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1 year ago

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The formula for percentage increase I (given as a decimal) of an investment is I=S−PP, where P is the purchase price and S is th

e sale price. You sell a stock at a price of $75, earning a percentage increase of 25%. What was the purchase price of the stock?
Solve the formula for P.

P=

The purchase price of the stock was $_

2 answers:

sattari [20]1 year ago

5 0

18.75/75=(75/75) -
p =(75-18.5)/75
p=56.5/75
p=0.75(3recurring)

vlabodo [156]1 year ago

3 0

Answer: $60

Step-by-step explanation:

Given : The formula for percentage increase I (given as a decimal) of an investment is $I=\dfrac{S-P}{P}$ , where P is the purchase price and S is the sale price.

If Price of stock S= $75 and the percentage increase of 25% i.e. I=0.25.

Then, to find P , we substitute the values of S and I in the given equation, we get

$0.25=\dfrac{75-P}{P}\\\\\Rightarrow\ 0.25P=75-P\\\\\Rightarrow\ P+0.25P=75\\\\\Rightarrow\ (1.25)P=75\\\\\Rightarrow\ P=\dfrac{75}{1.25}=60$

Hence, the purchase price of the stock was $60.

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The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a s

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Answer:

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 12.6, \sigma = 2.5$

What is the probability that randomly selected homework will require between 8 and 12 minutes to grade?

This is the pvalue of Z when X = 12 subtracted by the pvalue of Z when X = 8. So

X = 12

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

$Z = \frac{12 - 12.6}{2.5}$

$Z = -0.24$

$Z = -0.24$ has a pvalue of 0.4052

X = 8

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

$Z = \frac{8 - 12.6}{2.5}$

$Z = -1.84$

$Z = -1.84$ has a pvalue of 0.0329

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37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

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2 years ago

Natasha had a $922.93 balance on her credit card at the beginning of September. Her credit card has an APR of 9.89%, compounded

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Answer:

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Step-by-step explanation:

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The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge

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- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

$D(t) = 300t+125$ for $t< 2.5$

$D(t) = 880$ for $2.5 \leq 3.5$

$D(t) = 75t+612.5$ for $t\leq 6$

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

$D(0) = (300)(0)+125 = 125$

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

$D(2) = (300)(2)+125 = 725$

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

$D(6)) = 75(6)+612.5=1062.5$

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1 year ago

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Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?

sergeinik [125]

Solving RootIndex 3 StartRoot 8 EndRoot Superscript x we get $=2^x$

Step-by-step explanation:

We need to find equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x

Writing in mathematical form:

$(\sqrt[3]{8})^x$

Solving:

We know 8= 2x2x2= 2^3

and $\sqrt[3]{x}=x^{\frac{1}{3}}$

Applying these rules:

$=((2^3)^{\frac{1}{3}})^x$

$=(2^{\frac{3}{3}})^x\\$

$=2^x$

So, solving RootIndex 3 StartRoot 8 EndRoot Superscript x we get $=2^x$

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1 year ago

25. To produce the graph of the function y=0.5cos(0.5x), what transformations should be applied to the graph of the parent funct

soldi70 [24.7K]

Answer:

C. A horizontal stretch to produce a period of $2\pi$ and a vertical compression.

Step-by-step explanation:

We are given the parent function as $y= \cot x$

It is given that, transformations are applied to the parent function in order to obtain the function $y=0.5\cot (0.5x)$ i.e. $y=\frac{1}{2}\cot (\frac{x}{2})$

That is, we see that,

The parent function $y= \cot x$ is stretched horizontally by the factor of $\frac{1}{2}$ which gives the function $y=\cot (\frac{x}{2})$ .

Further, the function is compressed vertically by the factor of $\frac{1}{2}$ which gives the function $y=\frac{1}{2}\cot (\frac{x}{2})$ .

Now, we know,

If a function f(x) has period P, then the function cf(bx) will have period $\frac{P}{|b|}$ .

Since, the period of $y= \cot x$ is $\pi$ , so the period of $y=\frac{1}{2}\cot (\frac{x}{2})$ is $\frac{\pi}{1/2}$ = $2\pi$

Hence, we get option C is correct.

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2 years ago