Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]
= 10 x [tex]\frac{75}{100}[/tex]
= [tex]\frac{750}{100}[/tex]
= 7.5 cm
Answer:
7.5 cm
Step-by-step explanation:
Decreased height = 25% of 10
[tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]
New height = 10 - 2.5 = 7.5 cm
2.
√3x + 7 + √x + 1 =2
Answer:
x = -1
Step-by-step explanation:
The usual approach to these is to square the radicals until they are gone.
[tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]
Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.
The solution is x = -1.
_____
Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.
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]
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...
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
Factor completely 6x to the second power - 36xy + 12x
Answer:
6x(x - 6y +2)
Step-by-step explanation:
Step 1: Write out expression
6x² - 36xy + 12x
Step 2: Factor out x
x(6x - 36y + 12)
Step 3: Factor out 6
6x(x - 6y + 2)
That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.
The following questions pertain to the properties of the STANDARD NORMAL distribution. (a) True or False: The distribution is bell-shaped and symmetric. True False (b) True or False: The mean of the distribution is 0. True False (c) True or False The probability to the left of the mean is 0. True False (d) True or False The standard deviation of the distribution is 1. True False
Answer:
a. The distribution is bell-shaped and symmetric: True.
b. The distribution is bell-shaped and symmetric: True.
c. The probability to the left of the mean is 0: False.
d. The standard deviation of the distribution is 1: True.
Step-by-step explanation:
The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].
It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.
We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where [tex] \\ x[/tex] is the raw score that we want to standardize.
Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:
(a) True or False: The distribution is bell-shaped and symmetric
Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.
(b) True or False: The mean of the distribution is 0.
Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
If [tex] \\ x = \mu[/tex]
[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{0}{\sigma}[/tex]
[tex] \\ z = 0[/tex]
Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.
(c) True or False: The probability to the left of the mean is 0.
Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].
(d) True or False: The standard deviation of the distribution is 1.
Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.
In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].
In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.
Answer:
A: true
B: true
C: false
D: true
Simplify the expression by combining like terms
15 + 12x – 5.2 + 4y - 7
9.8 +12x+y-7
2.8+12x+4y
there are only red counters and blue counters in a bag. Jim takes at random a counter from a bag. the probability that the counter is red is 0.45 Jim puts the counter back into the bag. Molly takes at random a counter from the bag. She puts the counter back in the bag. What is the probability that Jim and Molly take counters of different colours? Give your answer as a decimal
Answer:
0.495 probability that Jim and Molly take counters of different colours
Step-by-step explanation:
For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can 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.
The probability that the counter is red is 0.45
This means that [tex]p = 0.45[/tex]
Jim taken a counter, then Molly:
Two trials, so [tex]n = 2[/tex]
What is the probability that Jim and Molly take counters of different colours?
One red and one blue. So this is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]
0.495 probability that Jim and Molly take counters of different colours
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%
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.
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 order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50 with a standard deviation of $16.
a) Formulate the null and alternative hypotheses to determine whether or not the average room price is significantly different from $112.
b) Compute the test statistic.
c) Using the p-value approach, what is your conclusion? Let alpha = .05.
d) Using the critival value approach, what is your conclusion? Let alpha = .05.
e) Write a concluding statement based on your answers above.
Answer:
C
Step-by-step explanation:
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.
What is the value of (4-2): – 3 x 4?
-20
-4
4
20
Answer:
4
Step-by-step explanation:
A male student of the author has a measured pulse rate of 52 beats per
minute. According to a National Center for Health Statistics data set, males have a mean
pulse rate of 67.3 beats per minute and a standard deviation of 10.3 beats per minute.
Determine whether the student's pulse rate is significantly low or high by calculating the
z score. Consider usual pulse rates to be within 2 standard deviations of the mean.
Justify your answer.
Answer:
[tex]z=-1.49[/tex]
Step-by-step explanation:
[tex]\text{Standard Score, z} =\dfrac{X-\mu}{\sigma} $ where:\\\\Mean Pulse rate, \mu =67.3$ beats per minute\\Standard Deviation, \sigma = 10.3$ beats per minute.\\[/tex]
For a male student who has a measured pulse rate of 52 beats per minute.
Raw Score, X =52 beats per minute.
Therefore:
[tex]\text{Standard Score, z} =\dfrac{52-67.3}{10.3}\\z=-1.49[/tex]
Since the usual pulse rates are within 2 standard deviations of the mean, a z-score of -1.49 tells us that the selected student's pulse rate is within the usual pulse rates.
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]
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.
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
You're pretty sure that your candidate for class president has about 6565% of the votes in the entire school. But you're worried that only 100100 students will show up to vote. How often will the underdog (the one with 3535% support) win? To find out, you
Answer:
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.
a. describe-how-you-will-simulate a component.
b. describe-how-you-will-simulate a trial.
c. describe-the-response-variable
Step-by-step explanation:
Part A:
A component is one voter's voting. An outcome is a vote in favor of our candidate.
Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.
Part B:
A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.
And counted how many people voted for each candidate. Whoever gets the majority of the votes wins the trial.
Part C:
The response variable is whether the underdog wins or not.
To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.
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
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. The test scores of 40 students are listed below. Construct a boxplot for the data set.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Answer:
Minimum = 25
First quartile = 58
Second quartile = 72
Third quartile = 80
Maximum = 98
Step-by-step explanation:
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°
Any help would be great
Hey there! :)
Answer:
[tex]-25m^{6}n^{9}[/tex]
Step-by-step explanation:
The product rule means that when multiplying variables with exponents, the exponents must be added together. Therefore:
[tex](-5m^{5}n^{6})(5mn^{3}) =[/tex]
[tex]-25m^{5+1}n^{6+3} =[/tex]
Simplify:
[tex]-25m^{6}n^{9}[/tex]
This is your answer!
Where is my phone? I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it. It started at the following coordinates A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12). My Mom told me she translated it 6 units to the left Then my little brother said he had reflected it over the Y-axis My friend many found it and translated it 9 units up Dad said he tripped over it and reflected it over the X-axis My sister then rotated it 900 clockwise Uncle Jose translated it 5 units left and 4 units down Cousin Michelle then said she rotated it 900 clockwise Finally my dog picked it up and translated it 5 units down and 10 units to the right Where is my phone? Using the scenario on this page do the following. Graph the preimage using the given points. Label points (A, B, C, ...) Transform the objects using the information provided. Show each transformation and label. (A', B', C', ...) Determine the final location. Write a 2 to 3 sentence explain on how you found the phone location.
Answer:
see attached
Step-by-step explanation:
The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.
The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.
__
Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.
90° CW does this: (x, y) ⇒ (y, -x)
Reflection across y does this: (x, y) ⇒ (-x, y)
Reflection across x does this: (x, y) ⇒ (x, -y)
Margo borrows $1700, agreeing to pay it back with 4% annual interest after 6 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
$1733.67
Step-by-step explanation:
Simple interest rate formula: A = P(1 + r)^t
Simply plug in your known variables
A = 1700(1 + 0.04)^0.5
A = 1733.67
Remember that t is time in years.
The weights of steers in a herd are distributed normally. The variance is 10,000 and the mean steer weight is 1400lbs. Find the probability that the weight of a randomly selected steer is between 1539 and 1580lbs. Round your answer to four decimal places.
Answer:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1539,1580)[/tex]
Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]
We are interested on this probability
[tex]P(1539<X<1580)[/tex]
And we can solve the problem using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 2 , 1 3 , 1 3 , 1 4 , 1 4 , 1 5 , 1 5 , 1 6 , ...
Answer:
if the sequence is:
12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.
Now, if the sequence is
1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5
so the terms after the first one repeat, we could group the terms with the same denominator and get:
1/2, 2/3, 2/4, 2/5..... etc.
So the terms after the first one are aₙ = 2/n.
Now, a criteria to see if a sequence converges if seing if:
[tex]\lim_{n \to \infty} a_n = 0[/tex]
and here we have;
[tex]\lim_{n \to \infty} 2/n[/tex]
that obviusly tends to zero, so we can conclude that this sequence converges.
then the limit is:
There exist a n' such that for any n > n' then IL -aₙI < ε
where L is the limit
I2/n - 0I = I2/nI < ε
then this is true if n > 2/ε = n'
. 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%
In general, shopping online is supposed to be more convenient than going to stores. However, according to a recent Harris Interactive poll, 87% of people have experienced problems with an online transaction (The Wall Street Journal, October 2, 2007). Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website. Fifty-three percent of people who experienced problems contacted customer-service representatives.
a. What percentage of people did not experience problems with an online transaction?
b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?
c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?
Answer:
a) 13% of people did not experience problems with an online transaction.
b) 36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website
c) 46.11% of people experienced problems with an online transaction and contacted customer-service representatives.
Step-by-step explanation:
a. What percentage of people did not experience problems with an online transaction?
87% of people have experienced problems with an online transaction. So 100 - 87 = 13% of people did not experience problems with an online transaction.
b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?
87% of people have experienced problems with an online transaction. Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website.
Then:
0.87*0.42 = 0.3654
36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website.
c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?
87% of people have experienced problems with an online transaction. Fifty-three percent of people who experienced problems contacted customer-service representatives.
Then:
0.87*0.53 = 0.4611
46.11% of people experienced problems with an online transaction and contacted customer-service representatives.
I NEED HELP ASAP PLEASE!!! I REALLY NEED HELP!
Answer:
D.
Step-by-step explanation:
One slope is positive and one negative, so one line should go up and one down. B or D.
y = 1/2 x - 1 line goes up and y-int. = - 1. Answer D.
y = - 1/2 x + 3 line goes up and y-int. = 3. Answer D.