Answer the questions about the following polynomial X +4

Answer:

-11 53/54

Step-by-step explanation:

3 x 18 = 54

1/54 - 12 = -11 53/54

To calculate Evan's AGI (Adjusted Gross Income) and taxable income if he files as a single taxpayer, we need to consider his income and deductible expenses.

Calculate Evan's total income:
  - Salary: $73,650
  - Part-time hourly pay: $700

  Total income = Salary + Part-time pay = $73,650 + $700 = $74,350

Deductible expenses:
  - Moving expenses: $1,200
  - Student loan interest: $2,890
  - Uniform cost: $1,490
  - Cash contribution: $1,345

  Total deductible expenses = $1,200 + $2,890 + $1,490 + $1,345 = $6,925

Calculate AGI:
  AGI = Total income - Total deductible expenses
  AGI = $74,350 - $6,925 = $67,425

Evan's taxable income is equal to his AGI since there were no other deductions mentioned in the question.

Therefore, Evan's AGI is $67,425, and his taxable income is also $67,425.

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Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

We have,

Income:

Salary: $73,650

Part-time work pay: $700

Total income: $73,650 + $700 = $74,350

Deductible Expenses:

Cost of moving possessions: $1,200

(This deduction applies if the move meets certain distance and time requirements. Since the move was 125 miles away, it meets the distance requirement.)

Interest paid on student loans: $2,890

Cost of purchasing a delivery uniform: $1,490

Cash contribution to State University deliveryman program: $1,345

Total deductible expenses:

$1,200 + $2,890 + $1,490 + $1,345

= $6,925

Now we can calculate Evan's AGI and taxable income:

AGI (Adjusted Gross Income)

= Total income - Deductible expenses

AGI = $74,350 - $6,925 = $67,425

Taxable Income = AGI - Standard Deduction

For a single filer in 2022, the standard deduction is $12,550.

Taxable Income = $67,425 - $12,550 = $54,875

Therefore,

Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

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The maximum volume of the box in terms of the height h is (30 - h/2)^2 x h, and the height that allows us to have the maximum volume is 40 inches

To answer your question, let's first understand that the volume of a box is given by the formula V = L x W x H, where L is the length, W is the width and H is the height. Since we are assuming the height is fixed, we can rewrite this formula as V = L x W x h.

Now, we know that the length plus width plus height of the box cannot exceed 60 inches. Therefore, we have the equation L + W + h = 60, which we can solve for L or W in terms of h. Let's solve for L: L = 60 - W - h.

Substituting this value of L into the formula for volume, we get V = (60 - W - h) x W x h. We can simplify this equation by expanding the brackets and collecting like terms to get V = -W^2h + 60Wh - h^2.

To find the maximum volume, we need to find the value of W that maximizes this equation. We can do this by differentiating the equation with respect to W and setting the derivative equal to zero. After some calculations, we get W = 30 - h/2.

Substituting this value of W back into the equation for volume, we get V = (30 - h/2)^2 x h. To find the height that gives us the maximum volume, we can differentiate this equation with respect to h and set the derivative equal to zero. After some calculations, we get h = 40 inches.

Therefore, the maximum volume of the box in terms of the height h is (30 - h/2)^2 x h, and the height that allows us to have the maximum volume is 40 inches.

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Answer:

0.4%

Step-by-step explanation:

If we are looking to have a number less than 3 rolled 4 out of 7 times.

Our winning numbers are 1 and 2. Our losing numbers are 3, 4, 5, and 6.

This means that our winning percentage is 33.3% and our losing percentage is 66.6%.

We need to multiply these numbers together taking our number of rolls into account.

.333 * .333 * .333 * .333 * .666 * .666  * .666 = 0.0036

Answer:

Mode of 3 median of 6, mean of 6, range of 8

Step-by-step explanation:

3, 3, 6, 7, 11

Perimeter of ΔABC is 12.41 units.

From the picture attached,

Since, cosθ = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\) and sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

For angle A,

Adjacent side = AC = 5 units

Opposite side = BC

and Hypotenuse = AB

By substituting the values in the cosine ratio,

cos(22°) = \(\frac{5}{AB}\)

AB = \(\frac{5}{\text{cos}(22^{\circ})}\)

      = 5.39

Since, sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

sin(22°) = \(\frac{BC}{5.39}\)

BC = 5.39[sin(22°)]

     = 2.02

Since perimeter of the given triangle ABC = AB + BC + AC

By substituting the measures of all sides in the expression of the perimeter,

Perimeter = 5.39 + 2.02 + 5

                 = 12.41 units.

         Therefore, perimeter of the given triangle is 12.41 units.

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Applying the two-tangents theorem, the value of x is: 5.

The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.

Since point J is formed by the two tangents, KJ and MJ, therefore:

KJ = MJ

Substitute:

4x + 7 = 7x - 8, find x

Combine like terms:

4x - 7x = -7 - 8

-3x = -15

-3x/-3 = -15/-3

x = 5

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The required value of x in the expression 2√51x is 25.

Given that,
An expression 2√51x,
To determine the value of x when the expression is equivalent to  10√51.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
2√51x = 10√51
√51x = 5√51
√x = 5√51 / √51
√x = 5
squaring both sides
x = 25

Thus, the required value of x in the expression 2√51x is 25.

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If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

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Answer: there is no picture again. just take a good guess

Step-by-step explanation:

To determine the number of hex digits required to represent decimal numbers up to 1,999, we need to find the largest decimal number within that range and convert it to hexadecimal representation.

The largest decimal number within the range is 1,999. To convert it to hexadecimal, we divide it by 16 repeatedly until the quotient is 0, and then concatenate the remainders in reverse order.

1,999 divided by 16 gives a quotient of 124 and a remainder of 15 (F in hexadecimal representation).

124 divided by 16 gives a quotient of 7 and a remainder of 12 (C in hexadecimal representation).

7 divided by 16 gives a quotient of 0 and a remainder of 7 (7 in hexadecimal representation).

Thus, 1,999 in hexadecimal representation is 7CF. It requires three hex digits (7, C, F) to represent 1,999.

To calculate the number of bits required, we need to know the number of bits in one hex digit. Since each hex digit represents 4 bits, three hex digits would represent 3 * 4 = 12 bits.

Therefore, to represent decimal numbers up to 1,999, three hex digits are required, and it would take 12 bits.

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Answer:

C. 3x + 5  = 2x -6

Step-by-step explanation:

Answer:

45 and 14 are the correct answer

Answer:

Step-by-step explanation:

Replace 8 for x.

3(8)=  24

Answer:

f(8) = 24

Step-by-step explanation:

To evaluate f(8) , substitute x = 8 into f(x) , that is

f(8) = 3(8) = 24

Answer:

Log7(1/49)=x  The first one

Step-by-step explanation:

I can't really explain how but hopeful this help

The sample size needed to estimate the average weight of all second-grade boys is 35.

To determine the sample size needed to estimate the average weight of all second-grade boys with a 95% confidence level and within 1 pound margin of error, we can use the following formula:

\($n = \frac{z^2 \sigma^2}{E^2}$\)

n = sample size

z = z-score for the desired confidence level (1.96 for 95% confidence level)

\($\sigma\) = population standard deviation

E = margin of error

Substituting the given values, we get:

\($n = \frac{(1.96)^2 \times (3)^2}{(1)^2}\)

  `= 34.57

Rounding up to the nearest integer, we get a required sample size of 35.

Therefore, a sample size of 35 second-grade boys is needed to estimate the average weight of all second-grade boys with a 95% confidence level and within 1 pound margin of error, assuming we know that the standard deviation of such weights is 3 pounds.

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Since Sophie can grade 11 papers per hour

Since she worked for 5 hours, then

Multiply 11 by 5 to find the number of the graded papers

Since the total number of papers is 86, then to find the number of the remaining papers subtract 55 from 86

There were 31 paper Sophie has to grade after working 5 hours

P-4 = -9 + p

Because there is the same quantity of the letter p on each side of the equal sign there is no solution to this problem.

Answer: no solution

The probability that a randomly selected LMU student would have a height greater than 68 inches is 0.0668 or 6.68%.

To determine the probability that a randomly selected LMU student would have a height greater than 68 inches, you can use the standard normal distribution.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To convert the given normal distribution with mean 65 inches and standard deviation 2 inches to the standard normal distribution, you can use the formula: z = (x - μ) / σ
where z is the z-score, x is the value you want to convert, μ is the mean, and σ is the standard deviation.Using this formula, you can find the z-score corresponding to a height of 68 inches as follows: z = (68 - 65) / 2 = 1.5. The probability of a randomly selected student having a height greater than 68 inches can be found by looking up the area to the right of the z-score of 1.5 in the standard normal distribution table. The table gives the area to the left of the z-score, so to find the area to the right of the z-score, you can subtract the area to the left from 1: P(z > 1.5) = 1 - P(z < 1.5)
Using the standard normal distribution table, you can find that the area to the left of the z-score of 1.5 is 0.9332. Therefore, the area to the right of the z-score is 1 - 0.9332 = 0.0668 or 6.68%.

Thus, the probability that a randomly selected LMU student would have a height greater than 68 inches is 0.0668 or 6.68%.

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Answer:

4x+2

Step-by-step explanation:

I'm not sure what they mean by defining a variable but this question could be modeled through the following equation

4x+2 where x (the variable) is a book

Answer:

It would take 15 years

Step-by-step explanation:

The length of time it takes to reach $1,000 savings can be determined from the future value formula given below:

FV=PV*(1+r/4)^n*4

FV is the target savings of $1,000

PV is the amount invested which is $600

r is the rate of interest of 3.4%

n is the unknown

1000=600*(1+3.4%/4)^4n

1000=600*(1+0.0085 )^4n

1000=600*(1.0085)^4n

1000/600=1.0085^4n

1.666666667 =1.0085^4n

take log of both sides

ln 1.666666667 =4n ln 1.0085

4n=ln 1.666666667/ln 1.0085

4n=0.510825624 /0.008464078

4n=60.35218768

n=60.35218768 /4

n= 15.09  

To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

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Answer:

Deductive Reasoning.

Step-by-step explanation:

Basically it’s logical thinking in simply terms.

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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Answer:

-14

Step-by-step explanation:

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations such as addition, subtraction, etc.

The expressions that give -9 are −12 − (−3),  −5 − 4, and 5 − 14.

Option (A), (C), and (F) are the correct answer.

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations such as addition, subtraction, etc.

We have,

A.

= −12 − (−3)

= -12 + 3

= -9

B.

= −10−1

= -11

C.

= −5 − 4

= -9

D.

= −1 − (−10)

= -1 + 10

= 9

E.

= 1 − (−8)

= 1 + 8

= 9

F.

= 5−14

= -9

We see that the expressions that give -9 are:

(A) −12 − (−3)

(C) −5 − 4

(F) 5−14

Thus,

The expressions that give -9 are:

Option (A), (C), and (F).

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The theoretical possibility of choosing a red earring is 1/10, 10%.

The experimental possibility of choosing a red earring is 8/25, 32%

The theoretical possibility of choosing a blue earring is 1/5, 20%.

The experimental possibility of choosing a blue earring is 7/15 or 28%.

Theoretical probability determines the chances that a random event would happen.

Theoretical probability = number of the earing in the box / total number of earrings

Red earrings = 2/20 = 1/10 = 10%

Blue earrings = 4/20 = 1/5 = 20%

Experimental probability is based on the result of an experiment that has been carried out multiples times

Experimental probability = number of times the earing was chosen / number of time the experiment was conducted

The experimental possibility of choosing a red earring= 16/50

=  8/25, 32%

The experimental possibility of choosing a blue earring = 14/50 = 7/25 = 28%

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Given:

The system of equations is

\(y=1.5x-3\)

\(y=1.5x+4\)

To find:

The true statement about the given system of equations.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

Where, m is the slope and b is the y-intercept.

We have,

\(y=1.5x-3\)

\(y=1.5x+4\)

On comparing these two lines with slope intercept form, we get

\(m_1=1.5,b_1=-3\)

\(m_2=1.5,b_2=4\)

Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.

Therefore, the correct option is A.

The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of each line,

LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,

Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3

Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.

Thus, the solution of the pair of lines has been shown above.

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Answer:

A. M= 20

B. r = 6

Step-by-step explanation:

M=kr³

where k is the constant

M= 160 , r 4

160= k(4)³

k = 160/4³= 2.5

A. when r= 2 , M= kr³

M= 2.5(2)³ = 20

B. when M= 540, find r

M= kr³

r³ = M/k

r³ = 540/2.5

r³= 216

r = 6

Answer:

First angle = 24'

Second angle = 156'

Third angle = 180'

Step-by-step explanation:

Given:

Ratio of circles angle = 2:13:15

Find:

All three angle

Computation:

Sum of all angle from center = 360'

So,

First angle = 360[2/(2+13+15)]

First angle = 360[2/(30)]

First angle = 24'

Second angle = 360[13/(2+13+15)]

Second angle = 360[13/(30)]

Second angle = 156'

Third angle = 360[15/(2+13+15)]

Third angle = 360[15/(30)]

Third angle = 180'