Project's cost at time 0 is $46,272.84
What is profitability index?
Profitability index is the present value of future cash flows divided by the project cost at time 0.
The present value of each future cash flow can be determined using the present value formula of a single cash flow as below;
PV=FV/(1+r)^N
FV=future cash inflows in years 1-4
r=discount rate=8.5%
N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.
PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4
PV of future cash flow=$41,553.01
Profitability index=PV of future cash flows/Project cost
Profitability index= .898
Project cost=unknown(assume it is X)
.898=$41,553.01 /X
X=$41,553.01/ .898
X=project's cost=$46,272.84
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Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
Someone pls help me, I’m so stuck lol
By solving a linear equation, we conclude that you bought 4 buns and 5 cakes.
How many of each did I buy?
We will define the two variables:
x = number of buns bought.y = number of cakes bought.We know that you spent exactly £4.35, then we only need to solve the linear equation:
x*0.40 + y*0.55 = 4.35
We need to solve that equation for x and y, such that the values of x and y can only be positive whole numbers.
We can rewrite the equation as:
y*0.55 = 4.35 - x*0.40
y = (4.35 - x*0.40)/0.55
Now we only need to evaluate it in different values of x, and see for which value of x, the outcome y is also a whole number.
We will see that for x = 4, we have:
y = (4.35 - 4*0.40)/0.55 = 5
So you bought 4 buns and 5 cakes.
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40p + 55p = 95p
435p ÷ 95p = 4.57...
So, the sum of the two pairs can go into £4.35 four times.
That meant if I increase the buns & cakes four times, it will help me get closer to the sum of £4.35 & work out which was extra
(40 x 4 = 160) & (55 x 4 = 220)
160 + 220= 380p or £3.80
Adding them up I get 380 pence & that's 55p short to getting to the sum of 435p or £4.35
(435-380=55p)
Thus, the extra is the cake, meaning you bought 4 buns and 5 cakes.
Hope this helps!
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y=60x+30
y=60x+30 represents what Health Club B charges. Health Club A charges a $50 sign-up fee and $27 per month.
Answer:
y = (constant variable x time) + independent variable
y = 60x + 30 ← Health Club B
y = 27x + 50 ← Health Club A
Step-by-step explanation:
I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.
ZA =
Round your answer to the nearest hundredth.
Answer:
Rounded to the nearest tenth would be 75.5 degrees
Step-by-step explanation:
Find the value of x.
Answer:
17
Step-by-step explanation:
i think its the right answer
The controller of MingWare Ceramics Inc. wishes to prepare a cost of goods sold budget for September. The controller assembled the following information for constructing the cost of goods sold budget: Direct materials: Enamel Paint Porcelain Total Total direct materials purchases budgeted for September $35,870 $7,530 $139,890 $183,290 Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 2,980 2,710 7,150 12,840 Direct labor cost: Kiln Department Decorating Department Total Total direct labor cost budgeted for September $51,550 $149,500 $201,050 Finished goods inventories: Dish Bowl Figurine Total Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850 Desired inventory, September 30 3,720 4,590 4,360 12,670 Work in process inventories: Estimated inventory, September 1 $3,540 Desired inventory, September 30 1,980 Budgeted factory overhead costs for September: Indirect factory wages $80,400 Depreciation of plant and equipment 10,550 Power and light 5,110 Indirect materials 3,390 Total 99,450 Use the preceding information to prepare a cost of goods sold budget for September. For those boxes in which you must enter subtracted or negative numbers use a minus sign. MingWare Ceramics Inc. Cost of Goods Sold Budget For the Month Ending September 30 Finished goods inventory, September 1 $Finished goods inventory, September 1 Direct labor $Direct labor Direct materials: $- Select - - Select - $- Select - - Select - $- Select - Direct labor fill in the blank 15 - Select - - Select - $- Select - Work in process inventory, September 30 fill in the blank 22 - Select - $- Select - - Select - $- Select - 4,100
The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:
Cost of Goods Sold Budget:Beginning inventory of finished goods $11,850
Cost of goods manufactured 485,310
Ending inventory of finished goods (12,670)
Cost of Goods Sold $484,490
What is the cost of goods sold budget?The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.
The cost of goods sold budget is based on the cost of goods manufactured budget.
Data and Calculations:Direct materials: Enamel Paint Porcelain Total
Total direct materials purchases
budgeted for September $35,870 $7,530 $139,890 $183,290
Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 (2,980) (2,710) (7,150) (12,840)
Materials used in production $183,250
Direct labor cost: Kiln Department Decorating Department Total
Total direct labor cost
budgeted for September $51,550 $149,500 $201,050
Finished goods inventories: Dish Bowl Figurine Total
Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850
Desired inventory, September 30 3,720 4,590 4,360 12,670
Cost of goods manufactured budget:Work in process inventories:
Estimated inventory, September 1 $3,540
Direct materials used in production $183,250
Direct labor costs $201,050
Total factory overhead costs $99,450
Desired inventory, September 30 (1,980)
Cost of goods manufactured $485,310
Budgeted factory overhead costs for September:Indirect factory wages $80,400
Depreciation of plant and equipment 10,550
Power and light 5,110
Indirect materials 3,390
Total 99,450
Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.
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In a study of 250,178 cell phone users,it was found that 81 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is 0.000412 probability of a person developing cancer of the brain or nervous system. We therefore expect about 104 cases of such cancer in a group of 250,178 people.Estimate the probability of 81 or fewer cases of such cancer in a group of 250,178. What do these results suggest about media reports that all cell phone cause cancer of the brain or nervous system?
P(x≤81)=[tex]P(x\leq 81)\\What do these results suggest about media reports?[/tex]
Using the normal distribution, the probability is given as follows:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For this problem, the proportion and the sample size are given by:
p = 0.000412, n = 250178
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 250178 \times 0.000412 = 103.1[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{250178 \times 0.000412 \times (1 - 0.000412)} = 10.15[/tex]The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]
Z = -2.13
Z = -2.13 has a p-value of 0.0158.
Hence:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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solve the algebraic equation 7 x - 2 equals to 2x + 13
Answer:
x = − 6
Step-by-step explanation:
I have my work
Use a table of values to graph the function ƒ(x) = |x + 2| – 1. Select the correct graph below.
Find the equation of the line parallel to y equals 1 half x plus 2 that passes through the point (4, 5) in slope-intercept form.
Answer: [tex]y=\frac{1}{2}x+3[/tex]
Step-by-step explanation:
We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form [tex]y=mx+b[/tex], and we can convert from point-slope form to this with simple algebra.
The point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope of the line, and [tex](x_1,y_1)[/tex] is the point.
We know that the line is parallel to [tex]y=\frac{1}{2}x+2[/tex], which means it will have the same slope. The slope of this line is [tex]\frac{1}{2}[/tex], so the slope of any line parallel to it will also be [tex]\frac{1}{2}[/tex].
[tex]y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3[/tex]
AN ARTICLE IN USA TODAY STATED THAT “INTERNAL SURVEYS PAID FOR BY DIRECTORY ASSISTANCE PROVIDERS SHOW THAT EVEN THE MOST ACCURATE COMPANIES GIVE OUT WRONG NUMBERS 15% OF THE TIME.” ASSUME THAT YOU ARE TESTING SUCH A PROVIDER BY MAKING 10 REQUESTS AND
ALSO ASSUME THAT THE PROVIDER GIVES THE WRONG TELEPHONE NUMBER 15%
OF THE TIME. FIND THE PROBABILITY OF GETTING ONE WRONG NUMBER.
Step-by-step explanation:
I assume this means exactly one wrong number in the 10 attempts.
the probability to get a wrong number is 0.15 (15%).
therefore, the probability to get a correct number is
1 - 0.15 = 0.85
in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :
0.15×0.85⁹ = 0.034742542...
this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.
how many different constellations can we have that way ?
10.
because the wrong number could be given at any of the 10 attempts.
so, the probability to get exactly 1 wrong answer is
10×0.15×0.85⁹ = 0.34742542... ≈ 35%
now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.
the probability to get all 10 numbers correctly is
0.85¹⁰ = 0.196874404... ≈ 20%
and therefore, the probability to get at least 1 number wrong is
1 - 0.196874404... = 0.803125596... ≈ 80%
FYI :
this would be, of course, also the result of we did it the complex way :
the sum of the probabilities of
exactly 1 number wrong
exactly 2 numbers wrong
...
exactly 9 numbers wrong
all 10 numbers wrong
and for each of the cases of n wrong numbers the probability is
(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)
this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.
and again, all this summed up (1 <= n <= 10) is the same as
0.803125596...
The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Now, Let q = probability of giving out wrong number = 15 % = 0.15
And, p = probability of not giving out wrong number = 1 - q
= 1 - 0.15 = 0.75
Hence, For a binomial probability,
P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.
With n = 10 and x = 1, the probability of getting a number wrong
P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
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How many values are in the range?
0 to 50
2. This month Tania saved
6 times as much money
as last month. Last
month she saved $24.
How much did Tania
save this month?
3.
Answer:
$144
Step-by-step explanation:
24*6 = 144
△ABC has vertices A(-2, 0), B(0,8), and C(4,2). Find the coordinates of the point of congruency of the altitudes (H)
Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the slope of BC, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2.
For the slope of CA, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3.
For the slope of AB, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4.
Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.
Since side AB is perpendicular to side QC, we have:
m₁ × m₂ = -1
Slope of AB × Slope of QC = -1
Slope of QC = (k - 4)/(h - 2)
4 × (k - 4)/(h - 2) = -1
(4k - 16)/(h - 2) = -1
4k - 16 = -h + 2
4k + h = 18 .......equation 1.
Similarly, we have the following:
Slope of BC × Slope of AH = -1
-3/2 × (k)/(h + 2) = -1
3k/(2h + 4) = 1
3k = 2h + 4
3k - 2h = 4 .......equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
8k + 2h = 36
3k - 2h = 4
11k = 40
k = 40/11.
For the value of h, we have:
h = -4k
h = -4 × (40/11)
h = -160/11
Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
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find r^-1 (x)
r(x) = 2/3 (4x -5)
Answer:
Step-by-step explanation:
Let r(y)=x.
[tex]x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}[/tex]
Write a linear function that passes through the points (3, -7) and (0, 15)
Answer:
The linear function for the given pts. will be
[tex]y = \frac{ - 22}{3}x + 15[/tex]
Step-by-step explanation:
Hello!
[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]
The following data were accumulated for use in reconciling the bank account of Mathers Co. for July: 1. Cash balance according to the company's records at July 31 $20,010. 2. Cash balance according to the bank statement at July 31, $21,110. 3. Checks outstanding, $4,060. 4. Deposit in transit, not recorded by bank, $3,260. 5. A check for $480 in payment of an account was erroneously recorded in the check register as $840. 6. Bank debit memo for service charges, $60. a. Prepare a bank reconciliation
The preparation of a bank reconciliation statement for Mathers Co. for July is as follows:
Bank Reconciliation StatementAt July 31
Cash balance per bank statement as at July 31, $21,110
Deposit in transit 3,260
Outstanding checks (4,060)
Balance as per adjusted cash balance $20,310
What is bank reconciliation?A bank reconciliation statement is a summary of banking and business cash transactions so that their balances can agree.
Bank reconciliations help the company to reconcile its bank account as per bank statements with its internal financial records.
The steps for preparing a bank reconciliation include:
Discover the discrepancies in both statements.Adjust the cash balance with entries from the bank statement and other accounting errors. Adjust the bank statements with uncredited deposits, checks not yet presented, and accounting errors. Compare the end balances.Data and Calculations:Cash balance per Cash Account at July 31 $20,010
Cash balance per bank statement at July 31, $21,110
Checks outstanding, $4,060
Deposit in transit $3,260
Transposed payment $360 ($840 - $480)
Bank service charges $60
Adjusted Cash Balance per Cash Account:Cash balance per Cash Account as at July 31 $20,010
Transposed payment 360
Bank service charges (60)
Adjusted cash balance per cash account $20,310
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I need help solving
The graph of the translated function can be seen in the image below.
How to translate the graph of a function?
For a given function f(x), we define a vertical translation of N units as:
g(x) = f(x) + N
Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.
In this case, we have:
y = f(x) - 2
Then we just need to translate the given graph 2 units below, we will get the graph you can see below.
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Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1 % interest compounded monthly. She just turned 33 and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time
Answer:
$152,419.36
Step-by-step explanation:
The future value of an ordinary annuity is given by the formula ...
FV = P((1 +r/12)^(12t) -1)/(r/12)
where P is the monthly payment, r is the annual interest rate, and t is the number of years.
Annuity valueFor P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...
FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36
The value of Jolene's retirement account when she turns 60 will be $152,419.36.
Really not sure what is meant by this when I'm only given one number, would appreciate help very much!!!!
Using continuous compounding, it is found that the value of r is of r = 7.7%.
What is continuous compounding?The amount of money after t years in continuous compounding is:
[tex]P(t) = P(0)e^{rt}[/tex]
In which:
P(0) is the initial amount.r is the exponential growth rate.The doubling time of 9 years means that P(9) = 2P(0), which is used to find r, hence:
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]2P(0) = P(0)e^{9r}[/tex]
[tex]e^{9r} = 2[/tex]
[tex]\ln{e^{9r}} = \ln{2}[/tex]
[tex]9r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{9}[/tex]
r = 0.077.
r = 7.7%.
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Use the function f(x) = 4x² - 7x-15 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph
a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The function has a minimum and grows in the + y direction.
d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.
How to analyze and interpret quadratic functions?
In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:
4 · x² - 7 · x - 15 = 0
4 · [x² - (7 / 4) · x - (15 / 4)] = 0
x² - (7 / 4) · x - (15 / 4) = 0
x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64
x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64
(x - 7 / 8)² = 289 / 64
x - 7 / 8 = ± 17 / 8
x = 7 / 8 ± 17 / 8
Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).
b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).
c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.
d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.
First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.
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jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did he sell?
Check what other students also ask
Answer:
300 tarts
Step-by-step explanation:
we must solve this equation by going backwards
3/4 of something (as 1/4 was given away) is 150
150 / 3/4 is what you must do
or
150 * 4/3
that is
200
3/5 was sold so 2/5 was left
2/5 of something is 200
200 / 2/5
200 * 5/2
that is
500
3/5 of that was sold
so
500 * 3/5 is 300
300 tarts were sold
How do you compute this? 4(-2, 3) - 2(6, -7)
Step-by-step explanation:
Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))
Classify each number below as an integer or not.
Using it's concept, the integer numbers in the data-set are given as follows:
6/1, -14, 56/7.
The other numbers, -74.48 and 3/17, are not integers.
What are integer numbers?Integer numbers are numbers that have no decimal part. They can be represented by pure numbers, either negative or positive, or also fractions that result in an exact division.
In this problem, we have that:
The division of 6 by 1 has a exact result of 6, hence 6/1 is an integer.The division of 56 by 7 has a exact result of 8, hence 56/7 is an integer.-14 is a pure number with no decimal part, hence it is an integer.-74.48 has a decimal part, hence it is not an integer.3/17 is not an exact division, hence it is not an integer.More can be learned about integer numbers at https://brainly.com/question/17405059
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On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1. Path Expected Duration (weeks) Variance A 10 1.21 B 8 2.00 C 12 1.00 D 15 2.89 E 14 1.44 Click here for the Excel Data File Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.) a. Graduation time? b. The end of week 15? c. The end of week 13?
The probability that the project will be completed before the graduation time is 0.6873.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event.
From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.
Also, the probability that the project will be completed before the end of week 15 will be 0.3983.
Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.
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Please help!!!!! Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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3x - 2(2x - 5) = 2(x + 3) - 8
Answer:
x = 4
Step-by-step explanation:
Hello!
We can solve for x by expanding the parentheses and isolating x.
Solve for x3x - 2(2x - 5) = 2(x + 3)-83x - 4x + 10 = 2x + 6 - 8-x + 10 = 2x - 210 = 3x - 212 = 3xx = 4The value of x is 4.
What is in simplest form?
A.
B.
C.
D.
Answer:
C. 8√3
Step-by-step explanation:
* = multiply or times
To find √192 in its simplest form we need to divide it by a square number like 64.
192/64 = 3
√192 = √64 * √3 = 8√3
what is the solution I need help
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Square root of numbersThe square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.
For the square root of √0.09
√0.09 = 0.3
Similarly for the square root of √0.16
√0.16 = 0.4
Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
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A balloon has a circumference of 28 in use the circumference to approximate the surface area of the ballon to the nearest square inch
The surface area of the balloon is 249 in².
What is the surface area of the balloon ?A balloon has the shape of a sphere. The distance round the sphere is equal to the circumference of the sphere.
Circumference of the sphere = 2πr
Where:
r = radius π = pi = 22 / 7Radius - circumference / 2π
28 / ( 2 x 22/7) = 4.45 inches
Surface area of a sphere = 4πr²
4 x 22/7 x 4.45² = 249 in²
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