Does 4f+2(12 f−4)=3(2f−4)−f+3 have one solution, no solution, or infinitely many solutions?

The calculation of the ratios, resulting from the square feet occupied by both departments, and the amounts of overhead allocated to the two departments are as follows:

                            Ratio      Amount

Department A       1/5        $10,000

Department B      4/5       $40,000

The ratio is the numerical relationship shared by two or more values.

Ratios are fractional values and are depicted using fractions, decimals, and percentages.

Ratios, like proportions, show how much a value or variable is contained in another.

Total overhead = $50,000

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            20,000         A = 1      B = $10,000 ($50,000 x 1/5)

Dept. B            80,000         C = 4     D = $40,000 ($50,000 x 4/5)

Ratios = 20,000:80,000

= 1:4

Sum of Ratios = 5

Thus, based on the cost driver allocation ratios, Department A will bear $10,000, while Department B will be allocated $40,000.

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The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.

Function

The function is referred as a mathematical expression that defines a relationship between one variable and another variable.

Given,

Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.

Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.

Here the x = 3 is a vertical asymptote.  

So the one factor in the denominator is (x - 3),

And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.

Therefore, the rational function would be :

f(x)  = (x + 2)/(x - 3)(x + 2)

So, the rational function would be (x + 2)/(x - 3)(x + 2).

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If each has the same probability of performance. If the system is to have a .92 probability of performing, The minimum probability of performing needed by each of the individual components is: 0.97126.

Given data:

Number of identical component = 3

Probability of performing = .92

Now let determine the probability

Probability =  0.92 ^(1/3)

Probability = 0.92^0.3333

Probability =.9726

Therefore the probability is .9726.

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Answer:

[tex]-11[/tex]

Step-by-step explanation:

[tex]P(-1)[/tex] is the remainder when [tex]P(x)[/tex] is divided by [tex]x+1[/tex].

[tex]\frac{x^4 + 7x^3 - 6x-11}{x+1}=x^3 + 6x^2 - 6x-\frac{11}{x+1}[/tex].

The remainder is [tex]-11[/tex], so [tex]P(c)=-11[/tex].

The speed of the car is 40mph

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

Distance covered by car = 160 miles

distance covered by plane = 840 miles

let the time taken to cover 160 miles by car be x

speed of car = 160/x

speed of plane which is 170mph faster than speed of car = 170 + 160/x

time taken to cover 840 miles by plane,

time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]

By simplifying,

time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]

since it takes same time for both to get to their destination,

Then,

x =  [tex]\frac{840x}{170x + 160}[/tex]

By cross multiplying

x( 170x + 160) = 840x

divide both sides by x, it reduces to

170x + 160 = 840

170x = 840 - 160

170x = 680

x = 680/170

x = 4

Speed of car = 160/x

speed of car = 160/4

speed = 40mph

In conclusion, the care moves at the speed of 40mph

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3

x

2

−

3

x

−

60

=

0

Explanation:

A quadratic equation whose roots are

α

and

β

and leading coefficient is

a

is

a

(

x

−

α

)

(

x

−

β

)

=

0

Hence, the quadratic equation whose roots are

5

and

−

4

and leading coefficient is

3

is

3

(

x

−

5

)

(

x

−

(

−

4

)

)

=

0

or

3

(

x

−

5

)

(

x

+

4

)

=

0

or

3

(

x

2

−

5

x

+

4

x

−

20

)

=

0

or

3

(

x

2

−

x

−

20

)

=

0

or

3

x

2

−

3

x

−

60

=

0

Answer:

5x^2+5x-100=0

Step-by-step explanation:

5(x+5)(x-4)=0

(x+5)(x-4)= 0

x= -5

x= 4

Answer:

D. 3 3/7 ft²​

Step-by-step explanation:

A = LW

A = 4 ft × 6/7 ft²

A = 24/7 ft²

A = 3 3/7 ft²

The values of the variables x and y are 2 and -7.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is y = -2x + 5. We are given two sets of ordered pairs. The ordered pairs are (6, y) and (x, 1). These points satisfy the given equation. We need to find the values of the variables x and y. We will substitute the coordinates into the equation.

y = -2x + 5

First, we will put (6, y).

y = -2(6) + 5 = -12 + 5 = -7

Now, we will put (x, 1).

1 = -2x + 5

2x = 4

x = 2

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The mistakes that Claire made in solving the equation are;

1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.

2)  - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x

3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x

We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)

Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x

Step 2; Simplify the right hand side to get;

16 + 56x = -2x - 2

Step 3; Rearrange to get;

16 + 2 = -58x

Step 4; Add up the left hand side to get;

18 = -58x

Step 5; Divide both sides by -58 to get;

x = -9/29

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Complete question is;

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It

turns out Clare's work has three mistakes!

find all three mistakes explain the below

8(2 + 7x) = 3x - (2+5x)

10 + 56x = 3x - 2 + 5х

10 + 56x = 8x - 2

10 = 64x - 2

12 = 64x

x = 3/16

Answer:

x = -5

y = -2

Step-by-step explanation:

-3x + 4y = 7 ⇒ ( 1 )

7x - 12y = -11 ⇒  ( 2 )

Multiply the equation ( 1 ) by 3.

( 1 ) × 3

3( -3x + 4y = 7 )

-9x + 12y = 21  ⇒ ( 3 )

Let us find the value of x.

Add equations ( 2 ) & ( 3 ).

( 2 ) + ( 3 )

7x - 12y - 9x + 12y = - 11 + 21

Combine like terms.

-2x = 10

Divide both sides by -2.

x = -5

Let us find the value of y.

For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.

- 3x + 4y = 7

-3 × -5 + 4y = 7

15 + 4y = 7

Subtract 15 from both sides.

4y = 7 - 15

4y = -8

Divide both sides by 4.

y  = -2

Answer:

24/8 = 3/1

40/20 = 20/1

Step-by-step explanation:



I hope this helps!

Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;

The number of each currency Abigail plans to buy are;

A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.

The amount Abigail Henderson budgeted = $1,360

The per currency exchange rate for country A = $1.30

The per currency exchange rate for country B = $1.60

The number of currency A Abigail wants = 4 × The number of currency B

Which gives; x = 4·y

The equation that represents Abigail's total cost of buying currencies is presented as follows;

1.3·x + 1.6·y = 1,360

Plugging in the value of x gives;

1.3 × (4·y) + 1.6·y = 1,360

6.8·y = 1,360

y = 1,360 ÷ 6.8 = 200

The number of currency of country B, Abigail purchases, y = 200

The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800

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Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives

The perimeter of a rectangle, P is given by the formula

P = 2(L + W) ≤ 57 units of wire

width, W = 2 units

length, L = 1 + W

= 1 + 2

= 3

The perimeter of the rectangle is given by

P = 2(L + W)

plugging the values of L and W

P = 2 (3 + 1)

P = 2 (4 )

P = 8 units

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Answer:

Thank you,Hope you like it and it will help you

If an American is selected at random, the probability that he or she will disapprove or have no opinion on the issue is 33%.

Given data:

Approved human embryonic stem cell research = 67% or 0.67

Now let find the probability that the human embryonic stem cell research will be disapprove using this formula

P(disapprove or no opinion) = 1 - Approved

Let plug in the formula

P(disapprove or no opinion)  = 1 - 0.67

P(disapprove or no opinion) = 0.33 or 33%

Therefore 33% is the probability of disapprove or no opinion.

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(5-√5)² in the form a + b√5 can be written as 30 - 10√5 where, the integers a and b are 30 and -10 respectively.

What is integer?

Positive, negative, and zero are all examples of integers. The Latin word "integer" means to "whole" or "intact." Therefore, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.

We know that,

[tex](a-b)^2= a^2 + b^2 - 2ab[/tex]

Using this mathematical identity, putting the values from question,

(5-√5)² = 5² + √5² - 2(5)(√5)

(5-√5)² = 25 + 5 - 10√5

(5-√5)² = 30 - 10√5

This is in the form a + b√5 where, the integers a and b are 30 and -10 respectively.

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By the concept of percentage, 41 is [tex]10\frac{1}{4}[/tex] % of the number 400.

The percentage is a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. Percent is derived from the Latin word per centum, which means "by the hundred." In the 16th century, the Latin expression was adopted by English. Later, it was shortened to % with a period in the end. The present one-word form % was created after the period was eliminated and the two elements were combined. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage.

Let the number be x.

Then, according to the question

[tex]10\frac{1}{4}[/tex] can be written as 41/4

So,

41/400 × x = 41

41 x = 41 ×100

x =400

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The  total cost for the group of ten people after discount is 10 t - 0.5 t.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Discount = 5%

Total tickets= 10

We have t represents the cost of one ticket.

So, For 10 person the cost of the ticket = 10t

Now, after discount the price of tickets

= 5% of 10t

= 0.5 t

Hence, the total cost for the group of ten people after discount is 10 t - 0.5 t.

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After using conversion of measurements , the answer is

60 km = 37.28 miles and 600km = 372.83 miles.

What is conversion of measurements?

  By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet. We must convert between different units in order to have accuracy and prevent measurement confusion.

Here the given we need to convert them km into miles.

To convert km to miles we need to divide the value by 1.609 .

=> 60 km

=> 60/1.609

=> 37.28 miles.

Now ,

=> 600 km

=> 600/1.609

=> 372.83 miles.

Therefore after conversion of measurement answer is

60 km = 37.28 miles and 600km = 372.83 miles.

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The Probability of P(B│A) is 0.77

Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.

If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears

P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3

Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that

P(A ∩ B) = 1/6

P(B│A) = P(A ∩ B)/ P(A)

= 1/6 /1/2= 1/3 = P(B)

Therefore P(B│A) = P(B)

if A= 0.15 and P(B)= 0.77

P(B│A) = 0.77

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Answer:

7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer

Answer:

a) 7:13  b) 5:13

Step-by-step explanation:

There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13

do the same thing for b) using the same steps.

Answer:

80

Step-by-step explanation:

x/ -4 = -20

I hope this helps!

Answer:

81 people

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The equation of the parallel line t is y = -4x  - 9

The equation of line s given as

y = -4x - 5/3

Also, from the question

The point on line t is given as

Point = (-3, 3)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4

(x₁, y₁) = (-3, 3)

Substitute the known values in the above equation

y = -4(x + 3) + 3

Evaluate

y = -4x - 12 + 3

Evaluate the sum

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9

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The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.

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:

Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.

So, for x= 3 them Q(3)

Q(3)= 8.25 (3) - 24.75

Q(3) = 24.75 - 24.75

Q(3) = 0

Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.

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Answer: 13.9

Step-by-step explanation:

17.140 rounded to the nearest tenth is 17.1

03.179 rounded to the nearest tenth is 3.2

17.1 - 3.2 = 13.9

The midpoint of the segment with the given endpoints.-5 and 4 is -0.5.

What are coordinates?

A pair of numbers is used to express a point's position on a coordinate plane using the horizontal and vertical distinctions from the two reference axes.

What is a midpoint?

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line.

Here,

A midpoint can also be written as an average or mean of two points.

Mean of -5 and 4 = (- 5 + 4)/2 = -0.5

Hence "The midpoint of the segment with the given endpoints.-5 and 4 is -0.5".

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The expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7  is 7+(3-2).8

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer.

a + b = b + a

3(2x8) + 7 = 7 + 3(2x8)

The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.

a(b x c) = (a x b) c

7 + 3(2x8) = 7 + (3.2)8

Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7  is 7+(3-2).8

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