21. Mr. Li has 1,034 goats. He has 242 more sheep than goats. How many sheep does Mr. Li have?

You want to limit the amount of television you watch to an average of at most 2 hours per week during an 8-week period. How many

solniwko [45]

You have been given the information
2 hour per week
8 week period
So, to find out how many hours of television you can watch, multiply 8 by 2 = 16 hours of television in a 8 week period.
Hope this helps!!

5 0

3 years ago

A typist charges $0.98 a page and averages 30 pages per workday. If he works 5 days a week, how much does he earn in a week? $5.

juin [17]

$147.00

0.98x30 = 29.4
29.4x5 = 147

5 0

2 years ago

Read 2 more answers

Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

4 0

3 years ago

help. If 20 men can survive for 24 days on 15 cans of rations, how many cans will be needed for 16 men to survive for 36 days?

Semmy [17]

Answer: 29 cans.

Step-by-step explanation:

20 can survive 24 days with 15 cans.

If X is the number of days that a man can survive with one can of rations.

so X is in the units can/day

then we have that:

24/15*X = 20

X = 20*15/24 = 12.5

This means that a man can live 12.5 days with a can of food.

then, for 16 men and 36 days we have:

(36/C)*12.5 = 16

C = (36/16)*12.5 = 28.1215

And we can not have a 0.1215 of a can, so we should round it up to 29 cans.

4 0

2 years ago

Select all of the linear transformations from R3 to R3 that are invertible. A. Projection onto the xy-plane B. Reflection in the

sergeinik [125]

Answer: . Rotation about the y-axis by π

Step-by-step explanation:

4 0

3 years ago

21. Mr. Li has 1,034 goats. He has 242 more sheep than goats. How many sheep does Mr. Li have?​

21. Mr. Li has 1,034 goats. He has 242 more sheep than goats. How many sheep does Mr. Li have?