Ask question

Ask question

All categories

2 years ago

7

An antique store increases all of its prices by $40\%$, and then announces a $25\%$-off-everything sale. What percent of the ori

ginal prices (before the increase) are the new prices?

2 answers:

Nostrana [21]2 years ago

6 0

Let X be the original price.
Do a 40% increase we get the price: X+0.4X=1.4X
Doing a 25% off we get the new price:
(1.4X)-0.25(1.4X)=1.05X
=X+0.05X.
The new prices are 5% increase from the original price.

Aleks04 [339]2 years ago

3 0

The most likely solution is 105%

You might be interested in

The inside diameter of a randomly selected piston ring is a random variable with mean value 13 cm and standard deviation 0.08 cm

sweet-ann [11.9K]

Answer:

a) P(12.99 ≤ X ≤ 13.01) = 0.3840

b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the cental limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 13, \sigma = 0.08$

(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.

Here we have $n = 16, s = \frac{0.08}{\sqrt{16}} = 0.02$

This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.

X = 13.01

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{13.01 - 13}{0.02}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

X = 12.99

$Z = \frac{X - \mu}{s}$

$Z = \frac{12.99 - 13}{0.02}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?

P(X ≥ 13.01) =

This is 1 subtracted by the pvalue of Z when X = 13.01. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{13.01 - 13}{0.02}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

7 0

2 years ago

Read 2 more answers

Dudley’s credit card has an APR of 20.7%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the

Annette [7]

If the credit card Balance is of, lets say, $2000 and if the interest rate is 2.7% and then he has a minimum payment of 2% which in terms of money will be $40 then it will take 9 years and 9 months to payoff his balance and the total interest wil be of $2640.45. If the credit card balance is not $2000 then you can take the amount they give you and do a cross multplication.

7 0

2 years ago

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believ

olga_2 [115]

Answer:

Value of v that minimizes E is v = 3u/2

Step-by-step explanation:

We are given that;

E(v) = av³L/(v-u)

Now, using the quotient rule, we have;

dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²

Expanding and equating to zero, we have;

[3av³L - 3av²uL - av³L]/(v - u)² = 0

This gives;

(2av³L - 3av²uL)/(v-u)² = 0

Multiply both sides by (v-u)² to give;

(2av³L - 3av²uL) = 0

Thus, 2av³L = 3av²uL

Like terms cancel to give;

2v = 3u

Thus, v = 3u/2

5 0

2 years ago

Nat2105 [25]

Answer:

x=10.25

Step-by-step explanation:

If the two angles are congruent, then the measures are equivalent. Therefore, we can set the measures equal to each other and solve for x.

5x+24=9x-17

We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

First, subtrct 5x from both sides.

5x-5x+24=9x-5x-17

24=9x-5x-17

24=4x-17

Next, add 17 to both sides.

24+17=4x-17+17

24+17=4x

41=4x

Lastly, divide both sides by 4, since 4 and x are being multiplied (4*x=4x).

41/4=4x/4

41/4=x

10.25=x

If the angles are congruent, then the value of x is 10.25.

3 0

1 year ago

Read 2 more answers

In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: Chapter Reference b The length of the

Butoxors [25]

Answer:

The length of the angle bisector of angle ∠A is 6.01.

Step-by-step explanation:

It is given that length of leg AC = 5 ft and the hypotenuse AB = 13 ft.

Using pythagoras theorem

$(AB)^2=(BC)^2+(AC)^2$

$(13)^2=(BC)^2+(5)^2$

$169=(BC)^2+25$

$BC=12$

$\sin A=\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\sin A=\frac{BC}{AB}$

$A=\sin ^{-1}\frac{12}{13}$

$A=67.38$

Bisector divides the angle in two equal parts, therefore,

$A'=\frac{67.38}{2} =33.69$

In triangle ACD.

$\cos A'=\frac{\text{Base}}{\text{Hypotenuse}}$

$\cos A'=\frac{AC}{AD}$

$\cos (33.69^{\circ})=\frac{5}{AD}$

$0.832=\frac{5}{AD}$

$AD=\frac{5}{0.832} =6.009\approx 6.01$

Therefore the length of the angle bisector of angle ∠A is 6.01.

4 0

2 years ago