Franklin Lyons is married and claims 3 withholding allowances. He gets paid overtime if he works over 40 hours in a week. His gross pay is $958.38. Find the Federal Withholding Tax.

Answer:

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.

This means that [tex]p = 0.18, n = 100[/tex]

So, by the Central Limit Theorem:

[tex]\mu = 0.18, s = \sqrt{\frac{0.18*0.82}{100}} = 0.0384[/tex]

How likely is the resulting sample proportion to be between 0.066 and 0.294?

This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So

X = 0.294

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.294 - 0.18}{0.0384}[/tex]

[tex]Z = 2.97[/tex]

[tex]Z = 2.97[/tex] has a pvalue of 0.9985

X = 0.066

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.066 - 0.18}{0.0384}[/tex]

[tex]Z = -2.97[/tex]

[tex]Z = -2.97[/tex] has a pvalue of 0.0015

0.9985 - 0.0015 = 0.997

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Answer:

A

Step-by-step explanation:

3/8

1/4× 2

3/8

-2/8

1/8

if that makes sense to you.

Answer:

x^2 - 100 = (x + 10) * (x - 10)

Step-by-step explanation:

Recall that 100 is the perfect square of 10:

10^2 = 100

then we can use the formula for factorization of a difference of squares:

x^2 - 10^2 = (x + 10) * (x - 10)

The image showing the trapezoid is missing, so i have attached it.

Answer:

C 54:18

Step-by-step explanation:

Formula for area of trapezoid is;

A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6

A_trap = ½(12 + 6) × 6

A_trap = 54 in²

Combined area of triangle:

A_tria = 2 × ½ × 3 × 6 = 18 in²

Thus;

A_trap:A_tria = 54 in²:18 in² = 54:18

The image showing the trapezoid is missing, so i have attached it.

Answer:

C 54:18

Step-by-step explanation:

Formula for area of trapezoid is;

A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6

A_trap = ½(12 + 6) × 6

A_trap = 54 in²

Combined area of triangle:

A_tria = 2 × ½ × 3 × 6 = 18 in²

Thus;

A_trap:A_tria = 54 in²:18 in² = 54:18

Answer:

Step-by-step explanation:

Given that:

The focal point = 18 inches

= (18 × 0.0254)m

= 0.4572 m

= 45.7 cm

For such a comfortable distance of 45.7 cm, the perfect lens power for grandfather can be determined.

Let's recall that, the accommodation amplitude usually decreases with age and eventually becomes 1 D after the age of 50.

Thus, +2.5D  or a convex lens appears to be a perfect one.

b. We will agree that Diopter illustrates the optical power or most at times the capability of the lens.

So, 3D is equally 1.75X magnification which is likely to be double the zoom as it will be helpful to the grandfather.

Now, for a 2.5D, approximately 1.5X zooming once(200%) will be perfect and equal to viewing with the reading glasses.

Answer:

A

Algebra For what values of the variables must ABCD be a parallelogram?

B

23. A 2y + 2 B 24. B

(3x + 10)

(8x + 5)º

3x + 6

54°

D

С

D

A

Зу - 9 с

ly+4

Answer:

One of the Numbers is -151 and the other is -144

Step-by-step explanation:

Set up the equations then solve

Answer:

47

Step-by-step explanation:

substitute the value of 5 in for c and 7 in for d;

(5) + 6(7)

5 + 42

47

Answer:

21

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

1 foot = 12 inches

length of board in inches = 8 ft × (12 in)/ft = 96 in

length of cut in inches = 5 ft + 8 in = 5 ft × (12 in)/ft + 8 in = 60 in + 8 in =  68 in.

96 - 68 = 28 inches left

Answer:

no se zorry ..............?..?

Answer:

A unique triangle will be produced if you are given: all three sides (Side-Side-Side) two sides and the included angle (Side-Angle-Side) two angles and the included side (Angle-Side-Angle)

Step-by-step explanation:

hope this helps! :D

Answer:

The similarity is they are using tools to help them make the lines, but the differences are they are using different tools to make different lines. While 1 of the tools is similar to the other

Step-by-step explanation:

Step-by-step explanation:

It's must be -3 ...............

Answer:

D) 4.9 units, 14.2 units

Step-by-step explanation:

I assume that we will be using trigonmetry as this is a right triangle

The two ratios that will be used are CAH (Cosine = adjacent/hypotneuse)

and SOH (Sine = opposite/hypotneuse)

While it does not matter which acute angle the problem is to, I decided to set up the triangle like so in the picture attached

This means x = adjacent and y = opposite here

Now we just need to plug in the numbers to find the missing variables

x) cos(19) = x/15

(15)cos(19) = x/15(15)

~14.2 = x

y) sin(19) = y/15

(15)sin(19) = y/15(15)

~4.9 = y

Hope that helps a bit

I took waaay too long to explain this lol

The value of x for the triangle is 14.2 and the value of y is 4.9. The correct option is D.

Trigonometry is the branch of mathematics that establishes a relationship between the sides and angles of a right-angle triangle.

The mathematical trigonometric functions, sometimes referred to as circle, angle, or goniometric functions, relate the angle of a right-angled triangle to the ratios of its two side lengths.

Calculate the value of x as below,

xcos(19) = x/15

(15)cos(19) = x/15(15)

14.2 = x

The value of y is calculated as,

ysin(19) = y/15

(15)sin(19) = y/15(15)

4.9 = y

To know more about trigonometry follow

https://brainly.com/question/20726216

#SPJ7

Answer:

x = 9

Step-by-step explanation:

6x = 4x + 18

6x - 4x = 18

2x = 18

x = 9

Answer:

-9

Step-by-step explanation:

3x−5x+8x=4x+18

Step 1: Simplify both sides of the equation.

3x−5x+8x=4x+18

3x+−5x+8x=4x+18

(3x+−5x+8x)=4x+18(Combine Like Terms)

6x=4x+18

6x=4x+18

Step 2: Subtract 4x from both sides.

6x−4x=4x+18−4x

2x=18

Step 3: Divide both sides by 2.

2x

2

=

18

2

Answer:

X = 4/3 Exactly one solution

Step-by-step explanation:

x-3 = 4x-7

x = 4x-4

-3x = -4

x = 4/3

Answer:

Fourth option: y = 2/5x - 3

Step-by-step explanation:

it is perpendicular :)

Answer:

Your answer y=-5/2x + 6

Mark it as brainlist answer. As soon as possible.

Ce clasă ești sa văd daca te pot ajuta

Answer:

C,D,F

Step-by-step explanation:

Answer:

8 hours and 175 minutes.

Step-by-step explanation:

So first add all the hours together: 2 + 2 + 1 + 2 + 1 = 8 Hours.

Then add all the minutes together: 17 + 48 + 53 + 19 + 38 = 175 Minutes.

Therefore, the team's score is 8 hours and 175 minutes.

I hope this helped!

Answer: 11hours 55minutes

Answer:

C. F(0)

Step-by-step explanation:

Add 5 to both sides. 5(x)=4(x)

5(0)=4(0) because 5 x 0 = 0 and 4 x 0 = 0.

Answer: 3 1/30

Step-by-step explanation:

Hi, IReady sucks. So I am gonna help you. I got 3 1/30 when you add them together. I would also recommend using a Fraction Calculator online. ;) it helps a lot!

Answer:

Part a: $0.40 per lemon,  Part b: $3.60

Step-by-step explanation:

Because the cost of five lemons is $2, it would be: 5 lemon = $2

$2/5 lemons = $x/1 lemon

so divide by 5 on the numerator and denominator. 2 divided by 5 = 0.4

So part a: 40 cents or $0.40 per lemon!

Part B:

cost of 1 lemon compared to 9 lemons:

$0.40/1 = x/9

Multiply both numerator and denominator by 9

So, it costs $3.60 for 9 lemons.

Answer:

Let's say that x is sam's age and y is Amy's age

x=y-4

and five years ago:

x-5=(y-5)/2

y-4-5=(y-5)/2

2y-18=y-5

y=13

x=9

then:

sam's age is 9 and Amy's age is 13

Answer:

Sam: 9, Amy: 13

Step-by-step explanation:

So five years ago, lets say Sam was 4, and Amy was 8. That would be half Amy's age. If we add on 5 to Sams age, as it says, Amy would then be 13, and Sam would be 9. This is also four years apart. Thus, the answers are Sam: 9 and Amy: 13

Answer:

136 people

Step-by-step explanation:

$462.40 divided by 3.40 is 136

Answer:

8125t^2-11250t^2+5625 greater than or equal to > 100

Step-by-step explanation:

PLATO

Answer:

150.80

Step-by-step explanation:

Answer:520.8

Step-by-step explanation:

Answer:

58.24

Step-by-step explanation:

9.1 x 6.4 = 58.2!!

bh = a

hope I helped

Answer:

58.24 :)

A=bh=9.1·6.4=58.24