracting 30 from both sides:

y = 15

Therefore, the two numbers are 30 and 15.

To know more about equation:

https://brainly.com/question/12788590

#SPJ1

The two numbers are 30 and 15.

What is equation?

An equation is a statement that asserts the equality of two mathematical expressions. It typically consists of two sides separated by an equal sign (=), where each side contains one or more variables and mathematical operations.

Let's call the two numbers "x" and "y".

From the problem statement, we know:

x=y=45 (equation 1)

x-y=15 (equation 2)

We can solve this system of equations by adding equation 1 and equation 2:

(x+y)+(x-y)=45+15

Simplifying the left side of the equation:

2x=60

Dividing both sides by 2:

x=30

Now that we know x, we can use equation 1 to solve for y:

30+y=45

Subtracting 30 from both sides:

y = 15

Therefore, the two numbers are 30 and 15.

To know more about equation:

brainly.com/question/12788590

#SPJ1

In Seventh grade, 30 students chose Music and 15 students chose World language while in Eight grade, 5 students chose Music and 50 students chose World language.

Total students is 100

Total students that chose music is 35

Total students that chose world language is 100-35 = 65

Total students in eight grade is 55

Total students in seventh grade is 100-55 = 45

Students in eight grade that chose world language is 50

Students in eight grade that chose music is 55 - 50 = 5

Students in seventh grade who chose music is 35 - 5 = 30 (total students who chose music - number of eighth grade students who chose music)

Students in seventh grade who chose world language = 45 - 30 = 15 (total student in seventh grade - students in seventh grade who chose music)

Learn more about linear algebra here:

https://brainly.com/question/30894110

#SPJ1

The requried length of the arc MN is evaluated as 6π.

From the figure,
The area of the shaded sector is given as:

A = ∠NLM/360×πr²

27π= ∠NLM/360×π9²
∠NLM = 120

Now,

length MN = 120/360*2πr

                  = 1/3×2π×9
                  = 6π

Thus, the requried length of the arc MN is evaluated as 6π.

Learn more about the area of a sector of the circle here:

https://brainly.com/question/29098110

#SPJ1

Answer:

The solution is 11/8

Step-by-step explanation:

3 1/4 - 1 7/8

= 13/4 - 15/8

= 26-15/8

= 11/8

The inverse of the function is g(x) = ( x - 2 )/5 and f(x) = 5x + 2 and g(x) = x - 2/5 are inverse functions of each other

Given data ,

Step 1:

Let the function be represented as f ( x )

Now , f(x) = 5x + 2 as an equation with the variable x:

f(x) = 5x + 2

Step 2:

Switch the variables in the equation from Step 1 and solve for y

Switching x and y:

x = 5y + 2

x - 2 = 5y

Dividing both sides by 5

y = (x - 2)/5

So, the equation with y as the variable is y = (x - 2)/5

Step 3:

Now , the inverse of g(x) = x - 2/5 and f(x) = 5x + 2

The inverse of a function g(x) is denoted as g⁻¹(x) and it is obtained by interchanging x and y and solving for y

Given g(x) = x - 2/5, we can switch x and y:

x - 2/5 = g^(-1)(x)

Now, we can solve for y by isolating it on one side of the equation

x - 2/5 = y

Hence , the inverse of g(x) is y = ( x - 2 )/5

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ1

The calculated value of the  length of the arc FG is 4π

From the question, we have the following parameters that can be used in our computation:

central angle = 60 degrees

Radius = 12

Using the above as a guide, we have the following:

Arc FG = central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

FG = 60/360 * 2 * π * 12

Evaluate

FG = 4π

Hence, the length of the arc FG is 4π

Read more about arc lengths at

brainly.com/question/16552139

#SPJ1

To obtain the quotient (4/27)⁻², (-3/2)⁻³ should be divided by -128/6561, and the result is -1/27.

To solve the problem, we need to simplify (-3/2)⁻³ and (4/27)⁻², and then find the quotient between them.

First, let's simplify (-3/2)⁻³

(-3/2)⁻³ = (2/-3)³ = -8/27

Next, let's simplify (4/27)⁻²

(4/27)⁻² = (27/4)² = 729/16

Now, we need to divide -8/27 by 729/16

(-8/27) ÷ (729/16) = (-8/27) × (16/729)

Multiply the numbers

= -128/6561

Therefore, we should divide (-3/2)⁻³ by -128/6561 to get the quotient (4/27)⁻².

(-3/2)⁻³ ÷ (-128/6561) = -1/27

So, (-3/2)⁻³ should be divided by -128/6561 to get the quotient (4/27)⁻², which is equal to -1/27.

Learn more about quotient here

brainly.com/question/16134410

#SPJ4

The given question is incomplete, the complete question is:

By what number should (-3/2)⁻³ be divided so that the quotient may be (4/27)⁻²

Answer:

Step-by-step explanation:

In the picture are 2 dots connect the line

I plugged in 0 for x and got (0,-3)

then i plugged in -3/2 for x and got (-3/2, -2)

plotted those 2 points and drew a line connecting those 2 dots

Answer:

The dimensions of the piece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95

Step-by-step explanation:

To determine the dimensions of the piece of carpet that Charlotte must purchase, we need to add the overlap to the length and width of the room.

The overlap is 3 inches, which is 0.25 feet (since there are 12 inches in a foot and 3/12 = 0.25).

So the length of the piece of carpet needed is 160.5 feet (160 + 0.25 + 0.25), and the width is 13.5 feet (13.25 + 0.25 + 0.25).

To find the area of the piece of carpet needed, we multiply the length by the width:

160.5 feet x 13.5 feet = 2166.75 square feet

Now we need to add the extra area needed for the overlap, which is:

0.25 feet x 0.25 feet x 4 (since there are 4 sides) = 0.25 square feet

So the total area of the piece of carpet needed is:

2166.75 square feet + 0.25 square feet = 2167 square feet

To determine the labor and material costs, we need to find the area of the plece (piece) of carpet, including the overlap.

The labor costs are $23 per hour, per person, and the crew can lay 50 square feet of carpet each hour. So the total labor cost will be:

4 people x $23 per hour per person = $92 per hour

To determine how many hours it will take to lay the carpet, we divide the total area of the plece by the rate at which the crew can lay carpet:

2167 square feet ÷ (4 people x 50 square feet per hour) = 10.835 hours

We will need to round up to the nearest whole number since the crew cannot work for a fraction of an hour. So it will take 11 hours to lay the carpet.

The cost of materials will be:

2167 square feet x $1.85 per square foot = $4001.95

The cost of labor and materials will be:

11 hours x $92 per hour = $1012

$1012 + $4001.95 + $75 equipment/materials/supplies fee = $5088.95

Therefore, the dimensions of the plece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95.

The probability that a person aged 40 or over has a master's degree is 6.15%

Given is table showing the educational qualification of a residential area, we need to find the probability that person aged 40 or over has a master's degree,

P(E) = favorable outcome / total outcome

P(person aged 40 or over has a master's degree) = 475+699 / 19076
= 1174 / 19076

= 0.06154

= 6.15%

Hence, the probability that a person aged 40 or over has a master's degree is 6.15%

Learn more about probability, click;

https://brainly.com/question/30034780

#SPJ1

Answer:

Circumference = 558π inches

= 1,752.12 inches

Area = π(279^2)

= 77,841π square inches

= 244,420.74 square inches

The total amount of wood needed would be -

X = 2w(l + b).

Assume that the total number of windows made by the carpenter are {w}.

Let the dimensions of each of the window be {l} x {b} respectively.

The total amount of wood needed for one window would be -

x = 2(l + b)

For all the windows, the total amount of wood needed would be -

X = 2w(l + b).

Therefore, the total amount of wood needed would be -

X = 2w(l + b).

To solve more questions on expressions, visit the link-

https://brainly.com/question/30361146

#SPJ1

A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon by proposing a theoretical framework or model. (option b).

Theoretical hypotheses are often used in scientific research to guide investigations and to help researchers make predictions about what they expect to observe. They are essential to the scientific method because they provide a basis for developing testable predictions and designing experiments to confirm or reject them.

A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon.

This statement is accurate. As discussed earlier, a theoretical hypothesis is a type of hypothesis that proposes a theoretical framework or model to explain a scientific question or phenomenon.

Therefore, statement b is the most accurate description of a theoretical hypothesis.

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

The interquartile range (IQR) is a measure of statistical dispersion, representing the difference between the first quartile (Q1) and the third quartile (Q3) in a dataset. It is used to assess the spread of the data and to identify potential outliers. The interquartile range (IQR) can be calculated as Q3 - Q1.

Interquartile range is a measure of dispersion that measures the range of the middle 50% of a dataset. It is commonly used in statistical analysis to summarize and compare the spread of different sets of data. The interquartile range is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) of a dataset.

To calculate the position of the quartiles, the dataset is first ordered from smallest to largest. The first quartile (Q1) is the value at the 25th percentile of the dataset, or the value that is one-quarter of the way through the dataset.

The third quartile (Q3) is the value at the 75th percentile, or the value that is three-quarters of the way through the dataset. The second quartile (Q2) is the median, or the value that is exactly in the middle of the dataset.

Overall, the interquartile range is useful because it is less sensitive to extreme values (outliers) than other measures of dispersion such as the range or standard deviation. This makes it a valuable tool for summarizing and comparing the spread of datasets with outliers or extreme values.

Know more about interquartile range here:

https://brainly.com/question/1210750

#SPJ11

The probability of choosing a letter from Q to W  is : 0.875

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

P(A) = Number of favorable outcomes/ total no. of possible outcomes

A box contains eight cards labeled  P,Q,R,S,T,U,V, and W.

There is eight in total cards.

To find the probability letter from Q to W.

From Q to W, there are 7 cards

The required probability = (7 / 8) = (3 / 5) = 0.875.

Learn more about Probability at:

https://brainly.com/question/30034780

#SPJ1

The given question is incomplete, complete question is:

A box contains eight cards labeled P,Q,R,S,T,U,V, and W. One card will be randomly chosen. What is the probability of choosing a letter from Q to W ? Write your answer as a fraction.

Answer:

The orange is 60 cents.

Step-by-step explanation:

1) Calculate the cost of an apple (45 cents).

2) Take away the cost of the 2 apples from the original problem (45+45=90 cents).

3) You get the cost of 60 cents for one apple.

3A + O - (2A + O) = 1.95 - 1.5
A = 0.45
Now we can substitute this value of A into one of the original equations to solve for O:
2(0.45) + O = 1.5
O = 0.6
Thus, an orange costs $0.60 at the local supermarket.

To find the cost of an orange, we can use the system of linear equations. Let's denote the cost of an apple as "a" and the cost of an orange as "o".

From the given information, we can write two equations:

1) 2a + o = $1.50
2) 3a + o = $1.95

Now, we can solve for "o" using the following steps:

Step 1: Subtract equation 1 from equation 2 to eliminate the "o" variable:

(3a + o) - (2a + o) = $1.95 - $1.50
a = $0.45

Step 2: Substitute the value of "a" back into equation 1 to find the value of "o":

2($0.45) + o = $1.50
$0.90 + o = $1.50

Step 3: Solve for "o":

o = $1.50 - $0.90
o = $0.60

So, the cost of an orange at the local supermarket is $0.60.

Learn more about Equation:

brainly.com/question/29657983

#SPJ11

There are two different normal forms, namely a single Jordan block of size 4 or two Jordan blocks of sizes 3 and 1, for nilpotent endomorphisms of a 4-dimensional vector space.

Cayley-Hamilton Theorem, states that every matrix satisfies its own characteristic polynomial. However, it is not directly related to the concept of normal forms.

To answer your question, we can use the Jordan Normal Form theorem, which states that every linear operator (or endomorphism) on a finite-dimensional vector space over an algebraically closed field (such as the complex numbers) is similar to a matrix in Jordan normal form.

For a nilpotent endomorphism on a 4-dimensional vector space, there are two possible Jordan normal forms: either a single Jordan block of size 4 with eigenvalue 0, or two Jordan blocks of sizes 3 and 1, also with eigenvalue 0.

Therefore, there are two different normal forms for nilpotent endomorphisms of a 4-dimensional vector space.

Learn more about Cayley-Hamilton Theorem here

brainly.com/question/31124382

#SPJ4

Answer:

262.8 feet

Step-by-step explanation:

To determine how much longer Sam walks, we need to calculate the distance of his actual path compared to the diagonal walkway. Using the Pythagorean theorem, we can calculate the diagonal walkway's length as follows:

diagonal walkway = √(1600² + 400²) = √(2560000) = 1600√2 ≈ 2,262.8 feet

To find Sam's actual path, we can add the distance from the entrance to the sports store (200 feet) and the distance from the sports store to the food court (800 feet):

actual path = 200 + 800 = 1000 feet

The difference between the actual path and the diagonal walkway is:

1000 - 1600√2 ≈ -262.8 feet

Since the result is negative, it means that Sam walks approximately 262.8 feet less than if he walks directly from the entrance to the food court along the diagonal walkway.

The fraction which exactly half-way between the fractions "2/3" and "1/6", expressed in simplest-form is "5/12".

To find the fraction exactly halfway between 2/3 and 1/6, we first convert the given fractions to fractions with a common denominator.

So, 2/3 = 8/12  and 1/6 = 2/12,

Now we have the fractions "8/12" and "2/12".

To find the fraction exactly halfway between them, we take their average.

So, Average of "8/12" and "2/12" is

⇒ (8/12 + 2/12)/2,

⇒ 5/12.

Therefore, "5/12" is the fraction exactly halfway between 2/3 and 1/6.

Learn more about Fraction here

https://brainly.com/question/13349591

#SPJ4

The given question is incomplete, the complete question is

Find the fraction which is exactly half way between 2/3 and 1/6 in it simplest form.

Answer: x = -3

Explanation did the test

Answer:

Triangle congruence cannot be determined with the given information.

An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(2 + 2)

Slope (m) = -2/4

Slope (m) = -1/2.

At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1/2(x - 2)

y = -x/2 + 1 + 1

y = -x/2 + 2

y ≤ (4 - x)/2 (since the solid line is shaded below)

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Answer:

R23

Step-by-step explanation:

1.6kg of bananas= R36.80

1kg= 36.80×1/1.6

= R23

Answer:

C.32%

Step-by-step explanation:

look at the column for grades 9-10 and add all of the different band preferences together: 40 + 30 + 55 = 125. Now, to find the percentage for rap music, divide the number of students for rap music by the total number of students in that grade group. 40 ÷ 125 = 0.32. Multiply by 100 to give it as a percentage. 0.32 × 100 = 32%

________________________________

________________________________

The area of the regular polygon with 4 sides and an apothem of 12 cm is 576 square cm.

The given apothem of the polygon is 12 cm.

The area of a regular polygon with 4 sides (a square):

Area = 2 × apothem × perimeter / 4

Since a square has four equal sides, the perimeter of the square is given by:

Perimeter = 4 × side length

So, the side length by using the formula for the apothem of a regular polygon with 4 sides:

Apothem = side length / 2

Solving for side length, we get:

side length = apothem × 2 = 12 × 2 = 24 cm

Now we can find the perimeter:

Perimeter = 4 × side length = 4 × 24 = 96 cm

Substituting the values of apothem and perimeter in the area formula, we get:

Area = 2 × 12 × 96 / 4 = 2 × 12 × 24 = 576 square cm

Learn more about the polygons here:

https://brainly.com/question/24464711

#SPJ1

The statements that are true based on the variables around the centroid are; 1)The value of x is 2, 2)The value of y is 6 and 3) The length of KH is 7.6

To find the value of y with the information provided about the various lengths around centroid,

KW : KR - 1:2

(2y - 8.9)/ (0.5y + 3.2) = 1/2

4y - 17.8 = 0.5y + 3.2

3.5y = 21

y =21/3.5

y = 6

KR = 0.5 × 6 + 3.2 = 6.2.

KT : KW = 1/2

7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2

9.2x = 18.4

x = 2

KW = 5 × 2 - 5.2 = 4.8

KD : KH = 1/2

9w - 23.2/ 4.5w - 5.9 = 1/2

18w - 46.4 = 4.5w -5.9

13.5w = 40.5

w = 3

KH 4.5 x 3 - 5.9 = 7.6

The length of KN

KN = (5x - 5.2)

KN = (5 × 2 - 5.2)

KN = 4.8

Find more exercises on centroids;

https://brainly.com/question/10708357

#SPJ1

Answer: 1,404 Non-Purple Candies

Step-by-step explanation:

First, you must figure out how many are non-purple in the box of 50:

50*0.22=11

Then, you must figure out how many are NOT purple:

50-11=39

Next, since you are trying to calculate how many non-purples are in 36 boxes of that candy, you must multiply the number of non-purple found in 1 box by 36:

39*36= 1404

So, there are 1,404 Purple Candies in 36 Boxes of Candy (approximately)

The best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

If 22% of the candy pieces in one box of fruit candy are purple, then 78% (100% - 22%) of the candy pieces are non-purple. To find the best estimate of the total number of non-purple candy pieces in 36 boxes of the same candy, we need to use proportions.

Let x be the total number of candy pieces in one box of fruit candy. Then, the number of non-purple candy pieces in one box is 0.78x. Therefore, the total number of non-purple candy pieces in 36 boxes is:

36 boxes x 0.78x non-purple candy pieces per box = 28.08x non-purple candy pieces

To find the value of x, we can use the fact that the box contains 50 candy pieces in total. Therefore:

22% of x = 0.22x purple candy pieces
78% of x = 0.78x non-purple candy pieces
Total number of candy pieces = 50

Using these equations, we can solve for x:

0.22x + 0.78x = 50
1x = 50 / 0.78
x = 64.1 (rounded to one decimal place)

Therefore, each box contains approximately 64 candy pieces. And the total number of non-purple candy pieces in 36 boxes is:

28.08x non-purple candy pieces = 28.08 x 64.1 = 1802.728 non-purple candy pieces

So the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1803 (rounded to the nearest whole number).

Let's use the terms you've provided to solve the problem step-by-step.

Step 1: Determine the number of purple candies in one box.
22% of the 50 fruit candy pieces are purple. To find this, multiply 50 by 0.22 (the decimal equivalent of 22%):
50 * 0.22 = 11 purple candy pieces

Step 2: Determine the number of non-purple candies in one box.
There are 50 fruit candy pieces in total. Subtract the 11 purple candies to find the number of non-purple candies:
50 - 11 = 39 non-purple candy pieces

Step 3: Estimate the total number of non-purple candies in 36 boxes.
To find this, multiply the number of non-purple candies in one box (39) by the number of boxes (36):
39 * 36 = 1,404

So, the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

Learn more about proportions at: brainly.com/question/30657439

#SPJ11

Answer: 1/4

Step-by-step explanation:

There are 8 possible outcomes

there are 2 possible times that the number is greater than 3

so you have a 2 out of 8 chance of getting a number greater than 3

2/8=1/4