t is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $310 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?

Answer:

The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:

x f(x) g(x)

-2 1/108 12

-1 1/18 2

0 1/3 1/3

1 2 1/18

2 12 1/108

To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).

Answer:

Its A.

Step-by-step explanation:

Other one was not clear enough lol ^

As Brian and his wife earned $550,000 in wages during 2020. The amount he pays in income taxes would be $167,700.

An income tax is a type of tax levied by governments on the earnings of businesses and individuals within their jurisdiction.

The amount of income tax that Brian and his wife paid in 2020 depends on several factors, such as their filing status, deductions, credits, and the tax rates that apply to their income.

Assuming that Brian and his wife filed jointly and did not have any significant deductions or credits, we can use the following tax brackets and rates for the 2020 tax year: 35% on taxable income between $414,701 and $622,050.

. Assuming that they did not have any significant deductions or credits, their taxable income would be $550,000 (their wages) minus the standard deduction for joint filers, which was $24,800 in 2020.

The income taxes will be calculated as:

= (35% * $550,000) - $24,800

= $192,500 - $24,800

= $167,700

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15 is area of Side of Square .

What is a square, exactly?

All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.

Length of diagonal of Square =15√2 cm-------------(1)

Let side of Square = a cm

So, Length of Diagonal

By Using Pythagorean Theorem

       = √a² + a²

        =  a√2        ........................(2)

  Equating (1) and (2)

    a√2   =  15√2

      a = 15

 cancelling root 2 from both sides.

     a = 15

Side of Square= 15 cm

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The complete question is -

Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.

P(X ≤ 2) = 0.636, P(X ≥ 4) = 1 - 0.990 = 0.010

Use the cumulative distribution function for the binomial distribution, 2 or fewer defective products:

P(X ≤ 2) = Σ P(X = k) for k = 0, 1, 2

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20

P(X ≤ 2) = 0.636

To find the probability of finding 4 or more defective products in this batch, we can use the complement rule:

P(X ≥ 4) = 1 - P(X ≤ 3)

Using the cumulative distribution function as before, we can calculate:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X ≤ 3) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20 + (22!/(3!19!))(0.039)^3(0.961)^19

P(X ≤ 3) = 0.990

Therefore, P(X ≥ 4) = 1 - 0.990 = 0.010

If the company finds 5 defective products in this batch, they should consider stopping production, as this is much higher than the expected rate of 3.9%.

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The recursively defined function has a first term equal to 10 and a common difference of 4 is f(n) = 6 + 4n.

When a recursive procedure gets repeated, it's called recursion. A recursive is a type of function or expression stating some conception or property of one or further variables, which is specified by a procedure that yields values or cases of that function by constantly applying a given relation or routine operation to known values of the function.

We have first term = a = 10

And the common difference of d = 4

We have the formula for the t terms of a as 10 and d as 4

f(n) = a + (n - 1)d

f(n) = 10 + (n-1) x 4

f(n) = 10 + 4n - 4

f(n) = 6 + 4n

So, the defined function is f(n) = 6 + 4n.

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The livable square footage of the house is 1,850 square feet.

To determine the livable square footage of the house, we need to exclude areas that are not considered living spaces. The main level of the house has 1,200 square feet and is considered livable space.

The top level has 650 square feet, but since it is not clear if the entire space is livable or if there are non-livable areas (such as an attic), we cannot assume that the entire space is livable.

Therefore, we will exclude the top level from our calculation of livable square footage. The garage is also not considered livable space, so we will exclude the 335 square feet of the garage as well.

Thus, the livable square footage of the house is 1,200 square feet (main level) + 0 square feet (top level) + 0 square feet (garage) = 1,200 square feet. Therefore, the total livable square footage of the house is 1,850 square feet.

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The length of the altitude drawn to the hypothenuse, WY as required to be determined is; 6.

As evident from the task content, it follows that the length of the altitude, WY drawn to the hypothenuse is to be determined.

Let WY be represented as a;

By observation; it follows that the triangles WXY and WXY are similar triangles.

Hence, the ratio which holds in the figure is;

12 / a = a / 3

Therefore by cross-multiplication, we have that;

a² = 36

a = 6.

Ultimately, the length of the altitude drawn to the hypothenuse is; 6.

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The population of foxes in the region in 2020 is predicted to be 40,174.

The population of foxes in the region in 2020 can be calculated using the formula [tex]P = P0 (1+r)^n[/tex], where P is the population at the end of n years, P0 is the initial population, and r is the annual growth rate. The fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area.In this case, P0 = 23900 and r = 0.09. Since the starting year is 2012, the number of years since then is n = 8. Plugging these values into the formula, P = 23900 (1.09)^8 = 40,174. Therefore, the population of foxes in the region in 2020 is predicted to be 40,174.

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The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.

The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:

[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]

This is the total number of possible outcomes.

To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:

[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]

So the probability of getting 0 toppings is:

[tex]$$P(\text{0 toppings}) =[/tex]  [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]

However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.

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A multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor A and three levels for factor B can be written as:

Y = b0 + b1A + b2B + b3AB + e

where Y is the dependent variable, A is the independent variable for factor A, B is the independent variable for factor B, A*B is the interaction between A and B, and e is the error term.

The variables can be defined as follows:

Y: The dependent variable that is being measured in the study.

A: The independent variable representing factor A, which has two levels (A1 and A2).

B: The independent variable representing factor B, which has three levels (B1, B2, and B3).

A*B: The interaction term between factor A and factor B.

e: The error term that captures the variability in the dependent variable that is not explained by the independent variables.

This equation allows us to examine the main effects of both factors (A and B) as well as their interaction (A*B) on the dependent variable Y in a two-factorial design.

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Answer: D

Step-by-step explanation: It is going up in a strait trend line, making it where it has no relation ship unless very closely  examined.

Answer: $840

Step-by-step explanation:

The formula for calculating simple interest is:

I = P * r * t

where:

I is the interest earned

P is the principal (the initial deposit)

r is the interest rate (as a decimal)

t is the time (in years)

Using this formula, we can find the interest earned on Ms. Leon's account over 4 years:

I = 750 * 0.03 * 4

I = 90

So Ms. Leon will earn $90 in interest over 4 years. To find the total amount in her account at the end of 4 years, we need to add the interest earned to the initial deposit:

Total amount = Initial deposit + Interest earned

Total amount = 750 + 90

Total amount = $840

Therefore, Ms. Leon will have a total of $840 in her savings account at the end of 4 years.

Answer:

Step-by-step explanation:

1) Cut the picture up into two rectangles

The larger rectangle has a length (15in+2in) of 17 and a width of 13. The smaller rectangle has a length of 2 and a width of 5.

2) Find the area of both rectangles

Rectangle 1: 17 x 13 = 221

Rectangle 2: 5 x 2 = 10

3) Add the area of both rectangles

221 + 10 =231

4) The answer is 231 inches squared

The only number between 18 and 30 that is a multiple of 5 and satisfies this condition is 20, Therefore, the mystery number is 20

The GCF of 18, 36, and the mystery number is 2.

This means that the mystery number is divisible by 2.

The mystery number is also a multiple of 5, so it must end in either 0 or 5.

The mystery number is greater than 18 and less than 30, so it can only be 20 or 25.

Let's check if the GCF of 18, 36, and 20 is 2.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

The only factor that 18, 36, and 20 have in common is 2, so the mystery number is 20.

Therefore, the mystery number is 20.

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Kendra cost $0.60 for each egg and $0.30 for each piece of toast.

Let's assume that the cost of one egg is x and the cost of one piece of toast is y.

From the given information, we can set up two equations:

2x + y = 1.5

x + y = 0.9

We can solve this system of equations by either substitution or elimination method.

Using the elimination method, we can multiply the second equation by -2 to eliminate y:

-2x - 2y = -1.8

2x + y = 1.5

Adding these two equations, we get:

-1y = -0.3

y = 0.3

Substituting y = 0.3 in either of the two equations, we get:

x = 0.6

Therefore, Kendra charges $0.60 for each egg and $0.30 for each piece of toast.

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a) Michael's z-score is 1.83.

b) Josh's z-score is 2.

A z-score (also known as a standard score) is a statistical measurement that represents the number of standard deviations a data point is from the mean of the population. It's a way to standardize scores from different populations or datasets, allowing for easier comparisons.

To find the z-score, we use the formula

z = (x - μ) / σ

where

x = the individual score

μ = the mean of the population

σ = the standard deviation of the population

For Michael's score

x = 83

μ = 72

σ = 6

z = (83 - 72) / 6 = 1.83

Therefore, Michael's z-score is 1.83.

For Josh's score

x = 61

μ = 55

σ = 3

z = (61 - 55) / 3 = 2

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The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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Using the division,

a) 363 ÷ 14 = 25 13/14

b) 636 ÷ 21 = 30 2/7

c) 908 ÷ 52 = 17 11/13

a) 363 ÷ 14, we first divide 363 by 14 to get a quotient of 25 with a remainder of 13. We then use the que board with 14 beads to represent this division. We start with the first digit of the dividend, which is 3. We count out 2 sets of 14 beads, which we move to the top of the board. We then move 1 more bead to the top, representing the remaining 13. The final result is 25 with a remainder of 13/14.

b) 636 ÷ 21, we divide 636 by 21 to get a quotient of 30 with a remainder of 6. We then use the que board with 21 beads to represent this division. We start with the first digit of the dividend, which is 6. We count out 3 sets of 21 beads, which we move to the top of the board. We then move 3 more beads to the top, representing the remaining 6. The final result is 30 with a remainder of 6/21, which can be simplified to 2/7.

c) 908 ÷ 52, we divide 908 by 52 to get a quotient of 17 with a remainder of 44. We then use the que board with 52 beads to represent this division. We start with the first digit of the dividend, which is 9. We count out 17 sets of 52 beads, which we move to the top of the board. We then move 44 more beads to the top, representing the remaining part of the dividend. The final result is 17 with a remainder of 44/52, which can be simplified to 11/13.

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Answer:

y = -3x + 3

Step-by-step explanation:

Knowing that;

Slope Intercept form : y = mx + b

To Find the Slope:

Used any given ordered pair given and use- m =  [tex]\frac{y_2-y_1}{x_2- x_1}[/tex]

Given Table:

X                  Y

1                   0

2                  -3

3                  -6

4                  -9

Solve:

I will use the ordered pair:

(1,0)

(2, -3)

1 and 2 are "x"

0 and -3 are "y"

m [tex]=\frac{-3-0}{2- 1}[/tex]

m [tex]=\frac{-3}{1}[/tex]

m [tex]=[/tex] -3

Now putting the value of m in equation

y = -3x + b

To find the y intercept (b) in the slope intercept formula:

Choose any ordered pair and substitute it in the slope intercept.

Let's choose the first point, (1,0) for calculating y-intercept.

Now plug it in the slope intercept formula:

y = mx + b

y = -3x + 3

Hence, the slope intercept form for that table is:

y = -3x + 3.

RevyBreeze

The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.

This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.

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Each piece is 24 inches long. One yard is equal to 36 inches, so two yards are equal to 72 inches.

To solve this problem, we need to convert the length of the board from yards to inches and then divide it into 3 equal parts.

First, we convert 2 yards to inches by multiplying by 36 (since there are 36 inches in a yard):

2 yards × 36 inches/yard = 72 inches

So, the board is 72 inches long.

Next, we divide 72 inches by 3 to find the length of each piece:

72 inches / 3 = 24 inches

Therefore, each piece is 24 inches long. In summary, to find the length of each piece of a board that is 2 yards long and cut into 3 equal pieces, we convert 2 yards to inches by multiplying by 36 and then divide by 3 to get each piece's length, which is 24 inches.

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The ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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When on a stem and leaf plot and it does not show a number on the right side and only on the right side, the number on the right side would be zero.

A stem and leaf plot is a method of organizing numerical data into groups. It is a visual representation of a dataset in which each value is separated into a stem and a leaf. A stem is the left-hand digit(s) of the value, while a leaf is the right-hand digit(s).

The stem and leaf plot contains two columns, one for the stem and the other for the leaf. The stem values are arranged vertically in the left-hand column, and the leaf values are arranged horizontally in the right-hand column. The leaf column should be read from left to right to extract the values.

When a value appears multiple times, its leaves are stacked on top of one another. The stem and leaf plot is an effective method for representing data, particularly when dealing with large datasets.

Hence, If a stem and leaf plot displays a number only on the left side and not on the right side, then the number on the right side would be interpreted as zero.


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Answer:

We can use the trigonometric ratios of a 30-60-90 triangle to find the length of XY. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Since ∠X is 60°, we know that ∠Z is 30°, and we can set up the following equation:

XY / 4 = 2 / √3

To solve for XY, we can multiply both sides of the equation by 4√3:

XY = 4 * 2 / √3

Simplifying the right side, we get:

XY = 8 / √3

To rationalize the denominator, we can multiply the numerator and denominator by √3:

XY = (8 / √3) * (√3 / √3)

Simplifying, we get:

XY = 8√3 / 3

Therefore, the length of XY is 8√3 / 3, which is approximately 4.62 units.

Mobile ladder stands with a top step over 10 feet high and 20 inches or more in depth must be equipped with a safety cage or body belt and lanyard to provide protection against a fall.

The cage should be at least 30 inches tall and should be fully enclosed on all four sides. Additionally, the top step should be enclosed and provided with a grab bar. The ladder must be securely supported and stabilized. Non-skid materials should be applied to the steps and platform. Finally, the ladder must meet safety requirements outlined in the Occupational Safety and Health Administration's (OSHA) regulations.

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a. The exit pressure is 19.76 lbf/in².

b. The ratio of the inlet area to the exit area is 3.125.

C. The exit area ratio (0.32) is less than the critical area ratio (1.89), the nozzle is converging-diverging in cross section.

To solve this problem, we need to apply the conservation equations for mass, momentum, and energy along with the isentropic relations.

a. To determine the exit pressure, we can use the isentropic relation for pressure ratio across a nozzle:

[tex]P_2/P_1 = (T_2/T_1)^{\frac{\gamma}{\gamma -1}}[/tex]

where [tex]P_1[/tex] and [tex]T_1[/tex] are the inlet pressure and temperature,

[tex]P_2[/tex] and [tex]T_2[/tex] are the exit pressure and temperature, and

γ is the specific heat ratio of air.

Using Table A-22E, we find that γ = 1.4 for air at 800°R.

Substituting the given values and solving for P2, we get:

[tex]P_2[/tex] = [tex]P_1 \times (T_2/T_1)^\frac{\gamma}{\gamma -1}[/tex] = [tex]45 \times (1500/480)^{(1.4/0.4)}[/tex]= 19.76 lbf/in²

b. To determine the ratio of the exit area to the inlet area, we can use the continuity equation:

[tex]A_1V_1 = A_2V_2[/tex]

where [tex]A_1[/tex] and [tex]A_2[/tex] are the inlet and exit areas, and

[tex]V_1[/tex] and [tex]V_2[/tex] are the inlet and exit velocities.

Substituting the given values, we get:

[tex]A_2/A_1 = V_1/V_2[/tex] = 480/1500 = 0.32

The ratio of the exit area to the inlet area is 0.32, or equivalently, the ratio of the inlet area to the exit area is 1/0.32 = 3.125.

c. To determine whether the nozzle is diverging only, converging only, or converging-diverging in cross section, we can compare the exit area ratio to the critical area ratio.

The critical area is the minimum area that allows the flow to reach sonic conditions, and it depends on the pressure and temperature of the flow.

For a converging-diverging nozzle, the exit area ratio is less than the critical area ratio, which is given by:

A* / [tex]A_1[/tex] = [tex](2/(\gamma+1))^{(\gamma+1)}/(2(\gamma-1)/(\gamma+1))^{(\gamma+1)/(\gamma-1)}[/tex]

where A* is the critical area,

[tex]A_1[/tex] is the inlet area, and

γ is the specific heat ratio.

Using the given values and γ = 1.4, we find that:

A* / [tex]A_1[/tex] = 1.89

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Question:-

Air enters a nozzle operating at steady state at 45 lbf/in.2, 800°R, with a velocity of 480 f/s, and expands isentropically to an exit velocity of 1500 ft/s. Using data from Table A-22E as needed, determine

a. the exit pressure, in lbf/in². 19.76

b. the ratio of the exit area to the inlet area. 0.577

c. whether the nozzle is diverging only, converging only, or converging-diverging in cross section. conv-div

Answer:

n=12

Step-by-step explanation:

sum of interior angles of polygon with n sides = (n-2)180

measure of an interior angle of a polygon times the number of sides (n) = sum of interior angles of polygon with n sides, therefore:

(n - 2)180 = 150n

180n - 360 = 150n

30n = 360

n = 360/30 = 12

Answer:

Mr Park has enough money to pay his rent.

Step-by-step explanation:

The amount of the monthly rent paid  = $1000

The account balance after depositing the paycheck = $1441.33

Now, to pay the rent,account should have more than the rent money $1000

Also, $1441.33  >  $1000

⇒ The amount in the bank after depositing the paycheck   >  The rent to be paid

Hence, Mr Park has enough money to pay his rent.