Simplify the following problem.

7) Mofor invests $3,101 in a savings account

Vika [28.1K]

Answer:

4%

Step-by-step explanation:

$A = P(1+r/n)^{nt}$

A = final amount

P = initial amount

r = interest rate per time period

n = number of times compounded per time period

t = number of time period

A = 3932.82

r = what we want to find

n = 2

t = 6

$A = P(1+r/n)^{nt}\\3932.82 = 3101(1+r/2)^{12}$

divide both sides by 3101 to isolate the exponent and its parts

$3932.82/3101 = (1+r/2)^{12}$

put both sides to the power of (1/12) to help isolate the variable

$(3932.82/3101)^{1/12}= (1+r/2)$

subtract 1 from both sides to isolate the variable and its coefficient

$(3932.82/3101)^{1/12}-1= (r/2)$

multiply both sides by 2 to get r

$((3932.82/3101)^{1/12}-1) * 2= r$

r ≈ 0.04 = 4%

7 0

2 years ago

-2x-107-7x=3 I need help

inysia [295]

Start off by combining like terms, then get x by itself.
Lemme know if you still need help.

7 0

3 years ago

Heights of 10 year-olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6

IRISSAK [1]

Answer:

A normal probability plot of heights of a random sample of 500 10 year- old people should show a fairly straight line

Step-by-step explanation:

We are given that heights are normally distributed with mean=55 and standard deviation=6.

Now explaining all the given statements.

Roughly 95% of 10 year-old are between 37 and 73 inches tall.

This statement is not true. We know that approximately 95% of data lies within interval mean±2*standard deviation (empirical rule).

mean±2*standard deviation=55±2*6=55±12=(43,67)

So, 95% of 10 year-old are between 47 and 67 inches tall. Thus, the above statement is wrong.

A 10 year-old who is 65 inches tall would be considered more unusual than a 10 year-old who is 45 inches tall.

If the heights of 10 years old lie more than 2 standard deviation away then it will considered as unusual and If the heights of 10 years old lie more than 3 standard deviation away then it will considered as more unusual.

As 65 and 475 lies within two standard deviation from mean, so these are not unusual data values. So, the above statement is not true.

A normal probability plot of heights of a random sample of 500 10 year- old people should show a fairly straight line.

A normal probability plot shows straight line when the data is normally distributed and we know that if the population is normally distributed then then sample selected from this population is also normally distributed with mean μxbar and standard deviation σxbar. So, this statement is true.

We would expect more 10 year-old to be shorter than 55 inches than taller than 55 inches

Last few words were missing from the statement and i gathered them through web search.

The probability of 10 years old shorter than 55 is 50% and probability of 10 years old taller than 55 as area under the normal curve is 1 and given mean is 55. The area above mean and below mean in the normal curve is 0.5. So, we can't say that We would expect more 10 year-old to be shorter than 55 inches than taller than 55 as they have equal probabilities. Thus, the above statement is not true.

8 0

4 years ago

Please help as fast as you can.

weeeeeb [17]

Answer:

$cos\theta$ = $\sqrt{\frac{85}{121}}$

$tan\theta$ = $\frac{6}{\sqrt{85}}$

Step-by-step explanation:

given, $sin\theta$ = $\frac{6}{11}$

since, $sin^2\theta$ + $cos^2\theta$ =1

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

$cos^2\theta[/tax]=1-[tex]\frac{36}{121}$

= $\frac{121-36}{121}$

= $\frac{85}{121}$

$cos\theta$ = $\sqrt{\frac{85}{121}}$ answer

$tan\theta$ = $\frac{sin\theta}{cos\theta}$

$tan\theta$ = $\frac{6}{\sqrt{85}}$ answer

7 0

3 years ago

A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tic

dalvyx [7]

Answer:

The expected revenue of the tour operator is 985.

Step-by-step explanation:

There are two outcomes:

Either less than 21 tourists show up and the operator does not have to pay anything. Or 21 tourists show up and the operator has to repay 100.

Anyways, initially he gets the price of all the tickets sold. That is 21 each at 50, so $R = 21*50 = 1050$ .

Then, we need to find the probability that all of the 21 tourists show up. In this case, we have to subtract 100 from the revenue.

Each tourist has a 0.02 probability of not showing up. This means that each has a 1-0.02 = 0.98 probability of showing up. So the probability P that all 21 tourists show up is $P = (0.98)^{21} = 0.6542$ .

So, the expected revenue of the tour operator is

$R = 1050 - 100P = 1050 - 100(0.6542) = 984.58$

Rounded up, the expected revenue of the tour operator is 985.

6 0

3 years ago

Simplify the following problem. | -48 – (-5) |