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3 years ago

O PERCENTS

Mathematics

1 answer:

Sedbober [7]3 years ago

3 0

Answer:

Commission rate = 15%

Step-by-step explanation:

Given that:

Amount of merchandise sold = $2700

Commission earned = $405

We can find the commission rate by dividing the commission with total sales and multiplying it with 100.

Commission rate = $\frac{Commission}{Total\ sales}*100$

Commission rate = $\frac{405}{2700}*100$

Commission rate = 0.15 * 100

Commission rate = 15%

Hence,

Commission rate = 15%

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The ratio of kids to adults in a dollar store is 2:1. Suppose there is a total of 50 kids to adults. How many kids are there?

Taya2010 [7]

The correct answer is 71 kids

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3 years ago

Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.

Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

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for n=1

P(n) = $1^{3}+2(1)+3(1)^{2}$ = 6

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Now, for n=k, $n > 0$

P(k) = $k^{3}+2k+3k^{2}$

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

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P(k+1) = $k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3$

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Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = $n^{3}+2n+3n^{2}$ is divisible by 2 and 3 for all positive integer n.

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3 years ago

6 pounds of potatoes cost $11.34. What is the unit price?

AveGali [126]

Your answer would be $1.89

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3 years ago

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)