Answer:
a. 0.1024
b. 0.8976
Step-by-step explanation:
The probability that x generators don't fail when they are needed follows a binomial distribution, because we have n identical and independent events (2 backup generators) with a probability p of success (1-0.32=0.68) and a probability q of failure (0.32).
So, the probability that x generator success are calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*q^{n-x}\\P(x)=\frac{2!}{x!(2-x)!}*0.68^{x}*0.32^{2-x}[/tex]
Then, the probability that both generators fail during a power outage is equal to the probability that 0 generators success. It is calculated as:
[tex]P(0)=\frac{2!}{0!(2-0)!}*0.68^{0}*0.32^{2-0}=0.1024[/tex]
At the same way, the probability of having a working generator in the event of a power outage is equal to the probability that at least 1 generator success. It is calculated as:
[tex]P(x\geq1)=P(1)+P(2) \\P(1)=\frac{2!}{1!(2-1)!}*0.68^{1}*0.32^{2-1}=0.4352\\P(2)=\frac{2!}{2!(2-2)!}*0.68^{2}*0.32^{2-2}=0.4624\\P(x\geq1)=0.4352+0.4624=0.8976[/tex]
This probability is not high enough for the hospital, both generators fail approximately the 10% of the time when needed.
Esther, Vida, and Clair were asked to consider two different cash flows: GH¢1000 that they could receive today and GH¢3000 that would be received 3 years from today. Esther wanted the GH¢1000 today, Vida chose to collect GH¢3000 in 3 years, and Clair was indifferent between these two options. Which of the three women made the right choice? Explain
Answer:
Esther made the right option which gives her maximum value at the end of 3 years than Vida and Clair.
Step-by-step explanation:
The life is all about making the right choices. Esther has made a decision to collect GH¢1000 now. To calculate future value of Esther choice at the end of 3 year we will use formula below,
FV = PV [tex](1 + r)^{t}[/tex]
discount factor at year 3 t 10% is 0.751
FV = 1000 (0.751) / (1.1)3
FV = GH¢2487.
Vidha choose to collect GH¢3000 at end of 3 year, the present value of GH¢3000 at 10% discount rate will be;
PV = FV [tex](1 + r)^{-t}[/tex]
PV = 3000 (0.751)
PV = GH¢2253.
Clair is indifferent from the choices given but this is also not a smart choice.
Esther has made the right choice among the three women and she gets maximum value of GH¢2487.
A box-contains 3 blue and 2 red marbles while another box contains 2
blue and 5 red marldes. A marble drawn at random from one of the boxes
turns out to be blue. what is the probability that it came from the first box?
Answer:
3/5
Step-by-step explanation:
(3/5) · (1/2) over (3/5) · (1/2) + (2/5) · (1/2)
= 3/5
Not sure if I got it right...I know it is one of the first 2.
Answer:
Step-by-step explanation:
-6x^2 + x -3 + 2x + 4
________________________
x^2 + 9
-6x^2 + 3x + 1
__________
x^2 + 9
the solution is the first one
Answer:
D.[tex]\frac{-6x^{2}-x-7 }{x^{2}+9}[/tex]
Step-by-step explanation:
since the [tex]x^{2}+9=x^{2} +9[/tex] you just have to add [tex]\frac{-6x^{2}+x-3-2x-4 }{x^{2}+9 }[/tex] so the answer will be: [tex]\frac{-6x^{2}-x-7 }{x^{2}+9 }[/tex]
Makayla invested $630 in an account paying an interest rate of 5.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,860?
Answer:
19.7 or 20 rounded
Step-by-step explanation:
A = $ 1,861.65
A = P + I where
P (principal) = $ 630.00
I (interest) = $ 1,231.65
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pe^rt
Calculate Principal Amount, solve for P
P = A / e^rt
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
You are building a curio cabinet in the form of a rectangular prism that must be 4 feet tall with a volume of 48 cubic feet. The length and with each must be no more than tot. Which of the following dimensions are the possible width and length of the cabinet? a) 15 foot by feet b) 24 feet by 5 foot c) 25 feet by 4.8 feet d) 3 feet by 4 feet e) 4 feet by 12 feet 19
Answer:
d) 3 feet by 4 feet
Step-by-step explanation:
Volume of the prism = 48 feet³
Height if the prism = 4 feet
To determine the possible values of the length and width of the prism let's divide the volume by the height.
So 48/4 = 12
So we'll be looking for a product of two numbers to give us 12
And it's between 12 and 1, 4 and 3 , and 6 and 2.
We have only 4 and 3 in the option.
If 8-2x<12 is -2 a solution to the inequality
Answer:
no
Step-by-step explanation:
Let's plug in -2 for x.
8 - 2 (-2) <12
8 + 4 < 12
12 < 12
Since this is a false statement, -2 is not a solution to the inequality.
Answer: No
Step-by-step explanation: To determine whether x = -2 is a solution to the inequality, substitute a -2 in for r.
So we have 8 - 2(-2) < 12.
Notice that I used parentheses.
This is a great habit to get into when
substituting numbers in for variables.
So we have 8 - (-4) which can be changed to 8 + (+4) or +12.
Since 12 is not less than 12, -2 is not a solution.
What is the difference between a centroid, orthocenter, and a circumcenter?
Giving Brainliest. :D
Please help.
Answer:
Take an example in a triangle:
The orthocenter is the intersection point of 3 altitudes.
The centroid is the intersection point of 3 medians.
The circumcenter is the intersection point of 3 bisectors.
Centroid, orthocenter, and circumcenter are collinear.
Hope this helps!
:)
There are 2 new seats in each row in a school auditorium. There are 20 rows in the auditorium. Each new seat costs $84 what is the cost for the new seats
Answer:
$3360
Step-by-step explanation:
First you have to do 20 times 2 to find out how many new seats there are.
Then you have to multiple that number by the cost to get the cost of all the new seats.
I hope this helped ;)
Find the value of x.
Answer:
x = 98
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
x + 24 = 122
Subtract 24 form each side
x+24-24 =122-24
x =98
Answer:
[tex] x = 98 \: \: degrees \\ [/tex]
Step-by-step explanation:
The exterior angle is equal to sum of opposite interior angles in a triangle.
[tex]24 + x = 122 \\ x = 122 - 24 \\ x = 98 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Isaac is working as a security guard. He earns $8.45 an hour. He earns double time for any overtime over 40 hours. Last week he worked 44 hours. How much did he earn last week? ( HInt: double time means 2 times the regular hourly rate. )
Answer:
$405.60
Step-by-step explanation:
If Isaac works for 40 hours will earn $8.45×40=$388. Since he worked 4 extra hours, he will earn $8.45×2×4 since he worked 4 extra hours. $8.45×2=$16.90, which is the amount he earns for every extra hour he works. $16.90×4=$67.60. Now if we add $67.60+$388=$405.60.
Hope this helps!
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. p(x) = 19x - 15
Step-by-step explanation:
→Set it up, like so:
[tex](25x)-(6x+15)[/tex]
[tex]25x - 6x-15[/tex]
→Add like terms (25x and -6x):
[tex]19x - 15[/tex]
What is the domain of g?
Answer:
domain is [-6,6] or -6 ≤ x ≤6
Step-by-step explanation:
domain is x value of given function
dark circle means that that number is included in domain
Find f(-7) if f(x) = 2x + 8
Answer:
-6
Step-by-step explanation:
f(x) = 2x + 8
Put x as -7.
f(-7) = 2(-7) + 8
Multiply first.
f(-7) = -14 + 8
Add.
f(-7) = -6
Adrian makes $36.50 per day plus tips. His average tip is 17% of the total amount of money customers spend. Which equation could be used to determine x, the total amount of money customers would need to spend for Adrian to earn a daily income of $150? A. 150 = 36.50 + 17x B. 150 = 0.17 + 36.50x C. 150 = x(17 + 36.50) D. 150 = 36.50 + 0.17x
Answer:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope m would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
Step-by-step explanation:
For this case we know that the fixed cost is $36.50 and the variable cost is 17% of the total amount of money customers spend, let's asusme that this variable is x. And we can create a model like this one:
[tex] y = mx +b[/tex]
Where y represent the income and x the the total amount of money customers would need to spend. For this case the value for b = 36.50 and the slope would be 0.17 since if we convert the % into a fraction we got 0.17. So then the best option is:
[tex] 150 = 36.5 +0.17x[/tex]
D. 150 = 36.50 + 0.17x
Scientists use carbon-14 dating to determine the age of a sample of organic material. a. The amount C (in grams) of a 100-gram sample of carbon-14 remaining after t years is represented by the equation C=100(0.99988)t C = 100 ( 0.99988 ) t . Use a calculator to find the amount of carbon-14 remaining after 4 years. Round your answer to the nearest hundredth. The amount of carbon-14 remaining is about grams. b. What percent of the carbon-14 remains after 4 years? Round your answer to the nearest hundredth. The percent of carbon-14 remaining is about %.
Answer:
a) 99.95 grams are remaining after 4 years.
b) The percent of carbon-14 remaining is about 99.95%
Step-by-step explanation:
The amount of carbon 14 remaining after t years is given by the following equation:
[tex]C(t) = 100(0.99988)^{t}[/tex]
a) Amount remaining after 4 years.
[tex]C(t) = 100(0.99988)^{4} = 99.95[/tex]
99.95 grams are remaining after 4 years.
b) Percentage remaining after 4 years:
[tex]p = \frac{100*C(4)}{C(0)} = \frc{100*99.95}{100} = 99.95[/tex]
The percent of carbon-14 remaining is about 99.95%
a) 99.95 grams are remaining after 4 years.
b) The percent of carbon-14 remaining is about 99.95%
The calculation is as follows:a.
The amount of carbon should be
[tex]C=100(0.99988)^4[/tex]
= 99.95 grams
b. The percent is
[tex]= 100 \times 99.95100[/tex]
= 99.95%
Learn more: https://brainly.com/question/6269728?referrer=searchResults
Please help! Correct answer only, please! I need to finish this assignment this week. Determine the value of the following if it is possible. If it is not possible, explain. Matrix P has a dimensions of 3 X 4 and Matrix Q has the dimensions 4 X 5. Determine the dimensions of the matrix PQ if it is possible. Explain why if it is not. (refer to video part 4) Group of answer choices A. Matrix PQ would have the dimensions 3 X 4 B. Matrix PQ would have the dimensions 4 X 5 C. Matrix PQ would have the dimensions 3 X 5 D. These matrices can not be multiplied because their dimension don't align.
Answer: c) 3 x 5
Step-by-step explanation:
When multiplying matrices of dimension m x n, the "inside" values MUST be the same. The dimension of their product is the "outside" values.
P = 3 x 4
Q = 4 x 5
The "inside" values are both 4 so the product can be found.
The "outside" values are 3 & 5 so the dimension of the product is 3 x 5.
If the problem was flipped to: find QP, we would get the following:
Q = 4 x 5
P = 3 x 4
the "inside" values of 3 & 5 are not the same so the product does not exist.
Which equation has the same solution as x^2+8x-33 =0 ?
1) (x+4)2 =49
3) (x+4)2 =17
2) (x-4)2 =49
4) (x-4)2=17
Please show work
Answer:
1) (x+4)2 =49
Step-by-step explanation:
x^2+8x-33 = 0 Factor this equation
(x + 11)(x - 3) = 0 Set each equation equal to 0
x = -11 and 3
Test the first equation to see if it has the same solution
(x+4)2 = 49 Simplify the parentheses
(x+4)(x+4) = 49 FOIL the equation
x^2 + 8x + 16 = 49 Subtract 49 from both sides
x^2 + 8x - 33 = 0 This is the correct solution.
Answer: correct answer is A
Step-by-step explanation:
Urgent help!
QUESTION 1
A fruit basket has both mangoes and oranges and can accommodate only 80 mangoes and oranges when
full. If there are x mangoes in a full basket,
(i) Write an expression for the number of oranges in it.
(ii) If an orange costs 50 cents and a mango costs 40 cents, write an expression for the amount of
money collected (in dollars) for the sale of all the mangoes and oranges in the full basket, S ( x ) .
(iii) Find the total amount collected from selling all the fruits in the full basket if there are 35 mangoes
in it.
Answer:
(i) [tex]80-x[/tex]
(ii) [tex]S(x) = 40 - 0.10x[/tex]
(iii) $36.5
Step-by-step explanation:
Given that:
1. Total Number of fruits = 80
2. Number of mangoes = x
3. Both mangoes and oranges are there in the basket.
Solution (i):
Only mangoes and oranges are there in the basket and the basket is full.
so, Number of mangoes + Number of oranges = Total number of fruits
x + Number of oranges = 80
Number of oranges = [tex]80 -x[/tex]
Solution (ii):
Given:
Cost of an orange = 50 cents = $0.50
Cost of a mango = 40 cents = $0.40
Cost for x mangoes = [tex]\$ 0.40x[/tex]
Cost for ([tex]80-x[/tex]) oranges = [tex]\$ 0.50 \times (80-x)[/tex]
[tex]\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x[/tex]
Solution (iii):
Put value of x = 35 in S(x)
[tex]S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5[/tex]
Hence, answers are:
(i) [tex]80-x[/tex]
(ii) [tex]S(x) = 40 - 0.10x[/tex]
(iii) $36.5
Find the area of the triangle
Need help fast
Answer:
118.3
Step-by-step explanation:
area = base * height / 2
The two sides forming a right angle can be used as base and height.
area = 13 m * 18.2 m / 2
area = 118.3 m^2
Answer:it is 118.2977011m^2 because the instruction says do not round
Step-by-step explanation:
The polynomial P(x) = 3 – 2x2 + 5x5 – 7x7 has what order?
Answer:
This, polynomial has order 7.
Step-by-step explanation:
Given the polynomial
P(x) = 3 – 2x2 + 5x5 – 7x7
[tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
Order for any polynomial is highest exponential value for variables . The exponent for polynomial is also called as degree.
Hence in terms of degree, the term in polynomial which has the highest degree . That degree is the order of the polynomial.
For example ,
in [tex]x^5 + x^8 + x^9[/tex]
here we see that variable x has highest power of 9. Thus, order of the given equation is 9.
Similarly for the polynomial given we see that
in the polynomial [tex]P(x) = 3 - 2x^2+ 5x^5 - 7x^7[/tex]
x has three power 2, 5 and 7 .
As 7 is the highest power of P(x) = 3 - 2x^2+ 5x^5 - 7x^7
This, polynomial has order 7.
Bob raked 30 bags of leaves in 3 hours. If he raked the same leaves did he rake per hour
Divide total bags by total hours:
30 bags / 3 hours = 10 bags per hour
HDTV screens usually have a width-to-heigh ratio of 16:9. Which screen dimensions are in the same proportion?
Answer:
4: 3
Step-by-step explanation:
In this case, we have that there is a relationship between width and height, which is 16: 9, which means that any screen that has the same ratio would be an identical screen.
How would we do this? it must either be raised to a power or rationalized on both sides of the ratio.
If we raise to a power, it would give very large dimensions for an HDTV, therefore, it is best to remove the square root on both sides, since it has more common values for a TV.
[tex]\sqrt{16} :\sqrt{9}[/tex]
4: 3
Therefore, a 4: 3 screen is a good choice for an HDTV with the same ratio.
Answer:
Ideiidididid
Step-by-step explanation:
Cici
Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of 120120120 square centimeters, and she wants it to weigh 400400400 grams. The density of the clay she is using is 1.61.61, point, 6 grams per cubic centimeter.
What should be the height of the paperweight?
Answer:
Step-by-step explanation:
We would determine the volume of the
pyramid-like paperweight. Formula for volume is expressed as
Volume = mass/density
From the information given,
mass = 400g
Density = 1.61g/cm³
Volume = 400/1.61 = 248.45cm³
The formula for determining the volume of a pyramid us expressed as
Volume = 1/3 × base area × height
From the information given,
Base area = 120 cm²
Volume = 248.45cm³
Therefore,
248.45 = 1/3 × 120 × height
248.45 = 40 × height
height = 248.45/40 = 6.2 cm
A survey of 250 homeless persons showed that 14 were veterans. Find a point estimate for the population proportion of homeless persons who are veterans.
Answer:
[tex] \hat p =\frac{14}{250}= 0.056[/tex]
And for this case that represent the 5.6% of the homeless persons who are veterans
Step-by-step explanation:
We know that in a survey of 250 homeless persons 14 were veterans. We can find the estimated proportion of homeless persons who are veterans with the following formula:
[tex] \hat p =\frac{X}{n}[/tex]
The last one is an unbiased estimator of the true population proportion p
And replacing the info given we got:
[tex] \hat p =\frac{14}{250}= 0.056[/tex]
And for this case that represent the 5.6% of the homeless persons who are veterans
Drew writes down a number between 1 and 1000. Mary must determine that number by asking "yes/no" questions of Drew. Mary knows that Drew always tells the truth. If Mary uses an optimal strategy, then she will determine the answer at the end of exactly how many questions in the worst case?
Answer: 10 questions.
Step-by-step explanation:
The optimal aproach would be divide the total range in half, for example, she can ask:
Is the number equal or greater than 500?
if he answers no, now she knows that the numer is in the range 1 to 499
if he says yes, she can know that the number is in the range 500 to 1000.
Now, suppose that the answer is yes.
Now she can ask if the number is equal or greater than 750.
Now we have two possible sets. (500, 749) and (750 , 1000).
Now we can divide those sets again, depending on the answer.
suppose we got the set of (750, 1000)
we can divide it into two sets and so on.
So, we have 999 options and we want to divide it by 2 until we reach to 1., the number of divisions by 2 is the number of times that she asked a question.
999/2^n ≤ 1.
we must find the smaller n that keeps the above inequality true.
999 ≤ 2^n
knowing that 2^10 = 1024.
999/1024 = 1024
So in the worst case, she should ask 10 questions.
The cone-shaped container for the echidna treats holds to 218 cubic centimeters of ants and has a radius of 4 cm. rounded to the nearest whole number, what is the height of the container? use 3.14 for pie symbol
Answer:
13 cm
Step-by-step explanation:
To find the answer, you can use the formula to calculate the volume of a cone and isolate the height:
V= πr^2[tex]\frac{h}{3}[/tex]
V= volume= 218 cubic centimeters
π= 3.14
r= radius= 4 cm
h=height
218= 3.14*4^2*[tex]\frac{h}{3}[/tex]
218*3=3.14*16*h
654=50.24*h
h=654/50.24
h=13
According to this, the height of the container is 13 cm.
the answer to this !!!
Answer: A=12, B=2, C=11
Step-by-step explanation:
With the given problem, you would first expand the numerator.
[tex]\frac{x^1^5y^3z^1^2}{x^3yz}[/tex]. Then you can simply from there. You can subtract the exponents. [tex]x^1^2y^2x^1^1[/tex]
The Trapezoidal rule Tn on the interval [0,5) will be exact for
all polynomial of degree at most
Select one
O A 5
OB. None
C. 3
O 0.9
OE
Answer:
degree 1
Step-by-step explanation:
The trapezoidal rule is exact when the second derivative is zero. This occurs when the polynomial is degree one or less
What to you think 28.6×100
Answer:
28.6 × 100
⇒ 286/10 × 100
⇒ 286 × 10
⇒ 2860
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?
The student got____problems correct on the test.
Answer:
The student got 16 problem correct
Step-by-step explanation:
Take the number of problems and multiply by the percent correct
20 * 80%
20 *.80
16
The student got 16 problem correct
Answer: The student got 16 problem correct.
Step-by-step explanation: To solve this problem, you first want to take the number of problems that are on the math test and multiply that by the percent the student got correct.
So we have 20 × 80%
Now write 80% as a decimal to get .80.
So we have 20 × .80 which is equal to 16.
So the student got 16 problems correct
and 4 problems incorrect on their test.