The payback period for Product A is 2.21 years and the payback period for Product B is 1.85 years, NPV of A = $21,215 and NPV of B = -$50,256. Product A: IRR = 28.28%, Product B: IRR = 29.58%, A: PI = 1.00, B: PI = 0.91, A: SRR = 0.49 or 49%, B: SRR = 0.44 or 44%.
What is payback period?Payback period is a financial metric used to evaluate the time required to recover the initial investment made in a project or investment opportunity.
According to given information:To calculate the payback period, we need to find out how long it takes for the initial investment to be recovered by the annual cash inflows. We calculate the cumulative cash inflows for each year and determine in which year the cumulative cash inflows exceed the initial investment.
Product A:
Year 1: $380,000 - $170,000 - $68,000 - $86,000 = $56,000
Year 2: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $56,000 = $112,000
Year 3: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $112,000 = $168,000
Year 4: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $168,000 = $224,000
Year 5: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $224,000 = $280,000
The payback period for Product A is 2.21 years (rounded to two decimal places).
Product B:
Year 1: $460,000 - $206,000 - $108,000 - $66,000 = $80,000
Year 2: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $80,000 = $160,000
Year 3: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $160,000 = $240,000
Year 4: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $240,000 = $320,000
Year 5: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $320,000 = $400,000
The payback period for Product B is 1.85 years (rounded to two decimal places).
To calculate the net present value (NPV), we need to discount the cash inflows and outflows using the company’s discount rate of 20% and then subtract the initial investment.
Product A:
[tex]NPV = -$340,000 + ($56,000/(1+0.20)^1) + ($112,000/(1+0.20)^2) + ($168,000/(1+0.20)^3) + ($224,000/(1+0.20)^4) + ($280,000/(1+0.20)^5)[/tex]
NPV = -$340,000 + $38,611 + $64,357 + $79,396 + $81,193 + $77,658
NPV = $21,215
Product B:
[tex]NPV = -$540,000 + ($80,000/(1+0.20)^1) + ($160,000/(1+0.20)^2) + ($240,000/(1+0.20)^3) + ($320,000/(1+0.20)^4) + ($400,000/(1+0.20)^5)[/tex]
NPV = -$540,000 + $66,667 + $111,111 + $114,882 + $99,425 + $97,659
NPV = -$50,256
To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV of the cash inflows and outflows equal to zero. We can use a financial calculator or spreadsheet software to solve for the IRR.
Product A: IRR = 28.28%
Product B: IRR = 29.58%
To calculate the profitability index (PI), we divide the present value of the future cash inflows by the initial investment.
Product A:
PV of future cash inflows = $38,611 + $64,357 + $79,396 + $81,193 + $77,658 = $341,215
PI = $341,215/$340,000
PI = 1.00
Product B:
PV of future cash inflows = $66,667 + $111,111 + $114,882 + $99,425 + $97,659 = $489,744
PI = $489,744/$540,000
PI = 0.91
To calculate the simple rate of return (SRR), we divide the average annual cash inflow by the initial investment.
Product A:
Average annual cash inflow = ($56,000 + $112,000 + $168,000 + $224,000 + $280,000)/5 = $168,000
SRR = $168,000/$340,000
SRR = 0.49 or 49%
Product B:
Average annual cash inflow = ($80,000 + $160,000 + $240,000 + $320,000 + $400,000)/5 = $240,000
SRR = $240,000/$540,000
SRR = 0.44 or 44%
6a.
Based on the payback period, Product B is preferred because it has a shorter payback period of 1.85 years compared to Product A’s payback period of 2.21 years.
Based on the net present value, Product A is preferred because it has a positive NPV of $21,215 compared to Product B’s negative NPV of -$50,256.
Based on the internal rate of return, Product B is preferred because it has a higher IRR of 29.58% compared to Product A’s IRR of 28.28%.
Based on the profitability index, Product A is preferred because it has a PI of 1.00, indicating that for every dollar invested, we receive one dollar in return. Product B has a PI of 0.91, indicating that for every dollar invested, we receive only $0.91 in return.
Based on the simple rate of return, Product A is preferred because it has a higher SRR of 49% compared to Product B’s SRR of 44%.
6b. Based on the simple rate of return, Lou’s division should accept Product A because it has a higher SRR of 49% compared to Product B’s SRR of 44%. However, other measures such as the net present value and internal rate of return suggest that Product A may not be the best choice.
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Evaluate and simplify the expression
when X = 3 and y = 5.
2y + 3(x - y) + x2 = [?]
Answer:
Step-by-step explanation:
substitute:
2(5) + 3(3-5) + 3² Do PEMDAS order (parenthesis, exponent, mult/div, add/sub
2(5) + 3(-2) +3²
2(5) + 3(-2) + 9
10 + 3(-2) +9
10-6+9
4+9
13
(CLASSKICK) 7k+8=71 and -9=3-y.
show the answer and steps.
Answer:
k = 9 y = -6Step-by-step explanation:
7k+8=71
7k=71-8
7k=63
k=63/7
k=9
-9=3-y
-9+3=y
-6=y
y=-6
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Salut! Comment allez-vous? Comment s'est passée ta journée?
Three-year-old boys in the United States have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches.
Mrs. Davis has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall.
Which of Mrs. Davis' children is more unusually tall for his
or her age and gender? Explain, showing any calculations you perform.
The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.
To solve this problemA z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.
For the 3-year-old boy, the z-score is:
z = (43 - 38) / 2 = 2.5
The z-score for the 10-year-old girl is:
z = (57 - 54.5) / 2.5 = 1
The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .
Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.
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whats angle A pls help
Answer :
Angle A = 19.6°
Step-by-step explanation :
According to the question It is given that,
Angle A = x
Angle B = 5x
Angle C = 4x - 16
We will apply angle sum property in the question.
Angle sum property states that sum of all the angles of triangle is 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180
[tex]\: :\implies [/tex] 10x - 16 = 180
[tex]\: :\implies [/tex] 10x = 180 + 16
[tex]\: :\implies [/tex] 10x = 196
[tex]\: :\implies [/tex] x = 196/10
[tex]\: :\implies [/tex] x = 19.6
Hence,
Angle A = x
[tex]\: :\implies [/tex] 19.6 °
Angle B = 5x5 × 19.6
[tex]\: :\implies [/tex] 98
Angle c = 4x - 16
[tex]\: :\implies [/tex] 4 × 19.6 - 16
[tex]\: :\implies [/tex] 78.4 - 16
[tex]\: :\implies [/tex] 62. 4
We must also check our answer.
Sum of all angles = 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] 19.6 + 98 + 62.4 = 180
[tex]\: :\implies [/tex] 117.6 + 62.4 = 180
[tex]\: :\implies [/tex] 180 = 180
Hence, Verified.
Therefore, The Measure of Angle A is 19.6°
Answer:
angle A = 19.6°
Explanation:
angle ABC + angle ACB + angle BAC = 180°
5x + (4x - 16)° + x = 180°
Simplifying:
5x + x + (4x + -16) = 180
Reorder the terms:
5x + x + (-16 + 4x) = 180
Remove parenthesis around (-16 + 4x)
5x + x + -16 + 4x = 180
Reorder the terms:
-16 + 5x + x + 4x = 180
Combine like terms: 5x + x = 6x
-16 + 6x + 4x = 180
Combine like terms: 6x + 4x = 10x
-16 + 10x = 180
Solving
-16 + 10x = 180
Solving for variable 'x'.
Add '16' to each side of the equation
-16 + 16 + 10x = 180 + 16
Combine like terms: -16 + 16 = 0
0 + 10x = 180 + 16
10x = 180 + 16
Combine like terms: 180 + 16 = 196
10x = 196
Divide each side by '10'
x = 19.6
The measure of angle A is 19.6°
Simplify remove all perfect squares from inside the square root assume b is positive
Answer:
Step-by-step explanation:
You take items out of a square root if you have a pair of numbers or if you know the square root.
[tex]\sqrt{48b^{7} }[/tex]=[tex]\sqrt{4*4*3*bbbbbbb}[/tex]
So I know the [tex]\sqrt{4}[/tex]=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3
Now for the b's for every pair there are, you can take that out. There are 3 pairs of b's so b³ is outside and one b is left inside.
Answer:
4b³[tex]\sqrt{3b}[/tex]
evaluate x^2-2x+3 when x= -3
Answer:
18
Step-by-step explanation:
[tex]x^{2}[/tex] -2x + 3 x = -3
[tex](-3)^{2}[/tex] - 2(-3) + 3
9 + 6 + 3
18
Helping in the name of Jesus.
Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is $62, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?
The expression of total amount paid in the first 12 months for the big screen TV is C. [tex]\frac{62*(1 - 1.04^{12})}{(1-1.04)}[/tex]
How to find expression of total amount paid in the first 12 months?To find the expression of the total amount paid in the first 12 months, we can use the formula for the sum of a geometric series which states: S = a(1-r^n) / (1-r)
Data:
First term (a) is $62
Common ratio (r) is 1.04
We have 12 terms (n) in the series.
Substituting the values, we get:
[tex]S = 62*(1 - 1.04^{12}) / (1-1.04)\\S = 62 * 15.0258054642\\S = 931.59993878\\S = $931.60[/tex]
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The function f(x) = 12x - 4.8x^2 models the height of a beach ball x seconds after it is tossed.
Find the average rate of change over the interval 0 < x < 2.
_____ feet per second
The average rate of change of a beach ball thrown according to the function[tex]f(x) = 12x - 4.8x^2[/tex] over the interval 0 < x < 2 is -9.6 feet per second.
To find the average rate of change, we need to find the height of the ball at x = 0 and x = 2, and then find the change in height over the time interval.
At x = 0, the height of the ball is:
[tex]f(0) = 12(0) - 4.8(0)^2 = 0[/tex]
At x = 2, the height of the ball is:
[tex]f(2) = 12(2) - 4.8(2)^2 = -19.2[/tex]
The change in height over the time interval 0 < x < 2 is:
-19.2 - 0 = -19.2
Therefore, -19.2/2 = -9.6 feet per second is the average rate of change over the range 0 x 2.
The average change throughout the range of 0 x 2 is therefore -9.6 feet per second.
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in a meeting 100 politicians are there 35 support rk 45 support js and 20 support both how many support js and how
Okay, here are the steps to solve this problem:
* There are 100 politicians total
* 35 support RK
* 20 support both RK and JS
* So 35 + 20 = 55 support RK in some way
* That means the remaining 100 - 55 = 45 politicians support JS
* So 45 politicians support JS
In summary:
RK supporters: 35
Both RK and JS: 20
Remaining JS supporters: 45
Total politicians: 100
So the answer is:
45 politicians support JS
Let me know if this helps explain the problem and solution. I can provide more details if needed.
Which description compares the domains of Function A and Function B correctly? Function A: f(x)=logx Function B: A square root function graphed on a grid in Quadrant One, with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The function, labeled g of x, contains a filled in point at begin ordered pair one comma zero end ordered pair and passes through begin ordered pair eight comma two end ordered pair as a smooth curve while extending to infinity. Responses The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1. The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1. The domain of both functions is the set of real numbers greater than or equal to 1. The domain of both functions is the set of real numbers greater than or equal to 1. The domain of Function A is the set of real numbers greater than or equal to 1. The domain of Function B is the set of real numbers greater than 1. The domain of Function A is the set of real numbers greater than or equal to 1. The domain of Function B is the set of real numbers greater than 1. The domain of both functions is the set of real numbers.
The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.
What is a function?
A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.
The domain of a function refers to the set of all possible input values for which the function can produce an output.
In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.
In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.
This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.
It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.
Therefore, the correct statement is A.
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Find a degree 3 polynomial with real coefficients having zeros x = 3 and x = 1 − 2 i and a lead coefficient of 1. Write in expanded form.
Step-by-step explanation:
(x-3)(x-1 +2i)(x-1-2i) The imaginary roots always come in pairs : 1+- 2i
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School Riverside School
0 5, 6, 9
9, 7, 2, 0 1 0, 2, 4, 5, 6, 7
8, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 5
0 3
4 2
Key: 2 | 1 | 0 means 12 for Sky View and 10 for Riverside
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning. (2 points)
Part A: For Sky View School: The median is 50. The mean is 50.8. For Riverside School: The median is 20.5. The mean is 9.93. Part B: The variability is For Sky View School: 1,298.16. For Riverside School: 477.0.
What is IQR?Interquartile Range, or IQR, is a measure of a dataset's variability or spread. It is determined by subtracting the dataset's third quartile (Q3) from its first quartile (Q1), where the quartiles divide the dataset into four equally sized segments. When compared to the range, the IQR contains the median 50% of the data and is less impacted by extreme values or dataset outliers. As a result, IQR is a valuable metric for describing a dataset's central tendency and variability.
Part A: The measure of the center is obtained by determining the mean and median for each school.
For Sky View School:
The median is (50 + 50) / 2 = 50.
The mean is 762 / 15 = 50.8.
For Riverside School:
The median is (20 + 21) / 2 = 20.5.
The mean is 139 / 14 = 9.93.
Part B:
The measure of variability is determined using IQR:
For Sky View School:
The range is 96 - 12 = 84.
IQR:
The 25th percentile is the 4th value when the data is arranged in ascending order, which is 20. The 75th percentile is the 12th value, which is 60. So the IQR is 60 - 20 = 40.
Variance is:
Square of mean = -38.8, -33.8, -28.8, -25.8, -25.8, -25.8, -23.8, -20.8, -9.8, -7.8, 11.2, 11.2, 14.2, 21.2, and 45.2.
Now summation of the square of mean is:
19,472.4
Now, dividing by 15 we have:
19,472.4 / 15 = variance of 1,298.16.
For Riverside School:
The range is 25 - 2 = 23.
The 25th percentile is the 4th value when the data is arranged in ascending order, which is 5. The 75th percentile is the 11th value, which is 21. So the IQR is 21 - 5 = 16.
The deviations from the mean are: -19.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, 0.3, 0.3, 10.3, 20.3, 20.3, 20.3, 27.3.
The sum of squared deviations is 6678.7.
Variance = 6678.7 / 14 = 477.0
Part C:
If you are interested in a larger class size, Riverside School is a better choice because it has a higher maximum class size (57) compared to Sky View School (69).
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I need help with this problem
Answer:
its 32 square units
Step-by-step explanation:
The Shape is a rectangle. Area of a rectangle is Length x Width
8 x 4 = 32
Answer:
32 Square units
Step-by-step explanation:
You can see that there are 8 spaces of width by using the graph. And 4 spaces of height. So, assuming each space is 1 Square unit. All you have to do is 8×4 which is 32.
Write MARIE code that accepts your last university ID number and displays all the
sequence of numbers from the entered number till 10.
Provide a screenshot of the simulation result (A screenshot of the MARIE Simulator
window after running the program, showing the values at the output window).
Instructions:
- Use “ORG” instruction to start your program at an address equivalent to 33610.
- Use your last university ID number as an input.
For example, if your ID is 2315161678235, then you will use the number 5 as the
value.
- Do not forget to change the Input and output boxes to decimal!
- You should include the necessary labels and directives at the end of your program.
The program that would be run in the MARIE Simulator to get the desired output is given below:
How to write the MARIE ProgramThe MARIE Program with the given requirements is as follows
ORG 33610
InputStore ID_LAST_DIGIT
Load ID_LAST_DIGIT
Loop:
Output
Add ONEStore ID_LAST_DIGIT
Load ID_LAST_DIGIT
Subt TEN
Skipcond
800Jump
Loop:
HaltI
D_LAST_DIGIT:
DEC 0ONE:
DEC 1TEN:
DEC 10
END
The program starts at 33610.
Input your last university ID digit (e.g., 5)
The program will show numbers from the input to 10.
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Michael invested $380 into an account that earns 8% interest, compounded continuously. How much will be in the account after eight years round to the nearest cent.
Answer:
Step-by-step explanation:
The formula for continuous compound interest is:
A = P(1 + r/100)^t
where A is the amount after t years, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.
In this case, we have P = $380, r = 0.08 (8%), and t = 8 years. Plugging in these values, we get:
A = 380 x (1+8/100)^8
A= 380 x (1+0.08)^8
A=380 x (1.08)^8
A= 380 x 1.8509..
A= $703.35
Therefore, the amount in the account after eight years, rounded to the nearest cent, is $703.35.
How can you write 10/3 as a division expression and as a mixed number?
Show your work!
Answer:
[tex] \frac{10}{3} = 10 \div 3 = 3 \frac{1}{3} [/tex]
Answer: Mixed Number Form: 3[tex]\frac{1}{3}[/tex]
Decimal Form: 3.3 repeating
can i have brainliest please i need it
What is the slope of the line?
Answer:
It could be 0, is the question multiple choice?
a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}[/tex]
8TH GRADE MATH: what is the distance from the store to the park? ‼️PLS ANSWER ASAP i’ll give any amount of points❕
Answer:
Step-by-step explanation:
assuming that every square is 1 unit, the distance from the store to home should be 5 units, I hope this helped
If the quotient of a number and 8 is added to 1/2, the result is 7/8. Find the number.
Answer:
Let's call the number we're looking for "x".
The problem states that the quotient of x and 8 is added to 1/2, and the result is 7/8. We can write this as an equation:
x/8 + 1/2 = 7/8
To solve for x, we need to isolate it on one side of the equation.
First, we can simplify the left side of the equation by finding a common denominator of 8:
8(x/8 + 1/2) = 8(7/8)
x + 4 = 7
Next, we can isolate x by subtracting 4 from both sides:
x = 3
Therefore, the number we're looking for is 3.
What is the angle SWY
The angle SWY is 59°.
What is points of tangency?
Points of tangency is a point When a line is tangent to a circle.
It intersects the circle at exactly one point.
This point is always perpendicular to the radius of the circle which passes through it which means that the tangent line and the radius form a right angle.
The measure of an arc is equal to the measure of the central angle which delete it. This means that if you know the measure of an arc.
We can find the measure of the central angle that subtends it.
If we assume that point Y is on the tangent line and is between point W and point S, then angle SWY is an inscribed angle that intercepts arc WS. In a circle, the measure of an inscribed angle that intercepts an arc is half the measure of the arc.
So, if the measure of arc WS is 118 degrees, then the measure of angle SWY is half of 118 degrees, which is 59 degrees.
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Y+8=2 solve for y show your work
Answer:
-6
Step-by-step explanation:
Y + 8 = 2
Subtract 8 from both sides
Y = -6
help! offering 20 points!!!
Data is given to represent the number of each of the types of clubs three different schools in your area offer. Academic Clubs Service Clubs Sporting Clubs Eastern High School 6 3 10 Central High School 8 9 9 West-Side High School 4 7 12 Which of the following matrices can be used to accurately represent the data? (2 points) matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 12, row 3 showing 4 and 7 and 9
Answer:
The matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 can be used to accurately represent the data.
The following matrix that can be used to accurately represent the data is the matrix:
[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]
What is the matrix?A matrix is a collection of numbers, encompassed by brackets.
The numbers are known as matrix elements or entries. The components are organized in rows (horizontal) or columns (vertical), which determine the matrix's size (dimension or order).
As per the question, the entry in row i and column j represents the number of type j clubs offered by school i.
The matrix that can be used to accurately represent the data is the matrix:
[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]
This is because the rows represent the three different schools, and the columns represent the number of each of the types of clubs they offer.
The given data matches the entries in this matrix, so it can be used to accurately represent the data.
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Question 2 (Essay Worth 10 points)
(02.02, 02.05 MC)
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents
the average test score in your science class, where x is the number of the test taken.
g(x)
81
83
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 polnts)
The science class had a higher average of 85 compared to te math's average of 81
Maths class
The function si given as
f(x) = 0.5x + 80
After completing test 2, we have
f(2) = 0.5 * 2 + 80
f(2) = 81
Science class
The function si given as
The table
The equation of the table is
g(x) = 2x + 81
After completing test 2, we have
g(2) = 2(2) + 81
g(2) = 85
This means that the science class had a higher average
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Use synthetic division to find the result when 2x^4-8x³ - 27x² + 14x + 24 is divided by x-6
First, write the coefficients of the polynomial in order of decreasing degree and include a placeholder for missing terms:
2 -8 -27 14 24
6
Bring down the leading coefficient:
2 -8 -27 14 24
6
2
Multiply the divisor by the result of the previous step and subtract from the corresponding coefficients:
2 -8 -27 14 24
6
2 -12
48
2 -12 21
-42
2 -12 21 -28
168
2 -12 21 -28 192
The result of the division is 2x³ - 12x² + 21x - 28 with a remainder of 192.
unit 7 homework 3 rectangles
Using the figure the missing sides are
∠ BCD = 90 degrees ∠ ABD = 6 degrees∠ CBE = 84 degrees∠ ADE = 84 degrees∠ AEB = 168 degrees∠ DEA = 12 degreesHow to find the missing values in the rectangleA rectangle is a type of quadrilateral that has four right angles and two pairs of opposite sides that are parallel and equal in length. Some of the properties of a rectangle will b used to find the value of the missing sides as follows
∠ BCD = 90 degrees (All four angles are right angles (90 degrees)).
∠ ABD = 6 degrees (alternate angles are equal)
∠ CBE = 90 - 6 = 84 degrees
∠ ADE = ∠ CBE = 84 degrees (alternate angles are equal)
∠ AEB = ∠ DEC (vertical angles)
∠ DEC = 180 - 6 - 6= 168 degrees (Diagonals are equal, isosceles triangle)
∠ DEA = 180 - ∠ DEC (Linear pair theorem)
∠ DEA = 180 - 168 = 12 degrees
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I need this ASAP!!
Find x, y, and z
The values of x, y, and z in the triangle are y = 7.8, z = 1.25 and x = 3.25
Finding the values of x, y, and zFrom the question, we have the following parameters that can be used in our computation:
the right triangle
So, we have
y^2 = 7.2^2 + 3^2
Evaluate
y = 7.8
For z, we have
3^2 = 7.2z
So, we have
z = 1.25
For x, we have
x^2 = (z + 7.2)^2 - y^2
So, we have
x^2 = (1.25 + 7.2)^2 - 7.8^2
x = 3.25
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find the product
-5(-8)
Answer:
40
Step-by-step explanation:
In order to find your answer, you would need to multiply -5, by -8 which equals 40.
:)
-5(-8) = 40
Because both the 5 and 8 being multiplied are negative, the commutative multiplication property states that the product should be positive. Since 5*8=40, -5*-8=40
Mark used the computer for 12 hours. If the average power use of a computer per hour is 299 watts, how much power did Mark use?
Answer:
Step-by-step explanation:
f(x)=-1/2x+3. G is a quadratic function with the following properties: g has lesser y-intercept than f; the maximum value of g and y-intercept are not equal; first g increases and the it decreases. Graph function g
The equation is [tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex] Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).
Define the term graph?To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.
To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:
[tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]
Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).
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