A barn is in the shape of a pentagonal prism with the dimensions shown. The volume of the barn is 9072 cubic feet. Find the dimensions of each half of the roof.

(Help I cannot solve this-)

The equivalent fraction for 12/16 will be A. 3/4, 24/32

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

It should be noted that equivalent fraction for 12/16 will be found by reduction to lowest term. This will be:

12/16 = 3/4

Also multiply the numerator and denominator by 8 will give 24/32. In conclusion, the correct option is A.

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The inequality which represents the range of temperature at which water boils is 100 ≤ b thus, option (C) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Water boils at a minimum temperature of 100 degrees Celsius.

Suppose b is the temperature at which water boils.

100 ≤ b

Hence "The inequality which represents the range of temperature at which water boils is 100 ≤ b".

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Answer:

Answer:

Step-by-step explanation:

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Given numbers :

[tex]0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Let's convert percent and fraction into like decimals.

[tex]\frac{4}{9}\ = 0.444[/tex]

We know that to convert percentage into decimals, we need to divide it by 100, we get

[tex]40.5 = \frac{40.5}{100} = 0.405[/tex]

[tex]\frac{11}{25} = 0.400[/tex]

Now , placing the above decimal numbers in order  from least to greatest

[tex]0.400, 0.405, 0.440, 0.444[/tex]

[tex]=0.4, 40.5, \frac{11}{25}, \frac{4}{9}[/tex]

Answer:

ong

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5*1 = 5

5*2 = 10

5*3 = 15

5*4 = 20

5*5 = 25

Based on the Pythagorean theorem, the set of side of lengths that will form a right triangle are:

2, √5, 3

2, 2, √8

Based on the Pythagorean theorem, any set of side lengths that will form a right triangle would have the following relationship:

b² = a² + c², where b is the longest side or the hypotenuse of the right triangle and "b and c" are the lengths of the legs of the triangle.

For side lengths, 4, 8, and 12, we have:

12² = 4² + 8²

144 = 16 + 64

144 = 80 [not true, cannot form a right triangle]

For side lengths, 2, √5, 3, we have:

3² = (√5)² + 2²

9 = 5 + 4 [true, this set will form a right triangle]

For side lengths, 2, 2, √8, we have:

(√8)² = 2² + 2²

8 = 4 + 4

8 = 8 [true, this set will form a right triangle]

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Answer: 132 degrees

Step-by-step explanation:

Because the lines are parallel, and the line intersecting them is straight, the angle on top should be the same as the angle on the bottom.

So that makes x=132

Twenty-five people in a survey were asked to give their current checking account balances and the frequency = 4.

What is frequency and example?

Given that;

Class intervals              Class frequency

(Account Balance)          (No of people)

 $0 - $99                                ?

Entries in this ($0 - $99) range are $29 , $60 , $28 , $83 = 4

Therefore, class frequency (no of people) = 4

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Answer:

-9

Step-by-step explanation:

(y2-y1)/(x2-x1)

[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9

Answer:

Step-by-step explanation: To find the x let y=0

We substitute into the equation 3x+2y=15

3x+2 *0=15

3x=15

x=15/3=5

To find the y let x=0

we substitute into the equation x =0

3*0+2y=15

2y=15

y=15/2

The option that best describes the data is B; The data is univariate and numerical.

This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In this case, the one variable is World History scores exam

Since we are given vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.

A numerical data is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.

Numerical data, also known as quantitative data, that is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.

Hence, the correct one is B; The data is univariate and numerical.

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Answer:

it is univariate and numerical

Step-by-step explanation:

univariate vs bivariate thsi is univariate because it only deals with one varialbe and its numberical because it is numbers ( that parts a litle clear)

hope i helped a litle i tried to explain it bc i know how tought this class can be (this is flvs from 4.09 from lesson4.05  incase that helps)

Step-by-step explanation:

in a fraction as exponent the numerator defines the pure exponent of the base, and the denominator gives the degree of root of the base.

so, this is

[tex] \sqrt[5]{y^{3} } [/tex]

Answer:

[tex] \sqrt[5]{ {y}^{3} } [/tex]

Step-by-step explanation:

When converting an expression with a fractional exponent to its radical form, the base number goes inside the radical(which means it becomes the radicand) along with the numerator(which remains an exponent). Whereas the denominator of the exponent becomes the index, or what dictates whether the radical is a square root, cube root, etc.

EX:

[tex] {y}^{ \frac{a}{m} } = \sqrt[m]{ {y}^{a} } [/tex]

The computation of the depreciation expense using the following methods are as follows:

                                                      2022          2023

A) Straight-line Method              $2,472        $2,472

B) Units Of Activity Method       $3,048        $2,448

C) Declining Balance method   $5,200        $4,160

The depreciation expense is the periodic recognition of the cost for a long-term asset over its useful life.

The costs of long-term assets are spread over their estimated life through depreciation, depletion, or amortization.

The various depreciation methods include:

The cost of the delivery truck on January 1, 2022 = $26,000

Expected salvage value = $1,280

Depreciable amount = $24,720

Estimated useful life = 103,000 miles or 10 years

Depreciation Expenses:

Straight-line method = $2,472 annually ($24,720/10)

Units of activity method per mile = $0.24 ($24,720/103,000)

2022 = $3,048 (12,700 x $0.24)

2023 = $2,448 (10,200 x $0.24)

Declining-balance method rate = 20% (100/10 x 2)

2022 = $5,200 ($26,000 x 20%)

2-23 = $4,160 ($20,800 x 20%)

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The equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is  y = 3x - 5.

The equation of a line can be represented in slope intercept form, point slope form, standard form and general form.

Linear equation in slope intercept form is as follows:

y = mx + b

where

Therefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x −2.

parallel lines have the same slope.

Therefore, the slope of the line is 3.

The y-intercept can be found as follows:

using (3, 4)

y = 3x + b

4 = 3(3) + b

b = 4 - 9

b = -5

Therefore, the equation in slope intercept form is y = 3x - 5.

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Evan made a mistake to add. As the sign of 4 positive and the sign of [tex]2\frac{1}{2}[/tex]. The subtraction operation must be performed for this.

What is a number line?

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever.

The given expression is

[tex]-2\frac{1}{2}[/tex] +4

It can be written as 4  [tex]-2\frac{1}{2}[/tex] .

Now perform the subtraction operation:

= 4 - 5/2

= (8-5)/2

=3/2

= [tex]1\frac{1}{2}[/tex]

The number line that represents the given operation is attached below.

Evan added 4 and  [tex]2\frac{1}{2}[/tex] which is incorrect way.

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Answer

2617.

Step-by-step explanation

To estimate the number of people that can fit into a circular arena with a diameter of 100 yards, we first need to find the area of the arena. To do this, we can use the formula for the area of a circle, which is equal to pi times the radius squared. Since the diameter of the arena is 100 yards, the radius would be half of that, or 50 yards. Plugging this value into the formula for the area of a circle, we get:

Area = pi * 50^2

Since pi is approximately equal to 3.14, we can plug this value into the equation to get:

Area = 3.14 * 50^2

This simplifies to:

Area = 3.14 * 2500

Which gives us an area of approximately 7850 square yards.

Since one person requires a personal space of 3 square feet, we can divide the total area of the arena by 3 to find the number of people that can fit in the arena. This gives us:

7850 square yards / 3 square feet/person = 2616.666... people

Rounded to the nearest whole number, this means that approximately 2617 people could fit in the circular arena with a diameter of 100 yards.

The percentage equation states that the part equals the percent multiplied by the whole.

What is percent?

A percentage is a number that indicates how much is 100 and can also be expressed as a decimal or fraction.

What is Percentage Equation?

Percentage equations allow you to find parts or ratios of amounts (or wholes). Percentages are specified with a % sign after the number of hundredths.

The formula for percentage equation is given below

Percent=(Part/Whole)x100

Example: 45 is 60% of what number?

Modifying the above percentage equation, we get

Whole= (Part/Percent) x 100

⇒Whole= (45/60) x 100

⇒Whole= (3/4) x 100

⇒Whole= 3 x 25

⇒Whole= 75

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Answer:

x = 2 or –6

Step-by-step explanation:

x² + 4x –12 = 0

x² +6x –2x –12 = 0

x(x + 6) –2( x + 6) = 0

(x–2)(x+6)= 0

x–2= 0

x= 2.

x+6= 0

x= –6

x = 2 or –6

Answer:

3 3/4 cups of sugar per cup of salt

Step-by-step explanation:

To find the unit rate of salt to sugar in the recipe, we need to divide the number of cups of sugar by the number of cups of salt. In this case, the unit rate of salt to sugar is 1 1/4 cups of sugar divided by 1/3 of a cup of salt, which can be simplified to 3 3/4 cups of sugar per cup of salt.

Answer:

The unit rate of cups per teaspoon is 1 1/3

Step-by-step explanation:

-A recipe calls for 2 by 3 cup of sugar for every 1 by 2 teaspoon of vanilla.

Based on the above information, the calculation is as follows:

=(2/3)/(1/2)

=(2/3)/(1/2)

=(2/3)x(2/1)

=(2x2)/(3x1)

=(4/3)

= 1 1/3

a) Figure                 1             2            3  

Number of tiles      8            12          16

b) The number of tiles is 8 more than 4 times of 1 less than the number of figure.

c) The equation of model the number of yellow tiles is y = 4x + 4.

d) The number of tiles in figure 24 is 100.

e) Figure 43 has 176 yellow tiles.

f) No.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given that

the number of yellow tile in figure 1 is 8.

The number of yellow tile in figure 2 is 12.

The number of yellow tile in figure 3 is 16.

(a) The table is

Figure                     1             2            3  

Number of tiles      8            12          16

(b)

The number of tiles increase at a constant rate.

The rate is (12 - 8) = (16 - 12) = 4

The relation with the figure and number of tiles is

The number of tiles is = 4 + (the number of figure - 1)4

C)

Assume that y represents total number of tiles.

x = Number of figure

Rewrite "The number of tiles is = 4 + (the number of figure - 1)4" in term of x and y:

y = 8 +(x - 1)4

y = 8 + 4x -4

y = 4x + 4

d) Putting x = 24 in y = 4x + 4

y = 4×24 + 4

y = 96 + 4

y = 100

e)

Putting y = 176 in y = 4x + 4

176 = 4x + 4

Subtract 4 from both sides:

172 = 4x

Divide both sides by 4

x = 43

f)

Putting y = 54 in y = 4x + 4

54 = 4x + 4

Subtract 4 from both sides:

50 = 4x

Divide both sides by 4

x = 50/4

The value of x is not a whole number. Thus it is not possible that a figure has with 54 yellow tiles.

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Using the exponent's rule we know that x = 5.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bn and is pronounced as "b to the n."

A number's exponent indicates how many times to multiply that particular number.

It appears as a little number above and to the right of the basic number.

For instance, 82 = 8 x 8 = 64.

(The exponent "2" instructs us to multiply by two and use the number eight.)

Another illustration is 53 = 5 * 5 * 5 = 125.

So, we have: 2ˣ = 32

We know that:

2 * 2 * 2 * 2 * 2 = 32

2 is multiplied 5 times which means:

2⁵ = 32

Hence, x = 5.

Therefore, using exponents we know that x = 5.

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Therefore the given function is a polynomial function consisting of the constant 0 and the leading term 1.

A polynomial function is a function in an equation that only employs non-negative integer powers or only positive integer exponents of a variable, such as in a quadratic equation, cubic equation, etc. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

Exponents are positive integers for the polynomial function given.

The positive integer 2x has an exponent of 1.

[tex]x^{5}[/tex], where is a positive integer with exponent 5, and.

Real numbers like 5 and 1 are among the coefficients in the function.

Consequently, a polynomial describes the function.

Having a degree of 5, it is a polynomial.

A polynomial is written in standard form by beginning with the term with the highest exponent and writing the remaining terms in descending order of terms with lower exponents.

Standard form for the polynomial is f(x)=2x+ [tex]x^{5}[/tex].

consisting of the constant 0 and the leading term 1.

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The required polynomial is x⁵ - 2x⁴ - 35x³ + 36x² + 180x.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, We have to construct a polynomial of degree 5, a positive lead

co-efficient and zeros or roots are -5, -2, 0, 3, 6.

If roots are -5, -2, 0, 3, 6 factors are (x + 5), (x + 2), (x + 0), (x - 3), (x - 6).

∴The required polynomial is  (x + 5)(x + 2)(x + 0)(x - 3)(x - 6).

= x(x + 5)(x + 2)(x - 3)(x - 6).

= (x² + 5x)(x² - 3x + 2x - 6)(x - 6).

=  (x² + 5x)(x² - x - 6)(x - 6).

=  (x² + 5x)(x³ - 6x² - x² + 6x -6x + 36).

=  (x² + 5x)(x³ - 7x²+ 36).

= x⁵ - 7x⁴ + 36x² + 5x⁴ - 35x³ + 180x.

= x⁵ - 2x⁴ - 35x³ + 36x² + 180x.

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If her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.

The full name of APR is the annual percentage rate. It is defined as the percentage rate applied on borrowing money in the form of interest but APR is applied annually.

It is given that, Jody takes out a 30-year mortgage for $300,000 at 3.524% APR. Her monthly payment is $1,350. She pays $186,175 in interest over those 30 years.

1 year = 12 month

30 year = 360 month

We have to find the total amount she will pay for the house,

Total amount = Monthly payment × 360 + intreast over 30 years

Total amount =1,350 × 360 + 186,175

Total amount =$ 672175

Thus, if her monthly payment is $1,350. She pays $186,175 in interest over those 30 years. The total amount she will pay for the house will be $ 672175.

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The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1<x<0

x<0

so x is negative.

Hence -x is positive.

and -1<x

or

x>-1

or

x+1>0

x+5=x+1+4>0+4

hence x+5 is positive.

x is negative .

∴x-2 is negative.

f(x)=(+)×(+)×(+)×(-)=-

B

The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.

Given that,

James is keeping an eye on the fish population in the pond he created. He constructed a pond and added 900 fish to it. Every year, the fish population doubles.

We have to find the equation by using x represent the number of years and y represent the number of fish.

We know that,

We get

Number of fish at starting =900

Number of fish after 1 year =900×2=1800

Number of fish after 2 year =1800×2=3600=900×(2)²

Number of fish after 3 year =3600×2=7200=900×(2)³

So,

Here we can see that the number of fish are in Geometric progression (G.P) with a=900 and r=2

So,

Tₙ=arⁿ⁻¹

We get

y=900×(2)ˣ

Therefore, The equation by using x represent the number of years and y represent the number of fish is y=900×(2)ˣ.

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Two possible numbers are 6 and 12.

6 would mean she bought one box, and 12 would mean she bought 2 boxes.

The length of the segment AE on the triangle is 45/7

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

DE parallel to BC,

Also, we have

AD/DB=3/4

The above parameters mean that

AD/AB = AE/AC

Also, we know that

AB = AD + DB

From the ratio values, we have

AB = 3 + 4

Evaluate the sum

AB = 7

Updating the initial ratio, we have

AE/15 = 3/7

Multiply both sides by 15

So, we have the following representation

AE = 15 * 3/7

Evaluate the products

AE = 45/7

Hence, the length of AE is 45/7

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Answer:

29 hrs

Step-by-step explanation:

439 = 14t + 29

439-29 = 14t

410 = 14t

t = 410/14

t= 29.28

t = 29