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Anuta_ua [19.1K]
2 years ago
12

If the cost of an item increased by a percentage and decreased by the same percentage, what would that percentage be if the new

cost was 84% of the original?
Mathematics
1 answer:
Orlov [11]2 years ago
8 0

The percentage, if the new cost was 84% of the original is 40%

Let the cost of the item be x.

When the price increased by y%, the new price is:

New =x \times (1 + y\%)

When the price decreased by the same percentage (i.e. y%), the new price is:

New =x \times (1 + y\%) \times (1 - y\%)

The cost is said to be 84% of the original price.

So, we have:

x \times (1 + y\%) \times (1 - y\%) =84\% \times x

Divide both sides by x

(1 + y\%) \times (1 - y\%) =84\%

Apply the difference of two squares

1 - (y\%)^2 =84\% \\\\

Subtract 1 from both sides of the equation

- (y\%)^2 =-16\%

Cancel out the common factors

(y\%)^2 =16\%

Take the square root of both sides

y\% =0.4

Multiply both sides by 100

y =40

Hence, the percentage is 40%

Read more about percentage change at:

brainly.com/question/809966

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Answer:

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Step-by-step explanation:

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Distribute

8*11i + 8*2

88i +16

Writing in the proper form

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6 0
3 years ago
A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon
fiasKO [112]

Answer:

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.

This means that n = 603, \pi = \frac{142}{603} = 0.2355

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

8 0
2 years ago
I NEED THIS PLEASE EXPERS.
kipiarov [429]

Answer: The answer is 24 :)

Give brainlest if I’m right

7 0
3 years ago
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Elvira was trying to find out the number of students in the courtyard during lunch. She doesn’t remember how many students were
il63 [147K]

Answer:

2x3=6+9=15?

Step-by-step explanation:

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4 0
2 years ago
The length of a rectangular garden is 3 yd less than twice its length. The perimeter of the garden is 78 yd. What are the width
Alenkasestr [34]

Complete question :

Answer:

Width = 14 yards ; length = 25 yards

Step-by-step explanation:

Given that :

The length of a rectangular garden is 3 yd less than twice its length. The perimeter of the garden is 78 yd. What are the width and length of the garden?

Width of garden (W) = w

Lenght of garden (L) = 2w - 3

Perimeter of a rectangle : 2 (L + W)

2(2w - 3 + w) = 78

2(3w - 3) = 78

6w - 6 = 78

6w = 78 + 6

6w = 84

w = 14 yards

Length = 2(14) - 3

Length = 28 - 3 = 25 yards

3 0
3 years ago
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