Answer:
1.41421356237
Step-by-step explanation:
-3 + 5 = 2
square root of 2 = 1.41421356237
Can someone help me please
Answer:
Slope: -1/2 Y-intercept: 1
Step-by-step explanation:
Slope: The line goes across 2 units, for every 1 unit down, so -1/2
Y-intercept: The line intersects the Y axis at 1
Answer: Choice B. slope = -1/2, y intercept = 1
=======================================================
Explanation:
The line goes downhill as we move from left to right. This means the slope is negative. We can rule out anything that has a positive slope. The answer is between A and B.
We can rule out choice A because the y intercept is actually 1 (not 2) because it crosses the y axis here. The only thing left is choice B.
The slope is -1/2 because moving from (0,1) to (2,0) means we move down 1 unit and over to the right 2 units.
slope = rise/run = -1/2
rise = -1 indicates a drop of 1
run = 2 means we move to the right 2 units
-----------
You can use the slope formula to get the same result
I'll use the two points (0,1) and (2,0)
m = (y2 - y1)/(x2 - x1)
m = (0 - 1)/(2 - 0)
m = -1/2
You could use any other two points you want as long as they are on the diagonal line.
Let y=tan(3x+4) Find the differential dy when x=5 and dx=0.3 Find the differential dy when x=5 and dx=0.6
Problem 1
y = tan(3x+4)
f(x) = tan(3x+4)
f ' (x) = 3sec^2(3x+4) .... apply derivative chain rule
dy/dx = f ' (x)
dy = f ' (x) * dx
dy = ( 3sec^2(3x+4) ) * dx
Now plug in x = 5 and dx = 0.3
dy = ( 3sec^2(3*5+4) ) * 0.3
dy = 0.920681 which is approximate
Make sure your calculator is in radian mode. Calculus textbooks will be in radian mode for the special sine limit definition [tex]\lim_{x\to0}\frac{\sin x}{x} = 1[/tex] to be true.
===========================================================
Problem 2
We'll have the same derivative function and same x value. The only difference is that dx = 0.6 this time.
dy = f ' (x) * dx
dy = ( 3sec^2(3*5+4) ) * 0.6
dy = 1.84136 approximately
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. In a talent competition, half of the contestants are eliminated in each round. At the end of the nth round, 32 contestants remain. If there were 1,024 contestants at the start of the competition, what is the value of n? The value of n is .
Answer:
n =32
Step-by-step explanation:
If 1 contestant is eliminated each round
then of 1024contestants
32 left
1024/32=32
Answer:
n=32
Step-by-step explanation:
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph
Answer:
15.74% of the player's serves were between 115 mph and 145 mph
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
What percentage of the player's serves were between 115 mph and 145 mph
This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.
X = 145
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{145 - 100}{15}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 115
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
15.74% of the player's serves were between 115 mph and 145 mph
What is the distance between (8, -3) and (4, - 7)?
Answer:
[tex]distance=\sqrt{32}[/tex] , which agrees with answer "c" in your list of possible options
Step-by-step explanation:
Use the formula for distance between two points [tex](x_1,y_1)[/tex], and [tex](x_2,y_2)[/tex] on the plane:
[tex]distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance= \sqrt{(4-8)^2+(-7-(-3))^2} \\distance= \sqrt{(-4)^2+(-4)^2} \\distance=\sqrt{16+16}\\distance=\sqrt{32}[/tex]
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Required:
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than $7.75?
c. What is the probability that the sample mean will be less than $8.10?
d. What is the probability that the sample mean will be more than $8.20?
Answer:
(a) The standard error of the mean is 0.091.
(b) The probability that the sample mean will be less than $7.75 is 0.0107.
(c) The probability that the sample mean will be less than $8.10 is 0.9369.
(d) The probability that the sample mean will be more than $8.20 is 0.0043.
Step-by-step explanation:
We are given that the average price for a movie in the United States in 2012 was $7.96.
Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Let [tex]\bar X[/tex] = sample mean price for a movie in the United States
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean price for a movie = $7.96
[tex]\sigma[/tex] = population standard deviation = $0.50
n = sample of theaters = 30
(a) The standard error of the mean is given by;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{0.50}{\sqrt{30} }[/tex]
= 0.091
(b) The probability that the sample mean will be less than $7.75 is given by = P([tex]\bar X[/tex] < $7.75)
P([tex]\bar X[/tex] < $7.75) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{7.75-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < -2.30) = 1 - P(Z [tex]\leq[/tex] 2.30)
= 1 - 0.9893 = 0.0107
The above probability is calculated by looking at the value of x = 2.30 in the z table which has an area of 0.9893.
(c) The probability that the sample mean will be less than $8.10 is given by = P([tex]\bar X[/tex] < $8.10)
P([tex]\bar X[/tex] < $8.10) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{8.10-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < 1.53) = 0.9369
The above probability is calculated by looking at the value of x = 1.53 in the z table which has an area of 0.9369.
(d) The probability that the sample mean will be more than $8.20 is given by = P([tex]\bar X[/tex] > $8.20)
P([tex]\bar X[/tex] > $8.20) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{8.20-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z > 2.63) = 1 - P(Z [tex]\leq[/tex] 2.63)
= 1 - 0.9957 = 0.0043
The above probability is calculated by looking at the value of x = 2.63 in the z table which has an area of 0.9957.
A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing vs , where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting 11 from the sample data to move the mean down to the null mean of results in the following data: .
57, 64, 70, 82, 84, 123
Use StatKey or other technology to create the randomization distribution for this test. Find the p-value.
Answer:
The p-value of the test is 0.1515.
Step-by-step explanation:
The hypothesis for the test can be defined as follows:
H₀: The mean level of arsenic is 80 ppb, i.e. μ = 80.
Hₐ: The mean level of arsenic is greater than 80 ppb, i.e. μ > 80.
As the population standard deviation is not known we will use a t-test for single mean.
It is provided that the sample mean was, [tex]\bar X=91[/tex].
The adjusted sample provided is:
S = {57, 64, 70, 82, 84, 123}
Compute the sample standard deviation as follows:
[tex]\bar x=\farc{57+64+70+82+84+123}{6}=80\\\\s=\sqrt{\frac{1}{6-1}\times [(57-80)^{2}+(64-80)^{2}+(70-80)^{2}+...+(123-80)^{2}]}=23.47[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar X-\mu}{\s/\sqrt{n}}=\frac{91-80}{23.47/\sqrt{6}}=1.148[/tex]
Thus, the test statistic value is 1.148.
Compute the p-value of the test as follows:
[tex]p-\text{value}=P(t_{n-1}<t)[/tex]
[tex]=P(t_{6-1}<1.148})\\\\=P(t_{5}<1.148})\\\\=0.1515[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.1515.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.1515 > α = 0.05
The null hypothesis will not be rejected at 5% level of significance.
Thus, concluding that the mean level of arsenic in chicken from the suppliers is 80 ppb.
Someone help me please
Answer:
3.5
Step-by-step explanation:
To find the mean, add up all the numbers
(8+0+3+3+1+7+4+1+4+4) = 35
Then divide by how many numbers there are
35/10 = 3.5
The mean is 3.5
Answer:
Step-by-step explanation:
- Mean- The AVERAGE OF ALL NUMBERS: You add up all the numbers then you divide it by the TOTAL NUMBER of NUMBERS!
8+0+3+3+1+7+4+1+4+4=35
35/10=3.5
35
Find the fifth term of an=(-1)^n/2n-1
a.-1/7 b.-1/9 c.1/9 d.1/7
Answer:
b) -1/9
Step-by-step explanation:
Given
[tex]a_{n} = \frac{(-1)^{n} }{2n-1}[/tex]
First term
[tex]a_{1} = \frac{(-1)^{1} }{2(1)-1} = -1[/tex]
second term
[tex]a_{2} = \frac{(-1)^{2} }{2(2)-1} = \frac{1}{3}[/tex]
Third term
[tex]a_{3} = \frac{(-1)^{3} }{2(3)-1} = \frac{-1}{5}[/tex]
Fourth term
[tex]a_{4} = \frac{(-1)^{4} }{2(4)-1} = \frac{1}{7}[/tex]
Fifth term
[tex]a_{5} = \frac{(-1)^{5} }{2(5)-1} = \frac{-1}{9}[/tex]
Answer:
B
Step-by-step explanation:
right on edge 2021
determine whether these two functions are inverses.
Answer:
No The reactions are not inverses to each other
Step-by-step explanation:
f(x) = 3x + 27
Let f(x) be y
y= 3x+27
subtracting 27 on both sides
3x = y - 27
x= (y-27)/3
= y/3 - 9
inverse function is x/3 -9 not x/3 + 9
Therefore, not an inverse
Hope it helps...
Simplify the expression by combining like terms
15 + 12x – 5.2 + 4y - 7
9.8 +12x+y-7
2.8+12x+4y
Justin spent $23 on fruit at grocery store. He spent a total of $25 at the store. What percentage of the total did he spend on fruit?
Step-by-step explanation:
In my opinion maybe he has spent 98%
State the size of angle 'n' in the triangle illustrated below.
Answer:
Option B
Step-by-step explanation:
<r = 32 degrees (alternate angles )
<r = <n = 32 degrees (vertical angles)
Please answer this correctly
Answer:
The number of employees classified into groups as shown below:
1 - 10: 3 6 (2companies)
11-20: 16 (1 company)
21-30: 25, 26, 27 (3 companies)
31-40: 34, 35, 35, 35, 36 (5 companies)
41-50: 41, 43, 48, 48 (4 companies)
Hope this helps!
Answer:
11-20 is 1
31-40 is 5
Step-by-step explanation:
Just count the amount
Hope that helps :D
What is the equation of the line with an X intercept of negative 2 and Y intercept of one
Answer:
y = 1/2x + 1
Step-by-step explanation:
Step 1: Find slope
(1-0)/(0+2) = 1/2
Step 2: Write equation
y = 1/2x + 1
I need help with this question please
Answer:
Just connect points Y and D with a straight line to make YD. Do the same for YE and YF, just attach Y to points E and F with a straight line.
GIVING 45points What is the measure of angle 1?
129
65
12
36°
086°
0899
094°
Answer:
94
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
<1 = 29+65
=94
Answer:
94°
Step-by-step explanation:
Angles in a triangle add up to 180°
[tex]180-65-29=86[/tex]
Angle 2 = 86°
Angles on a straight line add up to 180°
[tex]180-86=94[/tex]
Angle 1 = 94°
B
Round your answer to the nearest hundredth.
A
9
B
5
Answer:
56.25°
Step-by-step explanation:
The definition of the cosine function tells you that
cos(B) = BC/BA
B = arccos(BC/BA) = arccos(5/9)
B ≈ 56.25°
Pls help marking Brainliest! (x-1)(x-1)=?
Answer:
Brainleist!Step-by-step explanation:
x^2-2x+1thats the answer...
just: Expand the polynomial using the FOIL method.
Answer:
(x-1)(x-1)=(x-1)² because it's the same thing multiplied by itself
Using FOIL method:
(x-1)(x-1)=
x²-x-x+1=
x²-2x+1
Rewrite the expression using exponents .Then find the product
Answer:
[tex]m ^ {3/7}[/tex]
Step-by-step explanation:
=> [tex]\sqrt[7]{m^3}[/tex]
[tex]\sqrt[7]{}= ^\frac{1}{7}[/tex]
=> [tex]m^{3*1/7}[/tex]
=> [tex]m ^ {3/7}[/tex]
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly generally pass the course. She also knows that 85% of her students pass the course.
a. What is the probability that a student will do homework regularly and also pass the course?
b. What is the probability that a student will neither do homework regularly nor will pass the course?
c. Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
d. Are the events "pass the course" and "do homework regularly" independent? Explain.
Answer:
a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12
c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.
d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.
Step-by-step explanation:
Let the event that a student does homework regularly be H.
The event that a student passes the course be P.
- 60% of her students do homework regularly
P(H) = 60% = 0.60
- 95% of the students who do their homework regularly generally pass the course
P(P|H) = 95% = 0.95
- She also knows that 85% of her students pass the course.
P(P) = 85% = 0.85
a) The probability that a student will do homework regularly and also pass the course = P(H n P)
The conditional probability of A occurring given that B has occurred, P(A|B), is given as
P(A|B) = P(A n B) ÷ P(B)
And we can write that
P(A n B) = P(A|B) × P(B)
Hence,
P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')
From Sets Theory,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
P(H n P) = 0.57 (from (a))
Note also that
P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)
0.60 = P(H n P') + 0.57
P(H n P') = 0.60 - 0.57
Also
P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)
0.85 = P(H' n P) + 0.57
P(H' n P) = 0.85 - 0.57 = 0.28
So,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
Becomes
0.03 + 0.28 + 0.57 + P(H' n P') = 1
P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12
c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,
P(A n B) = 0.
But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.
Hence, the two events aren't mutually exclusive.
d. Are the events "pass the course" and "do homework regularly" independent? Explain
Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when
P(A|B) = P(A)
P(B|A) = P(B)
P(A n B) = P(A) × P(B)
To check if the events pass the course and do homework regularly are mutually exclusive now.
P(P|H) = 0.95
P(P) = 0.85
P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671
P(H) = 0.60
P(H n P) = P(P n H)
P(P|H) = 0.95 ≠ 0.85 = P(P)
P(H|P) = 0.671 ≠ 0.60 = P(H)
P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)
None of the conditions is satisfied, hence, we can conclude that the two events are not independent.
Hope this Helps!!!
Select a composite number to break into factors. Continue factoring until all factors are prime
Answer:
2*2 * 2*2 * 2*3
Step-by-step explanation:
96 =16 *6
Break these down, since neither 16 nor 6 are prime
= 4*4 * 2*3
4 in not prime, but 2 and 3 are prime
= 2*2 * 2*2 * 2*3
All of these are prime
Answer:
22, 23
Step-by-step explanation:
Just got it right on edge 2021
In a large population, 81% of the households have cable tv. A simple random sample of 144 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 77%
Answer:
The probability that the sampling distribution of sample porportions is less than 77% is P(p<0.77)=0.1106.
Step-by-step explanation:
We know that the population proportion is π=0.81.
We want to know the probability that the sampling distribution of sample proportions, with sample size n=144, is less than 0.77.
The sampling distributions of sampling proportions has a mean and standard deviation calculated as:
[tex]\mu_p=\pi=0.81\\\\\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.81\cdot 0.19}{144}}=\sqrt{0.001068}=0.0327[/tex]
Then, we calculated the z-score for p=0.77:
[tex]z=\dfrac{p-\pi}{\sigma_p}=\dfrac{0.77-0.81}{0.0327}=\dfrac{-0.04}{0.0327}=-1.2232[/tex]
The probability that the sample proportion is less than 0.77 is:
[tex]P(p<0.77)=P(z<-1.2232)=0.1106[/tex]
Butler Trucking Company has developed a regression equation to predict the delivery time for its drivers (y). The model is based on the miles traveled (x 1), the number of deliveries (x 2) and whether or not the travel will occur during rush hours (x 3 - 1 if during rush hour and 0 if not during rush hour). The regression equation that they use is y
Answer:
The answer is Y = 6.3973.
Note: Kindly find an attached document of the complete question to this solution
Sources: The complete question was researched from Quizlet site.
Step-by-step explanation:
Solution
Given that:
The regression equation is given below:
Y = - 0.3302 + 0.0672 x₁ + 0.6735 x₂ + 0.9980 x₃
Now,
When x₂ = 5, x₁ = 50, x₃ = 0
Y = - 0.3302 + 0.0672 * 50 +0.6735 * 5
Y= - 0.3302 + 3.36 + 3.3675
Y = 6.3973
Therefore the time (hour) it will take for the driver to make five deliveries on a 50 mile journey not during rush hour is 6.3973.
N
Write the rate as a unit rate
729 riders in 9 subway cars
А
The unit rate is
This
(Simplify your answ
riders/car
Answer:
Unit rate = 81 riders/ car.
Step-by-step explanation:
Given
729 riders in 9 cars
we have to find unit rate in terms of riders per car
let the the riders per car (i.e rate) be x.
If there are 9 cars then
total no. of riders in 9 cars = no. of cars * riders per car = 9*x = 9x
given that 729 riders in 9 cars
then
9x = 729
=> x = 729/9 = 81
Thus, riders per car = x = 81.
Unit rate is 81 riders per car.
Suppose that the regression for predicting weight (in pounds) from Height (in inches) is given by Weight -115+3.6 (Height) Which of the following statements is correct?
I. A person who is 61 inches tall will weigh 104.6 poulds.
II. For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds
III. The correlation between weight and height is negative.
A. II only
B. Iand II only
C. I only
D. II and III only
E. III only
Answer:
B. I and II only.
Step-by-step explanation:
A person who is 61 inches tall is predicted to weight 104.6 pounds according to the regression model.
[tex]y(61)=-115+3.6(61)=-115+219.6=104.6[/tex]
The slope of the linear regression model indicates the rate of change of the predicted variable in function of a unit change in the independent variable. In this case, for each additional inch in height, the predicted weight will increase, on average by 3.6 pounds, as indicated by the slope of this model.
As the slope m=3.6 is positive, the correlation is positive: when the independent variable increases, the predicted variable also increases.
A] Both I and II are correct.
Weight = - 115 + 3.6 (Height)
Here, 115 is the autonomous weight at 0 level of height, it is the intercept. 3.6 is the slope, representing change in weight due to change in height. Slope implies that : For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds. So, II is True
At height = 61 inches, weight = - 115 + 3.6 (61) = - 115 + 219.6 = 104.6 So, I is True
Regression shows cause effect relationship (of height on weight). Correlation shows just co-relationship in direction of variables' movement. Nevertheless, positive regression correlation increases the probability of positive correlation (instead of negative correlation) So, III is false
https://brainly.com/question/7656407?referrer=searchResults
how to determine the volume of a cone
Answer:
V= 1/3 h π r²
hope it helps
Rod's quiz grades are 72, 74, 89, and90. What score on a fifth quiz will make his average woz grade at least 84?
Answer: He would need at least a 95
Step-by-step explanation:
First I found the current average by adding 72, 74, 89, and 90 which equals 325.
Second, I worked backwards to see what the sum of his grades had to be by multiplying 84 times 5. 84 times 5 = 420
Now that we have both the current and the target sum, we find the difference by doing 420-325 which equals 95.
. A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line. Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?
Answer:
P(F | D) = 47.26%
There is a 47.26% probability that the foreman forgot to shut off the machine the previous night.
Step-by-step explanation:
A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line.
Let F denote the event that foreman forgets to shut off the machine.
Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%.
Let D denote the event that the mold is defective.
If the foreman forgets to shut off the machine then 15% molds get defective.
P(F and D) = 0.23×0.15
P(F and D) = 0.0345
If the foreman doesn't forget to shut off the machine then 5% molds get defective.
P(F' and D) = (1 - 0.23)×0.05
P(F' and D) = 0.77×0.05
P(F' and D) = 0.0385
The probability that the mold is defective is
P(D) = P(F and D) + P(F' and D)
P(D) = 0.0345 + 0.0385
P(D) = 0.073
The probability that the foreman forgot to shut off the machine the previous night is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(F | D) = P(F and D)/P(D)
Where
P(F and D) = 0.0345
P(D) = 0.073
So,
P(F | D) = 0.0345/0.073
P(F | D) = 0.4726
P(F | D) = 47.26%
(−p 2 +4p−3)(p 2 +2)
Answer:
[tex]-p^4+4p^3-5p^2+8p-6[/tex]
I hope this help you :)