MATHEMATICS COLLEGE

After an 80% reduction you purchase a new sofa on sale for $108 what was the original price

Answers

Answer 1
Answer:

Answer:

$540

Step-by-step explanation:

Define x as:

x = the Original Price, in dollars ($)

Then,

x - (80%)x = 108, where we note that (80%)x is the reduction amount, so that

20%x = 108,

0.2x = 108,

x = 108/0.2 = $540
Answer 2
Answer:

Final answer:

The original price of the sofa was $540.

Explanation:

Question:

After an 80% reduction, you purchase a new sofa on sale for $108. What was the original price?

Detailed Answer:

To find the original price, we need to determine what the 80% reduction represents in terms of the original price. If the sale price is 80% of the original price, then we can set up the equation: sale price = 0.2 * original price. We know the sale price is $108, so we can solve for the original price by dividing both sides of the equation by 0.2: original price = $108 / 0.2 = $540. Therefore, the original price of the sofa was $540.

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How do you do this question?

Answers

Answer:

z = -ln│5eᵗ + C│

Step-by-step explanation:

dz/dt + 5eᵗ⁺ᶻ = 0

dz/dt = -5eᵗ⁺ᶻ

dz/dt = -5eᵗeᶻ

-e⁻ᶻ dz = 5eᵗ dt

e⁻ᶻ = 5eᵗ + C

-z = ln│5eᵗ + C│

z = -ln│5eᵗ + C│

What is the least What is the least common multiple of four and 12

Answers

Answer: LCM(4,12) = 12

Step-by-step explanation:

This of this as singing all the multiples of 4

4, 8, 12.

4 + 4 + 4.

Answer:

2

Step-by-step explanation:

4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answers

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

\begin{gathered} A=l* b \n l=\text{length} \n b=\text{breadth or width} \end{gathered}

Now, let us calculate the area of FACE 1, 3 and 5.

\begin{gathered} \text{FACE 1:} \n A_1=18*4=72in^2 \n \text{FACE 3:} \n A_3=4*7=28in^2 \n \text{FACE 5:} \n A_5=18*7=126in^2 \end{gathered}

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

\begin{gathered} A_S=2*(72+28+126) \n \therefore A_S=452in^2\text{ } \end{gathered}

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

\begin{gathered} V=l* w* h \n l=\text{length} \n w=\text{width or breadth} \n h=\text{height or depth} \end{gathered}

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

\begin{gathered} V=7*18*4in^3 \n \therefore V=504in^3 \end{gathered}

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches

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Answers

Answer:

sorry i dont have insta

Step-by-step explanation:

hope you find help!

Answer:

What do u need help with

Off the production line, there is a 4.6% chance that a candle is defective. If the company selected 50 candles off the line, what is the standard deviation of the number of defective candles in the group?

Answers

Answer: 1.48

Step-by-step explanation:

From binomial distribution, the formula to find the standard deviation is given by :-

\sigma=√(np(1-p)), where n is the sample size and p is the proportion of success.

Given : The percent of chance that a candle is defective. If the company selected 50 candles off the line : 4.6%

i.e. The proportion of success : p=0.046

Sample size : n=50

Then, Standard deviation = \sigma=√(50(0.046)(1-0.046))

\sigma=1.48128322748\approx1.48

Hence, the standard deviation of the number of defective candles in the group=1.48

Can the range of a function be written like this {6,7,8,10} instead of like this 6\leq x\leq 10?

Answers

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.
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