You and your friend are talking about your solutions to problem 2. Your friend said that there are exactly 12 different pairs of numbers with a difference of 12 and that he had found them all. How would you respond to him?

A) The number of unsold cans of soup (ending inventory) is 19.

B) The various costs of the ending inventory under LIFO, FIFO, and the weighted average are as follows:

                                    Ending Inventory

LIFO                                  $17.15

FIFO                                 $25.65

Weighted average          $21.47

FIFO assumes that the physical flow of goods sold should follow the chronological sequence of purchases or production.

LIFO assumes that the first goods acquired are the last to be sold.

The Weighted Average uses an average to determine the cost of ending inventory and the cost of goods sold.

Description                 Units Unit Cost  Total

Beginning inventory     12     $0.85     $10.20

Purchases                      4     $0.95       $3.80

Purchases                      6     $1.05        $6.30

Purchases                      7     $1.35        $9.45

Purchases                     8     $1.50       $12.00

Total                            37                     $41.75

Sales                            18

Ending inventory        19 (37 - 18)

Average cost = $1.13 ($41.75/37)

LIFO:

Ending inventory = $17.15 ($10.20 + $3.80 + 3 x $1.05)

Cost of goods sold = $24.60 ($41.75 - $17.15)

FIFO:

Ending inventory = $25.65 (4 x $1.05 + $9.45 + $12.00)

Cost of goods sold = $16.10 ($41.75 - $25.65)

Weighted Average:

Ending inventory = $21.47 (19 x $1.13)

Cost of goods sold = $20.34 (18 x $1.13)

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Answer:

138.16 inches

Step-by-step explanation:

C=Circumference. r=radius. d=diameter

C=2πr

C=2π(d/2)  ==> a radius is half of a diameter

C=2(d/2)π

C=dπ ==> simplify

C=44π

C=44*3.14

C=138.16 inches

The constant of proportionality in the equation c = 8m is 8.

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

since C = 8m is an equation and the relationship between c and m is direct.

It means that dividing both sides of the equation by m we have

C/m = 8m/m

c/m = 8

Therefore the constant of proportionality is 8

In conclusion the constant of proportionality for which c = 8m is 8.

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Answer: 104.1

Step-by-step explanation:

If [tex]P(t)[/tex] represents the initial population in millions. [tex]t[/tex] years after 1990, then [tex]P(t)=64e^{0.027t}[/tex].

2008 is 18 years after 1990, so [tex]P(18)=64e^{0.027 \cdot 18} \approx 104.1[/tex]

The exponential growth of population in 2008 is 95.4 million

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the population of the country in 1993 be = 64 million

The exponential growth rate r = 2.7 %

So , the population of the country in 2008 is calculated by

The time t in years = 2008 - 1993

                               = 15 years

So , the equation for exponential growth rate is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

And substituting the values in the equation , we get\

x ( 15 ) = 64 × ( 1 + 0.027 )¹⁵

x ( 15 ) = 64 × ( 1.027 )¹⁵

x ( 15 ) = 64 × 1.49127

x ( 15 ) = 95.4413

So , the value of x ( 15 ) = 95.4 million

Hence , The exponential growth of population in 2008 is 95.4 million

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Answer:

x = -4

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } = 2[/tex]

[tex] {( \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } )}^{3} = {2}^{3} [/tex]

[tex] \frac{6x}{2x + 5} = 8[/tex]

[tex]6x = 8(2x + 5)[/tex]

[tex]6x = 16x + 40[/tex]

[tex] - 10x = 40[/tex]

[tex]x = - 4[/tex]

[tex] \frac{ \sqrt[3]{6( - 4)} }{ \sqrt[3]{2( - 4) + 5} } = 2[/tex]

[tex] \frac{ \sqrt[3]{ - 24} }{ \sqrt[3]{ - 3} } = 2[/tex]

[tex] \sqrt[3]{ \frac{ - 24}{ - 3} } = 2[/tex]

[tex] \sqrt[3]{8} = 2[/tex]

Answer: ima say something so hopefully this gets more noticed

Step-by-step explanation:

The Scale factor of ΔADC to ΔCDB is 2  .

In the question ,

a right triangle ABC is given (the figure is shown below )

h is the length of the altitude , AD = 12 , DB = 3 ,

to find the scale factor , we first need to find the value of h ,

since triangles ADC is similar to triangle CDB ,

we have , CD / AD = DB / CD

on cross multiplication , we get

CD² = AD × DB

CD² = 12 × 3 = 36

CD = 6

For the scale factor we divide the length of the original triangle ADC with the length of the image triangle CDB .

we get

Scale factor = AD / CD

= 12/6

= 2

Therefore , The Scale factor of triangle ADC to triangle CDB is 2  .

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Step-by-step explanation:

% in calculations are always represented as hundredths, as 100% represents the whole, and n% = n/100 of the whole.

x = pounds of 35% alloy.

y = pounds of 52% alloy.

x + y = 45

0.35x + 0.52y = 0.47(x + y)

from the first equation we get e.g.

x = 45 - y

now we use this in the second equation :

0.35(45 - y) + 0.52y = 0.47((45 - y) + y)

15.75 - 0.35y + 0.52y = 0.47(45 - y + y)

15.75 + 0.17y = 0.47×45 = 21.15

0.17y = 5.4

y = 5.4/0.17 = 31.76470588... pound

x = 45 - y = 13.23529412... pound

he needs to use

31.76470588... pounds of the 52% alloy

13.23529412... pounds of the 35% alloy.

S= 0.0625t² is the composition of a function to represent the area of the puddle as a function of time.

The defined region represents the extent of the area on a plane or curved surface. The area of ​​a planar region refers to the area of ​​a shape or planar layer, while surface area refers to the area of ​​an open surface or boundary of a three-dimensional object. Area can be defined as the amount of material of a certain thickness required to model the mold, or the amount of paint required to cover the surface in a single layer. This is a two-dimensional equivalent of the length of a curve or the volume of a solid..

We obtain the data from the equation.

The radius is increased by 0.25 Cm for each t min.

Assume that the puddle's area is S.

We all know that.

Circle area =  πr²

So, S= πr²

S= π(0.25t)²

S= π0.0625t²

S= 0.0625πt²

Therefore, the area of the puddle is S= 0.0625πt²

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Answer:

The 5 consecutive odd integers are 11 , 13 , 15 , 17 , 19

Step-by-step explanation:

The Difference between any odd Integer and its consecutive Integer = 2

So let the 3rd Odd Integer be x

Then the 1st Odd Integer is x - 2

and the 2nd Odd Integer is x - 4

and the 4th Odd Integer is x + 2

and the 5th Odd Integer is x + 4

Since the Sum of the 1st three integers is 3 more than the sum of the last two

Then 1st + 2nd + 3rd = 4th +5th +3

Then (x) + (x - 2) + (x - 4) = (x + 2) + ( x + 4) +3

Then 3x - 6 = 2x + 9

subtract 2x from both sides

3x - 2x -6 = 9

x - 6 = 9

Add 6 for both sides

Then x = 9 + 6 = 15

So the 3rd odd Integer is 15

So the five consecutive odd integers are 11 , 13 , 15 , 17 , 19

By using exponent, it can be verified that

[tex](2.9 \times 10^5) \times (3.4 \times 10^3)[/tex] in standard form is [tex]9.86 \times 10^8[/tex]

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a ... \times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^{m + n} = a^m \times a^n\\a^{m - n} = \frac{a^m}{a^n}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\(ab)^m = a^m b^m\\a^0 = 1\\a^{-n} = \frac{1}{a^n}[/tex]

The given exponent is

[tex](2.9 \times 10^5) \times (3.4 \times 10^3)\\9.86 \times 10^{5+ 3}\\9.86 \times 10^8[/tex]

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a. The ratio of the height of the building to the number of floor is 14:1

b. the unit rate is 14ft per floor and this means that each floor is 14ft high.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.

if h is the height of the building and n is the number of floor.

Therefore h:n= h/n

h:n = 112/8

divide through by 8

h:n= 14/1=14:1

the unit rate is therefore 14feet per floor and this means that one floor has a height of 14 feet.

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the number of ways of selecting and matching nine banners with a country is 36.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

Given, 9 of the 20 banners with the word “Hello” in different languages with the 9 countries

Toatl ways for arranging the 9 banners will be 9C2

And as the matching nine banner with the country is 9/20

So the number of ways of selecting is 9c2 = 36.

Hence the number of ways to select and matching the banner is 36.

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The percentage of white pumpkin is 25%.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

There are three times as many orange pumpkins at the pumpkin patch as there are white pumpkins.

Hence,

let

x = Number of white pumpkin

orange pumpkin = 3x

The percentage of pumpkin that are whiter can be calculated as follows:

The full percentage is 100%.

Therefore, percentage of white pumpkin is 25%.

Orange pumpkin = 25%(3) = 75

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Answer:

6a - 3

Step-by-step explanation:

Dividend: A number/expression that is divided by the divisor.

Divisor: The number/expression that divides the dividend.

Quotient: The result obtained by the division.

Remainder: The number/expression left behind.

Long division method

The solution is the quotient plus the remainder divided by the divisor.

Given dividend:  

Given divisor:  

[tex]\large \begin{array}{r}2a+1\phantom{)}\\6a-3{\overline{\smash{\big)}\,12a^2\phantom{))..)))}-3\phantom{)}}}\\{-~\phantom{(}\underline{(12a^2-6a)\phantom{)))))}}\\6a-3\phantom{)}\\-~\phantom{()}\underline{(6a-3)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]

Therefore, the quotient is 6a - 3.

The regular price of the table based on the information is $177.41.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Let the regular price be x.

Since the table is on sale for 100.80, which is 76% less than the regular price, that will be illustrated as:

x = 100.80 × (100% + 76%)

x = 100.80 × 1.76

x = 177.408

The value is $177.41.

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Answer:

406$

Step-by-step explanation:

Answer:

$20,222 and $6,362

Step-by-step explanation:

I took the test

The solution for A(3) in the function when the function A(x) = 4 − (x + 3)⁵ is -772

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

A ( x ) = 4 − ( x + 3 )^5

To make the equation legible, we need to rewrite it

So, we have the following representation

A(x) = 4 − (x + 3)⁵

Also from the question, we have

A(3)

This means that the value of x is 3, and we calculate A(x) when x = 3

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

A(3) = 4 − (x + 3)⁵

So, we have the following equation

A(3) = 4 − (3 + 3)⁵

There are constants to add or subtract to both sides of the equation

However, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

A(3) = 4 − (6)⁵

Solving further, we have

A(3) = 4 − 7776

Evaluate the difference

A(3) = −7772

Hence, the solution is −7772

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Possible question

Given A ( x ) = 4 − ( x + 3 )^5, find A(3).

Answer:

Step-by-step explanation:

You want the minimum number of pie slices and the amount of sugar in each such that the sugar in each slice is less than 22 grams when the whole pie has 187.64 grams of sugar.

The sugar in each of n slices is 1/n times the sugar in the whole pie. You want ...

  (187.64 g)/n < 22 g

Multiply by n/(22 g) to get

  n > 187.64/22

  n > 8.53

The smallest whole number that satisfies this inequality is n = 9.

The minimum number of pie slices is 9.

When the sugar in the pie is divided into 9 equal parts, each part is ...

  (187.64 g)/(9 slices) = 20.85 g/slice

Each slice of pumpkin pie will contain about 20.85 grams of sugar.

Answer:

Step-by-step explanation:

the answer is 9

The value of the expression, (-3x)(-6)*(-10)/(-9), after simplification is 20x.

According to the question,

We have the following expression:

(-3x)(-6)*(-10)/(-9)

Now, we will first solve the numerator of this expression.

We know that the multiplication of two negative integers always gives us the positive results.

So, the multiplication of -6 and -3x will give us the positive results.

18x*(-10)/(-9)

When two negative integers are in division then their results is also positive.

18x*10/9

Dividing 18 in the numerator by 9 in the denominator, we will get 2as the result:

2x*10

20x

Hence, the value of the expression, (-3x)(-6)*(-10)/(-9), after simplification is 20x.

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Answer: 18 hours

Step-by-step explanation: There are 6 working machines at first, and it takes 36 hours to complete this.

If there are double the machines, it takes half the time to complete the order, because double the amount of fudgemaking is being done per hour.

36 divided by 2 = 18 hours with twice the machines.

Answer: 25

Step-by-step explanation:

10           6

/       =      /

x             15

Just cross multiply, so do 10*15 = 6*x

10*15 = 6*x

150 = 6*x

Divide by 6 on both sides to isolate x.

25 = x

Answer:

x = 25

Step-by-step explanation:

first simplify the 6/15 by dividing 6 and 15 both with 3
10/x = 2/5
then multiply with 5x on both sides to get rid of the fraction:
5x * (10/x) = 5x * (2/5)
then shorten and solve:
5 * 10 = x * 2
50 = x * 2
25 = x

The value of x is=-1

acc to our question-

hence,The value of x is=-1

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Answer:

  1/3

Step-by-step explanation:

You want to know the fraction that are poodles when 5/9 of animals are dogs, and 3/5 of dogs are poodles.

We can write the equations ...

  dogs = (5/9)·(animals)

  poodles = (3/5)·(dogs)

Using the first equation to substitute into the second, we get ...

  poodles = (3/5)·(5/9)·(animals) = 3/9·animals = 1/3·animals

Then the fraction that are animals is found by dividing by "animals":

  poodles/animals = 1/3

1/3 of the animals in the pet show are poodles.

Answer:

4

Step-by-step explanation:

slope intercept form is y=Mx+b

4x-y=0

   +y.  +y

4x=y

y=4x

So slope is 4

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The value of x, given the angles m and n can be found to be 30.

Given the fact that m || n, it means that when m and n are added, they equate to 180 degrees.

The reason for this is that m and n are supplementary angles and such angles will always add up to 180 degrees.

This means the value of x can be found as:

180 = m + n

180 =  (6x - 5 ) + ( x - 25 )

180 = 6x + x - 5 - 25

180 = 7x - 30

180 + 30 = 7x

x = 210 /7

x = 30

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when the correlation coefficient has a positive value , it means that when x increases , y increases and when x decreases , y decreases , the correct option is (b) .

in the question ,

it is given that

the value of correlation coefficient has a positive value .

it means that the variables have a direct relation with each other,

which means when one variable increases , the other variable also increases and when one variable decreases  , the other variable also decreases ,

Therefore , the positive value of correlation coefficient means that  When x increases, y increases, and when x decreases, y decreases.

The given question is incomplete , the complete question is

Select the correct answer. What does it mean when the correlation coefficient has a positive value?

(a) When x increases, y decreases, and when x decreases, y increases.

(b) When x increases, y increases, and when x decreases, y decreases.

(c) When x increases, y decreases, and when x is constant, y equals zero.

(d) When x increases, y increases, and when x is constant, y decreases.

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Comparing the linear expressions it shows that  

3x - 2(2,3x + 2.5) = -1.6x - 5     - equivalent

5 - 3(-1.6x - 2.1) = 4.8x - 1.3       - not equivalent

Information given in the question include

3x - 2(2,3x + 2.5) = -1.6x - 5

5 - 3(-1.6x - 2.1) = 4.8x - 1.3  

The equations are equivalent if the values on the left hand side of the equation is equal to the values on the right hand side of the equation

3x - 2(2,3x + 2.5) = -1.6x - 5

expending gives

3x - 4.6x - 5 = -1.6x - 5

-1.6x - 5 = -1.6x - 5

The expression above is equivalent

5 - 3(-1.6x - 2.1) = 4.8x - 1.3

expending gives

5 + 4.8x + 6.3 = 4.8x - 1.3

4.8x + 11.3 = 4.8x - 1.3

The expression above is not equivalent

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