Answer:
1/9 or 0.11
Step-by-step explanation:
1/3 divided by 3
= 1/3 / 3
= 1/3 / 3/1
= 1/3 x 1/3 (the rule is a/b / c/d = a/b * d/c)
= 1/9 or 0.11(1 continues repeating for ever so just make it 0.11)
What would be the arc length of 1/5 of a circle with a radius of 4 ft?
Answer:
5.029ft
Step-by-step explanation:
[tex](titer \div 360) \times \pi \times diameter[/tex]
[tex](75degrees \div 360) \times \pi \times 8[/tex][tex] = 5.029[/tex]The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answer: 82
Step-by-step explanation:
72 times 6 is equal to 432
6 plus 2 is 8
74.25 times 8 is equal to 594
If you minus 594 and 432 you get 162
162 is total marks for both subjects
162 minus 80 you get 82 which is the marks for the 8th subject
Hope it taught you something..
In a spelling test the scores are 15,8,11,16,10,5and 10. what is the range
Solution,
Given data=15,8,11,16,10,5,10
Highest score= 16
lowest score= 5
Range=highest score- lowest score
=16-5
=11
Answer:
[tex]10[/tex]
Step-by-step explanation:
Given data =
[tex]15 \: \: 8 \: \: 11 \: \: 16 \: \: 10 \: \: 5 \: \: 10[/tex]
[tex]range = height \: \: - \: lowest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: score \: \: \: \: \: \: \: \: \: \: \: \: \: score \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \: \: \: \: \: - \: \: \: \: 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 10[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Does Anyone know how to do this It’s very difficult for me
Answer: D
Step-by-step explanation: y int is when x=0, thus when there are no chirps.
Y=(1/6)x + 50
put in 0
Y=(1/6)*0 + 50
Y=50
Slope is the rate at which x changes, in this case, 1/6
Professor Melendez has 10 students in her college algebra class. Their ages are shown below.
19, 27, 19, 18, 18, 18, 47, 19, 20, 18
The mean age of the students in the class is 22.3. The median age of the students is 19.
There are two outliers in the data from Professor Melendez’s class: 27 and 47.
When the outliers are removed, what is the mean age of the remaining students? Round your answer to the nearest tenth
What is the median age of the remaining students?
Answer:
Mean: 18.6 years old
Median: 18.5 years old
Step-by-step explanation:
Mean = average (add all numbers then divide by the number of numbers in the data set)
To find the mean, start by adding all of the numbers except for the outliers.
19 + 19 + 19 + 18 + 18 + 18 + 18 + 20 = 149
We added 8 numbers, so divide the sum by 8.
149/8 = 18.6
Therefore, the mean without outliers is 18.6 years old.
Median = middle (order numbers from least to greatest, then find the middle)
To find the median, order the numbers from least to greatest.
18, 18, 18, 18, 19, 19, 19, 20
Now, find the middle.
(Since there are an even number of numbers, select the two numbers in the middle.)
18, 18, 18, 18, 19, 19, 19, 20
Now, add these numbers and divide by 2.
18 + 19 = 37
37/2 = 18.5
Therefore, the median without outliers is 18.5 years old.
Solve.
y = x – 8
2x + 3y = 1
Use the substitution method.
Substitute [tex]y=x-8[/tex] into the second equation to get [tex]2x+3(x-8)=1,[/tex] which simplifies to [tex]5x=25,[/tex] so [tex]\boxed{x=5}.[/tex] It easily follows that [tex]\boxed{y=-3}.[/tex]
Answer:
x=5, y=-3
Step-by-step explanation:
Divide these polynomials (8x^3+2x^2-7x+2)/(2x-1)
Answer:
[tex]4x^2+3x-2[/tex]
Step-by-step explanation:
We are given that
[tex]\frac{8x^3+2x^2-7x+2}{2x-1}[/tex]
We have to divide the polynomials.
We have
Divisor polynomial=[tex]2x-1[/tex]
Dividend polynomial=[tex]8x^3+2x^2-7x+2[/tex]
[tex]\frac{8x^3+2x^2-7x+2}{2x-1}=4x^2+3x-2[/tex]
Quotient=[tex]4x^2+3x-2[/tex]
Remainder=0
(+20) + (-4) [(+3) 2 - (+6)]
A homeowner is designing a rectangular pool for her backyard. Due to the size of the yard, the width of the pool will be one-third its length, and the pool will have a uniform depth of 5 feet. Which of the following equations can be used to describe l, the length of the pool, in terms of its volume, V?
Answer:
Step-by-step explanation:
What is the rvalue of the following data, to three decimal places?
Answer:
b
Step-by-step explanation:
According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions, in a certain country each year from 1980 to the present can be approximated by f’(t) = 0.001155t(t-1980)^0.50, where t is the year.
a. Using the fact that in 1980 there were 264,034,000 outpatient visits, find a formula giving the approximate number of outpatient visits as a function of time.
b. Use the answer to part a to forecast the number of outpatient visits in the year 2015.
Answer:
a) [tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000[/tex]
b) f(t=2015) = 264,034,317.7
Step-by-step explanation:
The rate of change in the number of hospital outpatient visits, in millions, is given by:
[tex]f'(t)=0.001155t(t-1980)^{0.5}[/tex]
a) To find the function f(t) you integrate f(t):
[tex]\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt[/tex]
To solve the integral you use:
[tex]\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}[/tex]
Next, you replace in the integral:
[tex]\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C[/tex]
Then, the function f(t) is:
[tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'[/tex]
The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.
Hence C' = 264,034,000
The function is:
[tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000[/tex]
b) For t = 2015 you have:
[tex]f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7[/tex]
solve 2x-4÷ 5 = 4
really need help fast
Step-by-step explanation:
here is the answer u can get help from it.....
The solution to the equation (2x-4)/5 = 4 is x = 12.
What is the solution of the equation?To solve the equation (2x-4)/5 = 4, we will use the following steps.
Multiply both sides of the equation by 5 to eliminate the denominator as;
5[(2x-4)/5] = 5 x 4
This simplifies to:
2x - 4 = 20
Add 4 to both sides of the equation to isolate the term with x:
2x - 4 + 4 = 20 + 4
This simplifies to:
2x = 24
Divide both sides of the equation by 2 to solve for x:
(2x)/2 = 24/2
This simplifies to:
x = 12
Thus, the solution to the equation (2x-4)/5 = 4 is x = 12.
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Which of the following is an arithmetic sequence?
Answer: choice D
Step-by-step explanation:
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
in this exampke the constant(d) is -3
Answer:
D is the correct answer.
Step-by-step explanation:
because the numbers are decreased by -3
Defination: in arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
sector with a radius of \maroonD{10\,\text{cmd}}10cm start color #ca337c, 10, start text, c, m, end text, end color #ca337c has a central angle measure of \purpleD{252\degree}252°start color #7854ab, 252, degree, end color #7854ab. \theta=252\degreeθ=252°r=10\,\text{cm}r=10cm
Answer:
219.91cm²
Step-by-step explanation:
The question is not properly structured. Here is the complete question.
A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.
Area of a sector = theta/360 × πr²
theta is the angle substended by the circle
r is the radius of the circle.
Given radius = 10cm
theta = 252°
Area of a sector = 252°/360° × π(10)²
Area of a sector = 252/360 × 100π
Area of a sector = 79168.13.360
Answer:
Step-by-step explanation:
The question is not properly structured. Here is the complete question.
A sector with a radius of 10cm and has a central angle of 252°. Calculate the area of the sector.
Area of a sector = theta/360 × πr²
theta is the angle substended by the circle
r is the radius of the circle.
Given radius = 10cm
theta = 252°
Area of a sector = 252°/360° × π(10)²
Area of a sector = 252/360 × 100π
Area of the sector = 219.91cm²
Answer:
70pi
Step-by-step explanation:
That is the answer on khan academy
18. Which inequality is equivalent to
3x + 2 > 5?
A) x <1
B) x>-1
C) x 1
D) X > 3
Answer:
C)
Step-by-step explanation:
3x+2>5
3x>3
x>1
I believe that you mistyped C so I think its C
uppose that Mary's utility function is U(W) = W0.5, where W is wealth. She has an initial wealth of $100. How much of a risk premium would she want to participate in a gamble that has a 50% probability of raising her wealth to $115 and a 50% probability of lowering her wealth to $77? Mary's risk premium is $ nothing. (round your answer to two decimal places)
Note that [tex]U(W) = W^{0.5}[/tex]
Answer:
Mary's risk premium is $0.9375
Step-by-step explanation:
Mary's utility function, [tex]U(W) = W^{0.5}[/tex]
Mary's initial wealth = $100
The gamble has a 50% probability of raising her wealth to $115 and a 50% probability of lowering it to $77
Expected wealth of Mary, [tex]E_w[/tex]
[tex]E_{w}[/tex] = (0.5 * $115) + (0.5 * $77)
[tex]E_{w}[/tex] = 57.5 + 38.5
[tex]E_{w}[/tex] = $96
The expected value of Mary's wealth is $96
Calculate the expected utility (EU) of Mary:-
[tex]E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75[/tex]
The expected utility of Mary is $9.75
Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where
U(EW - P) is equal to Mary's expected utility from the risky gamble.
U(EW - P) = EU
U(94 - P) = 9.63
Square root (94 - P) = 9.63
If Mary's risk premium is P, the expected utility will be given by the formula:
[tex]E_{u} = U(E_{w} - P)\\E_{u} = U(96 - P)\\E_u = (96 - P)^{0.5}\\(E_u)^2 = 96 - P\\ 9.75^2 = 96 - P\\95.0625 = 96 - P\\P = 96 - 95.0625\\P = 0.9375[/tex]
Mary's risk premium is $0.9375
The midpoint of (-2,1) and (-1,1)
Answer:
The midpoint of (-2,1) is -1. The midpoint for (-1,1) is 0.
Step-by-step explanation:
To find the midpoint you will have to add x+y then divide by 2.
00:00
Gavin counted the number of days until the end of school.
If he counted the days in groups of 7, which list shows the numbers Gavin could have
named?
O
A. 7, 15, 22, 30
B. 7, 14, 21, 30
O
C. 7, 14, 21, 28
D. 14, 21, 32, 38
Answer:
C. 7, 14, 21, 28
Step-by-step explanation:
We want to find the multiples of 7
7*1= 7
7*2 = 14
7*3= 21
7*4 = 28
Answer:
The answer is, C. 7, 14, 21, 28
A recent survey collected information on television viewing habits from a random sample of 1,000 people in the United States. Of those sampled, 37 percent indicated that their favorite sport to watch on television was American football. Construct and interpret a 95 percent confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football. Based on your answer to the previous problem, is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football
Answer:
The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40). This means that we are 95% sure that the true proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is between (0.34 and 0.40).
The lower bound of the confidene interval is higher than 0.33. So it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football, this estimate should be higher than 33%.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1000, \pi = 0.37[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 - 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.34[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 + 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.40[/tex]
The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40). This means that we are 95% sure that the true proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is between (0.34 and 0.40).
Based on your answer to the previous problem, is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football
The lower bound of the confidene interval is higher than 0.33. So it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football, this estimate should be higher than 33%.
The 95% Confidence Interval we will found for given case is:
(0.34, 0.40)
It is Not reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football
Given that:Total size of sample = n = 1000Percent of people in sample indicating that their favorite sport on TV is to watch American football = p = 37% = 0.37 probability.To find:95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.
Finding the Confidence Interval:When there is n sample size and the probability of success is p with level of significance [tex]\alpha[/tex]calculated as:
[tex]CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}[/tex]
Where [tex]z_0[/tex] is the z score [tex]1- \dfrac{\alpha}{2}[/tex] .
1 - [tex]\alpha[/tex] = 0.95 ( since it is given to find 95% CI)
Thus, [tex]\alpha[/tex] = 0.05
The z score at p value = 1 - [tex]\alpha[/tex]/2 = 1 -0.025 = 0.975 is 1.96
Thus we have:
[tex]CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}}\\\\CI = 0.37 \pm 1.96 \sqrt{\dfrac{0.37 \times0.63 }{1000}}\\\\CI = 0.37 \pm 1.96 \times 0.0152 = 0.37 \pm 0.03\\[/tex]
Lower limit of CI = 0.34 and Upper limit of CI = 0.40.
The case to decide to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football can be solved as:
33% = 0.33 probability of actually liking watching american probability.
Since 0.33 is lower than the lower limit of CI for 0.37 probability, thus we reject the null hypothesis that both 0.37 and 0.33 are approximately same, and thus decide that it is false that 0.33 percent believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football.
Thus it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football.
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Tina must select and answer in any order three of seven
seven essay questions on a test.
In how many ways can she do so?
Tina can select and answer the essay questions on her test in_____ ways.
(Simplify your answer. Type an integer or a fraction.)
Answer:
Tina can select and answer the essay questions on her test in 35 ways.
Step-by-step explanation:
The order in which she chooses the questions is not important. For example, choosing questions 1, 3 and 7 is the same as choosing 7, 3 and 1. So we use the combinations formula to solve this question.
Combinations formula:
[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]
In this question:
Three questions from a set of 7. So
[tex]C_{7,3} = \frac{7!}{3!(7-4)!} = 35[/tex]
Tina can select and answer the essay questions on her test in 35 ways.
Tina can select and answer the essay question on her test in 35 ways.
Number of ways to select 'r' objects out of 'n' objects is given by the expression,
Number of ways = [tex]^nC_r[/tex]
Since, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
If n = 7 and r = 3,
Number of ways to select 3 essays out of 7 will be,
Number of ways = [tex]^7C_3[/tex]
[tex]=\frac{7!}{3!(7-3)!}[/tex]
[tex]=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}[/tex]
[tex]=35[/tex]
Therefore, Tina can select and answer the essay question on her test in 35 ways.
Learn more.
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"According to a 2018 Gallup poll, 5% of U.S. adults consider themselves to be vegetarian. Nonwhite Americans (9%) are three times as likely as white Americans (3%) to describe themselves as vegetarian." This statement is based on a random sample of 1033 American adults interviewed in July 2018, in which 270 respondents identified as "nonwhite" and 742 as "white.
The cited value 5% is part of the:
a. Experimental
b. Conditional
c. Observational
d. Anecdotal
e. Marginal
and distribution of the:
a. Ethnicity, given diet choice
b. Diet choice, given ethnicity
c. Ethnicity, D. Diet
Answer:
(c) Observational Distribution
(d) Diet Choice
Step-by-step explanation:
Out of 1033 American adults interviewed in July 2018, 5% consider themselves to be vegetarian.
Since the poll observes the diet habit of the respondents, the cited 5% is part of the Observational distribution of whether the respondent is a vegetarian or not (which is the Diet Choice).
If on the other hand, the poll seeks to manipulate the conditions of the study, it would have been an experimental distribution.
A goal is to get at least 10% of daily calories from polyunsaturated fats as are found in various nuts, oils, and fish. One serving of walnuts (about 15 pieces) has about 20 g of polyunsaturated fat. Each fat gram has 9 calories. About what percent of daily calories does one serving of walnuts provide, assuming a 2,000-calorie diet?
The percent of daily calories does one serving of walnuts provide is 9%.
This question is solved using proportions.
We have:
A diet of 2,000 calories.To find the percentage of daily calories provided by one walnut, we have to find the amount of calories in the walnut, and find it's percentage relative to 2,000.-----------------
Walnut:
Has 20 grams of polyunsaturated fat.Each gram has 9 calories.Thus, the amount of calories of fat is:
[tex]A = 20 \times 9 = 180[/tex]
-----------------
Percentage:
180 calories out of a daily diet of 2000 calories, so:
180*100%/2000 = 9%
The percent of daily calories does one serving of walnuts provide is 9%.
A similar question is found at https://brainly.com/question/10491646
What is (-3)x(5-7)-9(39/3)
Answer:-111
Step-by-step explanation:
0.09 is smaller than 0.001
Answer:
no
Step-by-step explanation:
A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?
Answer:
She is 215 m from the starting point
Step-by-step explanation:
Let's begin by constructing a figurative representation of the information given (figure attached)
We know 2 sides of the triangle and the inner angle, we can therefore use the Cosine Rule
Mathematically represented as:
b² = a² + c² - 2ac(CosB)
b = ?, a = 60 m, c = 180, B = 118° (the sum of the 90° right angle at B + the interior angle of 28° from A)
b² = 60² + 180² - 2(60)(180)Cos 118°
b² = 3600 + 32400 - (- 10140.586)
b² = 46140.586 ⇒ b = [tex]\sqrt{46140.586}[/tex]
b = 214.8 m ≈ 215 m
b = 215 m (to the nearest whole number)
∴ the student is 215 m from the starting point
Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.
Answer:
Step-by-step explanation:
The person receives 10000 every month
for one year total principal 10000 * 12 = 120000
r= 12%p.a and t is 1yr
simple interest= 120000*12*1/100 = 14400
total money received in present year 120000 + 14400 = 134400
for 20 yrs principal becomes 10000*12*20= $2400000
simple interest = 2400000*12*20/100= $5760000
total amount received for 20 yrs = 2400000+ 5760000=8160000.
present value of principal as money receive 10000 for 10 yrs = 10000*10 = 100000
si = 100000*10*12/100= 120000
amount = $220000
What is the value of the expression?
458+56−134
Enter your answer as a mixed number in simplest form
Answer:
Step-by-step explanation:
Apply the priority rule,
(458+56)-134=514-134=380
Parallel lines m and n are cut by transversal l. On line m where it intersects with line l, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: blank, blank, 45 degrees, blank. On line n where it intersects with line l, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are blank, (2 x minus 5) degrees, blank, blank.
What is the value of x?
Answer:
X=70 :) Good Luck!!
Step-by-step explanation:
Using the concept of supplementary angles, it is found that the value of x is of 70 degrees.
-----------------
The situation is modeled by the graph at the end.The angles of 45º and (2x - 5)º are on the same side, thus they are supplementary.If two angles are supplementary, the sum of their measures is of 180º.Thus:
[tex]45 + 2x - 5 = 180[/tex]
[tex]2x + 40 = 180[/tex]
[tex]2x = 140[/tex]
[tex]x = \frac{140}{2}[/tex]
[tex]x = 70[/tex]
The value of x is of 70 degrees.
A similar problem is given at https://brainly.com/question/22826236
A drink is a mixture of three parts water to 1 part orange concentrate. How much water should be added to 100ml of orange concentrate? *
Answer:
300 mL
Step-by-step explanation:
If one part is 100 mL, then 3 parts will be 300 mL.
300 mL of water should be added.
Suppose that 80% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. Consider groups of 17 trucks and let X be the number of trucks in a group that have passed the inspection. What is the probability that at least 10 but fewer than 13 trucks pass the inspection
Answer:
0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection
Step-by-step explanation:
For each truck, there are only two possible outcomes. Either they pass the inspection, or they do not. The probability of a truck passing the inspection is independent of other trucks. 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.
80% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection.
This means that [tex]p = 0.8[/tex]
17 trucks:
This means that [tex]n = 17[/tex]
What is the probability that at least 10 but fewer than 13 trucks pass the inspection
[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{17,10}.(0.8)^{10}.(0.2)^{7} = 0.0267[/tex]
[tex]P(X = 11) = C_{17,11}.(0.8)^{11}.(0.2)^{6} = 0.0680[/tex]
[tex]P(X = 12) = C_{17,12}.(0.8)^{12}.(0.2)^{5} = 0.1361[/tex]
[tex]P(10 \leq X < 13) = P(X = 10) + P(X = 11) + P(X = 12) = 0.0267 + 0.0680 + 0.1361 = 0.2308[/tex]
0.2308 = 23.08% probability that at least 10 but fewer than 13 trucks pass the inspection