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3 years ago

Mark got a loan of $77000 which he will complete repayment in

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

7 0

Answer:

A = $94652.66

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), where r is the annual interest rate and n is the number of compounding periods per year.

Here, A = ($77000)(1 + 0.07/2)^(2*3), or

A = $77000(1.035)^6, or

A = $77000(1.229), or

A = $94652.66

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Udrey used compensation to mentally solve the subtraction problem 5.35−0.07

Licemer1 [7]

The last step you need to do is 5.25+0.03, because you took away 0.03 more than what the question asked so you need to add the 0.03 back, which gets you the final result of 5.28.

6 0

3 years ago

A square room has walls that are each 6 feet long. How much carpet would be needed to cover the floor of this room.

Helga [31]

36 feet of carpet cause its a square so 6x6 is 36

4 0

3 years ago

Read 2 more answers

Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5

Shtirlitz [24]

Answer:

(b) ln(33/5)

Step-by-step explanation:

$\int\limits_{5}^{33} \frac{1}{x} \, dx = \ln(x) \Big|\limits_{5}^{33} = \ln(33) - \ln(5) \\\\= ln(33/5)$

Remember that in general

$\ln(a) - \ln(b) = \ln(a/b)$

4 0

3 years ago

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

In the New York State daily lottery game, a sequence of 4 (not necessarily different) digits in the range of 0-9 is selected at

devlian [24]

Answer:

50.40% probability that all 4 are different.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

4 digits, all different

For the first digit, it can be any of them, so there are 10 possible

For the second digit, it can be any of them other than the first digit. So there are 9 possible.

For the third digit, it can be any of them, other than the first and the second. So there are 8 possible.

By the same logic, 7 possible digits for the fourth. So

$D = 10*9*8*7 = 5040$

Total outcomes:

4 digits, each can be any of them(10 from 0 - 9).

$T = 10*10*10*10 = 10000$

Probability:

$p = \frac{D}{T} = \frac{5040}{10000} = 0.5040$

50.40% probability that all 4 are different.

5 0

3 years ago