Answer:
30 PS4 in the shipment are likely to be defective
Step-by-step explanation:
We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.
From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?
50PS4 - 3 defective
500 PS4 - x defective
[tex]50x = 3*500[/tex]
[tex]x = \frac{1500}{50}[/tex]
[tex]x = 30[/tex]
30 PS4 in the shipment are likely to be defective
Answer:
don't take my word but I think 150
Step-by-step explanation:
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8. Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.
Answer:
The 95% confidence interval for the mean is (3.249, 4.324).
We can predict with 95% confidence that the next trial of the paint will be within 3.249 and 4.324.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean.
As the population standard deviation is not known, we will use the sample standard deviation as an estimation.
The sample mean is:
[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4+5.2+3+4.8)\\\\\\ M=\dfrac{56.8}{15}=3.787[/tex]
The sample standard deviation is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(3.4-(3.787))^2+(2.5-(3.787))^2+(4.8-(3.787))^2+...+(4.8-(3.787))^2]}\\\\\\[/tex][tex]s=\sqrt{\dfrac{1}{14}\cdot [(0.15)+(1.66)+(1.03)+...+(1.03)]}[/tex]
[tex]s=\sqrt{\dfrac{13.197}{14}}=\sqrt{0.9427}\\\\\\s=0.971[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=3.787.
The sample size is N=15.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.971}{\sqrt{15}}=\dfrac{0.971}{3.873}=0.2507[/tex]
The t-value for a 95% confidence interval is t=2.145.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.145 \cdot 0.2507=0.538[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 3.787-0.538=3.249\\\\UL=M+t \cdot s_M = 3.787+0.538=4.324[/tex]
The 95% confidence interval for the mean is (3.249, 4.324).
To estimate a 95% prediction interval, calculate the sample mean and standard deviation, then use the t-distribution to apply the formula that includes the t-value for 95% confidence level and the sample size.
Explanation:To find a 95% prediction interval for the drying time for the next trial of latex paint, we need to use the measurements provided with the assumption that they represent a random sample from a normally distributed population.
However, before we can provide the prediction interval, we must first calculate the sample mean and the sample standard deviation from the given data. With those, we can then use the t-distribution to find the prediction interval, which will take the form of:
Sample Mean ± (t-value * Sample Standard Deviation * √(1 + 1/n))
Where 'n' is the number of observations and the t-value is determined from the t-distribution table for (n-1) degrees of freedom at the 95% confidence level.
Once calculated, this interval estimates the range within which we can expect the drying time for the next trial of paint to fall, with 95% confidence.
Question 5 (1 point)
A barrel contains 1256 liters of water.
Water is leaking out of the barrel at a rate of 3 liters per minute. At this rate, how many liters of water will
the barrel have after 27 minutes?
A. 81
B. 30
C. 1175
D. 1337
Answer:
C. 1175
Step-by-step explanation:
At 3 liters per minute, the amount leaked in 27 minutes is ...
(3 L/min)(27 min) = 81 L
Then the amount remaining is ...
1256 L - 81 L = 1175 L
There will be 1175 liters in the barrel after 27 minutes.
Linda invests $3000 in a bond trust that pays 8% interest compounded monthly. Her friend Lyla invests $3000 in a certificate of deposit that pays 7.75% compounded continuously. For Linda: a. State which formula should be used to solve this problem. _____________________ b. Write the function for Linda. _____________________ c. Determine how much Linda would have in her account after 20 years
Answer:
a) The interest is compounded monthly, so should use the compound interest formula.
b) [tex]A(t) = 3000(1.0067)^{12t}[/tex]
c) Linda would have $14898.33 in her account after 20 years.
Step-by-step explanation:
Compound Interest Formula:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years for which the money is invested.
Continuous Interest Formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial amount invested and r is the interest rate, as a decimal.
For Linda: a. State which formula should be used to solve this problem.
The interest is compounded monthly, so should use the compound interest formula.
b. Write the function for Linda.
Invests 3000, so [tex]P = 3000[/tex]
8% interest, so [tex]r = 0.08[/tex]
Compounded monthly. An year has 12 months, so [tex]n = 12[/tex]
Then
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 3000(1 + \frac{0.08}{12})^{12t}[/tex]
[tex]A = 3000(1.0067)^{12t}[/tex]
c. Determine how much Linda would have in her account after 20 years
This is A(20)
[tex]A = 3000(1.0067)^{12*20} = 14898.33[/tex]
Linda would have $14898.33 in her account after 20 years.
For Linda the formula that would be used to solve this problem is: FV = A (1 + r)^nm
For Linda, the function is: $3000(1.0067)^12n.
The amount Linda would have in her account after 20 years is $14,780.41.
The formula for determining the future value of an amount of money is: FV = A (1 + r)^nm
Where:
FV = Future value A = Amount deposited R = interest rate = 8%/12 = 0.067 m = number of compounding = 12 N = number of years = 20Value after 20 years $3000(1.0067)^(12 x 20) = $14,780.41.
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how do i Find the volume of the composite figure.
4 ft2 ft7 ft5 ft2 ft
The volume of the composite figure is cubic feet.
Answer:
You have to break apart the shape into individual shapes to find the volume of each one. Then you add.
hope this helped :)
When rolling two fair 6 sided dice, what is the probability that the difference between the scores is more than 3?
Answer:
[tex]1/6[/tex]
Step-by-step explanation:
When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.
Case 1: The difference of scores is 4.
The possible outcomes can be [tex](1,5), (5,1), (2,6) \text{ and }(6,2).[/tex] i.e. 4 number of cases are possible.
Case 2: The difference of scores is 5.
The possible outcomes can be [tex](1,6) \text{ and } (6,1)[/tex]. i.e. 2 number of cases.
Here, total number of favorable cases are 4 + 2 = 6.
Total number of cases, when two fair dice are rolled, are 36.
These cases are:
[tex][(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\..\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]}[/tex]
Formula:
[tex]\text{Probability of an event = } \frac{Number\ of\ favorable\ cases}{Total\ number\ of\ cases}[/tex]
Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is [tex]\frac{6}{36}[/tex] i.e. [tex]\frac{1}{6}[/tex].
Hence, the required probability is [tex]\frac{1}{6}[/tex].
An auto repair shop charges $50 plus $25 per hour. How much money would you have to pay if your car takes 4 hours to get repaired?
Answer:
150
Step-by-step explanation:
Answer: You would pay $150
Step-by-step explanation: Take 25 times 4, then add on the additional fee.
Vector wants to create a new box he wants the new box to be 2 inches wide the length and volume is 4 and 64. How tall should he make the new box?
9514 1404 393
Answer:
8 inches
Step-by-step explanation:
The product of length, width, and height is the volume.
V = LWH
H = V/(LW) = 64/(2·4) = 8
The height of the new box should be 8 inches.
To create a box that is 2 inches wide, 4 inches long, and has a volume of 64 cubic inches, the box should be made 8 inches tall.
The question asks how tall a new box should be if it is 2 inches wide, has a length of 4 inches, and must have a volume of 64 cubic inches. To find the height of the box, we use the formula for the volume of a rectangular prism (box), which is Volume = length × width × height.
Given the volume (V) is 64 cubic inches, the width (w) is 2 inches, and the length (l) is 4 inches, we can rearrange the formula to solve for the height (h):
h = V / (l × w)
= 64 / (4 × 2)
= 64 / 8
= 8 inches
Therefore, to create a new box with the specified dimensions and volume, Vector should make the box 8 inches tall.
In a 2008 article by Hsiu-Ling Lee, data from 147 colleges from 1995 to 2005 were used to predict endowments to a college from the average SAT score of students attending the college, among other variables. The resulting regression equation for these variables was Ŷ = –20.46 + 4.06(X). Using the regression equation, what would be the endowments (in billions) to a college whose students' average SAT score is 1050?
Answer:
4283.46 billion
Step-by-step explanation:
According to the information of the problem
[tex]\hat{Y} = 20.46 + 4.06(X)[/tex]
Therefore you are looking for
[tex]\hat{Y} = 20.46 + 4.06(1050) = 4283.46[/tex]
Determine which numbers could not be used to represent the probability of an event. Select all that apply. A. StartFraction 64 Over 25 EndFraction , because probability values cannot be greater than 1. B. 0.0002, because probability values must be rounded to two decimal places. C. minus1.5, because probability values cannot be less than 0. D. 0, because probability values must be greater than 0. E. 33.3%, this is because probability values cannot be greater than 1. F. StartFraction 320 Over 1058 EndFraction , because probability values cannot be in fraction form.
Answer:
A. [tex]\frac{64}{25}[/tex] , because probability values cannot be greater than 1.
C. -1.5, because probability values cannot be less than 0.
Step-by-step explanation:
Probability is the extent to which an event is likely to happen. It ranges from 0(impossible) to 1(certain). Probability values can be written in decimal form or in fractional form.
The following numbers could not be used to represent the probability of an event.
A. [tex]\frac{64}{25}[/tex] , because probability values cannot be greater than 1.
C. -1.5, because probability values cannot be less than 0.
In a certain normal distribution of scores, the mean is 40 and the standard deviation is 3. Find the s-score corresponding to a score
of 54.
a. 4.67
C. 4.67
b. 18.0
d. 13.33
Please select the best answer from the choices provided
Answer:
The s-score corresponding to a score of 54 is 4.67
Step-by-step explanation:
In a certain normal distribution of scores:
Mean = [tex]\mu = 40[/tex]
Standard deviation = [tex]\sigma = 3[/tex]
We are supposed to find the z-score corresponding to a score of 54.
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
x=54
Substitute the values
So,[tex]Z= \frac{54-40}{3}[/tex]
Z=4.67
So, Option A is true
Hence the s-score corresponding to a score of 54 is 4.67
Use Random number generator and simulate 1000 long columns, for each of the three cases. Example: for the Car type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty. Next: use either sorting to construct the appropriate histogram or rule of thumb to answer the questions: 13. What is approximate probability that Car Type 3 has annual cost less than $550?
Answer:
Step-by-step explanation:
The question is incomplete since they do not give information about the Car type 3.
We will do it in a generic way, we will say that the Car type 3 has a mean of M and a standard deviation SD.
We would be:
P (CT3 <550) = P [z <(550 - X) / SD]
Now if we give it values, for example that X = 600 and SD = 120
It would remain:
P (CT3 <550) = P [z <(550 - 600) / 120]
P (CT3 <550) = P [z <-0.42]
We look for this value in the normal distribution table (attached) and it shows us that the probability is approximately 0.3372, that is, 33.72%
What you need to do is replace the X and SD values of theCar type 3 in the equation above how I just did and you will get the result.
Point A is located at 11 on the number line. Point B is 5 less than Point A, where on the number line is Point B
Answer:
11-5 = 6
Step-by-step explanation:
Sunnyside Middle School wanted to add a new school sport, so they surveyed the students to determine which sport is most popular. Students were able to choose among soccer, football, lacrosse, or swimming. The same number of students chose lacrosse and swimming. The number of students who chose soccer was double the number of students who chose lacrosse. The number of students who chose football was triple the number of students who chose swimming. If 434 students completed the survey, how many students chose each sport?
Answer:
Lacrosse = 62 students
Swimming = 62 students
Soccer = 124 students
Football = 186 students
Step-by-step explanation:
Based on the information, we can draw some equations
1. Lacrosse = Swimming
2. Soccer = 2 * Lacrosse
3. Football = 3 * Swimming
4. Football + Soccer + Swimming + Lacrosse = 434
Lets solve for once sport at a time, I will start with Football.
I will put equation 1, 2 and 3 into equation 4
3Sw + 2L + L + L = 434
We can now again put equation 1 into the new equation 4
3L + 2L + L + L = 434
Simplify
7L = 434
L = 434 ÷ 7
L = 62 students
Since L = Sw, 62 students did swimming also
We can put L into equation 2 to solve for So
So = 2 * 62
So = 124 students
And now we can put Sw into equation 3 to solve for F
F = 3 * 62
F = 186 students
find the slope passing through to two points -5, 2 and 7,-1
PLEASE HURRY
Answer:
-1/4
Step-by-step explanation:
The slope is found by
m = (y2-y1)/(x2-x1)
= (-1-2)/(7- -5)
= (-1-2)/(7+5)
= -3/12
= -1/4
Who to write 26.46 as a fraction?
Answer:
2646/100 or 260 46/100 or 260 23/50
Which rigid transformation would map the
pre-image ΔABC to the image ΔA'B'C'?
a rotation by 90°
a reflection
a translation to the right
a translation up
Answer:
A Reflection on Edg
Step-by-step explanation:
Answer:B reflection
Step-by-step explanation:
edg 2022
Is this irrational or rational?
Answer:
irrational
Step-by-step explanation:
because √3 is irrational
Answer:
irational
Step-by-step explanation:
The he average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average.
1. State the null and alternative hypotheses to be tested.
2. Compute the test statistic.
3. The null hypothesis is to be tested at 95% confidence. What do you conclude?
Answer:
a) Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
c) The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=170[/tex] represent the sample mean in minutes
[tex]s=80[/tex] represent the standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =140[/tex] represent the value to verify
[tex]\alpha[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Part a
We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:
Null hypothesis:[tex]\mu = 140[/tex]
Alternative hypothesis:[tex]\mu \neq 140[/tex]
Part b
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]
Part c
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
Now we can calculate the p value, since we are conducting a two tailed test:
[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]
Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
Explanation:This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:
Null hypothesis (H0): The average internet usage in Soddy-Daisy is not significantly different from the U.S. average. This can be represented as H0: m = 140 minutes.Alternative Hypothesis (H1): The average internet usage in Soddy-Daisy is significantly different from the U.S. average. This can be represented as H1: m ≠ 140 minutes.For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.
For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.
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(i) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.
(ii) If volume is low this week then it will be high next week with a probability of 0.4. The manager estimates that the volume is five times as likely to be high as to be low this week.
Assume that state 1 is high volume and that state 2 is low volume.
(1) Find the transition matrix for this Markov process.(2) If the volume this week is high, what is the probability that the volume will be high two weeks from now?
A Markov chain is used to model this situation. The transition matrix based on the given probabilities will be [[0.9, 0.1],[0.4, 0.6]]. Also, to calculate the probability of being in a high-volume state two weeks from now given that it is in a high-volume state now, we square the matrix and look at the upper-left entry.
Explanation:A Markov process, in particular, a Markov chain, is a stochastic process that undergoes transitions from one state to another on a state space following the Markov property, stating that future states depend only on the current state and not on events that occurred before it. The transition matrix in these cases provides the probabilities between state transitions.
Given the data:
The probability of switching from hia gh volume (state 1) to a high volume (state 1) is 0.9The probability of switching from high volume (state 1) to low volume (state 2) is 1-0.9 =0.1The probability of switching from low volume (state 2) to high volume (state 1) is 0.4The probability of switching from low volume (state 2) to low volume (state 2), therefore, is 1-0.4 = 0.6Based on these probabilities the transition matrix will be of the form:
[[0.9, 0.1],[0.4, 0.6]].
To find the probability that the volume will be high two weeks from now, we will need to square the matrix as we are considering two steps ahead. The top left element of the resulting matrix will give the desired probability. In general, the i,j-th entry of the square of a transition matrix gives the 2-step transition probability from state i to state j.
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An ice cream truck began its daily route with 95 gallons of ice cream. The truck driver sold 78% of the
ice cream. How many whole gallons of ice cream were sold?
Answer:
74.1 or 74
Step-by-step explanation:
there is an antenna on the top of a building. From a location 300 ft from the base of the building, the angle of elevation to the top of the building is measured to be 40 degrees. From the same location the angle of elevation to the top of the antenna is measured to be 43 degrees. find the height of the antenna
Answer:
300tan43 - 300tan40
Step-by-step explanation:
Use tangent to find the height of the building:
tan40 = b/300
b = 300tan40
The use tangent to find the height to the top of the antenna:
tan43 = a/300
a = 300tan43
The antenna height = a - b
Find the dot product of the given vectors.
u=9i+4j
v=3i−j
The dot product of u = 9i+4j and v = 3i- j is 23.
Explanation:The dot product of two vectors can be calculated by multiplying their corresponding components and then summing them up. In this case, the dot product of u = 9i+4j and v = 3i- j is:
u · v = (9)(3) + (4)(-1) = 27 - 4 = 23
So, the dot product of u and v is 23.
An association was formed by students to protest labor exploitation in the apparel industry. There were 18 student "sit-ins" for a "sweat-free campus" organized at several universities. Data were collected for the duration (in days) of each sit-in, as well as the number of student arrests. The data for 5 sit-ins in which there was at least one arrest and the results of a simple linear regression are found below. Let y be the number of arrests and x be the duration. Complete parts a through d Click the icon to view the data table E Click the icon to view the results of the simple linear regression. a. Write the equation of a straight-line model relating y to x.A. y = beta1xB. y = beta1x^2 + beta0C. y = beta0 + beta1x + {D. y = beta1x + {b. Use the results of the linear regression to find the least squares prediction equation Type an integer or decimal rounded to three decimal places as needed)
Data for complete question is attached.
Answers
Therefore .
A. The regression equation is
y = beta0 + beta1+ ∈
B. From the given output regression line
y= 2.478+7.717x
The question addresses using a simple linear regression model to determine the relationship between two variables, and how to interpret the parameters of that model, as well as the significance of the correlation coefficient in the context of a hypothetical student protest situation.
Explanation:The subject of this question is about linear regression analysis in mathematics, particularly in the context of statistical analysis. The question demonstrates the application of a simple linear regression to decipher the relationship between the duration of student sit-ins (independent variable) and the number of arrests (dependent variable).
Answers to the Linear Regression Exercise:The equation of the straight-line model relating number of arrests (y) to duration (x) is C. y = beta0 + beta1x, where beta0 is the y-intercept, and beta1 is the slope of the regression line.To find the least squares prediction equation, use the provided regression output to plug in the estimated coefficients for the y-intercept (beta0) and slope (beta1). The form it should take is ý = a + bx, where 'a' is the estimated y-intercept and 'b' is the estimated slope.The y-intercept, or the constant 'a', has meaning if it has a context within the scope of the study. For example, it might represent the expected number of arrests when the duration of the sit-in is zero, if such a scenario makes sense within the context of the study.To find the correlation coefficient, typically denoted as 'r', refer to the regression output and assess its significance level. A significant correlation coefficient indicates a strong relationship between the dependent and independent variables.When engaging in weight-control (fitness/fat burning) types of exercise, a person is expected to attain approximately 60% of his or her maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of thirty 20-year-olds was taken, and the sample mean was found to be 107 bpm, with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. Report a 95% confidence region for the mean level of heart rate for this group. the mean level of heart rate is greater than 117.67 the mean level of heart rate is lower than 120.96 the mean level of heart rate is lower than 114.47 the mean level of heart rate is greater than 114.47
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Mr. Good Wrench advertises that a customer will have to wait no more than 30 minutes for an oil change. A sample of 26 oil changes had a standard deviation of 4.8 minutes. Use this information to calculate a 90% confidence interval for the population standard deviation waiting time for an oil change.
Answer:
The 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
Step-by-step explanation:
The (1 - α)% confidence interval for the population standard deviation is:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
The information provided is:
n = 26
s = 4.8 minutes
Confidence level = 90%
Compute the critical values of Chi-square as follows:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652[/tex]
[tex]\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611[/tex]
*Use a Chi-square table.
Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
[tex]=\sqrt{\frac{(26-1)\times 4.8^{2}}{37.652}}\leq \sigma\leq \sqrt{\frac{(26-1)\times 4.8^{2}}{14.611}}\\\\=3.9113\leq \sigma\leq 6.2787\\\\\approx 3.9 \leq \sigma\leq6.3[/tex]
Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
A customer in a shoe store bought a pair of shoes that were on sale for $15.00. He gave the salesman a $20.00 bill. Since he did not have change, the salesman went to an adjoining store and asked the lady in charge to give him change. She obligingly gave him a $10.00 bill and two $5.00 bills. The shoe man then returned and gave the customer his shoes and $5.00 change. The customer left.
Up to this point the story is very ordinary, but here is where "the plot thickens."
After the customer left, the lady who gave the salesman the change came into the store and told him that the $20.00 bill was a counterfeit. He looked at the bill, agreed that it was indeed worthless, and immediately repaid her with a good $20.00 bill.
That night, as he was closing the store, the shoe man began thinking about what he had lost in this series of transactions.
What did he lose?
Answer:
He lost $5.
Step-by-step explanation:
When the customer gives him the $20, the salesman does not gain any money because it is fake.
Then, he gets real money summing up to $20. So he gains that, but then gives $5 away. Now he has $15.
Then, the lady tells him the $20 bill is fake, so he must give the lady $20. So, 15 - 20 = -5. He lost $5.
Answer: He lost $35. $15 for the pair of shoes and $20 for having to repay the joined store for the counterfit money.
Step-by-step explanation:
Find the dot product of the given vectors.
u=2i−6j
v=3i+9j
u = 2i - 6j
v = 3i + 9j
Take the dot product:
u • v = (2i - 6j) • (3i + 9j)
u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)
u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)
The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to
u • v = 6 + 0 - 0 - 54
u • v = -48
Find the volume of a right circular cone that has a height of 11.1 in and a base with a circumference of 17.6 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
91.2
Step-by-step explanation:
use formula v=1/3 by pie r squared then the hieght
Final answer:
To calculate the volume of a cone given its height and the circumference of its base, first find the radius using the circumference formula, then apply the volume formula for a cone. In this case, the volume is approximately 92.4 cubic inches.
Explanation:
To find the volume of a right circular cone with a height of 11.1 inches and a base circumference of 17.6 inches, we first need to calculate the radius of the base. The formula for the circumference of a circle is C = 2πr. We can solve for r (radius) by rearranging the formula: r = C / (2π). Plugging in the given circumference, we get r = 17.6 / (2π) ≈ 2.8 inches.
Next, we use the formula for the volume of a cone, which is V = (1/3)πr²h. Substituting in our values for r (2.8 inches) and h (11.1 inches), we obtain V = (1/3)π(2.8)²(11.1) ≈ 92.4 cubic inches.
Therefore, the volume of the right circular cone is approximately 92.4 cubic inches, rounding to the nearest tenth.
Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.
Find the probability:
The probability that Joshua beats Eric in ping pong AND pool?
The probability that Joshua beats Eric in ping pong OR pool?
Answer:
P(pp & pool) = 22%
There is 22% probability that Joshua beats Eric in ping pong AND pool.
P(pp OR pool) = 50%
There is 50% probability that Joshua beats Eric in ping pong OR pool.
Step-by-step explanation:
The probability Joshua beats Eric in ping pong is given by
P(pp) = 0.48
The probability Joshua beats Eric in pool is given by
P(pool) = 0.46
The probability that Joshua beats Eric in ping pong AND pool is given by
P(pp & pool) = P(pp)×P(pool)
P(pp & pool) = 0.48×0.46
P(pp & pool) = 0.22
P(pp & pool) = 22%
Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.
The probability that Joshua beats Eric in ping pong OR pool is given by
P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54
Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)
Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)
P(pp OR pool) = 0.48×0.52 + 0.46×0.54
P(pp OR pool) = 0.25 + 0.25
P(pp OR pool) = 0.50
P(pp OR pool) = 50%
Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.
To calculate the probability of Joshua beating Eric in at least one game of ping pong or pool, taking into account the probabilities for each game.
Probability plays a key role in analyzing the chances of events happening. In this case, we have two independent events: winning ping pong and winning pool. The probability of Joshua winning at least one game can be calculated using the probabilities given for each game.
Calculate the probability of Joshua winning both games: 0.48 × 0.46 = 0.2208
Subtract this value from 1 to find the probability of Joshua winning at least one game: 1 - 0.2208 = 0.7792
Therefore, Joshua has a 77.92% chance of beating Eric in at least one of the games.
Maya mowed 4 lawns in 12 hours. What was her rate of mowing in hours per lawn?
Answer:
1 Lawn per 3 Hours
Step-by-step explanation:
In 'Lawns : Hours' the work that she has done = 4 : 12 = 1 : 3
With this workout, we can conclude that Maya mowed 1 Lawn every 3 Hours.
Maya's rate of mowing is 3 hours per lawn, calculated by dividing the total time spent (12 hours) by the number of lawns mowed (4 lawns).
Maya mowed 4 lawns in 12 hours, so to find her rate of mowing in hours per lawn, we divide the total hours by the number of lawns mowed. The calculation is 12 hours / 4 lawns, which equals 3 hours per lawn. Therefore, Maya's mowing rate is 3 hours per lawn.