Your aunt bought a new television. The television screen is a
rectangle.
The length of the television screen is 54 inches and the width is
30.4 inches.
What is the area of the television screen? What is the perimeter
of the television screen?
Use the given information to complete the worksheet.
Problem apr20 Client Version 7.7.14 Server Version 73.14
O
Length of the Television Screen
Width of the Television Screen
Perimeter of the Television Screen
Area of the Television Screen
DELL
Diagram Label
SC
CR
Area Formulas:
• Parallelogram: A = bh
• Square: A = s²
.
Value
54
30.4
168.8
Triangle: A = bh
•Trapezoid: A=h(b₁+ b₂)
Units
inches
inches
inches
square inches
©2021 Carneg
Oct 13

Polynomial equation 3 -x + 2x -4 + 2x is equivalent to 6 +(-x) + 2x + (-7) + 2x

The example of a first-degree polynomial is f(x) = MX + b of a linear function.

Consider a equation 1, to 6 +(-x) + 2x + (-7) + 2x, and simplify it.

6 +(-x) + 2x + (-7) + 2x

= 6 -x + 2x -7 + 2x

Take likely terms and add or subtract according to the equation.

6-7-x+2x+2x

-1+3x

Consider 3 – x + 2x – 4 + 2x as equation 2.

3 – x + 2x – 4 + 2x

Take likely terms and add or subtract according to the equation.

= -1+ 3x

Here equation 1 is equal to equation 2.

∴6 +(-x) + 2x + (-7) + 2x = 3 – x + 2x – 4 + 2x

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y = 3x - 1 is the equation in slope-intercept form.

What exactly does slope intercept mean?

y = 3x +b  passes through the point (2,5)

5 = 3 * 2 + b

5 = 6 + b

b = 5 -6

b = -1

y = 3x +b

y = 3x - 1 is the equation in slope-intercept form.

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The 95% confidence interval for the mean of the population lies between

(17.61, 62.39)

Construct a 95% confidence interval for the mean:

To construct a 95% confidence interval for the mean of the population, we must start with finding the following:

Mean

n=4

Mean=(25+47+32+56)/n

         =(160)/4

         =40

Mean is 40

Standard deviation σ

                             = [tex]\frac{1}{n-1}( \sum x^{2} -n(mean)^{2} )[/tex]

                             = [tex]\frac{1}{3} (6994-4(40)^{2} )[/tex]

                            σ= 14.07

Now, we construct 95% confidence interval CI:

Confidence interval=mean± t-table value*(standard deviation/√n)

Given a t-table value of 3.1824 from z-distribution table, mean=40, n=4, and standard deviation=14.07, we have:

Confidence interval=(40±3.1824(14.07/√4)

                               =(40±22.39)

                               =(40-22.39, 40+22.39)

Confidence interval=(17.61, 62.39)

The question was incomplete, below is the complete question:

You are given the following information obtained from a random sample of four observations taken from a large, normally distributed population.

25 47 32 56

Construct a 95% confidence interval for the mean of the population

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The remainder of the polynomial 4x³-20x-50 / (x - 3) would be the expression 4x²+20x+52.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

We have to determine the remainder of the quantity 4 x cubed minus 20 x minus 50 end quantity divided by the quantity x minus 3 end quantity.

4x³-20x-50 = (4x³-4x²-16x-50) + (4x²+16x)

Divide both sides by (x - 3) to get

4x³-20x-50 = (4x³-4x²-16x-50)/(x-3)+(4x²+16x)/(x-3)

⇒ 4(x²+4x+12)+(4x²+16x)/(x-3)

⇒ 4x²+16x+48+(4x²+16x)/(x-3)

⇒ 4x²+16x+48+4(x+4)

⇒ 4x²+20x+52

Therefore, the remainder of the polynomial 4x³-20x-50 / (x - 3) would be the expression 4x²+20x+52.

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In the given groups of Relative Frequencies the best represented by a pie chart would be Option D. 25%; 24%; 26%; 25%.

Relative frequencies are more commonly used because they allow you to compare how frequently values occur relative to the overall sample size. They are calculated by dividing the total number of responses by the number of responses for each category. Pie charts depict relative frequencies by showing how much of the total pie each category represents. Raw frequencies and relative frequencies can be displayed in frequency tables and bar charts.

According to the question we can get,

25% = [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{4}[/tex] × 360° = 90°

24% approach 25%

26% approach 25%

So Option D would be the group of relative frequency best represented by a pie chart.

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They will together take 18 minutes to finish the sanitization work together.

It is mentioned that Liana can sanitize the guest room in 45 minutes only and Gab, her brother, can do the same in 30 minutes.

Let they take y minutes to finish the work together.

Let the total work be m

Workdone by Liana in 45 mintues = m

∴Workdone in 1 minute = m / 45

Workdone by Gab in 30 minutes = m

∴Workdone by Gab in 1 minute = m / 30

Let the total time taken by them = x minutes.

Total time taken by them together = m / 45 + m / 30

∴ [tex]\frac{m}{45} +\frac{m}{30} = \frac{m}{x}[/tex]

⇒ [tex]\frac{1}{45} +\frac{1}{30} = \frac{1}{x}[/tex]

LCM of 45 and 30 is 90

⇒ [tex]\frac{2}{90} +\frac{3}{90} = \frac{1}{x}[/tex]

⇒ [tex]\frac{5}{90}= \frac{1}{x}[/tex]

⇒ [tex]\frac{1}{18}= \frac{1}{x}[/tex]

⇒ x = 18 minutes

Hence they both can do the same given work in 18 mintues.

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Answer:

76:9

Step-by-step explanation:

because because because

On solving the inequality we get -6>5 which is not possible; hence there is NO SOLUTION possible for s.

We solve the given inequality for s as follows

2(4s-3) ≥ 5+8s

⇒8s - 6≥ 5 +8s

⇒ -6 > 5               (on subtracting 8s from both sides)

the last statement shows that variables cancel out from both sides of the inequality and we get -6>5 which is not possible. Because -6>5 is not possible or false, hence no value of s will be able to satisfy the given inequality. Thus the answer for s is NO SOLUTION.

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The number of liters that are in 13.39 gallons is 51.5 liters

In order to determine the liters that are in 13.39 gallons, divide the amount of gallons by the unit of conversion.

Division is the mathematical process of grouping a number into equal parts using another number. The sign used to represent division is ÷. Division is one of the basic mathematical operations. Other  mathematical operations are addition, subtraction and division.

Number of liters in 13.39 gallons = 13.39 / 0.26 = 51.5 liters

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Answer:

x = 1

Step-by-step explanation:

Let's solve your equation step-by-step.

3x+5=6x+2

Step 1: Subtract 6x from both sides.

3x+5−6x=6x+2−6x

−3x+5=2

Step 2: Subtract 5 from both sides.

−3x+5−5=2−5

−3x=−3

Step 3: Divide both sides by -3.

−3x−3=−3−3

x=1

Answer:

x=1

Hope this helps! <3

Answer:

stuff, look to the explanation for your answers

Step-by-step explanation:

Procedures for the left side: dividing 3 and subtracting 5

Procedures on the left side: subtracting 2 and dividing by 6.

You do these procedures to both sides to get your answer.

Raising 4,929 to the place value of the underlined digit will give a value of 4930.

It should be noted that rounding up of numbers simply means raising the number to the nearest ten, hundred, or thousand.

In this case let's assume that the underlined number is 2. Therefore, raising 4929 will give 4940. It should be noted that the number beside it is more than 5. Therefore, 1 will be added to 2 making 3. The new number is 4930.

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Answer:

3. parallel

4. they have the same slope

Answer:

x = 115°

Step-by-step explanation:

Line a and line b are parallel lines

x° and the angle with measure 115° are alternate exterior angles so they have same measurement and each is 115°

The sets of lengths that are Pythagorean triples are:

A. 10, 24, 26

D. 9, 40, 41

E. 15, 20, 25

A Pythagorean triple can be described as a set of three numbers of the side lengths of a right triangle whereby the square of the longest side is equal to the sum of the squares of the two other sides.

For 10, 24, 26, we have:

10² + 24² = 26²

676 = 676 [true]

The set, 10, 24, 26 is a Pythagorean triple.

For 14, 48, 49, we have:

14² + 48² = 49²

2,500 = 2,401 [not true]

The set, 14, 48, 49, is NOT a Pythagorean triple.

For  9, 12, 16, we have:

9² + 12² = 16²

225 = 256 [not true]

The set, 9, 12, 16, is NOT a Pythagorean triple.

For  9, 40, 41, we have:

9² + 40² = 41²

1,681 = 1,681 [true]

The set, 9, 40, 41, is a Pythagorean triple.

For  15, 20, 25, we have:

15² + 20² = 25²

625 = 625 [true]

The set, 15, 20, 25, is a Pythagorean triple.

The correct set of options are, A, D, and E.

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The given graph is of the function of the form y = 3(2ˣ )

A function is a set of rules that assigns each element of a set a unique element of another set.

If f is a function and f(x) = x+2, then if we have to check x= 1 , y=3 put these values in y = x + 2 , 3 =1+2 (true)

Given that the graph of a function in the form y =f(x) = a b ˣ

From the graph in the question : The function passes through two points

(1,6) and  (0, 3 )

From point (0,3 ) it gives that  when x= 0 ⇒ y = f(x) =3

⇒ 3 = ab⁰

⇒ 3 = a

From point (1,6) it gives that when x =1 then y = f(x) =6

⇒ 6= ab¹

⇒ 6 = 3 b

⇒ 2 = b

Therefore, the given graph is of the function y = 3 ×2ˣ

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1. The value of the expression 5/8 - (-2/8) will be 7/8.

2. The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. The value of the expression 5/8 - (-2/8) will be 7/8.

What is Addition?

The process of combining the two or more number is called Addition.

Given that;

The expression are;

1. 5/8 - (-2/8)

2. -3 1/5 + (-6 1/2)

3. 5/8 - (-2/8)

Now, Solve the expression as;

1. 5/8 - (-2/8) = 5/8 + 2/8

                   = 7/8

Thus, The value of the expression 5/8 - (-2/8) will be 7/8.

2. -3 1/5 + (-6 1/2) = - 16/5 - 13/2

                          = -32/10 - 65/10

                          = - 97/10

Thus, The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. 5/8 - (-2/8) = 5/8 + 2/8

                   = 7/8

Thus, The value of the expression 5/8 - (-2/8) will be 7/8.

So, The solution are;

1. The value of the expression 5/8 - (-2/8) will be 7/8.

2. The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. The value of the expression 5/8 - (-2/8) will be 7/8.

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Answer:

10/9

Step-by-step explanation:

We can calculate f(3) and g(-4)

f(3) = 4*3 - 2 = 12 - 2 =10

and g(-4) = -2 * (-4) + 1 = 8 + 1 = 9

Then it is easy to calculate f(3)/g(-4):

f(3)/g(-4) = 10/9

where we use the values which we calculated before.

⇒In the equation f(x) given f(3) plug in the value 3 in the place of x and simplify

[tex]f(3)=4(3)-2\\f(3)=12-2\\F(3)=10[/tex]

⇒For g(-4) in the place of x plug in -4 in the equation of g

[tex]g(-4)=-2(-4)+1\\g(-4)=8+1\\g(-4)=9[/tex]

Now we can find the value of  of the problem as done BELOW:

[tex]\frac{f(3)}{g(-4)} \\\frac{f(3)}{g(-4)} =\frac{10}{9}[/tex]

Answer:

[tex]h = \dfrac{T - r}{n}\\\\\text{Hourly rate } = \$45\;\;\text{if T = 200, r = 20 and n= 4}[/tex]

Step-by-step explanation:

We have from #14 that
T = r + nh

where T = amount charged, n = hours worked, r = fixed rate and h = hourly rate

Subtract r from both sides:
T - r = r + nh - r

The r terms on RHS of the equation cancel out
T - r = nh

Divide both sides by n:
(T - r)/n = h

Or we can write it as
h = (T - r)/n

If r = 20, , T = 200 and n =4 we get by substitution

h = (200-20)/4

h = 180/4

h = 45

So hourly rate = $45

Answer:

1080 total inches of ribbon. 60 pieces of ribbon can be cut.

Step-by-step explanation:

Firstly, the dressmaker has 15 rolls of ribbon that are 6 feet in length. Multiply those to see how many feet in total, 90. Then multiply this by 12 (there are 12 inches in a foot) to get the amount of total inches: 1080.

This is the answer to the question below the problem.

To answer the bigger question at hand:

You would need to take 1080 divided by 18 to find how many pieces the dressmaker can cut. She can cut exactly 60 pieces from her 15 rolls of ribbon.

Answer:

The opposite of an integer and negative number is a positive integer number. In this case, the opposite of -4 is +4.

The cost of renting the meeting room by the manager for the hours 1,2,3 and 4 defined by the function of (t) = function of (t-1) + 20, given that function of (1) = 100 is 520.

A function can be defined as a mapping whose co-domain is the set of real numbers.

Given the mapping defined as function of (t) = function of (t-1) + 20, for function of (1) = 100

Hence,

.f (2) = function of (2-1) + 20

.f (1) + 20

100 + 20 = 120

.f (3) = function of (3-1) + 20

.f (2) + 20

120 + 20 = 140

f (4) = f (4-1) + 20

.f (3) + 20

140 + 20 = 160

This can be seen in a table as shown above!

We can conclude with the proper mapping of the defined function of (t) = function of (t-1) + 20 for function of (1) = 100 that the total cost for the hours 1,2,3 and 4 for renting the meeting room is 520.

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Given the function:

The given function is a linear function

The rate of change of the linear function = the slope of the function

The slope = the coefficient of x = -1/4

So, from the given options, you will select the function that has a slope that is greater than (-1/4)

a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

1) we calculate the volume of the first carton:

volume=length x width x height

volume=3 ft * 3 ft * 1 ft=9 ft³

Therefore:

A machine can fill 9 ft³ in 3 seconds.

2) we calculate the volume of the second carton.

volume=length x width x heigth

volume=4 ft * 4 ft * 6 ft=96 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

9 ft³---------------------3 seconds

96 ft³--------------------      x

x=(96 ft³ * 3 seconds) / 9 ft³=32 seconds.

Hence , a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

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The sequence of the decorative fence boards would be 66.48 feet which is the infinite geometric sequence.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio

The first fence board will be 2 feet tall, and each successive fence board will be 25% taller than the previous fence board which is given in the question.

aₙ = arˣ⁻¹   (n ≠ 0)

a₁ = 2

x = (1 +25%) = 125%

n = 10

aₙ = 2 × (125%)

The sum of the terms in a finite or infinite geometric sequence as

Sₙ = a₁ + a₂ + ... +aₙ

= a₁(1 -xⁿ)/(1-x)

= 2(1 -1.25¹⁰)/(1-1.25)

= 2(-8.31)/(-0.25)

=  66.48 feet

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The law which makes this argument true is referred to as the Law of Syllogism.

The Law of Syllogism is also referred to as reasoning by transitivity and it states that if two (2) statements are true, then a third true statement can be logically derived.

Mathematically, the Law of Syllogism follows a specific pattern and can be represented by the following conditional statements:

In this context, we can reasonably infer and logically deduce that the Law of Syllogism makes the conclusion based on the two premises.

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Fill in the missing 6 groups of_ number. equal 42.

because 6 × 7 = 42 then

6 groups of 7 equals 42.

Reason:

The fraction 3/2 converts to 1.5 in decimal form

This is larger than 1 which is not possible for probability values. They must be between 0 and 1 inclusive of both endpoints.

Answer: 3/2

Step-by-step explanation: It will be 3/2 because 3/2 is 150 percent

Hope this helps!

The $2 and $3 profits from the sale of sandwiches and wraps respectively, and the equation that is used to calculate the profit gives;

1. The equation is; [tex] \displaystyle{y = 490 - \frac{2}{3} \cdot x}[/tex]

The slope, m = [tex] \displaystyle{ - \frac{2}{3}}[/tex]

The y–intercept, c = 490

2. The graph can be drawn by joining the y–intercept to a point found by moving along the slope from the y–intercept

3. [tex] \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}[/tex]

4. Please find attached the graph of the number of wraps to the number of sandwiches

5. Please find attached the combined graph of the two functions

The similarity is the common slope

The difference is the y–intercept

The slope is the ratio of the rise to the run of the graph.

The given function is; 2•x + 3•y = 1470

Where;

x = The number of sandwich sold

y = The number of wraps sold

The profit per sandwich sale = $2

Profit per each wrap sale = $3

1. The slope and intercept form is; y = m•x + c

Where;

m = The slope

c = The y–intercept

Therefore, 2•x + 3•y = 1470 gives;

3•y = 1470 - 2•x

y = (1470 - 2•x)÷3 = 490 - (2/3)•x

[tex] \displaystyle{y = \frac{1470-2\cdot x}{3} = 490 - \frac{2}{3} \cdot x}[/tex]

Therefore;

By comparison, we have;

2. Using the slope and intercept method to graph the line involves the following steps.

3. The equation in function notation is; [tex] \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}[/tex]

The meaning of the function is that the number of wraps sold is given by the difference between 490 and two thirds of the number of sandwiches sold, or that as the number of sandwiches sold increases by by 1, the number of wraps sold decreases by 2/3

4. The graph can be created using a spreadsheet application

Please find attached the graphs of the function

5. With a profit next month of $1,593, we have;

2•x + 3•y = 1593

Which gives;

[tex] \displaystyle{y = 531 - \frac{2}{3} \cdot x}[/tex]

Given that the equation of the graph of the previous month is y = 490 - (2/3)•x, we have;

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