Answer:
The best option is to buy Japanese Car.
Step-by-step explanation:
Fuel usage per year is 150000/ 8 = 18750 miles per year
Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5
Japanese Car:
Fuel usage 18750 / 23 = 815 * $3 = $2446
Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372
Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860
Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804
Present value of cost at 5% = 24674.07
Cost of car is $30,000
Total cost = $54674.07
Amercian Car:
Cost $35,000
Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.
Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208
Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301
Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934
Present value of cost at 5% = 25302.18
Cost of car is $35,000
Total cost = $60302.
German Car:
Cost = $45,000
Fuel usage 18750 / 21 = 892 * $3 = $2678
Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171
Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316
Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976
Present value of cost at 5% = 27105.73
Cost of car is $45,000
Total cost = $72105.
A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (a) Compute the probability that 2 or fewer will withdraw. If required, round your answer to four decimal places. (b) Compute the probability that exactly 4 will withdraw. If required, round your answer to four decimal places. (c) Compute the probability that more than 3 will withdraw. If required, round your answer to four decimal places. (d) Compute the expected number of withdrawals.
Answer:
a) 0.206 = 20.6% probability that 2 or fewer will withdraw.
b) 0.2182 = 21.82% probability that exactly 4 will withdraw.
c) 0.5886 = 58.86% probability that more than 3 will withdraw.
d) The expected number of withdrawals is 4.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they withdraw without completing the introductory statistics course, or they do not. Each student is independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% of its students withdraw without completing the introductory statistics course.
This means that [tex]p = 0.2[/tex]
Assume that 20 students registered for the course.
This means that [tex]n = 20[/tex]
(a) Compute the probability that 2 or fewer will withdraw.
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115[/tex]
[tex]P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576[/tex]
[tex]P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0115 + 0.0576 + 0.1369 = 0.206[/tex]
0.206 = 20.6% probability that 2 or fewer will withdraw.
(b) Compute the probability that exactly 4 will withdraw.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{20,4}.(0.2)^{4}.(0.8)^{16} = 0.2182[/tex]
0.2182 = 21.82% probability that exactly 4 will withdraw.
(c) Compute the probability that more than 3 will withdraw.
Either less than 3 withdraw, or more than 3 withdraw. The sum of the probabilities of these events is 1. So
[tex]P(X \leq 3) + P(X > 3) = 1[/tex]
We want P(X > 3). So
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.2)^{0}.(0.8)^{20} = 0.0115[/tex]
[tex]P(X = 1) = C_{20,1}.(0.2)^{1}.(0.8)^{19} = 0.0576[/tex]
[tex]P(X = 2) = C_{20,2}.(0.2)^{2}.(0.8)^{18} = 0.1369[/tex]
[tex]P(X = 3) = C_{20,3}.(0.2)^{3}.(0.8)^{17} = 0.2054[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0115 + 0.0576 + 0.1369 + 0.2054 = 0.4114[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.4114 = 0.5886[/tex]
0.5886 = 58.86% probability that more than 3 will withdraw.
(d) Compute the expected number of withdrawals.
The expected value of the binomial distribution is:
E(X) = np
In this question:
E(X) = 20*0.2 = 4
The expected number of withdrawals is 4.
Four different positive integers have a product of 110.
What is the sum of the four integers?
Given:
Four different positive intergers as a product of 110
To find:
The sumnof the four numbers whose product is 110
Solution:
1) To find the number we have to find the prime factorization of the given number 110
2) Prime factorization of 110 is
110 = 1×2 × 5 = 11
3) So the four numbers whose product is 110 are 1,2,5 and 11
4) The sum of number's are
1+2+5+11=19
SO THE FINAL ANSWER IS 19What is the missing value from the set of data if the mean is 4?
{5,2,_,2,4,8}
Answer: The missing value from the data set is 4.
Step-by-step explanation: Let's put it from least to greatest to figure it out...
2, 2, (4, 4,) 5, 8,
It would have to be 4, because 8 divided by 2 will equal 4. And because there's an even amount of numbers we have to add two numbers then divide it by 2.
4 + 4 = 8
8 ÷ 2 = 4
The mean is 4, and the missing value from the data set is 4.
I hope this helps!
A store that sells skis buys them from a manufacturer at a wholesale price of $87 The store's markup rate is 50% A. What price does the store charge its customers for the skis? B. What percent of the original price is the final price? C. What is the percent INCREASE from the original price to the final price?
Answer:
A. $130.50
B. 150%
C. 50%
Step-by-step explanation:
First, find 50% of 87 and add it to find the new price.
87 x 0.5 = 43.5
87 + 43.5 = 130.5
Then, find the percent by doing 130.5 ÷ 87, which is 150%
Calculate the percent increase by doing (130.5-87) ÷ 87, which is 50%
Answer:
see below
Step-by-step explanation:
First find the markup
87* 50%
87*.50
43.50
Add this to the wholesale price
87+43.50 =130.50
This is what they charge the customer
This is 150% percent of the wholesale price
100% + 50% = 150%
To find the percent increase
Take the new price and subtract the wholesale price
Then divide by the wholesale price
(130.50-87)/87 =50 % increase
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. The point estimate of the mean content of the bottles is:__________.
Select one:
a. 0.02
b. 0.22
c. 121
d. 4
Answer:
option D is correct, 4 ounces.
Step-by-step explanation:
In this case we have a random sample of 121 cologne bottles that showed an average content of 4 ounces.
The point estimate of the mean content of the bottles is average value.
What 4 ounces means is the correct answer since this is the mean, therefore the option D is correct
5 Samir wants to work out the cost of the tiles needed to replace a roof.
The roof has 4 identical faces.
Each face is a triangle.
Each triangle has a base length of 7.6 m and a height of 4.8 m.
Samir has this information,
roof tiles
1 pack of tiles covers 13.8 m² (including overlaps)
each pack costs £716.10
Answer:
Step-by-step explanation:
Since the roof has 4 identical faces and each face is a triangle, we would determine the area of each face of the triangle by applying the formula,
Area of triangle = 1/2 × base × height
Area of each triangular face = 1/2 × 7.6 × 4.8 = 18.24m²
Area of the 4 faces = 4 × 18.24 = 72.96 m²
Since 1 pack of tiles covers 13.8 m², the number of packs needed to cover 72.96 m² is
72.96/13.8 = 5.29 packs
Since samir can only buy whole packs of these tiles, the number of packs of tiles that he needs to buy would be 6.
If 1 pack costs £716.1, then the total cost of the tiles needed for the 4 faces of this roof is
6 × 716.1 = £4296.6
Solve the system of equations. 3x + 4y = 8 x + 2y = 4
Answer:
x=0, y=2
Step-by-step explanation:
3x+4y=8
x+2y=4
Multiply the second equation by 2:
2x+4y=8
Subract it from the first equation:
x=0
y=2
Hope this helps!
HELPPP The number of members in the Triathlon Club was 36 in 2001 and has increased by 20% each year. Which exponential growth model shows the club's membership in terms of t, the number of years since 2001? s since 2001?
A. y=20(36)t
B. y=36(0.2)t
C. y=36(1.2)t
D. y=36(20)t
Answer:
C. y=36(1.2)t
Step-by-step explanation:
The number of members in the Club in t years after 2001 is given by an equation in the following format:
[tex]y = y(0)(1+r)^{t}[/tex]
In which y(0) is the number of members in 2001 and r is the growth rate, as a decimal.
The number of members in the Triathlon Club was 36 in 2001 and has increased by 20% each year.
This means that [tex]y(0) = 36, r = 0.2[/tex]
So
[tex]y = y(0)(1+r)^{t}[/tex]
[tex]y = 36(1+0.2)^{t}[/tex]
[tex]y = 36(1.2)^{t}[/tex]
The correct answer is C.
The driving distance from Chicago to San Francisco is 2,142 miles. The Hathaway family left Chicago on Monday morning, December 6. They averaged 50 miles an hour and drove 6 hours each day. On what day and date did they reach San Francisco?
Answer:
They arrive on Monday, December 13th
Step-by-step explanation:
First, we know that this family must drive a total of 2,142 miles.
They average 50 miles per hour and drive 6 hours each day, thus we can see that they drive (50)(6)=300 miles per day.
Now, to know how many days it will take them to drive the total of 2,142 miles we are going to divide the total amount of miles between the number of miles driven per day:
2,142÷300= 7.14
Thus, it takes them 7.14 days to drive 2,142 miles.
If we round this (since the number is greater than 7 this would mean it takes them more than 7 days and they would stop at 7 for the day) to the next digit, we would have that it will take them 8 days to get to San Francisco.
Thus, since they start on December 6th (day 1), December 7th would be day 2 and following this pattern we would have that the eighth day would be December 13th.
Now, since the days repeat every 7 days and we now that December 6th was monday, we would have that the day they arrive to San Francisco (December 13th) is monday too.
NEED HELP ASAP!!!!
The steps below show the work of a student used to calculate the number of yards in 6,436 meters.
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)
Step 1: 6,436 meters multiplied by conversion factor 1 mile over 1,609 meters equals 4 miles
Step 2: conversion factor of 1,760 yards over 1 mile divided by 4 miles equals 440 yards
Step 3: 440 yards
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)
How can the error in the student's work be corrected? (1 point)
a
The 6,436 meters and the 1,609 meters in Step 1 should be switched.
b
The 1 mile and the 1,609 meters in Step 1 should be switched.
c
The conversion factor should be multiplied in Step 2 instead of being divided.
d
The conversion factor should be added in Step 2 instead of being divided.
Answer:
You usually wouldn't divide lengths
Step-by-step explanation:
What is fo)?
O O only
0 -6 only
0-2, 1, 1, and 3 only
0 -6, -2, 1, 1, and 3 only
Answer:
-6 only
Step-by-step explanation:
f(0) is the value of y when x=0. This is the graph of a 4th-degree polynomial, so is a function. There is only one y-value for x=0. That is where the graph crosses the y-axis, at y = -6.
f(0) = -6 . . . . only
Annie was told that her math test score was 3 standard deviations below the mean. If test scores were approximately normal with μ=99 and σ=4, what was Annie's score? Do not include units in your answer. For example, if you found that the score was 99 points, you would enter 99.
Answer:
[tex]X \sim N(99,4)[/tex]
Where [tex]\mu=99[/tex] and [tex]\sigma=4[/tex]
We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:
[tex] X = \mu -3\sigma[/tex]
And replacing we got:
[tex] X = 99 -3*4 = 87[/tex]
So then the Annie's score would be 87
Step-by-step explanation:
Let X the random variable that represent the test scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(99,4)[/tex]
Where [tex]\mu=99[/tex] and [tex]\sigma=4[/tex]
We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:
[tex] X = \mu -3\sigma[/tex]
And replacing we got:
[tex] X = 99 -3*4 = 87[/tex]
So then the Annie's score would be 87
Answer: 87
Step-by-step explanation:
We can work backwards using the z-score formula to find the x-value. The problem gives us the values for z, μ and σ. So, let's substitute these numbers back into the formula:
z−3−1287=x−μσ=x−994=x−99=x
We can think of this conceptually as well. We know that the z-score is −3, which tells us that x is three standard deviations to the left of the mean, 99. So we can think of the distance between 99 and the x-value as (3)(4)=12. So Annie's score is 99−12=87.
Lataycia has 188 but she is spending 14 per week.
Answer:
90
Step-by-step explanation:
14×7=98
188-98=90 so she had 90 left
Answer:
90
Step-by-step explanation:
14×7=98
188-98=90 so she had 90 left
Angie and Irene had the same amount of money at first.At a shopping mall, Angie spent $2595 while Irene spent $297.Irene then had thrice as much money as Angie. How much money did Irene have at first?
Answer:
Irene had $3744 at first.
Step-by-step explanation:
Let Angie and Irene had the money initially = $a
At a shopping mall Angie spent money = $2595
Money left with Angie = $(a - 2595)
Similarly, Irene spent the money = $297
Money left with Irene = $(a - 297)
Money left with Irene was thrice as much as Angie,
(a - 297) = 3(a - 2595)
a - 297 = 3a - 7785
3a - a = 7785 - 297
2a = 7488
a = [tex]\frac{7488}{2}[/tex]
a = $3744
Therefore, Irene had $3744 at first.
Answer:
$3746
Step-by-step explanation:
A=2595. I=2595
(x-293)=(x-2595)
X-293=3x-7785
-293+7785=2x
7492/2=x
So. x=3746
which fraction is equivalent to 5/12+1/4
Answer:
2/3
Step-by-step explanation:
5/12+1/4
Make the fractions have the same denominator.
5/12 + 1×3/4×3
5/12 + 3/12
Add the fractions.
(5+3)/12
8/12
Simplify.
2/3
Answer:
[tex] = \frac{2}{3} \\ [/tex]
Step-by-step explanation:
[tex] \frac{5}{12} + \frac{1}{4} \\ \frac{5 + 1 \times 3}{12} \\ \frac{5 + 3}{12} \\ = \frac{8}{12} \\ = \frac{2}{3} [/tex]
What’s the correct answer for this?
Answer:
The answer is option 2.
Step-by-step explanation:
Given that the formula for length of arc is :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
Answer:
B
Step-by-step explanation:
It could also be
[tex] \frac{\pi \times r \times m}{180} [/tex]
Which of the following expressions represents the distance between -4/3 and 1/3?
Answer:
none of the above
Step-by-step explanation:
Take the absolute value of the second point and subtract the first point
| 1/3 -( -4/3)|
Since this answer does not match any of the above choices
Answer:
None of the above.
Step-by-step explanation:
The distance between -4/3 and 1/3 is
|1/3-(-4/3)| =|1/3 + 4/3|
This is not in the option so;
None of the above.
Identify the table of values which represents the function y=x+2
Answer:
Option 1.
Step-by-step explanation:
y = x + 2
Put x as 1, 2 and 3 to find y.
y = (1) + 2
y = 3
y = (2) + 2
y = 4
y = (3) + 2
y = 5
When x = 1, y = 3.
When x = 2, y = 4.
When x = 3, y =5.
The values that represent the function is the first table.
Use the function rule f(x)=x^2
Find f(2.5)__
Answer:
6.25
Step-by-step explanation:
f(x)=x^2
f(2.5) = (2.5)^2
=6.25
Answer: 6.25
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(2.5).
We find f(2.5) by plugging 2.5 in for x
everywhere that x appears in the function.
So we have f(2.5) = (2.5)².
(2.5)² is 6.25.
So our answer is 6.25.
what is a unit rate?
Answer:
5
Step-by-step explanation:
Answer:
the answer is-
Step-by-step explanation:
When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
HOPE IT HELPS!!!
what is the solution of this equation 4(x-8)+10=-10
Start by subtracting 10 from both sides.
This gives us 4x - 32 = -20.
Now add 32 to both sides to get 4x = 12.
Now divide both sides by 3 to get x = 3.
There are 500 people in a building. 20% of half of them went out. 15% of those who went out came back in. How many people are in the building now?
Answer:
415people
Step-by-step explanation:
20%of250=100people
15%of the 100people=15people
So 100 went out remaining(500-100)400
Then 15 returned=400+15
415
Answer:
458 people in the building now.
Step-by-step explanation:
20%x500/2 = 20% x 250=50
15% x 50 = 7.5
7.5 + (500 - 50) =457.5 =458people.
Tell me if it's correct plz.
Hope this helps..
Please answer this question !! 20 points and brainliest !! Thank u !!
Answer:
Step-by-step explanation:
The system of equations (a) is the correct one for this situation. We must now solve this system for x and y, which are the unit costs.
Multiplying the 2nd equation by (-3/2) yields -12x - 18y = -168.
Now eliminate x by combining the two equations
12x + 5 y = 116
-12x -18y = - 168
-------------------------
-13y = -52, or y = 4.
If y = 4 then 12x + 5y = 116, or
12x +5(4) = 116, or
12x + 20 = 116, or
12x = 96, or x = 8
Roller pens are $8/dozen and ball point pens are $4 per dozen.
I think it’s A:
Cause it is what it is
What’s the correct answer for this?
Answer:
YT AND RQ
Step-by-step explanation:
Solve the equation for the indicated variable.
660w
C=
for w
h2
W=
(Simplify your answer.)
The first step is to multiply both sides by h^2. Afterwards, divide both sides by 660 to fully isolate w.
c = 660w/(h^2)
ch^2 = 660w
660w = ch^2
w = (ch^2)/660 is the answer
Recently, FHA mortgages, which are insured by the federal government, accounted for 28% of all home-purchase mortgages that were approved. A random sample of 150 mortgage applications was selected. What is the probability that 48 or more from this sample were insured by the FHA?
Answer:
15.87% probability that 48 or more from this sample were insured by the FHA
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]p = 0.28, n = 150[/tex]
So
[tex]\mu = E(X) = np = 150*0.28 = 42[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.28*0.72} = 5.5[/tex]
What is the probability that 48 or more from this sample were insured by the FHA?
Using continuity correction, this is [tex]P(X \geq 48 - 0.5) = P(X \geq 47.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 47.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{47.5 - 42}{5.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
1 - 0.8413 = 0.1587
15.87% probability that 48 or more from this sample were insured by the FHA
Wendy has only nickels and dimes in her pocket. The number of dimes is 8 less than triple the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.
Answer:
The number of dimes is 3n - 8
Step-by-step explanation:
Here, we are interested in writing an expression for the number of dimes.
We proceed as follows;
Now, there are n nickels with the number of dimes been 8 less than 3 times the number of nickels
That would be;
3(n) -8 = 3n -8
A collection of 36 coins consists of nickels, dimes and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin are there?
Answer:
9 quarters, 12 nickels, and 15 dimes.
Step-by-step explanation:
Let's start by naming the number of quarters x.
That means that the number of nickels is x+3.
(There are three fewer quarters than nickels)
The number of dimes would be x+6.
(There are six more dimes than quarters)
We know the total number of coins is 36.
We can set up an equation.
quarters+nickels+dimes=36
x+x+3+x+6=36
Combine like terms.
3x+9=36
Subtract 9 from both sides.
3x=27
Divide both sides by 3.
x=9
There are 9 quarters.
Use given info to find the number of other coins.
9+3=12
There are 12 nickels.
9+6=15
There are 15 dimes.
A national college researcher reported that 65% of students who graduated from high school in 2012 enrolled in college. Twenty nine high school graduates are sampled. Round the answers to four decimal places.
(a) What is the probability that exactly 17 of them enroll in college? The probability that exactly 17 of them enroll in college is_______
(b) What is the probability that more than 14 enroll in college? The probability that more than 14 enroll in college is_______ .
(c) What is the probability that fewer than 11 enroll in college? The probability that fewer than 11 enroll in college is_______ .
(d) Would it be unusual if more than 24 of them enroll in college? It (Choose one) be unusual if more than 24 of them enroll in college since the probability is ________.
Answer:
a) The probability that exactly 17 of them enroll in college is 0.116.
b) The probability that more than 14 enroll in college is 0.995.
c) The probability that fewer than 11 enroll in college is 0.001.
d) It would be be unusual if more than 24 of them enroll in college since the probability is 0.009.
Step-by-step explanation:
We can model this with a binomial distribution, with n=29 and p=0.65.
The probability that k students from the sample who graduated from high school in 2012 enrolled in college is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{29}{k} 0.65^{k} 0.35^{29-k}\\\\\\[/tex]
a) The probability that exactly 17 of them enroll in college is:
[tex]P(x=17) = \dbinom{29}{17} p^{17}(1-p)^{12}=51895935*0.0007*0=0.116\\\\\\[/tex]
b) The probability that more than 14 of them enroll in college is:
[tex]P(X>14)=\sum_{15}^{29} P(X=k_i)=1-\sum_{0}^{14} P(X=k_i)\\\\\\P(x=0)=0\\\\P(x=1)=0\\\\P(x=2)=0\\\\P(x=3)=0\\\\P(x=4)=0\\\\P(x=5)=0\\\\P(x=6)=0\\\\P(x=7)=0\\\\P(x=8)=0\\\\P(x=9)=0\\\\P(x=10)=0.001\\\\P(x=11)=0.002\\\\P(x=12)=0.005\\\\P(x=13)=0.013\\\\P(x=14)=0.027\\\\\\P(X>14)=1-0.005=0.995[/tex]
c) Using the probabilities calculated in the point b, we have:
[tex]P(X<11)=\sum_0^{10}P(X=k_i)\approx0.001[/tex]
d) The probabilities that more than 24 enroll in college is:
[tex]P(X>24)=\sum_{25}^{29}P(X=k_i)\\\\\\ P(x=25) = \dbinom{29}{25} p^{25}(1-p)^{4}=23751*0*0.015=0.007\\\\\\P(x=26) = \dbinom{29}{26} p^{26}(1-p)^{3}=3654*0*0.043=0.002\\\\\\P(x=27) = \dbinom{29}{27} p^{27}(1-p)^{2}=406*0*0.123=0\\\\\\P(x=28) = \dbinom{29}{28} p^{28}(1-p)^{1}=29*0*0.35=0\\\\\\P(x=29) = \dbinom{29}{29} p^{29}(1-p)^{0}=1*0*1=0\\\\\\\\P(X>24)=0.007+0.002+0+0+0=0.009[/tex]
find a in a=6b if b=2
Answer:
a=12
Step-by-step explanation:
if a=6b
and b=2
a=2×6
a=12
