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4 years ago

Casey paid $32 for a book that was on a sale at 20% off. What was the original price for that book?

Mathematics

2 answers:

Elis [28]4 years ago

8 0

Answer:

$40

Step-by-step explanation:

If it was 20% off, you are paying 80% of the original price.

So .80 * Original price = $32

32/.8 = 40

Dvinal [7]4 years ago

4 0

Answer:

$40

Step-by-step explanation:

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The A store has the price for 2/$ 5 and the B one has 5.99 who should i buy from and why?

Aloiza [94]

You should purchase from the store that is selling the 2/$5. You spend less money per item. The A store has you pay $2.50 per item with the deal while the B store has you pay almost $6 per item.

3 0

3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

3 years ago

A large university accepts 60% of the students who apply. Of the students the university accepts, 40% actually enroll. If 30,

kykrilka [37]

Answer:

7,200

Step-by-step explanation:

Let's start by calculating how many students the university accepts. The problem says they accept 60% of the students. 60% as a decimal is 0.6. To calculate 60% of something, you multiply .60 by whatever quantity. In this case, it would be the students.

Number of accepted students = $.6 * 30000$ = 18,000

The university accepts 18,000 students.

Now, the next problem is that of those accepted students, we need to find out how many actually enroll. The problem says they accept 40% of the accepted students. Applying the same principle,

Number of enrolled students = $.4 * 18000$ = 7,200