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New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
Answers
Answer:
I can explain how the relationship between the amount of money the painter earns and the number of rooms he paints can be represented in a graph.
The amount of money the painter earns depends on the number of rooms he paints. The painter charges $25 for each room he paints, so the amount of money he earns can be calculated by multiplying the number of rooms painted by $25. However, he also has to pay $100 for supplies regardless of the number of rooms painted.
Therefore, the relationship between the amount of money the painter earns and the number of rooms painted is a linear function, where the y-intercept (when no rooms are painted) is -$100 and the slope (how much he earns per room painted) is $25. This relationship can be represented in a graph as a straight line with a positive slope that intersects the y-axis at -$100.
I hope this helps
Option C is the correct graph for the given condition.
What is the significant use of graphs in real life?Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.
Let's assume that the number of rooms painted is represented by the variable "x". The cost of painting x rooms can be calculated using the following equation:
Cost = 100 + 25x
The $100 is a fixed cost for the supplies, and the $25 is the cost per room painted. The variable "x" represents the number of rooms painted, which can vary.
We can draw a graph of this equation by plotting points for different values of "x" and connecting them with a straight line. For example:
If x = 0, then Cost = 100 + 25(0) = $100, which is the y-intercept (where the line intersects the y-axis).If x = 1, then Cost = 100 + 25(1) = $125, which gives us the point (1, 125) on the line.If x = 2, then Cost = 100 + 25(2) = $150, which gives us the point (2, 150) on the line.If x = 3, then Cost = 100 + 25(3) = $175, which gives us the point (3, 175) on the line.We can continue this process to find additional points, and then plot them on a coordinate grid. Here's what the graph might look like:
The line passes through the point (0, 100), which is the y-intercept. As we move to the right along the x-axis (increasing the number of rooms painted), the cost increases at a constant rate of $25 per room. The slope of the line is therefore 25.
The equation for the line is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this case, we have:
Cost = 25x + 100
This equation gives us the cost of painting x rooms, where x can be any non-negative integer.
The correct graph is option C
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Related Questions
Every number has only one quality: its distance from zero.
O A. True
OB. False
Answers
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Every number has multiple qualities beyond its distance from zero. Some of the qualities of a number include its sign (positive or negative), its magnitude (Absolute Value), its parity (whether it is even or odd), and its relationship to other numbers (greater than, less than, or equal to). Additionally, numbers can have properties such as being prime or composite, rational or irrational, and real or complex. Therefore, a number is characterized by more than just its distance from zero.
Last week, the value of an investment changed at a rate of -\$ 3.15−$3.15 each day. After how many days was the total charge in $ 12.60?−$12.60?
Answers
Based on the rate of change, the total charge will be $ 12.60 in 4 days
After how many days was the total charge in $ 12.60?From the question, we have the following parameters that can be used in our computation:
Rate of change of investment = $3.15
Value of the investment = $12.60
Using the above as a guide, we have the following:
Number of days = Value of the investment/Rate of change of investment
Substitute the known values in the above equation, so, we have the following representation
Number of days = 12.60/3.15
Evaluate
Number of days = 4
Hence, the number of days is 4
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apllo traveld 48 leauges in 3 day then he tripled his rate how long would it take him to travel 336 leagues at this new speed
Answers
48 leagues / 3 days = 16 leagues per day
Next, we know that Apollo tripled his rate, which means his new speed is:
16 leagues per day x 3 = 48 leagues per day
To find out how long it will take him to travel 336 leagues at this new speed, we can use the formula:
time = distance / speed
In this case, the distance is 336 leagues, and the speed is 48 leagues per day. So we have:
time = 336 leagues / 48 leagues per day = 7 days
Therefore, it would take Apollo 7 days to travel 336 leagues at his new speed.
Luciana bought a total of 7 textbooks at the bookstore. She bought four more textbooks than journals. How many journals did she buy
Answers
Given the vectors a and b. sketch the vector a+b
Answers
The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.
What is parallelogram law of vector addition?
Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.
For the given vector a, and vector, the resultant of the two vector is calculated as;
-----------> a and --------------->b = a + b
The diagram represents the addition of the two vectors, a and b;
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Krell Industries has a share price of $22.08 today. If Krell is expected to pay a dividend of $0.98 this year, and its stock price is expected to grow to $24.98 at the end of the year, what is Krell's dividend yield and equity cost of capital?
what is Krell's equity cost of capital, or expected total return ?
Answers
Krell's equity cost of capital, or expected total return, is 5.57%.
We have,
The dividend yield is the annual dividend divided by the current share price:
Dividend yield
= Annual dividend / Share price
= $0.98 / $22.08 = 0.0444 = 4.44%
The equity cost of capital is the expected total return on the stock, which includes both the dividend yield and the expected capital appreciation:
Equity cost of capital = Dividend yield + Capital Appreciation
= 4.44% + [(24.98 - 22.08) / 22.08]
= 4.44% + 0.1314
= 5.57%
Therefore,
Krell's equity cost of capital, or expected total return, is 5.57%.
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please help for question 3
Answers
Reflecting the triangle Q over the line y = 1 would map it onto triangle T
Reflecting the triangle PReflection 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 transformationUsing the same transformation rule above;
A reflection over the line y = 1 would map the triangle Q onto triangle T
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click on the region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2
Answers
Answer: The region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2 is the area bounded by the two lines and the x-axis.
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
W
X14
Determine if the proportion is true. If it is not true, correct the error.
A true
B.
Z
Mark this and return
V
X
Save and Exit
Next
Answers
Determining if the proportion is true. If is not true and correcting the error v/x = x/v+w is: B. false, it should be w/x = x/v+w.
What is the proportion?In order for us to know whether the proportion v/x = x/v+w is true or not we need to cross multiply and simplify both sides:
v(x + v + w) = x^2
Expand the left-hand side:
vx + v^2 + vw = x^2
Subtract vx from both sides:
v^2 + vw = x^2 - vx
Factor out v on the left-hand side and x on the right-hand side:
v(v + w) = x(x - v)
Divide both sides by (v + w)x:
v/(v + w) = x/(x - v)
Therefore the correct option is B.
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I still have no clue what the teacher wants us to do
Answers
The objective of the above task to to check your ability to compute various parts of a parallelogram given various inputs. See the solution attached.
What is parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.
Note that the corners angles (AB,C,D)are derived as follows;
A = C = θ
B = D = Φ
A + B = 180° = π radians
for a parallelogram that is not a rectangle or square,
0 < A< 90° (0 < A < π/2),
90° < B < 180° (π/2 < B < π)
The diagonals are derived as follows:
Diagonals: d, c
d = √( a² + b² - 2ab cos(A) ) = √( a² + b² + 2ab cos(B) )
c = √( a² + b² + 2ab cos(A) ) = √( a² + b² - 2ab cos(B) )
d² + c² = 2(a² + b²)
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Need problem please please
Answers
The formula for the nth term of the geometric sequence is given as follows:
[tex]a_n = 7(-3)^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The formula for the nth term of the sequence is given as follows:
[tex]a_n = a_1q^{n-1}[/tex]
The first term of the sequence is given as follows:
[tex]a_1 = 7[/tex]
Each term is the previous term multiplied by -3, hence the common ratio is given as follows:
q = -3.
Thus the formula for the sequence is given as follows:
[tex]a_n = 7(-3)^{n - 1}[/tex]
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A college student takes the same number of credits each semester. Before beginning college, the student had some credits earned while in high school. After 2 semesters, the student had 39 credits, and after 5 semesters, the student had 75 credits.
If C(t) is the number of credits after t semesters, write an equation that represents this situation.
Provide your answer below:
Answers
The equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.
Let x be the number of credits the student had before starting college, and let y be the number of credits the student takes each semester. We can use this information to write an equation that represents the number of credits the student has earned after t semesters.
After 2 semesters, the student had 39 credits, which means the student earned 2y + x credits in those two semesters. Similarly, after 5 semesters, the student had 75 credits, which means the student earned 5y + x credits in those five semesters.
Using this information, we can write the following equation:
C(t) = yt + x
where C(t) represents the number of credits the student has earned after t semesters.
We know that C(2) = 2y + x = 39 and C(5) = 5y + x = 75. We can use these two equations to solve for x and y:
2y + x = 39
5y + x = 75
Subtracting the first equation from the second equation gives:
3y = 36
Therefore, y = 12, which means the student takes 12 credits each semester. Substituting y = 12 into either of the two equations above gives x = 15, which means the student had 15 credits before starting college.
Thus, the equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.
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Triangle LMN is an obtuse triangle with l = 6, n = 8.3, and m∠M = 132°. What is the area of ΔLMN?
Answers
The area of triangle LMN is 49.61 square units.
We have,
To find the area of triangle LMN.
Area = (1/2) x base x height
where the base and height are the sides of the triangle perpendicular to each other.
First, we need to find the length of side L.
We can use the Law of Cosines.
L² = M² + N² - 2MNcos(132°)
L² = 6² + 8.3² - 268.3cos(132°)
L² = 36 + 68.89 + 99.36
L² = 204.25
L = √204.25
L = 14.28
Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.
Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.
Let's call the foot of the perpendicular point P.
Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:
M∠LMP = 180° - M∠M
M∠LMP = 180° - 132°
M∠LMP = 48°
We can use trigonometry to find the length of MP:
tan(48°) = h/6
h = 6 x tan(48°)
h = 6.93
The area of triangle LMN is:
Area = (1/2) x base x height
Area = (1/2) x 14.28 x 6.93
Area ≈ 49.61
Thus,
The area of triangle LMN is 49.61 square units.
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answers
Answer:d
Step-by-step explanation:
Rearrange the formula = 2√
3
and make ‘’ the subject.
Answers
Making x as a subject, we get equation as x=(y+2)/5.
The given equation is y=5x-2.
To make x as the subject
y+2=5x
x=(y+2)/5
Therefore, making x as a subject, we get equation as x=(y+2)/5.
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"Your question is incomplete, probably the complete question/missing part is:"
Rearrange the formula to make x the subject y=5x-2.
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day. A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3. Which of the following data sets best represents what is displayed in the histogram? (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42) (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42) (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42) (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answers
The data set that best describes the histogram is
(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
We have,
The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.
From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.
Looking at the answer choices, we need to choose the data set that matches the histogram.
The first step is to check if the data set has the same range as the histogram.
The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.
Now,
The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.
The second answer choice has a range from 4 to 42, which matches the histogram.
We can check if the frequencies in the data set match the heights of the bars in the histogram.
For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.
The second data set has 4 passengers in the 11 to 20 interval, so it matches.
We can do the same for the other intervals and find that the second data set matches the histogram.
Therefore,
The data set that best describes the histogram is
(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
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A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
Answers
The frequency table is plotted and the order for the restaurant is given
Given data ,
A restaurant had 160 lunch customers last weekend.
90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both.
There were 45 customers who ordered seltzer and a veggie sandwich.
Eleven more people ordered a veggie sandwich than a tuna sandwich.
On simplifying the equation , we get
A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2
D=11
Thus C = 22
F = 45 + C
F = 45 + 22
F = 22
G = A + D = 18
Chicken Veggie Tuna Total
Seltzer 38 45 7 90
Iced Tea B 22 11 70
Total 75 67 18 160
Hence , the frequency is completed
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The complete question is attached below :
A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
Need help easy please give right answer
Answers
Answer: x < 5, see attached
Step-by-step explanation:
To solve for x, we will isolate the given variable.
Given:
[tex]\displaystyle 1 > \frac{x}{5}[/tex]
Multiply both sides of the equation by 5:
[tex]\displaystyle5 > x[/tex]
Flip equation:
[tex]\displaystyle x < 5[/tex]
To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.
Find the solution set for the following equation. - square root x =5
Answers
The solution set for the given equation is 25.
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
Next, we would determine the solution set for the given equation by translating the word problem into an equation and then divide both sides of the square root function as follows;
-√x = 5
√x = -5
By taking the square of both both sides of the square root function, we have:
x = (-5)²
x = 25
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10 points. please awnser
Answers
The angle measures for the triangles are given as follows:
m < G = 105º.m < H = 55º.m < I = 20º.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:
m < Z + 20 + 105 = 180
m < Z + 125 = 180
m < Z = 55º.
Hence the measures are given as follows:
m < G = 105º. -> equivalent to X.m < H = 55º. -> equivalent to Z.m < I = 20º. -> equivalent to I.More can be learned about similar triangles at brainly.com/question/14285697
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Help 100 pts. I don’t get it
Answers
The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
Given that, the dimensions of rectangular flower bed are length= 6 feet and width = 4 feet.
Dimensions of large rectangle are Length = 6+2x and width = 4+2x
Now, area of large rectangle = (6+2x)×(4+2x)
= 24+8x+12x+4x²
Area of a rectangular flower bed = 6×4
= 24 square feet
Tulips and Daisy have same area to plant
So, the equation is 24+20x+4x²=24
4x²+20x=0
Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
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FOUR CARS CRASH AT 5 MILES AN HOUR. Cost of the repairs are 422, 456, 401, and 215
COMPUTE RANGE
SAMPLE VARIANCE,
AND SAMPLE STANDARD DEVIATION
Answers
The range of the repairs to the cars is 241.
The sample variance is 11, 671.33
The sample standard deviation would be 108.03.
How to find the range ?Range = Maximum repair cost - Minimum repair cost
= 456 - 215
= 241
How to find the sample variance and standard deviation ?Find mean :
= (422 + 456 + 401 + 215) / 4
= 373. 5
Sample variance :
= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)
= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )
= 11, 671. 33
Sample standard deviation:
= √sample variance
= √11, 671. 33
= 108. 03
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(Time limit) Give me the domain and range and tell me if the graph is a function or not.
Answers
Yes, The given graph is shows a function.
And, Range = {y | y ≥ - 2}
Domain = (- ∞ , ∞)
We have to given that;
the graph is shown in image.
Now, We can check the graph is a function or not by vertical line test.
Hence, By vertical line test it's shows the function as it cut at one point for each value of y.
Thus, The given graph is shows a function.
Since, The set of all inputs of the function is called Domain of set.
Hence, We get;
Domain = (- ∞ , ∞)
And, The set of all outputs of the function is called range of set.
Hence, We get;
Range = {y | y ≥ - 2}
Thus, Yes, The given graph is shows a function.
And, Range = {y | y ≥ - 2}
Domain = (- ∞ , ∞)
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Find the x - and y -intercepts of the following equation: 3x-2y=5 ?
Answers
The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).
The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.
Given the equation: 3x - 2y = 5
Setting y = 0, we get;
3x - 2(0) = 5
3x = 5
x = 5/3
So, the x-intercept is (5/3, 0).
The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.
Setting x = 0, we get;
3(0) - 2y = 5
-2y = 5
y = -5/2
So, the y-intercept is (0, -5/2).
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For each of the following functions, match the function to the graph.
Answers
The function that matches the above graph is Option C - F(x) = (1/2)^x - 3
What are the properties ofthe function ?
Here are the properties of the function are given as follows
Domain - The domain of the function is all real numbers, as there are no restrictions on the input value x .
Range - the range of the function is (-3, infinity), as the output values approach but never reach - 3 as x approaches negative infinity, and the output values can be arbitrarily large as x approaches infinity.
x -intercept - The x-intercept of the function is (log(2, 3), 0), as F(log(2, 3)) = [( 1/2)^ (log(2, 3) ) ] - 3 = 0.
y-intercept - The y-intercept of the function is (0, -2.5), as F(0) = [(1/2)^0] - 3 = -2.5.
Asymptotes - The horizontal asymptote of the function is y = -3, as the output values approach but never reach -3 as x approaches infinity. There are no vertical asymptotes.
Decreasing function - The function is a decreasing function, as the output values decrease as x increases.
Continuous function - The function is continuous for all real numbers.
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The market mechanism might leave some people with too little income and others with too much. The government uses taxes and transfers to redistribute income more fairly.
Income Transfers are payments to individuals for which no current goods or services are exchanged (e.g., Social Security, welfare, unemployment benefits).
Program Recipient Group Number of Recipients Value of Transfers
Social Security Retired and disabled workers 70 million $ 1,156 billion
Medicare Individuals over age 65 61 million $ 820 billion
Medicaid Medically needy individuals 77 million $ 650 billion
Unemployment compensation Unemployed workers 18 million $ 150 billion
Food stamps Low-income households 43 million $ 105 billion
Earned Income Tax Credit Low-wage workers 25 million $ 62 billion
Temporary Aid to Needy Families Low-income families 3 million $ 30 billion
Calculate the average benefit a Medicaid recipient receives.
Instructions: Round your response to the nearest dollar.The market mechanism might leave some people with too little income and others with too much. The government uses taxes and transfers to redistribute income more fairly.
Income Transfers are payments to individuals for which no current goods or services are exchanged (e.g., Social Security, welfare, unemployment benefits).
Program Recipient Group Number of Recipients Value of Transfers
Social Security Retired and disabled workers 70 million $ 1,156 billion
Medicare Individuals over age 65 61 million $ 820 billion
Medicaid Medically needy individuals 77 million $ 650 billion
Unemployment compensation Unemployed workers 18 million $ 150 billion
Food stamps Low-income households 43 million $ 105 billion
Earned Income Tax Credit Low-wage workers 25 million $ 62 billion
Temporary Aid to Needy Families Low-income families 3 million $ 30 billion
Calculate the average benefit a Medicaid recipient receives.
Instructions: Round your response to the nearest dollar.
Answers
Taxes and transfers are used by the government to more equitably share revenue. A Medicaid participant typically receives $1500 in benefits.
We know that,
Medicare is a health insurance program for seniors, disabled individuals under 65, and dialysis patients. Medicaid is a program that provides financial aid for low-income patients' medical costs.
The federal government and the states share funding for the Medicaid program. The amount that the federal government reimburses states for program costs is known as the Federal Medical Assistance Percentage, or FMAP (FMAP).
Spending on Medicaid is mostly targeted at the elderly and those with disabilities. Despite accounting for over two-thirds of Medicaid spending, seniors and individuals with disabilities make up one in four beneficiaries, which reflects the high per-enrollee expenses for both acute and long-term care.
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A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. z = -3, if the standard deviation is 80.
Answers
Answer:
260
Step-by-step explanation:
The z score for a normal distribution is given by the formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
where
X is the data point, μ is the mean and σ is the standard deviation
Given
Mean μ = 500
Standard deviation σ = 80
z-score = -3
and plugging in these values for z-score formula we get
[tex]-3 = \dfrac{X -500}{80}[/tex]
==>
-240 = X - 500
-240 + 500 = X
260 = X
or
X = 260
ASAPPPPPP 100 POINTS GUYS CMON LAST HW QUESTION
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 6 feet and a height of 9 feet. Container B has a radius of 5 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
Answers
Answer:
The nearest tenth, Container A is about 46.3% full after the pumping is complete.
Step-by-step explanation:
To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.
The volume of water in Container A can be found using the formula for the volume of a cylinder:
V_A = πr^2h = π(6^2)(9) = 324π cubic feet
The volume of Container B can also be found using the same formula:
V_B = πr^2h = π(5^2)(12) = 300π cubic feet
After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:
V_A' = πr^2h' = 300π
h' = 300/(36π) = 25/6 feet
So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:
(25/6) / 9 * 100% ≈ 46.3%
Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.
Rectangle BCDE has vertices B(-9,-4), C(-6,-8), D(10,4), and E(7,8). What is the area of BCDE?
Answers
Answer:
To find the area of the rectangle BCDE, we can use the formula:
Area = length x width
First, we need to find the length and width of the rectangle.
The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:
distance BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)
= sqrt(3^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
The width of the rectangle is the distance between points C and D:
distance CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((10 - (-6))^2 + (4 - (-8))^2)
= sqrt(16^2 + 12^2)
= sqrt(256 + 144)
= sqrt(400)
= 20
Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:
Area = length x width = 5 x 20 = 100
Therefore, the area of BCDE is 100 square units.
Step-by-step explanation:
Suppose you draw 6 samples of marbles from a jar and get these results for red marbles. 26,25,25,30,28,28 What is the mean number of red marbles drawn?
Answers
Answer:
Mean-27
Step-by-step explanation:
Add all of the numbers and it equals 162
Then divide 162 by the amount of numbers presented.
Since there are 6 numbers listed we divide by 6
162/6=27