In May 2003, JP Gas Co. had the following rate schedule for natural gas usage in single-family residences. Gas is
measured in units called therms. All customers pay a monthly charge. They also pay a distribution charge based on
the amount of gas they use and a supply charge that is also based on the amount of gas they use. The fees are as
follows:
Monthly Customer Charge $6.45
Distribution Charge
1st 20 therms $0.20/therm
Next 30 therms $0.11/therm
Over 50 therms $0.04/therm
Gas supply charge $0.73/therm
a) What is the charge for using 40 therms?
b) What is the charge for using 202 therms?
c) Construct a function that gives the monthly charge C for the x therms of gas.

The equation can be used to solve for x is 90-52 = (12x - 10)°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

In the diagram, since vertically opposite angles are equal. Thus, we can say:

∠UTW =  ∠VTZ

90 - 52 = (12x - 10)°

38 = 12x - 10

12x = 38 + 10

12x = 48

x = 48/12

x = 4

Therefore, the equation is 90-52 = (12x-10)°

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The dimensions of the rectangular field are given as follows:

The perimeter of a rectangle is given by twice the sum of the length and the width of the rectangle, as follows:

P = 2(l + w).

For this problem, the perimeter is of 582 yards, hence:

2(l + w) = 582

l + w = 291.

The length of the field is 4 yards less than quadruple the width, hence:

l = 4w - 4.

Then the width is obtained as follows:

4w - 4 + w = 295

5w = 295

w = 295/5

w = 59.

The length is obtained as follows:

l = 4 x 59 - 4

l = 232 yards.

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By the given explanation it is proven that ∠1 and ∠3 are supplementary from this, it has proven the Consecutive Interior Angles theorem.

According to the consecutive interior angle, if a transversal intersects two parallel lines each pair of consecutive interior angles is supplementary, meaning that the sum of the consecutive interior angles equals 180°  

Here we have

Line p and line q are two parallel lines and line 't' is a transversal on Line p and line q  

Theorem:

When a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary i.e added up to 180°.  

We can prove the above theorem as follows

Given p║q  

Let's take angles 4 and 5 on line 'p' as shown below

Here ∠4 + ∠3 = 180°     [∵  pair of linear angle ]    

Now substitute ∠1 in place of ∠4  

=> ∠1 + ∠3 = 180°     [ ∵ Corresponding angles ∠1 and ∠4 are equal ]  

Therefore,

By the given explanation it is proven that ∠1 and ∠3 are supplementary from this, it has proven the Consecutive Interior Angles theorem.

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The sales price of the item is £18

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

Discount = 1/3

Original price = 27

This means that

Sales price = original price * (1 - discount)

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

Sales price = 27 * (1 - 1/3)

Evaluate

Sales price = 18

Hence, the sales price is #18

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Evaluating the piecewise function we will get:

f(-1) = -13

f(0) =-8

f(2)  = 10

Here we have a piecewise function and we want to evaluate it on different values of x.

When x = -1, we need to use the first part, because -1 < 0.

f(-1) = 9*-1 - 4 = -13

when x  = 0, we need to use the second part, because 0 ≥ 0.

f(0) = 9*0 - 8 = -8

When x = 2 we also use the second part:

f(2) = 9*2 - 8

f(2) = 18 - 8 = 10

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answer = there are three photos. all answer in three photos

Answer:

Step-by-step explanation:

The lateral surface area of the pyramid can be found using the formula for the area of an equilateral triangle:

A = (s^2 * √3) / 4

where s is the length of one side of the equilateral triangle base.

For this pyramid, s = 50 feet

A = (50^2 * √3) / 4 = (2500 * √3) / 4 = 1250 * √3 ≈ 2129.28 ft^2

The total surface area of the pyramid can be found by adding the area of the base to the area of the lateral surface:

A = base area + lateral surface area

A = (side length^2 * √3) / 4 + (3 * triangle area)

A = (50^2 * √3) / 4 + (3 * (50^2 * √3) / 4)

A = 2500 * √3 + 3750 * √3 ≈ 5884.28 ft^2

To paint 75% of the pyramid, the painter needs to paint 75% * 5884.28 ft^2 = 4413.71 ft^2

Since the painter can paint 100 ft^2 in 18 minutes, he can paint 4413.71 ft^2 in 4413.71 / 100 * 18 minutes ≈ 786.96667 minutes

Rounding to the nearest tenth, the painter will take 786.967 minutes to paint 75% of the pyramid, which is approximately 13.1 hours.

Answer:

The water cycle involves the continuous movement of water on, above, and below the surface of the Earth. In the cycle, water can exist in three states: liquid, solid, and gas. During evaporation, liquid water changes into water vapor, the gaseous state of water, as it heats up and turns into steam. When water vapor cools, it can condense back into liquid form, such as when it forms clouds. Precipitation, such as rain or snow, occurs when water droplets in the clouds become heavy enough to fall from the sky. When precipitation reaches the ground, some of it may flow into rivers and streams and eventually make its way to the ocean. Some of it may also be taken up by plants or seep into the ground, becoming part of the groundwater system. Eventually, the water in the groundwater system may evaporate back into water vapor and start the cycle over again.

The total value of the loan with the quarterly compounded interest

is $117599.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded quarterly is,

A = P(1 + (r/4)/100)⁴ⁿ.

[tex]A = 50000(1 + 6.15/100)^{4\times\frac{43}{12}}[/tex].

[tex]A = 5000(1 + 0.0615)^{14.33}[/tex].

[tex]A = 5000(1.0615)^{14.33}[/tex].

[tex]A = 5000\times2.352[/tex].

A = $117,599.

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The area of the top of the second mattress , 3/2x²

The equation to model the problem is y= 1.22x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let the side of mattress one be x

and, the side of Mattress 2 be y.

So, area of Mattress 2 / Area of Mattress 1 = 1 1/2

area of Mattress 2 / Area of Mattress 1 = 3/2

y²/ x² = 3/2

(y/ x)² = 3/2

y/x = √3/2

y /x = 1.22

Hence, the equation is y= 1.22 x .

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The equation of the graph is y = -2/3x - 4

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

From the graph, we have

c = -4

So, the equation becomes

y = mx - 4

From the graph, we have the following point

(-6, 0)

So, we have

0 = -6m - 4

Evaluate

m = -2/3

So, we have

y = -2/3x - 4

Hence, the equation is y = -2/3x - 4

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Answer:

13

Step-by-step explanation:

Len n = number.

9n = 2n + 91

7n = 91

n = 13

Answer: 13

The dimensions that will maximize the enclosed area are 125 meters by 250 meters

Represent the dimensions with x and y

So, we have the following equations

Perimeter = 4x + 2y = 1000

Area = 2xy

So, we have

2x + y = 500

This gives

y = 500 - 2x

So, we have

Area = 2x(500 - 2x)

Expand

Area = 1000x - 4x^2

Differentiate and set to 0

1000 - 8x = 0

So, we have

8x = 1000

Divide

x = 125

Recall that

y = 500 - 2x

y = 500 - 2 * 125

y = 250

Hence, the dimension is 125 by 250

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Answer:

1st number linline

Step by step explanation:

x < -3 means x is less than -3

so it should be any number less than -3

In the 2nd number line represents

[tex]x \leqslant - 3[/tex]

so the answer is 1st one

When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.

Its precise nature is understood to be the figure is probably smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the median and excess. A fractional number can always be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the intermediate is referred to as a linear expression. Every variable's classes are listed in lowest to highest in the general form of any formula. The formula for a linear function is x + b = 0. The simplified version of a two-variable mathematical expression is an x + b y + c = 0. (or something similar). Either conditioned equations or identities provide categories for equations. An identity holds true because of whatever value of the variables.

given

The aforesaid issue is easily resolved by doing the following:

Considering that,

Four Bs are worth three As.

It can be written as;

3A = 4B

determining B's value

B = 3A/4 (Equation 1) (Equation 1)

Now,

A B is worth five Cs.

So, 5B = C (Equation 2) (Equation 2)

Calculating B's value in equation 1

= 15A/4 = C

= 4C = 15A

2C = (15/2)A

2C = 7.5A

Therefore, the solution is 2C = 7.5A

When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.

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Answer:

A

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given diameter = 14 then r = 14 ÷ 2 = 7

A = π × 7² = 49π m²

Answer:

49π

Step-by-step explanation:

area of circle=pie*radius²

and radius=diameter/2

therefore

r=14/2

=7m

Area =π*7²

Area=49π

9 miles for every ½ hour and 6 miles for every 20 minutes can be considered equivalent because they represent the same speed, just measured in different units.

To see this, we can convert the units to a common unit, such as miles per hour.

First, let's convert the 6 miles in 20 minutes to miles per hour:

[tex] \frac{6}{20} \times 60[/tex]= 18 miles/hour

Next, let's compare this speed to the 9 miles per ½ hour:

[tex] \frac{9}{ \frac{1}{2} } = \frac{9}{ \frac{1}{2} } \times \frac{1}{ \frac{1}{2} } = 18[/tex]

Since both speeds are equal to 18 miles per hour, we can conclude that they are equivalent. This means that the missing values are also equivalent.

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As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

Demorgan's law can be utilised in set theory and boolean algebra to make mathematical formulations simpler. Let's say that the universal set U has two subsets, A and B. A' is A's complement, and B' is set B's complement.

Given that, (An B)' UC'.

Using the De Morgan's law we have:

(A ∩ B)’ = A’ ∪ B’.

Substituting this in (An B)' UC'. we have:

A’ ∪ B’ U C'

A' = {f, p, x, y}

B' = {f, g, h, p}

C' = {f, g, x, z}

A’ ∪ B’ U C'  = {f}

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

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Answer:

x= - 52

Step-by-step explanation:

we need to multiply  both sides by 4 to leave the x alone

so

[tex]\frac{-x}{4} *4= 13*4\\-x= 52\\\frac{-x}{-1}=\frac{52}{-1}\\ x=-52[/tex]

Answer:

C

Step-by-step explanation:

Therefore , the solution of the given problem of fraction comes out to be Roman can thus perform 8 poster.

Any number of equal amounts or fractions can be used to represent a whole. In standard English, the quantity of a certain size is stated as a fraction. 8, 3/4. Wholes also include ratio. Numbers are represented in mathematics by the fraction to numerator ratio. These are all straightforward integer fractions. There is a fraction in the denominator of a difficult fraction. because the calculations, numerators, and numerators of actual fractions vary.

Here,

Given :

Roman divided a poster board sheet into ten equally sized pieces.

The entire sheet should be x.

then, one part of sheet=  1/1 0 of the sheet

Currently, only 8/10 of the poster is left after his brother used portion of it.

Roman can therefore use each remaining piece of the poster to create a sign if he so chooses.

The number of indications he is capable of making is then

=> 8/10/1/10

= > 8/10 * 10 = 8.

Roman can thus perform 8 signs.

Therefore , the solution of the given problem of fraction comes out to be

Roman can thus perform 8 poster.

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The expressions that can be used to find the area of the shaded portion of the circle are 9²·π  - (2 · 13.5π ) and 2/3 · 9²·π

Since the whole circle has a radius of 9 inches. The area of the whole circle will be 9²·π square inches (Remember: Area of circle = πr²)

Also, the area of a single section of the circle is equal to 13.5π square inches.

We can get the area of the shaded portion (blue ones) by subtracting the area of the unshaded portion (white ones) from the area of the whole circle. That is:

9²·π  - (2 * 13.5π )

Notice that we have 2 unshaded (whites)

Also, there 4 shaded portions out of the whole 6. We can write:

area of shaded portions = 4/6  ·  9²·π = 2/3 · 9²·π

Thus, the expressions are is 9²·π  - (2 · 13.5π ) and 2/3 · 9²·π

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The simplified expression of the given expression is 4√2

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

√32

Express 32 as 16 * 2

So, we have

√32 = √16 * √2

Evaluate the radicand

√32 = 4√2

HEnce, the solution is 4√2

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The decimals are less than 0.03.

All of the above.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

10 rows and 10 columns.

This means,

100 boxes.

Now,

3 boxes are shaded.

The fraction of shaded boxes.

= 3/100

= 0.03

Now,

0.02, 0.0, 0.00, and 0.01 are all less than 0.03.

Thus,

All the decimals are less than 0.03.

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The number of populations that he needs to answer this question is the number of classes that he teaches.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

Hence in this problem each population is the set of all students in each class, hence the number of populations that he needs to answer this question is the number of classes that he teaches.

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Answer:

BC = 18

Step-by-step explanation:

the diagonal AC is the perpendicular bisector of diagonal BD

this indicates the figure is a Kite with sides AB ≅ AD and BC ≅ DC

then

BC = DC = 18

Answer:18

Step-by-step explanation: Square root of 18²-8²= 16.124.........

The square root of 16.124..........²+8²=18

In the United States, 65% of cans are recycled.

A number or ratio that can be expressed as a fraction of 100 is called a percentage. Divide the number by its whole number and multiply it by 100 if we have to figure out the percentage of that number. Consequently, the percentage represents one part per hundred.

Given In the United States, 13 out of every 20  cans are recycled.

total cans = 20

recycled cans = 13

percent of recycled can = 100*recycled cans/total cans

percent of recycled can = 100*13/20

percent of recycled can = 60%

Hence 65% of cans are recycled.

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Correct question is In the United States, 13 out of every 20 cans are recycled. What percent of cans are recycled?

Answer:

w ≥ 87/7

Step-by-step explanation:

Step 1: Subtract 63 from both sides.

7w+63−63≥150−63

7w≥87

Step 2: Divide both sides by 7.

7w/7  ≥  87/7

w ≥ 87/7