A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15. From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively. Suppose that a cost overrun is experienced by the agency. What is the probability that the firm involved is firm B
Answer:
68.11% probability that the firm involved is firm B
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Cost overrun
Event B: Agency B used.
A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.
This means that [tex]P(B) = 0.45[/tex]
From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.
This means that [tex]P(A|B) = 0.14[/tex]
Probability of cost overrun.
Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.
So
[tex]P(A) = 0.4*0.01 + 0.45*0.14 + 0.15*0.17 = 0.0925[/tex]
What is the probability that the firm involved is firm B
[tex]P(B|A) = \frac{0.45*0.14}{0.0925} = 0.6811[/tex]
68.11% probability that the firm involved is firm B
The price of an item has risen to $282 today. Yesterday it was $120. Find the percentage increase.
Answer:
57.45% increase
Step-by-step explanation:
The formula for percent change is (new - old)/new x 100.
The new value is $282 and the old value is $120.
Plug that into the formula:
(282 - 120)/282 x 100
= 57.45%
I hope this helped!
Two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 95 mph. If they pass each other in 3 hours, what is the speed of each?
Answer:
325 mph and 420 mph
Step-by-step explanation:
If the speed of the slower plane is x, then the speed of the faster plane is x + 95.
The distance traveled by the slower plane is 3x.
The distance traveled by the faster plane is 3(x + 95).
The total distance is 2235 miles.
3x + 3(x + 95) = 2235
3x + 3x + 285 = 2235
6x = 1950
x = 325
x + 95 = 420
The speed of the planes is 325 mph and 420 mph.
How do you write 345,000,000,000 in scientific notation
Answer:
[tex] 3.45 \times {10}^{11} [/tex]
Step-by-step Explanation:
[tex]345,000,000,000 = 3.45 \times {10}^{11} \\ [/tex]
A tree harvester estimates the trunk of a tree to have a height of about 36 meters and a base diameter of about 0.5 meter. The wood of the tree has a density of about 610 kilograms per cubic meter. Find the mass of the trunk. Round your answer to the nearest hundred. in kilograms
Answer:
The mass of wood is 4309.65 kg.
Step-by-step explanation:
Volume of a cylinder is:
[tex]V = \pi r^{2} h[/tex]
Where [tex]r[/tex] is the radius of base of cylinder
and [tex]h[/tex] is the height of the cylinder
[tex]r=\dfrac{d}{2}[/tex]
[tex]d[/tex] is the diameter of base of cylinder.
A tree's trunk is in the shape of cylinder only. And we are given the following details:
[tex]d = 0.5m\\\Rightarrow r = \dfrac{0.5}{2} m[/tex]
[tex]h =36 m[/tex]
[tex]V = \pi (\dfrac{0.5}{2})^2 \times 36\\\Rightarrow V = 7.065\ m^3[/tex]
Density of wood of tree = 610 kg per cubic meter
Mass of trunk = Volume [tex]\times[/tex] density
[tex]\Rightarrow 610 \times 7.065\\\Rightarrow 4309.65\ kg[/tex]
Hence, mass of trunk is 4309.65 kg.
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?
Answer:
scale
Step-by-step explanation:
scales are used to measure weight
The tool that Caroline can use to Measure the mass of a dictionary is; Pan Balance.
What is the Correct Tool of Measurement?When discussing measurements, there are different tools and equipment's that can be used such as Ruler, Pan balance, Stopwatch, Liter container.
Now, the tools above can be used for measuring different things but our question wants the one that would be used to measure the mass of a dictionary and the correct tool is a Pan Balance.
Read more about Tools of Measurement at; https://brainly.com/question/17562905
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A cone has a height of 2.5 in. and a radius of 5 in. What is the volume of the cone? (Use 3.14 for Pi. Round the answer to two decimal places.) 32.71 Inches cubed 65.42 Inches cubed 196.25 Inches cubed 588.75 Inches cubed
Answer:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
And replacing we got:
[tex] V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3[/tex]
And the best option would be:
65.42 Inches cubed
Step-by-step explanation:
For this case we have the following info given:
[tex] h =2.5 in[/tex] represent the height of the cone
[tex] r = 5 in[/tex] represent the radius
And the volume of the cone is given by;
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
And replacing we got:
[tex] V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3[/tex]
And the best option would be:
65.42 Inches cubed
Answer:
32.71 Inches cubed
Step-by-step explanation:
Let's recall the volume of the cone to be = 1/3πr³h
So using the formula.
r= 5
h = 2.5
I = 3.14
Volume = 1/3 * 3.14 * 5³ * 2.5
Volume = 327.1 in³
h(n)=63(-1/3)^n Complete the recursive formula of h(n)
Answer:
h(n+1) = -⅓ h(n), h(0) = 63
Step-by-step explanation:
h(n) = 63 (-⅓)ⁿ
This is a geometric series where the first term is 63 and the common ratio is -⅓.
Therefore, each term is -⅓ of the previous term.
h(n+1) = -⅓ h(n), h(0) = 63.
Students are designing a new town as part of a social studies project on urban planning. ey want to place the town’s high school at point A and the middle school at point B. they also plan to build roads that run directly from point A to the mall and from point B to the mall. the average cost to build a road in this area is $550,000 per mile. . c. Draw the road from point A to the mall and find its length. d. Draw the road from point B to the mall and find its length. e. How much farther from the mall is point B than point A? How much more will it cost to build the longer road?
Answer:
c, d. see attached
e. about 2.96 miles; about $1.63 million
Step-by-step explanation:
e. The x-coordinates of points A and B are 1/3 and 2/3 of the x-coordinate of "Downtown", respectively. The y-coordinates of A and B are 2/3 and 1/3 of the y-coordinate of "Town pool", respectively. Then the distances from A and B to the Mall can be found using the Pythagorean theorem:
A to Mall = √(4² +(10/3)²) = √(244/9) ≈ 5.20683 . . . miles
B to Mall = √(8² +(5/3)²) = √(601/9) ≈ 8.17177 . . . miles
The difference in distance is ...
(BM -AM) = 8.17177 -5.20683 = 2.96493 . . . miles
The mall is about 2.96 miles farther from point B than from point A.
The additional cost is the difference in miles multiplied by the cost per mile:
(2.96 mi)($0.550 M/mi) = $1.63 M
The additional cost of the longer road is about $1.63 million.
Which expression is equivalent to 4 (x + 2)? 6 x 4 (x) + 4 (2) 4 (x) + 4 8x
Answer:
4x+8 or 4 (x) + 4 (2)
Step-by-step explanation:
Hope it helps.
Answer:
B
Step-by-step explanation:
4(x+2).
By expanding the expression we have;
4(x+2) = 4× x + 4× 2 = 4(x) + 4(2)
Your favorite team is in the World Series. You have assigned a probability of 63% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 72% of the time. When they lose the championship, they win the first game 27% of the time. The first game is over and your team has lost. What is the probability that they will win the World Series?
Answer:
0.3950
Step-by-step explanation:
Any team team will win the championship with probability 63% that is
P(W)=0.63
when teams win the championship, they win the first game of the series 72% of the time that is
P(F|W)=0.72
When they lose the championship, they win the first game 27% of the time.
P(F|W')=0.27
The probability that they will win the World Series when the first game is over and your team has lost that is
P(W|F')
Now, By Bayes theorem
[tex]\begin{array}{l}
P\left(W | F^{\prime}\right)=\frac{P\left(F^{\prime} | W\right) P(W)}{P\left(F^{\prime} | W\right) P(W)+P\left(F^{\prime} | W^{\prime}\right) P\left(W^{\prime}\right)} \\
\quad=\frac{[1-P(F | W)] P(W)}{[1-P(F | W)] P(W)+\left[1-P\left(F | W^{\prime}\right)\right][1-P(W)]} \\
\quad=\frac{[1-0.72] \times 0.63}{[1-0.72] \times 0.63+[1-0.27][1-0.63]} \\
\quad=\frac{0.28\times 0.63}{0.28\times 0.63+0.73 \times 0.37} \\
=0.3950\end{array}[/tex]
what is the value of the expression {4×[6+(18-7)]}÷1/3
Answer:
{4*[6+(18-7)] } ÷1/3
{4*[6+18+7] }÷1/3
{24+72+28}÷1/3
{124}÷1/3
124*3/1
372/1=372
ill give you brainiest if your right !!!!
Answer:
12m - 4
☆ putting the value of m in the above formula
12 × 4 - 4
= 48 - 4
= 44
6r - 4
☆ Putting the value of r in the above formula
6 × 6 - 4
= 36 - 4
= 32
Buying a house is most likely a long-term goal for a person of which of these
ages?
A. 19 years old
B. 79 years old
C. 69 years old
O
D. 59 years old
Answer:
A. 19 years old
Step-by-step explanation:
A person at the age of 19 is probably still in college . He/She is probably investing more time and finance in his/her education. A person at age 19 is still building his or her career . He/she is likely to have limited working experience. He/she has more years ahead of him to invest his little income(that is if he has any) for a longer term plan like owning a house and building a business.
In fact at age 19 a person is more concern in his/her career development and studies. Buying a house is most likely a long time goal for a person of 19 years old because he has so many year ahead of him to gather or create wealth for himself.
The other ages 59, 79 and 69 years are individuals who have probably amassed wealth . They probably have over 3 decades of working experience and this working years will reflect in their savings. people at this age have shorter time to work or are probably even retired.
Answer:
A. 19 years old
Step-by-step explanation:
19 years old because usually by the time someone between the ages of 59 and 79 should already own or be renting a house if they have set their financial goals correctly.
The growth in the mouse population at a certain county dump can be modeled by the exponential function A(t)= 906e0.012t, where t is the number of months since the population was first recorded. Estimate the population after 36 months.
Answer:
[tex] A(t) = 906 e^{0.012t}[/tex]
Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 months into the function and we got:
[tex] A(36) = 906 e^{0.012*36}= 1395.54[/tex]
So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.
Step-by-step explanation:
We know that the population can be represented with this formula:
[tex] A(t) = 906 e^{0.012t}[/tex]
Where t is the number of months since the population was first recorded. And we want to find the population after 36 months so we need to replace t=36 monthsinto the function and we got:
[tex] A(36) = 906 e^{0.012*36}= 1395.54[/tex]
So then we can conclude that after 36 months the population of mouse is between 1385 and 1396.
Q. Three horses A, B, and C are in a race, A is twice as likely to win
as B and B is twice as likely to win as C. What are their
respective probabilities of winning?
What would I get by solving by polynomials?
Answer:
x=0 or x=3 or x= -3⅘
Step-by-step explanation:
Please see attached picture for full solution.
Another way to solve it is to factorise x out from the equation from the beginning. This would leave you with
x(5x² +4x -57x)=0
Then you can factorise the quadratic equation.
x(x -3)(5x +19)= 0
And solve it just like we did above.
x=0 or x-3=0 or 5x+19=0
x=3 or 5x= -19
x= -3⅘
In the picture, I used synthetic division but long division works too!
What is the relationship between the value of the digit 3 in 4,231 and in the value of the digit 3 in the number 3,421?
A.
In 4,231, the value of the digit 3 is 110 the value of the digit 3 in 3,421.
B.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
C.
In 4,231, the value of the digit 3 is 1100 the value of the digit 3 in 3,421.
D.
In 4,231, the value of the digit 3 is 100 times the value of the digit 3 in 3,421.
Answer:
A.
In 4231, the value of the digit 3 is 110 less than the value of the digit 3 in 3421.
Step-by-step explanation:
We can see that the value of 3 In 4231 is in ten while the value of 3 in 3421 is in thousands.
So to get the actual division factor, let's take 3300 and divide it by 30,
3300/30 = 110
So it's clear already, that the value of 3 in 4231 is 110 times less to the value in 3421
Answer: C In 4,231, the value of the digit 3 is 1/100 the value of the digit 3 in 3,421
Step-by-step explanation:
3,000 divided by 30 equals 100
In the diagram, m 23 = 120° and mZ12 = 80°. Which
angle measures are correct? Check all that apply.
1
2
mZ1 = 60°
V
9 10
11 12
4
e
m2 13 = 80
56
13 14
m26 = 80
7
8 15 16
f
m25 = 60°
Om Z10 = 120°
'c
d
m2 14 = 100
Intro
Done
4 of 8
Answer:
A,B,D,F
Step-by-step explanation:
The angle measures that are true are:
m∠1 = 60
m∠13 = 80
m∠5 = 60
m∠14 = 100
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
m∠3 = 120
m∠12 = 80
Now,
1)
m∠1 = 60 (true)
m∠1 + m∠3 = 180
So,
m∠1 = 180 - 120 = 60
2)
m∠13 = 80 (true)
m∠12 and m∠13 are alternate angles.
So,
m∠13 = 80
3)
m∠6 = 80 ( false)
m∠6 and m∠3 are alternate angles.
So,
m∠6 = 120
4)
m∠5 = 60 (true)
m∠5 + m∠3 = 180
m∠5 = 180 - 120 = 60
5)
m∠10= 120 (false)
m∠10 + m∠12 = 180
m∠10 = 180 - 80 = 100
6)
m∠14 = 100 (true)
m∠14 + m∠12 = 180
m∠12 = 180 - 80 = 100
Thus,
The angle measures that are true are:
m∠1 = 60
m∠13 = 80
m∠5 = 60
m∠14 = 100
Learn more about corresponding angles here:
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Please answer this correctly
Answer:
6 cm^2
Solution,
Volume of cube=1 cm^3
Volume of cube=l^3
or,1=(l)^3
or,l=1*1*1
length=2 cm
Again,
Surface area of cube= 6(a)^2
=6*(1)^2
=6*1
=6 cm^2
hope it helps
Good luck on your assignment
If f(x) = 4x ^ 2 and g(x) = x + 1 , find (fg)(x) ).
a. 4x(x)
B. 4x ^ 3 + 4x ^ 2
C. 4(x + 1) ^ 2
D. 4x ^ 2 + 1
Answer:
[tex]\boxed{\sf \ C \ is \ the \ correct \ answer \ ! \ }[/tex]
Step-by-step explanation:
fog(x)=f(g(x))
so it comes
[tex]f(g(x))=f(x+1)=4(x+1)^2[/tex]
so C is the correct answer
Answer:
Option B
Step-by-step explanation:
[tex]f(x) = 4x^2\\g(x) = x+1[/tex]
Multiplying both will give us:
[tex](fg)(x) = 4x^2(x+1)[/tex]
=> [tex](fg)(x) = 4x^3+4x^2[/tex]
Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water is this per hour? (Round your answer to the nearest whole number.)
Answer:
16 cubic feet per hour
Step-by-step explanation:
We want to convert from cubic inch per minute to cubic feet per hour,
We can use the standard conversion rate:
1 cubic inch per minute = 0.0347222 cubic feet per hour
=> 462 cubic inch per minute = 462 * 0.0347222 = 16.04 cubic feet per hour
Approximating to whole number, it is 16 cubic feet per hour.
Answer: Option 16 cubic feet
Step-by-step explanation:
A rectangular board is 1.5 meters long and 1.2 meters wide. What is the area of the board in square millimeters?
1 meter = 1000mm
Convert the dimensions to mm:
1.5 x 1000 = 1500 mm
1.2 x1000 = 1200 mm
Area = length x width
Area = 1500 x 1200 = 1,800,000 square mm
The student council is planning the school carnival. Each ticket costs $2.50. Explain how to write an equation that represents this scenario. Let X represent the number of tickets sold, and Y represents the total amount of money raised.
Answer:
the answer is c.
Answer:
Let x represent the variety of tickets sold, and y represent the total amount of cash raised. Since each price tag is $2.50, the total amount of money raised is identical to $2.50 instances the wide variety of tickets. The equation would be y = 2.50x.
Step-by-step explanation:
The x variable represents the number of tickets sold.
The y variable represents the total amount of money raised from ticket sales.
The equation for the scenario is y = 2.50x.
Which is the best buy?
12 tins of fish at K7.80 or 6 tins of fish at K4.20?
Divide price by quantity of each and compare:
7.80 / 12 = o.65 per tin
4.20 / 6 = 0.70 per tin
12 for 7.80 is less per tin, so is the Best Buy.
the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer.
Answer:
Old adult
Step-by-step explanation:
Because about eighty percent of adult suffer from blood pressure.
Which expression represents 25!/(25-12)!12!
Answer:
Combination 25 to 12
Step-by-step explanation:
[tex]C^{12} _{25}[/tex]
The expression 25! / [(25 - 12)! x 12!] represents the combination.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Let a be the number of items selected from the group of n.
We know that the combination is given by,
ⁿCₐ = n! / [(n - a)! x a!]
The expression is given below.
⇒ 25! / [(25 - 12)! x 12!]
Then the expression can be written as,
⇒ ²⁵C₁₂
Then the expression 25! / [(25 - 12)! x 12!] represents the combination.
More about the permutation and the combination link is given below.
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The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2.Three scores extracted from the test are 148,102,152.What is the average of the extracted scores that are outliers
Answer:
102
Step-by-step explanation:
We have the mean (m) 128.5 and the standard deviation (sd) 8.2, we must calculate the value of z for each one and determine whether or not it is an outlier:
z = (x - m) / sd
In the first case x = 148:
z = (148 - 128.5) /8.2
z = 2.37
In the second case x = 102:
z = (102 - 128.5) /8.2
z = -3.23
In the first case x = 152:
z = (152 - 128.5) /8.2
z = 2.86
The value of this is usually between -3 and 3, therefore when x is 102 it goes outside the range of the value of z, which means that this is the outlier.
I need help with this please
Answer:
D
Step-by-step explanation:
The equations are similar and so if we compute the vertex we would see they are the same..
Let's try computing the maximum or minimum point of y= -3(x+2)^2 - 4 and y= 3(x+2)^2 - 4 ;
For y= 3(x+2)^2 - 4 ;
to compute the maximum or minimum point we find dy/dx of the expression equating it to 0; the value of x is determined and we substitute to the original expression for y.
If y is -ve we know it's a minimum graph and if y is +be it's a maximum graph.
From the foregoing;
For y= 3(x+2)^2 - 4 ;
dy/dx = 2× 3 ( x+2) ×1 = 6(x+2) = 6x + 12= 0
6x= -12=>x= -12/6= -2;
We substitute x= -2 in y =3(x+2)^2 - 4; y = 3(-2+2)^2-4 = -4
Since y = -4 is a hence y= 3(x+2)^2 - 4 is a minimum graph.
For y= -3(x+2)^2 - 4 ;
dy/dx = 2× -3 ( x+2) ×1 = -6(x+2) = -6x - 12= 0
-6x= 12=>x= -12/6= -2;
Substituting in the y= -3(x+2)^2 - 4 ;
We have;
We substitute x= -2 in y =-3(x+2)^2 - 4; y = -3(-2+2)^2-4 = -4
y= -4 ;
Since both graphs look like they are minimum that is the vertex is y= -4;
Let's explore a further step
The derivative of the previous derivative;
For y= 3(x+2)^2 - 4;
We means d/dy × [dx/dy] = d/dy [ 6x + 12 ] = 6
Hence y= 3(x+2)^2 - 4 is a maximum graph;
Similarly for y= -3(x+2)^2 - 4 ;
d/dy × [dx/dy]
d/dy [-6x-12 ] = -6
Hence y= -3(x+2)^2 - 4 is a minimum graph;
Conclusion: y= 3(x+2)^2 - 4 is a maximum graph and y= -3(x+2)^2 - 4 is a minimum graph;
Si: F(x) = 2x + 4 ; R(x) = x ; calcula : R(F(0))
Answer: 4
Step-by-step explanation:
Given
[tex]F(x)=2x+4[/tex]
[tex]R(x)=x[/tex]
We need to find [tex]R(F(x))[/tex] at [tex]x=0[/tex]
[tex]R(F(x))=[2x+4][/tex]
[tex]R(F(x))=2x+4[/tex]
[tex]R(F(0))=2\times 1+4=4[/tex]
[tex]R(F(0))=4[/tex]