Answer:
I)One to three roots.
ii)Two or zero extrema.
iii)One inflection point.
iv)Point symmetry about the inflection point.
v)Range is the set of real numbers.
vi)Three fundamental shapes.
vii)Four points or pieces of information are required to define a cubic polynomial function.
Roots are solvable by radicals.
Final answer:
The graph of a cube root function has several characteristics such as its domain, range, starting point, and symmetry.
Explanation:
A cube root function is represented by the equation y = ∛x. The graph of a cube root function has several characteristics:
The domain of the function is all real numbers because the cube root can be taken of any number.The range of the function is also all real numbers because the cube root of any number will give a real number.The graph starts in the fourth quadrant and passes through the origin.The graph is continuous, meaning there are no breaks or holes in the line.The graph is decreasing for negative values of x and increasing for positive values of x.The graph is symmetric about the origin, meaning if a point (x, y) lies on the graph, then (-x, -y) also lies on the graph.what is the area of the base.(area=6 square in.x 5 in.
Answer:
30 square inch
Step-by-step explanation:
[tex]area \: of \: base = 6 \times 5 = 30 \: {inch}^{2} \\ [/tex]
Kirk goes to the gym every 3 days. Deshawn goes to the
gym every 4 days. If they join the gym on the same day,
when is the first day that they'll be at the gym together?
The day when they would meet first time after joining the gym together will be 12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Kirk goes to the gym every 3 days.
Deshawn goes to the gym every 4 days.
If they join the gym on the same day.
Then the day when they would meet first time after joining the gym together will be
LCM of 4, 3 will be 12.
Then the day will be 12.
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Final answer:
Kirk and Deshawn will be at the gym together on the 12th day since they joined.
Explanation:
Gym memberships for Kirk and Deshawn occur every 3 days and 4 days respectively. To find the first day they'll be at the gym together, we need to find the lowest common multiple of 3 and 4.
LCM(3, 4) = 12. Therefore, Kirk and Deshawn will be at the gym together on the 12th day since they joined the gym.
A simple random sample of size nequals10 is obtained from a population with muequals63 and sigmaequals18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x overbar.
Answer:
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
If it is:
[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
What is the place value of 4 in 4.09
Which function does a criminologist perform?
Answer:
To find why the crimes were committed
Find BC if BC=x+2, AB=2x-6, and AC=17.
Answer:
BC = 9
Step-by-step explanation:
Assuming this is a straight line
AB + BC = AC
2x-6 + x+2 = 17
Combine like terms
3x -4 = 17
Add 4 to each side
3x-4+4 = 17+4
3x = 21
Divide each side by 3
3x/3 =21/3
x =7
We want to find BC
BC =x+2
=7+2
=9
A circle is centered on point B. Points A, C and D lie on it's circumference. If ADC measures 20 degrees, what does ABC measure
The Answer is : ABC = 40
Over the past year, the vice president for human resources at a large medical center has run a series of three-month workshops aimed at increasing worker motivation and performance. To check the effectiveness of the workshops, she selected a random sample of 35 employees from the personnel files and recorded their most recent annual performance ratings, along with their ratings prior to attending the workshops. If the vice president for human resources wishes to assess the effectiveness of the workshop in improving performance ratings, what sort of test should she use?
Answer: She should use THE PAIRED SAMPLE T-TEST.
Step-by-step explanation: The Paired sample t-test, is a method used in statistics to determine whether the mean difference in a statistics is zero. Which shows the accuracy of the two different recorded observation.
The paired sample t-test will help her to evaluate the recorded performance rating of the workers before the workshop, and after attending the workshop.
Example:
Let the mean in the workers performance rating before the workshop be Mb, and after the worship be Ma.
If she wants to find how significant the workshop was.
Ma - Mb = 0 means the workshop did not have any influence in their performance, as their performance remains the same.
Ma - Mb > 0 means that the workshop has improved the performance of the workers. As their mean performance after the workshop is greater than their mean performance before the workshop.
Ma - Mb <0 means that the workshop has reduced the performance of the workers. As their mean performance before the workshop is greater than their mean performance after the workshop.
Toby skated from his house to the beach at a constant speed of 8 88 kilometers per hour, and then skated from the beach to the park at a constant speed of 7 77 kilometers per hour. The total distance Toby skated was 20 2020 kilometers, and it took him twice as long to get to the park.
Answer:
8b+7p=20
p=2b
Step-by-step explanation:
You're welcome. Thou shall complete thou work without any trouble.
When telephone subscribers call from the National Magazine Subscription Company, 18% of the people who answer stay on the line for more than one minute. If 800 people are called in a day, find the probability that a. at least 150 stay on the line for more than one minute. (Use normal approximation to binomial). b. more than 200 stay on the line. (Use Normal approximation to Binomial).
Answer:
a) 30.50% probability that at least 150 stay on the line for more than one minute.
b) 0% probability that more than 200 stay on the line for more than one minute.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 800, p = 0.18[/tex]
So
[tex]\mu = E(X) = np = 800*0.18 = 144[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.18*0.82} = 10.87[/tex]
a. at least 150 stay on the line for more than one minute.
Using continuity correction, [tex]P(X \geq 150 - 0.5) = P(X \geq 149.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 149.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{149.4 - 144}{10.87}[/tex]
[tex]Z = 0.51[/tex]
[tex]Z = 0.51[/tex] has a pvalue of 0.6950
1 - 0.6950 = 0.3050
30.50% probability that at least 150 stay on the line for more than one minute.
b. more than 200 stay on the line.
Using continuity correction, [tex]P(X \geq 200 + 0.5) = P(X \geq 200.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 200.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200.5 - 144}{10.87}[/tex]
[tex]Z = 5.2[/tex]
[tex]Z = 5.2[/tex] has a pvalue of 1
1 - 1 = 0
0% probability that more than 200 stay on the line for more than one minute.
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Find the absolute value.
|-89= 0
please help thank you
the answer is 89
Step-by-step explanation:
it does not matter if the number is negative the absolute value is the number inside the lines
Answer:
The absolute value of this one is 89. Because for example: |-3|=3 because any number is in that sign || the number will turn to positive. For example, If it is |-3| it will turn to 3
Harper works as a carpenter for $20.87/h. How much will he earn in a 40-hour workweek? *
Answer:
$834.8 dollars that week
Step-by-step explanation:
All you have to do is multiply $20.87 by 10 hours to get your answer:)
By multiplying Harper's hourly wage ($20.87) by 40 hours, we determined that Harper will earn $834.80 in a 40-hour workweek.
Explanation:To calculate how much Harper will earn in a 40-hour work week, you simply need to multiply his hourly wage by the number of hours he works. In this case, that's $20.87 times 40. Using direct multiplication:
$20.87 x 40 = $834.80
So, Harper will earn $834.80 in a 40-hour workweek.
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A research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2824 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was x=14.6, with a standard deviation of s=10.3 . Complete parts a through d.a- Give a point estimate for μ.b- Give an interval estimate for μ. Use a confidence coefficient of 0.95c- Comment on the validity of the followingstatement: "95% of the time, the true mean number of people named per person will fall in the interval computed in part b."Choose the correct answer below.A. The statement is correct. 95% of the time, the true mean number of people named per person will fall within an interval computed with a confidence coefficient of 0.95.B. The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."C. The statement is incorrect. A correct statement would be"95% of the time, the true mean number of people named per person will fall outside the interval computed in part b.D. The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall outside the interval computed in part b.d- It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidenceinterval?A. It does impact the validity of the interpretation because the interpretation is based on highly skewed resultsB. It does impact the validity of the interpretation because the interpretation was based upon a sample instead of the entire population.C. It does not impact the validity of the interpretation because the interpretation is based on highly skewed results.D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
Answer:
a. [tex]\mu=\bar x =14.6[/tex]
b. The 95% CI for the population mean is (14.22, 14.98).
c. B. "The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b"
d. D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
Step-by-step explanation:
a) The sample mean provides a point estimation of the population mean.
In this case, the estimation of the mean is:
[tex]\mu=\bar x =14.6[/tex]
b) With the information of the sample we can estimate the
As the sample size n=2824 is big enough, we can aproximate the t-statistic with a z-statistic.
For a 95% CI, the z-value is z=1.96.
The sample standard deviation is s=10.3.
The margin of error of the confidence is then calculated as:
[tex]E=z\cdot s/\sqrt{n}=1.96*10.3/\sqrt{2824}=20.188/53.141=0.38[/tex]
The lower and upper limits of the CI are:
[tex]LL=\bar x-z\cdot s/\sqrt{n}=14.6-0.38=14.22\\\\UL=\bar x+z\cdot s/\sqrt{n}=14.6+0.38=14.98[/tex]
The 95% CI for the population mean is (14.22, 14.98).
c. "95% of the time, the true mean number of people named per person will fall in the interval computed in part b"
The right answer is:
B. "The statement is incorrect. A correct statement would be"One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b"
The confidence interval gives bounds within there is certain degree of confidence that the true population mean will fall within.
It does not infer nothing about the sample means or the sampling distribution. It only takes information from a sample to estimate a interval for the population mean with certain degree of confidence.
d. It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval?
The answer is:
D. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem.
The reliability of a confidence interval depends more on the sample size, not on the distribution of the population. As the sample size increases, the absolute value of the skewness and kurtosis of the sampling distribution decreases. This sample size relationship is expressed in the central limit theorem.
The point estimate for μ is 14.6. The confidence interval will provide the range where the true mean falls with 95% confidence. The Central Limit Theorem suggests that the deviation from the normal distribution will not significantly affect the answers.
Explanation:a- The point estimate for μ is x=14.6. This is calculated as the mean of all measured values.
b- An interval estimate can be calculated with the formula: x ± Z*(s/√n) where Z is the Z-value from a Z-table corresponding to desired confidence level, here, 0.95. The result would give you the range in which the true mean, μ, falls with 95% confidence.
c- The correct answer is B: The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."
d- If the personal network sizes of adults are not normally distributed and the distribution is highly skewed, it will have an impact on the validity of inferences derived from the confidence interval. The correct answer is D: It does not impact the validity of the interpretation as the sampling space of the sample mean will still be approximately normal due to the Central Limit Theorem.
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Help me plz
Solve for X
20 points*
Answer:
x = 4
Step-by-step explanation:
14x - 15 + 139 = 180
(Alternate & Supplementary angles)
14x = 56
x = 4
78.3 + -17 evaluate the expression
Answer:
it is 61.3
Step-by-step explanation:
A rectangular box is to have a square base and a volume of 72 ft3. If the material for the base costs $0.62/ft2, the material for the sides costs $0.15/ft2, and the material for the top costs $0.18/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
a. length
b. width
c. height
Answer:
a. length = 0.7211 ft
b. width = 0.7211 ft
c. height = 140.3846 ft
Step-by-step explanation:
This is an optimiztion with restriction problem.
We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.
As the cost for the sides is constant, we know that length and width are equal.
Then, we can express the volume as:
[tex]V=x\cdot y\cdot z=x^2z=73[/tex]
being x: length and z: height
We can express the height in function of the length as:
[tex]x^2z=73\\\\z=73x^{-2}[/tex]
Then, the cost of the box can be expressed as:
[tex]C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}[/tex]
To optimize C, we derive and equal to zero
[tex]\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211[/tex]
The height z is then
[tex]z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846[/tex]
An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 29 water samples and measure the pH of each. The sample mean and standard deviation are 6.7 and 0.35, respectively. Is there enough evidence to reject the company’s claim at the α = 0.05 level of significance?
The question asks to perform a hypothesis test about the mean pH level in a river. Given a sample size of 29, a sample mean of 6.7, a sample standard deviation of 0.35, and a significance level of α = 0.05, the provided reference suggests that there is insufficient evidence to reject the company's claim of a mean pH of 6.8, due to the calculated p-value being greater than α.
Explanation:In this problem, we are testing the hypothesis that the mean pH level of water in a nearby river is 6.8. The company claims this as the true population mean. The hypothesis under test is called the Null hypothesis.
Null Hypothesis H0: µ = 6.8Alternative Hypothesis HA: µ ≠ 6.8The level of significance is given as α = 0.05. We have a sample of size 29 with mean 6.7 and standard deviation 0.35.
In hypothesis testing, we calculate a test statistic and compare it with a critical value corresponding to the level of significance α. Here, we would be calculating a t-score because we have the sample standard deviation, not the population standard deviation and the sample size is less than 30. If the test statistic falls in the critical region, then we reject the null hypothesis.
Without specific calculations, the given reference suggests that the decision is to not reject the null hypothesis, citing p-value > α. In this case, the calculated p-value from testing statistics is higher than 0.05, meaning that the observed test statistic would be quite likely if the null hypothesis is true.
This results in the conclusion that there is insufficient evidence in the sampled data to reject the company's claim of a mean pH of 6.8.
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There is not enough evidence to reject the company's claim at the α=0.05 level of significance.
Given:
Population mean =6.8
Sample mean =6.7
Sample standard deviation s=0.35
Sample size n=29
Level of significance α=0.05
We'll perform a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30.
The hypotheses are:
Null hypothesis (o):
The mean pH level of the water in the river is 6.8 (μ=6.8).
Alternative hypothesis (H1):
The mean pH level of the water in the river is not equal to 6.8 (≠6.8)
We'll use the formula for the test statistic of a one-sample t-test:
t = (x- ) / [tex]\frac{s}{\sqrt{n} }[/tex]
t= -0.1/ 0.0651
t≈−1.535
Now, we'll find the critical value for a two-tailed test at α=0.05 significance level with n−1=28 degrees of freedom. Using a t-distribution table or statistical software,
we find the critical values to be approximately ±2.048.
Since −1.535 falls within the range −2.048 to 2.048, we fail to reject the null hypothesis.
So, there is not enough evidence to reject the company's claim at the α=0.05 level of significance.
Martin is playing a game . The probability of winning is 0.3 what is the probability of not winning
Answer:
0.7
Step-by-step explanation:
0.3+0.7=1.0=100%
Final answer:
The probability of not winning the game that Martin is playing is 0.7 or 70%, which is obtained by subtracting the probability of winning (0.3) from 1.
Explanation:
If Martin is playing a game where the probability of winning is 0.3, then the probability of not winning can be calculated by subtracting the probability of winning from 1. This is because the sum of the probabilities of all possible outcomes must equal 1. Since the probability of winning is 0.3, we calculate the probability of not winning as follows:
Probability of not winning = 1 - Probability of winningProbability of not winning = 1 - 0.3Probability of not winning = 0.7Therefore, the probability of not winning is 0.7 or 70%.
After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favored firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50.
(A) What is the P-value for this hypothesis test?
The P-value for this hypothesis test is 0.0228.
Explanation:To find the P-value for this hypothesis test, we need to calculate the proportion of alumni who favored firing the coach in the sample. Out of 100 alumni, 64 were in favor. So, the sample proportion is 64/100 = 0.64.
Now, we need to calculate the test statistic, which follows a normal distribution. The formula for the test statistic is: z = (p' - p) / sqrt(p * (1-p) / n), where p' is the sample proportion, p is the claimed proportion under the null hypothesis, and n is the sample size.
Plugging in the values, we get: z = (0.64 - 0.50) / sqrt(0.50 * (1-0.50) / 100) = 2.00
The P-value is the probability of observing a test statistic as extreme as 2.00, assuming the null hypothesis is true. We can look up this probability in a standard normal distribution table or use a statistical software. In this case, the P-value is 0.0228.
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
(a) What proportion of housing prices in Athens are less than $234,000? (3 decimal places)
(b) A realtor takes a random sample of 134 houses in Athens. Determine the probability the average selling price is greater than $239,000? (3 decimal places)
(c) A realtor in Asheville, NC wants to estimate the mean housing price of houses in Asheville. The realtor believes the distribution of housing prices in Asheville is similar to those in Athens.
If this realtor takes a random sample of 134 homes in Asheville, what is the standard error of the estimate? (3 decimal places)
How many homes in Asheville should the realtor sample to be 98% confident the estimate is within $500 of the true mean price? Use the critical value to exactly 3 decimal places.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes.
Step-by-step explanation:
The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
a) We need to know the proportion of housing prices in Athens that are less than $234,000. We can calculate this from the z-score for the population distribution.
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{234,000-238,000}{5,041}=\dfrac{-4,000}{5.041}=-0.793\\\\\\ P(x<234,000)=P(z<-0.793)=0.214[/tex]
The proportion of housing prices in Athens that are less than $234,000 is 0.214.
b) Now, a sample is taken. The size of the sample is n=134.
We have to calculate the probability that the average selling price is greater than $239,000.
In this case, we have to use the standard error of the sampling distribution to calculate the z-score:
[tex]z=\dfrac{\bar x-\mu}{\sigma/\sqrt{n}}=\dfrac{239,000-238,000}{5,041/\sqrt{134}}=\dfrac{1,000}{435.476}= 2.296 \\\\\\P(\bar x>239,000)=P(z>2.296)=0.011[/tex]
The probability that the average selling price is greater than $239,000 is 0.011.
c) We have another sample taken from a distribution with the same parameters.
We have to calculate the sample size so that the margin of error for a 98% confidence interval is $500.
The expression for the margin of error of the confidence interval is:
[tex]E=z\cdot \sigma/\sqrt{n}[/tex]
We can isolate n from the margin of error equation as:
[tex]E=z\cdot \sigma/\sqrt{n}\\\\\sqrt{n}=\dfrac{z\cdot \sigma}{E}\\\\n=(\dfrac{z\cdot \sigma}{E})^2[/tex]
We have to look for the critical value of z for a 98% CI. This value is z=2.327.
Now we can calculate the minimum value for n to achieve the desired precision for the interval:
[tex]n=(\dfrac{z\cdot \sigma}{E})^2\\\\\\n=(\dfrac{2.327*5,041}{500})^2= 23.461 ^2=550.410\approx551[/tex]
The realtor should sample at least 551 homes.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes
Step-by-step explanation:
In a bag of candy, there are 2 cinnamon, 1 butterscotch, and 2 peppermints. What is the probability of randomly selecting a peppermint?
Answer:
2/5
Step-by-step explanation:
The total number of candies are 2+1+2 = 5 candies
P (peppermint) = number of peppermints/total
=2/5
Answer:
2/5
Step-by-step explanation:
The probability is 2/5.There are five in all and two peppermint.Put it as a fraction and you get 2/5.
5(y+4)=6y need help in this math is for my son
Answer:
y =20
Step-by-step explanation:
5(y+4)=6y
Distribute
5y +20 = 6y
Subtract 5y from each side
5y-5y+20=6y-5y
20 =y
Answer:
solution
5y+20=6y
5y-6y=20
-y=20
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
Answer:
Approximately 20,579 units.
Two similar cylinders have surface areas of 24 cm2 and 54 cm2. The volume of the smaller cylinder is 16 cm2.
What is the volume of the larger cylinder?
Given:
Given that two similar cylinder have surface areas 24π cm² and 54π cm².
The volume of the smaller cylinder is 16π cm³
We need to determine the volume of the larger cylinder.
Volume of the larger cylinder:
The ratio of the two similar cylinders having surface area of 24π cm² and 54π cm², we have;
[tex]\frac{24 \pi}{54 \ pi}=\frac{4}{9}[/tex]
[tex]=\frac{2^2}{3^2}[/tex]
Thus, the ratio of the surface area of the two cylinders is [tex]\frac{2^2}{3^2}[/tex]
The volume of the larger cylinder is given by
[tex]\frac{2^2}{3^2}\times \frac{2}{3}=\frac{16 \pi }{x}[/tex]
where x represents the volume of the larger cylinder.
Simplifying, we get;
[tex]\frac{2^3}{3^3}=\frac{16 \pi }{x}[/tex]
[tex]\frac{8}{27}=\frac{16 \pi }{x}[/tex]
Cross multiplying, we get;
[tex]8x=16 \pi \times 27[/tex]
[tex]8x=432 \pi[/tex]
[tex]x=54 \pi \ cm^3[/tex]
Thus, the volume of the larger cylinder is 54π cm³
Answer:
54π cm³
Step-by-step explanation:
does this answer and help me with all subjects?
EXAMPLE 2 Prove that 9ex is equal to the sum of its Maclaurin series. SOLUTION If f(x) = 9ex, then f (n + 1)(x) = for all n. If d is any positive number and |x| ≤ d, then |f (n + 1)(x)| = ≤ 9ed. So Taylor's Inequality, with a = 0 and M = 9ed, says that |Rn(x)| ≤ (n + 1)! |x|n + 1 for |x| ≤ d. Notice that the same constant M = 9ed works for every value of n. But, from this equation, we have lim n → [infinity] 9ed (n + 1)! |x|n + 1 = 9ed lim n → [infinity] |x|n + 1 (n + 1)! = . It follows from the Squeeze Theorem that lim n → [infinity] |Rn(x)| = 0 and therefore lim n → [infinity] Rn(x) = for all values of x. By this theorem, 9ex is equal to the sum of its Maclaurin series, that is, 9ex = [infinity] 9xn n! n = 0 for all x.
Answer:
To Prove: [tex]9e^x[/tex] is equal to the sum of its Maclaurin series.
Step-by-step explanation:
If [tex]f(x) = 9e^x[/tex], then [tex]f ^{(n + 1)(x)} =9e^x[/tex] for all n. If d is any positive number and |x| ≤ d, then [tex]|f^{(n + 1)(x)}| = 9e^x\leq 9e^d.[/tex]
So Taylor's Inequality, with a = 0 and M = [tex]9e^d[/tex], says that [tex]|R_n(x)| \leq \dfrac{9e^d}{(n+1)!} |x|^{n + 1} \:for\: |x| \leq d.[/tex]
Notice that the same constant [tex]M = 9e^d[/tex] works for every value of n.
But, since [tex]lim_{n\to\infty}\dfrac{x^n}{n!} =0 $ for every real number x$[/tex],
We have [tex]lim_{n\to\infty} \dfrac{9e^d}{(n+1)!} |x|^{n + 1} =9e^d lim_{n\to\infty} \dfrac{|x|^{n + 1}}{(n+1)!} =0[/tex]
It follows from the Squeeze Theorem that [tex]lim_{n\to\infty} |R_n(x)|=0[/tex] and therefore [tex]lim_{n\to\infty} R_n(x)=0[/tex] for all values of x.
[tex]THEOREM\\If f(x)=T_n(x)+R_n(x), $where $T_n $is the nth degree Taylor Polynomial of f at a and $ lim_{n\to\infty} R_n(x)=0 \: for \: |x-a|<R, $then f is equal to the sum of its Taylor series on $ |x-a|<R[/tex]
By this theorem above, [tex]9e^x[/tex] is equal to the sum of its Maclaurin series, that is,
[tex]9e^x=\sum_{n=0}^{\infty}\frac{9x^n}{n!}[/tex] for all x.
a box of cookies contain 12 chocolate chip cookies, 6 peanut butter cookies, and 6 sugar cookies, what is the probability of randomly selecting a chocolate chip cookie, eating it, and then randomly selecting a sugar cookie?
The probability of first selecting a chocolate chip cookie and then selecting a sugar cookie from a box containing 24 cookies in total is 6/46 or approximately 0.1304.
The question refers to calculating the probability of selecting cookies of different flavors one after the other without replacement from a box. To begin with, we must find the probability of selecting a chocolate chip cookie followed by the probability of selecting a sugar cookie after one chocolate chip cookie has been removed.
Firstly, the total count of cookies is 12 chocolate chip + 6 peanut butter + 6 sugar cookies = 24 cookies. The probability (P) of selecting a chocolate chip cookie first is P(chocolate chip) = 12/24 = 1/2. After eating the chocolate chip cookie, there are 23 cookies left and the probability of then selecting a sugar cookie is P(sugar) = 6/23 since there are 6 sugar cookies left out of the remaining 23 cookies.
Since these events are sequential without replacement, we can find the combined probability of both events by multiplying the probabilities of each event. Thus, the combined probability is P(chocolate chip then sugar) = P(chocolate chip) *P(sugar) = (1/2) * (6/23) = 6/46.
The combined probability of first selecting a chocolate chip cookie and then selecting a sugar cookie is therefore 6/46 or about 0.1304.
Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint.
Answer:
The probability that none of the four cans selected contains an incorrect mix of paint is P=0.2545.
Step-by-step explanation:
We have 12 cans, out of which 3 are defective (incorrect mix of paint).
The man will choose 4 cans to paint his mother's house living room.
Let x = the number of the paint cans selected that are defective.
The variable x is known to follow a hypergeometric distribution.
The probability of getting k=0 defectives in a selected sample of K=4 cans, where there are n=3 defectives in the population of N=12 cans is:
[tex]P(X=k)=\dfrac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}\\\\\\\\ P(X=0)=\dfrac{\binom{4}{0}\binom{12-4}{3-0}}{\binom{12}{3}}=\dfrac{\binom{4}{0}\binom{8}{3}}{\binom{12}{3}}=\dfrfac{1*56}{220}=\dfrac{56}{220}=0.2545[/tex]
The probability that none of the four cans selected contains an incorrect mix of paint is P=0.2545.
Final answer:
The probability that none of the four randomly selected cans are defective is approximately 0.2545, or 25.45%, which is determined using the hypergeometric distribution.
Explanation:
The student is faced with a scenario where a man has twelve 1-gallon paint cans, out of which three contain an incorrect mix of paint. The man randomly selects four of these cans to paint with, and the question is to find the probability that none of the four selected cans are defective, which follows the hypergeometric distribution.
The relevant parameters for the hypergeometric distribution in this scenario are: the total number of cans (N=12), the number of defective cans (K=3), the number of cans selected (n=4), and the number of defective cans selected that we are interested in (x=0). To compute the probability, we use the hypergeometric probability formula:
P(X = x) = [(C(K, x) * C(N-K, n-x)) / C(N, n)]
Substituting the given values, we have:
P(X = 0) = [(C(3, 0) * C(12-3, 4-0)) / C(12, 4)]
= [(1 * C(9, 4)) / C(12, 4)]
= (1 * 126) / 495
≈ 0.2545
This means the probability that none of the four randomly selected cans are defective is approximately 0.2545, or 25.45%.
i need this answered asap
It's a parallelogram, opposite sides congruent.
6x - 7 = 2x + 9
4x = 16
x = 4
12 = y + 3
9 = y
Answer: x=4, y=9
Answer:
x = 4 and y = 9
Step-by-step explanation:
This is a parallelogram, which we can tell because of the arrows. Basically, opposite sides are parallel. By definition, then, opposite sides of this polygon are equal: LM = ON and LO = MN. That means we can set the various expressions equal to each other:
LM = ON ⇒ 6x - 7 = 2x + 9 ⇒ 4x = 16 ⇒ x = 4
LO = MN ⇒ 12 = y + 3 ⇒ y = 9
Thus, x = 4 and y = 9.
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