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iris [78.8K]
3 years ago
7

Vicky works in retail. Her annual gross salary is $24,000. From this, she must pay 15% income tax. In addition, she must repay a

loan at a rate of $120 per month. The loan amount is taken out of her post-tax pay (i.e. after the tax has been calculated). What is Vicky's take home pay per month?
Mathematics
2 answers:
Stella [2.4K]3 years ago
8 0

Answer: Vicky's take home pay per month is $1,580

Step-by-step explanation: If Vicky's annual gross salary (salary before any deductions) is given as 24000, then her monthly gross salary is derived as;

Salary Per month = 24000/12

Salary per month = 2000

She must pay 15 percent income tax and this derived as follows;

Income tax = 2000 x 0.15

Income tax = 300

Therefore her salary after tax deduction is derived as follows;

Salary after tax = 2000 - 300

Salary after tax = 1700

However, she must repay a loan (after tax deduction) at a rate of 120 per month, which is now derived as follows;

Salary after loan repayment = 1700 - 120

Salary after loan repayment = 1580

Therefore the calculations show that her take home pay after all adjustments comes down to $1,580 per month.

xenn [34]3 years ago
3 0

Answer:

Vicky's take home pay per month will be $1,580

Step-by-step explanation:

Given that her salary per annual i.e salary for the year = $24,000

Therefore salary per month would be $24,000/12 = $2,000.

From this, she must pay 15% income tax.

i.e 15% of salary

15/100 * 2000

= 0.15*2000

= $300.

Salary after paying tax = $2,000 - $300= $1,700.

Since, she must repay a loan at a rate of $120 per month we will reduct the loan from her salary,

$1,700 - $120 = $1,580

Vicky's take home pay per month will be $1,580

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Zepler [3.9K]

Answer:

a) \bar X=144.3

b) The 95% confidence interval would be given by (138.846;149.754)      

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3 represent the sample mean  

\mu population mean (variable of interest)

\sigma=8.8 represent the population standard deviation

n=10 represent the sample size  

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that t_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

144.3-1.96\frac{8.8}{\sqrt{10}}=138.846    

144.3+1.96\frac{8.8}{\sqrt{10}}=149.754

So on this case the 95% confidence interval would be given by (138.846;149.754)    

Part c

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (5) we got:

n=(\frac{1.960(8.8)}{3})^2 =33.05 \approx 34

So the answer for this case would be n=34 rounded up to the nearest integer

Part d

n=(\frac{1.960(8.8)}{1})^2 =297.493 \approx 298

So the answer for this case would be n=298 rounded up to the nearest integer

Part e

n=(\frac{1.960(8.8)}{0.5})^2 =1189.97 \approx 1190

So the answer for this case would be n=1190 rounded up to the nearest integer

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lbvjy [14]

Answer:I think its C but im not sure

6 0
2 years ago
In a certain state, fishing licenses are in the form of LLL NN, where L stands for a letter of the alphabet and N stands for a o
Pavel [41]
<h2>Answer:</h2>

There are 1757600 possibilities.

<h2>Step-by-step explanation:</h2>

In a certain state, fishing licenses are in the form of LLL NN

L stands for a letter of the alphabet (a to z)

N stands for a one-digit number from 0 to 9.

Now, for the series LLL, 3 alphabets are placed that can be any from a to z. This means at each place, 26 letters can be placed.

Similarly, for NN, 2 numbers are placed that can be any, between 0 and 9. At each place 0 to 9 can be placed.

Hence, the total possible outcomes will be :

26\times26\times26\times10\times10=1757600

Therefore the answer is 1757600 possibilities.

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3 years ago
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Julio can buy a box of 20 pencils<br> for $2.80. What is the unit rate in<br> dollars per pencil?
Mice21 [21]

Answer:

$0.14

Step-by-step explanation:

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zmey [24]

Answer:

9.103

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180 - (47 + 30) = 103

DEG = 180 - 103 = 77 angles on a straight line equals 180

An equilateral triangle has all 3 sides equal

if the sum of angles in a triangle is 180 degrees, each angle measures 180 / 3 = 60

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

5² + 4² = 41

squareroot of 41 = 6.4

b : √(25² - 15²) = 20

√(60² - 48²) = 36

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2 years ago
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