Answer:
a) 0.398 = 39.8% probability that the sample contains exactly one defective item.
b) 0.9021 = 90.21% probability that the sample contains at most one defective item.
Step-by-step explanation:
The itens are chosen without replacement, so we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Suppose there are 3 defective items in a lot (collection) of 50 items
This means that [tex]k = 3, N = 50[/tex]
Sample of 10
This means that [tex]n = 10[/tex]
(a) exactly one defective item.
This is P(X = 1). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,50,10,3) = \frac{C_{3,1}*C_{47,9}}{C_{50,10}} = 0.398[/tex]
0.398 = 39.8% probability that the sample contains exactly one defective item.
(b) at most one defective item.
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,50,10,3) = \frac{C_{3,0}*C_{47,10}}{C_{50,10}} = 0.5041[/tex]
[tex]P(X = 1) = h(1,50,10,3) = \frac{C_{3,1}*C_{47,9}}{C_{50,10}} = 0.398[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5041 + 0.398 = 0.9021[/tex]
0.9021 = 90.21% probability that the sample contains at most one defective item.
Please help! I’ll give BRAINLIEST and show ur work please
Answer:
M<E=T M<T=E
Step-by-step explanation:
As you can see in the trapezoid the show you only one two sides that are equals so that's mean that the angles are congruent each other.
Answer:
[tex]m\angle E=118^{\circ},\: m\angle T=118^{\circ}[/tex]
Step-by-step explanation:
As the diagram is marked, [tex]WE=WT[/tex] and [tex]SE=ST[/tex]. Therefore, [tex]m\angle E=m\angle T[/tex]. Since the interior angles of all quadrilaterals add up to be [tex]360^{\circ}[/tex], we can write the following equation:
[tex]29^{\circ}+95^{\circ}+m\angle E+m\angle T = 360^{\circ}[/tex]
Subtract 29 and 95 from both sides to get [tex]m\angle E+m\angle T=236^{\circ}[/tex].
As we found earlier, [tex]m\angle E=m\angle T[/tex].
Therefore [tex]m\angle E=m\angle T=\frac{236}{2}=\fbox{$118^{\circ}$}[/tex].
What is m∠P?
There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
Step-by-step explanation:
540 = 4x-10+5x-11+128+4x+2+132
23= x
RST=104
QRS=82
TPQ=94
The value of x from the figure is 23
PolygonsThe sum of the interior angle of the pentagon is 540 degrees
Taking the sum of all the angles:
4x+2+132+4x-10+128+5x-11 = 540
4x+4x+5x+241 = 540
13x = 540 - 241
13x = 299
x = 299/13
x = 23
Hence the value of x from the figure is 23
Learn more on polygons here: https://brainly.com/question/24966296
When you purchased 100 shares of Bio-Tech Sciences, the value per share was listed at $12.38. When Bio-Tech
Sciences sent out their daily report today, you see that they list the value of their stock at $45.16. If you were to sell all
your shares in Bio-Tech Sciences today, what would be the total value of your investment?
a $1,238.00
c. $5,754.00
b. $4,516.00
d. $3,278.00
Answer:
b
Step-by-step explanation:
4,516.00
Answer:
C.
Step-by-step explanation:
Edge2022
a.
Group
The intervals of the horizontal axis.
b. The break in the vertical axis.
c. The break in the horizontal axis.
d. The intervals of the horizontal axis are not labeled correctly.
A.) The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2. Find the EXACT volume of the sphere in terms of the diameter d. Be sure to fully simplify the expression.
B.) What is the EXACT volume of the sphere when the diameter is 2/3 centimeter?
Answer:
[tex]\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3[/tex]
Step-by-step explanation:
The Volume of a Sphere
The volume of a sphere of radius r is given by:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
A. )
If the diameter of the sphere is d, the radius is r=d/2. Substituting:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \left (\frac{d}{2} \right )^3[/tex]
Operating
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \frac{d^3}{8}[/tex]
Simplifying
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot d^3[/tex]
B.)
The diameter of the sphere is 2/3 cm, thus the volume is:
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \left (\frac{2}{3} \right )^3[/tex]
Operating:
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \frac{8}{27}[/tex]
[tex]\displaystyle V=\frac{8}{27}\frac{1}{6}\cdot \pi[/tex]
[tex]\boxed{\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3}[/tex]
Miranda cuts grass ( g ) for $ 20 and hour and trims hedges ( h ) for $ 25 an hour. She is trying to make enough money during the summer to buy a car for $ 4200 .
Which inequality represents the number of hours Miranda needs to cut grass and trim hedges?
what are the options
Situation
You are a financial advisor. Your clients include young couples who are looking for financial advice. During this pandemic, everyone is looking for the best option when saving their money. As a financial advisor, you help people determine the best options for their savings plan. Most banks offer saving plan options with compound interest.
The Jacksons
Eric and Amy Jackson wish to invest in a no-risk savings account. They currently have $55,000 in an account that has a 4.125% annual interest rate, compounded continuously. They have the following options:
a. keep their money in the account they already have
b. invest the money in an account that has 5% annual interest, compounded annually
c. invest the money in an account that has 4.5% annual interest, compounded quarterly
d. invest the money in an account that has 3.875% annual interest, compounded monthly
Write a function for each option, that represents the amount of money in the account after t years after the account is opened.
a. C(t) keep their money in the account they already have
b. A(t) invest the money in an account that has 5% annual interest, compounded annually
c. Q(t) invest the money in an account that has 4.5% annual interest, compounded quarterly
d. M(t) invest the money in an account that has 3.875% annual interest, compounded monthly
Answer:
egwegerhreherhsrhs
Step-by-step explanation:
thtrhrtsjsjhshjshhs
PLEASE HELP ME PLEASEEEEEEEEEEEEEE
(x - 3)2 + (y + 7)2 = 121 what's the radius
Answer:
[tex]r=11[/tex]
Step-by-step explanation:
The equation of a circle is commonly denoted as:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h, k)[/tex] is the center of the circle.
This equation is already written in that format, therefore:
[tex]r^2=121,\\r=\fbox{$11$}[/tex],
Guy is self employed. In one year, Guy generates a gross income of $44,500. When calculating his taxes, Guy is allowed to deduct $2,500 in expenses from his gross income (the result is his 'operating income'). Guy must then pay 10% tax on all operating income up to $20,000 and then 20% on any operating income over $20,000. Calculate the amount of tax that Guy must pay. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Answer:
20000÷20= the amount you need for the income price is 16000
Answer:
Step-by-step explanation:
Operating Income=$44,500−$2,500=$42,000.
So Guy will be taxed 10% on $20,000 and 20% on $(42,000−20,000)=$22,000, hence
Total Tax=10%×$20,000+20%×$(42,000−20,000)=$6,400.
Which functions are linear
Answer:
its c
Step-by-step explanation:
Solve for s.
9 − 2s − 10s = –10s − 7
Show work
Answer:
s=8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
answerrrrrr ??????????
Answer:
19
Step-by-step explanation:
Sub the x with 6
30 - 11 = 19
Part A
The data in the line plots show the number of hours volunteers work each week for two different organizations. Find the measures of center and variability of the two sets of data.
Part B
What conclusions can you draw from the two sets of data? Select all that apply
A. Volunteers in organization B spend more time volunteering than volunteers in organization A
B. The median of organization A's data and organization B's data is the same
C. The range of organization B's data is greater than the range of organization A's data
D. The mean and the median of organization A's data are the same
E. The mean and the median of organization B's data are the same
Answer:
line plots do you mean number line, cos no pic is attached
I will give brainiest to whoever answers correctly !!
Answer:
After 10 years, the population of the town will be of 5905.
After 50 years, the population of the town will be of 11487.
Step-by-step explanation:
The population of the town after x years is given by the following equation:
[tex]P(x) = 5000(1.181)^{0.1x}[/tex]
After 10 years, the population of the town will be of:
This is P(10). So
[tex]P(10) = 5000(1.181)^{0.1*10} = 5000(1.181)^1 = 5905[/tex]
After 10 years, the population of the town will be of 5905.
After 50 years, the population of the town will be of:
This is P(50). So
[tex]P(50) = 5000(1.181)^{0.1*50} = 5000(1.181)^5 = 11487[/tex]
After 50 years, the population of the town will be of 11487.
Which of the following is a proportion? 9/12 = 8/10 3/4 = 9/12 6/8 = 8/12 12/18 = 19/16
Answer:
3/4=9/12
Step-by-step explanation:
3x3= 9
4x3= 12
Next in sequence 9/16, -9/8, 9/4, -9/2, 9, ?
Answer:
-18
Step-by-step explanation:
*2, *(-2), *2, *(-2) ...
Answer:
-18
Step-by-step explanation:
4/5(x+1) write the expression in standard form
Solve ASAP. Giving 28 points.
Answer:
where is the question
Step-by-step explanation:
Answer:
what's the question I can't see it
what‘s the maximum and minimum
pls help！！！
Answer:
D.By finding the unit rate and multiplying it by 7.
Step-by-step explanation:
what is 14x three over seven
Explain why the expressions 8x(6-4) and 8x6-4 dont not have the same value even though they look very similar? HELP!! PLEASE EXPLAIN IT IN 2 complete sentences. (ITS ALGEBRA)
Answer:
Because the first has () and the second doesn't so if u multiply the first one you will have to start with the () but if u answer the second u can start with anything
what is the circumference of a 12mm circle
Answer:
The circumference is 37.7 mm.
help plz i’ll give brainliest
Answer: d
Step-by-step explanation:
Find the Error .A student is finding -1/2 ÷ (-4/5). Do you agree with student's solving?
Answer option no or yes
if 5/8 is given in the question, then YES. If not, then NO
PLEASE ANSWER ASAP WITH WORK FOR BRAINLEST!!!!!!!!!!!!!!!!1
Answer:
they need to wash 39 cars
Step-by-step explanation:
600-61=539
539/14=38.5
round to 39
find the value of x and y please help..
Answer:
this means this is a isosceles triangle so y is 44 and now -180
180-88
X=92
jose is working two summer jobs making $10 per hour washing cars and $9 per hour walking dogs. Last week Jose worked a total of 13 hours and earned a total of $122. Write a system of equations that could be used to determine the number of hours jose worked washing cars last week and the number of hours he worked walking dogs last week. define the variables that you use to write the system
Answer:
164
Step-by-step explanation:
add everything together 10+9+13+122 = 164.
Help plz:)))I’ll mark u Brainliest
Answer:
22-18-25,
19-24-30,
7-24-25
Step-by-step explanation:
In a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], any two sides must have a sum larger than the third.
Using this rule, the possible side lengths out of these choices that could form a triangle are:
22-18-25,
19-24-30,
7-24-25
The theoretical probability of an event occurring is 3/4. Fill in the blank with a
number to complete each statement so that it best describes the expected
chances of the event occurring in an experiment. Out of 400 trials, the desired
outcome will occur approximately
times. *
Answer:
300 times
Step-by-step explanation:
Answer:
The answer is out of every 5, the desired out come will be approximately 2 times.
Step-by-step explanation: