All categories

2 years ago

Please help!! With step by step

Mathematics

1 answer:

Sever21 [200]2 years ago

4 0

Answer:

$R=\$145.12$

Step-by-step explanation:

<u>Compound Interest</u>

This is a well-know problem were we want to calculate the regular payment R needed to pay a principal P in n periods with a known rate of interest i.

The present value PV or the principal can be calculated with

$P=F_a\cdot R$

Solving for R

$\displaystyle R=\frac{P}{F_a}$

Where Fa is computed by

$\displaystyle F_a=\frac{1-(1+i)^{-n}}{i}$

We'll use the provided values but we need to convert them first to monthly payments

$i=7\%=7/(12\cdot 100)=0.00583$

$n=3*12=36$

$\displaystyle F_a=\frac{1-(1+0.00583)^{-36}}{0.00583}$

$F_a=32.386$

Thus, each payment is

$\displaystyle R=\frac{4,700}{32.386}=145.12$

$\boxed{R=\$145.12}$

You might be interested in

Convert 3/11 to a decimal equivalent using long division. (Ex: 80-30 is what I need but I'm not sure.)

Virty [35]

.27 repeating.... you have to put three on the inside and 11 outside, so 11 goes into 3 zero times so put a zero at the top. Write a zero underneath and subtract 3-0 (obviously 3) and put a decimal point after the first three under the sign and the 0 above it. Add a zero after the threes decimal, and carry it down to the bottom most 3 to have 30. 11 goes into 30 two times so write a 2 at the top. Subtract the 30-22 at the bottom and get 8. Add another 0 after the 3 ( so now 3.00) and carry it to the 8 (80). 11 goes in 7 times, 77. So 7 on top and 80-77= 3 below. Add another zero to repeat process if necessary, but otherwise it repeats, just so you know ;) hope this helps

8 0

3 years ago

∠1 and ∠2 are supplementary angles. If m∠1 = 77°, then m∠2 =

posledela

Answer:

B. 103°

Step-by-step explanation:

Supplementary angles add up to 180°, so we can find the measure of angle 2 by subtracting 77 from 180

180 - 77

= 103

So, m∠2 is 103°

7 0

2 years ago

Various studies indicate that approximately 11% of the world's population is left handed. You think this number is actually high

Irina-Kira [14]

Answer:

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

d. z= 1.3322

Step-by-step explanation:

We formulate our hypothesis as

a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )

According to the given conditions

p`= 31/225= 0.1378

np`= 225 > 5

n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5

p = 0.4 x= 31 and n 225

c. Using the test statistic

z= p`- p / √pq/n

d. Putting the values

z= 0.1378- 0.11/ √0.11*0.89/225

z= 0.1378- 0.11/ √0.0979/225

z= 0.1378- 0.11/ 0.02085

z= 1.3322

at 5% significance level the z- value is ± 1.645 for one tailed test

The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept Ha : p >0.11 and conclude that the data indicates that the 11% of the world's population is left-handed.

The rejection region is attached.

The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.

which appears to be 0.95 and subtracting from 1 gives 0.04998

8 0

3 years ago

Use the point-slope form linear equation given.

Agata [3.3K]

y-3=3(x+1)

opening the bracket

y-3=3x+3

y=3x+3+3

equation of the line in the form y=mx+c;

y=3x+6

therefore gradient=3

parallel lines have same gradient therefore gradient of the other line is 3

y--3/x-0=3

y+3=3(x-0)

y+3=3x-0

y=3x-3.

8 0

2 years ago

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. Th

ankoles [38]

We have been given that the distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 6. We are asked to find the approximate percentage of lightbulb replacement requests numbering between 38 and 56.

First of all, we will find z-score corresponding to 38 and 56.

$z=\frac{x-\mu}{\sigma}$

$z=\frac{38-38}{6}=\frac{0}{6}=0$

Now we will find z-score corresponding to 56.

$z=\frac{56-38}{6}=\frac{18}{6}=3$

We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is $-3\sigma\text{ to }3\sigma$ .

We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.

We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.

$\frac{99.7\%}{2}=49.85\%$

Therefore, approximately $49.85\%$ of lightbulb replacement requests numbering between 38 and 56.

6 0

3 years ago