Mathematics College

Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.

Answers

Answer 1

Fwam and Eva are an equal distance of 69 miles away from the stadium when the time t = 3 hours

Given data ,

The formula for the distance (F) of Fwam from the stadium is:

F(t) = 327 - 42t

Since Fwam is travelling at a 42 mph pace, his distance from the stadium is reducing at a 42 mph rate.

The formula for Eva's separation from the stadium is:

E(t) = 396 - 65t

Eva's distance from the stadium also shrinks at a pace of 65 miles per hour as she drives at a speed of 65 mph.

Set F(t) = E(t) and solve for t to get the time at which Fwam and Eva are equally far from the stadium

On simplifying the equations , we get

327 - 42t = 396 - 65t

Adding 65t to both sides:

65t + 327 - 42t = 396

23t + 327 = 396

Subtracting 327 from both sides:

23t = 396 - 327

23t = 69

Dividing both sides by 23:

t = 69 / 23

t = 3 hours

Hence , at t = 3 hours after noon, both Fwam and Eva are an equal distance of 69 miles away from the stadium.

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The complete question is attached below :

Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.

Related Questions

Suppose x, y, z > 1 and integers, let :
p(x, y): x is a factor of y,
q(x, y, z): z = GCF(x, y), and
r(x): x is prime.
Check if the following argument is valid or not.
(∀x)(∃y)(p(x, y) ⇒ r(x)), (∀x)(∀y)(∀z)(¬q(x, y, z)), (∃x)(∀y)(p(x, y) ∨ r(x)).
Therefore, (∀y)(∃z)(∃x)q(x, y, z).

Answers

Yes, The argument is valid.

Now, We have;

(∀x) (∃y) (p(x, y) ⇒ r(x))

Means that for any integer x, there exists an integer y such that if x is a factor of y, then x is prime.

(∀x)(∀y)(∀z)(¬q(x, y, z)) means that for any integers x, y, and z, the greatest common factor of x and y is not z.

(∃x)(∀y)(p(x, y) ∨ r(x)) means that there exists an integer x such that for any integer y, either x is a factor of y or x is prime.

Therefore, (∀y)(∃z)(∃x)q(x, y, z) means that for any integer y, there exists integers z and x such that the greatest common factor of x and y is z.

To see why this conclusion follows, consider that if (∀y)(∃z)(∃x)q(x, y, z) were false, then there would be some integer y such that for all integers z and x, the greatest common factor of x and y is not z.

However, this would contradict (∀x)(∀y)(∀z)(¬q(x, y, z)), which states that for any integers x, y, and z, the greatest common factor of x and y is not z.

Therefore, the argument is valid.

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Determine whether the graph of the equation is symmetric with respect to the x axis, y axis and or the origin.
X^2 + Y -36 =0

Answers

The graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.

x² + y - 36 = 0

Symmetry with respect to the x-axis:

Replace y with -y: x² - y - 36 = 0

This equation is not equivalent to the original equation, so the graph is not symmetric with respect to the x-axis.

Symmetry with respect to the y-axis:

Replace x with -x: (-x)² + y - 36 = 0

Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.

Therefore, the graph is symmetric with respect to the y-axis.

Symmetry with respect to the origin:

Replace x with -x and y with -y: (-x)² + (-y) - 36 = 0

Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.

Therefore, the graph is symmetric with respect to the origin.

Hence, the graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.

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Please help !!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

It does not belong because like the other ones it is not side ways, as well as it's common sense.

Consider the quadratic function f (x) = 2x² - 16x + 24. Complete the square to rewrite the function in the form
f(x)= a(x-h)² + k.
f(x) =

Answers

The quadratic function f(x) = 2x² - 16x + 24 can be rewritten in the vertex form f(x) = 2(x - 4)² + 4.

What is the vertex form of the given function?

Given the function in the question:

f(x) = 2x² - 16x + 24

To determine the vertex form f(x) = a(x-h)² + k, we need to complete the square.

Factor out the leading coefficient of 2:

f(x) = 2x² - 16x + 24

f(x) = 2(x² - 8x + 12)

To complete the square, we need to add and subtract the square of half of the coefficient of x:

f(x) = 2[(x² - 8x + 16) - 4] + 8

Since (x² - 8x + 16) is a perfect square trinomial, we factored as (x - 4)².

f(x) = 2[(x - 4)² - 4] + 8

Now we can simplify and rewrite in the desired form:

f(x) = 2(x - 4)² - 4 + 8

f(x) = 2(x - 4)² + 4

Therefore, the vertex form is f(x) = 2(x - 4)² + 4.

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For the ordered stem-and-leaf plot given, find:
a. the minimum value
b. the maximum value
c. the number of data with values greater than 25.
d. the number of data with values of at least 40.
e. the percentage of the data with value less than 15.

Answers

From a stem-and-leaf plot,

1. The minimum value = 13

2. The maximum value = 62

3. The number of data with values greater than 25 = 16

4. The number of data with values of at least 40 = 4

5. The percentage of the data with value less than 15 = 6.25%

We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.

From the stem-and-leaf plot,

a) the minimum value is 13

b) the maximum value is 62

c) the number of data with values greater than 25:

26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62

So, the number of data with values greater than 25 = 16

d) the number of data with values of at least 40:

42, 43, 47, 62

So, the required number = 4

e) the percentage of the data with value less than 15:

the data with values less than 15 are: 13, 14

So, the number of the data with values less than 15 are: 2

The total number of data values = 32

So, the required percentage would be,

P = (2/32) × 100

P = 6.25%

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Factor cards is a one - player game using numbered cards. To begin with, all cards are in a central pile with their numbers visible. At each turn , exactly one card is moved from the central pile to the score pile and one or more cards are moved from central pile to the discard pile according to these rules.
Rule 1: A card may be moved to the score pile only if the number on the card has at least one of its factors, other than itself, still on the central pile.
Rule 2: When a card is moved to the score pile, all the cards that have factors of its number and are still in the central pile are moved to the discard pile.
Play stops when no card in the control pile has a factor other than itself in the central pile. The players score is the sum of all numbers on the cards in the score pile at the end of play.
In the following questions, the game starts with 20 cards numbered 1 to 20 and are therefore called 20-games.
A) Show steps that will produce a score of more than 100 points in a 20- game
B) What is the maximum score for a 20- game. Explain why it is the maximum
C) Explain why every 20- game ends with 8 or fewer cards in the score pile .

Answers

The match terminates as soon as the central heap runs out of cards whose factor are not present elsewhere, resulting in a score of 92 - falling short from 100.

How to explain the information

It should be noted that to acquire a higher point achievement, alternative approaches can be tested; however, reaching beyond the hundred mark is not guaranteed.

Conversely, with each 20-game, the final outcome should contain 8 or fewer pieces in the tally pile since there are strictly 17 cards eligible to be shifted into this collection. Subsequently, due to the 138 maximum points potential (stated in part B), and the entire set amounting for 210 points - the minimum count for items within the discard pool will be 3 (as calculated from 20 - 17).

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If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage e for a child of age a, pharmacists use the equation c = 0.0417D(a + 1).

Suppose the dosage for an adult is 150 mg.
(a) Find the slope of the graph of e. (Round your answer to two decimal places.)
P
What does it represent?

The slope represents the Select of the dosage for a child for each change of 1 year in age.
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
ma

Answers

a) The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.

b) The dose for newborn baby is: 6.225 mg

How to interpret the slope?

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

(a) Let a be an age of an child in years. Then:

c = 0.0417Da + 0.0417D

Where D is a constant

Since D = 150 mg, then we have:

The slope of the graph = 0.0417(150)

= 6.225 mg/year

The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.

(b) Newborn baby: a=0

Thus:

c(0) = 0 + 6.225

= 6.225 mg

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Question 1 (Multiple Choice Worth 6 points)
(02.08 MC)
The table of values forms a quadratic function f(x)
x f(x)
-5-28
-40
-3 20
-2 32
-1 36
0 32
1 20
What is the equation that represents f(x)?
Of(x)=x²-2x+8
Otx) = 4x² + 8x-32
Of(x)=x²+2x-8
Of(x)=-4x2²-8x+32

Answers

Answer:

The answer to this question is --> f(x) = -4x^2-8x+32

Hope this helps

please help for question 3

Answers

Reflecting the triangle Q over the line y = 1 would map it onto triangle T

Reflecting the triangle P

Reflection over line x = 1

This means that we draw a vertical line that passes through x = 1

And then we create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is attached

Reflection over line y = 2

This means that we draw a vertical line that passes through y = 2

As done in part (a), we then create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is also attached

Description of the transformation

Using the same transformation rule above;

A reflection over the line y = 1 would map the triangle Q onto triangle T

Answers

The function type of f(x) = √3x + 2 is A. square root

Classifying the function type of f(x)

From the question, we have the following parameters that can be used in our computation:

f(x) = √3x + 2

In the above function, we have the notation √

The notation √ is a square root notation

This means that the function type of f(x) is A. square root

Answers

The Probability of both balls being green is 0.36 or 36%

b) The Probability of neither ball being green is 0.16 or 16%

What is the Probability about?

Based on question A, To find the probability that both balls are green, we use the equation below:

P (both green) = P (first green) x P (second green)

= (6/10) x (6/10)

= 36/100

= 9/25

=0.36

b) To find the probability that neither ball is green, we use the formula below:

P (neither green) = P (first not green) x P (second not green)

= (4/10) x (4/10)

= 16/100

= 4/25

=0.16.

Therefore, the statement will be: The Probability of both balls being green: 0.36 and the probability of neither ball being green is 0.16

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(HURRY PLEASE!!) First, a graph of f(x) = -x + 3 is drawn. Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3. Which will be true of these three graphs? A. Their slopes will be the same as the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). B. Their slopes will be the same as the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x). C. Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). D. Their slopes will be different from the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x).

Answers

The true statement about the graphs:

Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).

The correct answer is an option (C)

First we draw a graph of function f(x) = -x + 3.

Find the graph in attached figure.

the x-intercept of f(x) is:

0 = -x + 3

i.e., x-intercept = (3, 0)

Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.

Let g(x) = -1(-x + 3)

The x-intercept of g(x) would be,

0 = -1(-x + 3)

i.e., x-intercept = (3, 0)

Let h(x) = -2(-x + 3)

The x-intercept of h(x) would be,

0 = -2(-x + 3)

2x = 6

i.e., x-intercept = (3, 0)

Let t(x) = -3(-x + 3)

The x-intercept of t(x) would be,

0 = -3(-x + 3)

3x = 9

i.e., x-intercept = (3, 0)

the graph of functions g(x), h(x) and t(x) is shown below.

We can observe that the x-intercept is same for all graphs but the slopes are different.

Therefore, the correct answer is an option (C)

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At a large university, 20% of students are enrolled in the nursing program. The dean of students selects a random sample of 20 students and records n the number of students enrolled in the nursing program. What is an appropriate assignment of digits to the outcomes for a simulation of this random process? = O Let 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6-9, and 0. ○ Let 0 and 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6, 7, 8, 9, and 0. O Let 1 = the student is enrolled in the nursing program. Let 2-9 = the student is not enrolled in the nursing program. Skip the digit 0. O Let 1 and 2 = the student is enrolled in the nursing program. Let 3-9 = the student is not enrolled in the nursing program. Skip the digit 0.

Answers

An appropriate assignment of digits to the outcomes for a simulation of this random process would be:

Option 1: Let 0 and 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6, 7, 8, 9, and 0.

This option assigns two digits, 0 and 1, to represent the two possible outcomes: a student is either enrolled in the nursing program (outcome 1) or not enrolled (outcome 2-5). The digits 2-5 represent the non-nursing program outcomes, and the digits 6-9 and 0 are skipped.

Option 1 is appropriate because it assigns a unique digit to each possible outcome, and the skipped digits are not relevant to the simulation. Additionally, the proportion of digits assigned to each outcome (2 out of 10) corresponds to the proportion of students in the nursing program (20%).

The two tables show the number of copies of album x y and z sold in outlets A , B C and D of w company.
Which outlet sold the greatest amount of copies of album x in July and august

Answers

To find the outlet that sold the greatest amount of copies of album X in July and August, we need to add the number of copies sold in each outlet for those two months.

Outlet A: 80 + 90 = 170
Outlet B: 60 + 70 = 130
Outlet C: 70 + 80 = 150
Outlet D: 90 + 80 = 170

Outlets A and D both sold the greatest amount of copies of album X in July and August, with 170 copies sold each. Therefore, the answer is either A or D.

Sarah's bird feeder holds 1/2 of a cup of birdseed. Sarah is filling the bird feeder with a scoop that holds 1/4 of a cup. How many scoops of birdseed will Sarah put into the feeder?

Answers

The number of scoops of birdseed Sarah puts in the feeder n = 2

Given data ,

Let the number of scoops of birdseed Sarah puts in the feeder be n

While utilizing a scoop that can contain 1/4 cup of birdseed, Sarah's bird feeder holds 1/2 cup of birdseed. We must divide the capacity of the bird feeder by the capacity of the scoop to determine how many scoops Sarah will add to the feeder.

On simplifying the equation , we get

1/2 ÷ 1/4 = n

n = 1/2 x 4/1

n = 4/2

n = 2 scoops

Hence , the equation is solved and n = 2

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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A or the total amount due at time t
P= 5000
r=4.5%
t = 6 months

Answers

The future value or the total amount due at time t for the loan is $5112.50.

To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;

A=P + (P × r × t)

where; A = future value or total amount due at time t

P = principal amount

r = simple interest rate

t = time period (in years)

Given the values; P = $5000

r = 4.5% (or 0.045 as a decimal)

t = 6 months (or 0.5 years)

We can substitute these values into the formula and calculate the future value;

A = 5000 + (5000 × 0.045 × 0.5)

A = 5000 + 112.5

A = $5112.50

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Give me the domain and range
Tell me if the graph is a function or not

Answers

The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function

Calculating the domain and range of the graph

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the x values to be

x = -2 to 5

On the graph, we have the y values to be

y = -6 to 2

This means that domain = [-2, 5] and range is [-6, 2]

If the graph is a function or not

The graph is the graph of a circle

A circle does not represent a function

Hence, the graph is not a function

Answers

The point on the number line that is 7/9 of the way from -3.6 to 10 is approximately 6.97777777778.

To find the point on the number line that is 7/9 of the way from -3.6 to 10, we can use the following formula:

Point = Starting point + (Fraction of distance) x (Total distance)

In this case, the starting point is -3.6, the total distance is the distance from -3.6 to 10 (which is 10 - (-3.6) = 13.6), and the fraction of distance is 7/9.

Plugging in these values, we get:

Point = -3.6 + (7/9) x (13.6)

Simplifying,

Point = -3.6 + (7/9) x (13.6)

Point = -3.6 + 9.9556

Point = 6.97777777778

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Four cars are for sale. The red car costs $15,000, the blue car costs $18,000, the green car costs $22,000, and the white car costs $20,000. Use the table to identify all possible samples of size n = 2 from this population and their sample minimums. The first sample is done for you.

Sample
n = 2 R, B R, G R, W B, G B, W G, W
Costs
($1000s) 15, 18 15, 22 15, 20 18, 22 18, 20 22, 20
Sample
Mean 15 15 15 18 18 20

What is the mean of all six sample minimums?

What is the value of the population minimum?

Is the sample minimum an unbiased estimator of the population minimum?

Answers

Answer:

Step-by-step explanation:The six sample minimums are 15, 15, 15, 18, 18, and 20.

To find the mean of all six sample minimums, we add them up and divide by 6:

(15 + 15 + 15 + 18 + 18 + 20) / 6 = 16.1667

So the mean of all six sample minimums is $16,166.67.

The population minimum is the smallest cost among the four cars, which is $15,000.

The sample minimum is a biased estimator of the population minimum. Since the samples are of size 2, the probability of obtaining the population minimum as the sample minimum is only 1/3 (when the minimum of the two cars selected is the population minimum). Therefore, the sample minimum tends to underestimate the population minimum.

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1252 with a standard deviation of 39 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.
(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between
and
A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between
and
A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between
and
A.D.

Answers

a) The range of years centered about the mean in which about 68% of the data in between 1291 or 1213.

b) The range of years centered about the mean in which about 95% of the data in between 1330 or 1174.

c) The range of years centered about the mean in which about 95% of the data in between 1369 or 1135.

We have,

Mean= 1252

Standard deviation= 39

a) The range of years centered about the mean in which about 68% of the data

= 1252 ±39

= 1252 + 39 or 1252 -39

= 1291 or 1213

b) The range of years centered about the mean in which about 95% of the data

= 1252 ± 2(39)

= 1252 + 78 or 1252- 78

= 1330 or 1174

c) The range of years centered about the mean in which about 95% of the data

= 1252 ± 3(39)

= 1252 + 117 or 1252- 117

= 1369 or 1135

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I need help! pls and thank u!

Answers

Evaluating the given function, we can see that the intensity at 35 cm is 0.816

How to find the intensity at 35 cm from the source?

The intensity at a distance d in centimeters is given by the function:

I = 100*d⁻²

Here we want to find the intensity at 35 centimeters from the source, then we need to evaluate the function above at d = 35, doing that we will get:

I = 100*35⁻²

I = 100/(35²)

I = 0.816

The intensity at 35 centimeters from the source is 0.816.

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solvesolveslvesolbesolve

Answers

The maximum value of z = 28. I occurs at (x, y) = 4

How to go about this ?

To solve thhis linear programming problem, we can use the graphical method..

Graph the feasible region defined by the constraints.....

x >= 0 and y >= 0 represent the non-negative quadrants.

x + y < = 8 represents the area below the line passing through ( 8, 0) and (0, 8).

x + y >= 2 represents the area above the line passing through ( 2 , 0) and (0 , 2).

Identify the corner points of the feasible region .....

(0, 2)

( 2, 0)

( 4, 4)

( 8, 0 )

Calculate tthe objective function at each corner point....

z(0, 2 ) = 3(0) + 4(2) = 8

z (2, 0 ) = 3(2) + 4(0) = 6

z(4, 4 ) = 3(4) + 4(4) = 28

z ( 8, 0) = 3(8) + 4(0) = 24

Determine the maximum value of the objective function and the values of x and y that give this maximum value

The maximum value of z is 28, which occurs at the corner point (4, 4).

So we c can be stated as follows --

Maximum value of z = 28

x = 4

y = 4

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Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college
with no student loan debt. This is her only job, and she makes a salary that allows her to
bring home $3,300 a month. She's not married and has no children or anyone else who
is supported by her income. Over the past year, she has given a total of $3,960 to charity.
Her address is 1234 Main St., New York, NY 12345, and her Social Security number is
123-45-6789.

Answers

Note that the above prompt requires you to under stand what a W-4 form is and how to complete one.

What is the process for comleting the W-4 form?

Rbecca needs to s tart by entering your personal information in boxes 1-4, including your name, address, Social Security number, and filing status. In this case, Rebecca Kate Foster's information is:

Box 1: Rebecca Kate Foster

Box 2: 1234 Main St.

Box 3: New York, NY 12345

Box 4: 123-45-6789

Box 5: Single

In box 6, write "1" since Rebecca only has one job.

Rebecca can claim the standard deduction or itemize deductions in box 7. She may benefit from itemizing deductions because she has donated $3,960 to charity in the last year.

Rebecca can claim whatever excess tax withholding she wants each paycheck in box 8. She may not need to withhold any further taxes because she has no dependents and is not married. If she prefers, she can leave this section blank.

Rebecca can claim any extra withholding for the year in box 9. If she anticipates to owing taxes at the end of the year, she may want to withhold more from each paycheck to prevent a hefty tax payment later. If she anticipates a reimbursement, she should withhold less. She can use the IRS's withholding calculator to determine the right amount.

Finally, sign and date the form in box 5 before submitting it to your company.

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DIRECTIONS Read the scenario below and fill out the W-4 form using the information provided. Then, read the W-2 form and answer the questions that follow. W-4 Form Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college with no student loan debt. This is her only job, and she makes a salary that allows her to bring home $3,300 a month. She’s not married and has no children or anyone else who is supported by her income. Over the past year, she has given a total of $3,960 to charity. Her address is 1234 Main St., New York, NY 12345, and her Social Security number is 123-45-6789.

A committee of four people is formed by selecting members from a list of 12 people.
How many different committees can be formed?

__ committees

Answers

The number of different committees that can be formed is 495

How many different committees can be formed?

From the question, we have the following parameters that can be used in our computation:

People = 12

Committee = 4

These can be represented as

n = 12 and r = 4

The number of different committees that can be formed is

Number = nCr

So, we have

Number = 12C4

Evaluate

Number = 495

Hence, the committee are 495

Answers

The three things that a personality test can tell you are:

A. How you prefer to interact with others.

C. What you might enjoy in a career.

D. How you recharge your energy.

What is personality test?

A personality test is a tool used to assess and measure an individual's traits, characteristics, and patterns of behavior.

It may be a series of questions or statements that the individual must respond to.

The results are used to determine the person's strengths and weaknesses, their communication and social interaction (like if they are extrovert or introvert), how they process information and decision-making, etc.

They can also tell of an individual's preferred methods of finding balance in their lives, like spending time alone or with friends and families, being in nature, etc.

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in a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win.

Answers

The calculated value of the probability of winning is 3.06501854e-7

Calculating the probability of winning

From the question, we have the following parameters that can be used in our computation:

Select 6 numbers out of 39 to win

This means that when a number is selected, the number is returned and the total numbers reduces by 1

i.e. P(Current) = n/(39 - n)

Using the above as a guide, we have the following:

P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34

Evaluate the product of tthe expressions

So, we have

P(Win) = 3.06501854e-7

Hence, the probability of winning is 3.06501854e-7

Answers

The greatest of the given integers is 64.

Given that, the sum of four consecutive integers is 250. We need to find what is the greatest of these integers.

Let the consecutive integers be = x, x+1, x+2, x+3

Therefore,

x + x+1 + x+2 + x+3 = 250

4x + 6 = 250

2x + 3 = 125

2x = 122

x = 61

Therefore, the greatest integer = 61 + 3 = 64

Hence, the greatest of the given integers is 64.

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What is the slope of the line that passes through
the points (2,-4) and (2, 4)?
A. -3 B.0. C.8. D. Undefined

Answers

The line is a vertical line, then the correct option is D, the slope is undefined.

How to find the slope of the line?

A general linear equation can be written as:

y = a*x + b

Where a is the slope, b is the y-intercept, and x is the variable.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the two points are (2, -4) and (2, 4)

Replacing that we would have a problem, that is because we have the same x-value in both points.

Then we have a vertical line at x = 2.

That line has no defined slope, thus, the correct option is D.

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The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.

Answers

Answer:

I helped you last time so I'll help you again.

Step-by-step explanation:

We can find the average rate of change of f(x) over the interval [10, 20] using the formula:

average rate of change = (f(b) - f(a))/(b - a)

where a = 10 and b = 20.

So, we have:

f(a) = f(10) = 1.85(10)^2 = 185

f(b) = f(20) = 1.85(20)^2 = 740

average rate of change = (740 - 185)/(20 - 10) ≈ 55.5

Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.

b) Find the value of w. Sive each answer as an integer or as a fraction in its simplest form 4 cm A 7 cm 12 cm 3 cm B W cm 9 cm

Answers

The calculated value of w from the similar triangles is 21/4

Calculating the value of w

From the question, we have the following parameters that can be used in our computation:

Similar triangles A and B

Also from the similar triangles, we have the following proportional relation

4 7 12

3 W 9

Using the above as a guide, we have the following equation

4/3 = 7/W = 12/9

So, we have

W * 12 = 7 * 9

Evaluate the products and divide both sides by 12

W = 21/4

Hence, the value of W is 21/4