Answer:
Mailing preparation takes 38.29 min max time to prepare the mails.
Step-by-step explanation:
Given:
Mean:35 min
standard deviation:2 min
and 95% confidence interval.
To Find:
In normal distribution mailing preparation time taken less than.
i.eP(t<x)=?
Solution:
Here t -time and x -required time
mean time 35 min
5 % will not have true mean value . with 95 % confidence.
Question is asked as ,preparation takes less than time means what is max time that preparation will take to prepare mails.
No mail take more time than that time .
by Z-score or by confidence interval is
Z=(X-mean)/standard deviation.
Z=1.96 at 95 % confidence interval.
1.96=(X-35)/2
3.92=(x-35)
X=38.29 min
or
Confidence interval =35±Z*standard deviation
=35±1.96*2
=35±3.92
=38.29 or 31.71 min
But we require the max time i.e 38.29 min
And by observation we can also conclude the max time from options as 38.29 min.
In a normal distribution, the 95th percentile is calculated by adding twice the standard deviation to the mean. Based on the given mean (35 minutes) and standard deviation (2 minutes), 95% of the time the envelope preparation should take less than 39 minutes.
The problem asks what time, in percentage terms, the preparation for mailing the weekly report to the executives is less than.
Given that the time taken to prepare the envelopes follows a normal distribution with a mean of 35 minutes and a standard deviation of 2 minutes, we need to determine the time that occurs at the 95th percentile of this distribution.
The 95th percentile is found by adding 2 standard deviations to the mean in a normal distribution (this is due to the empirical rule, which states that about 95% of values lie within 2 standard deviations of the mean in a normal distribution).
Here's how you calculate it:
Determine the mean: The mean is given as 35 minutes.
Determine the standard deviation: The standard deviation is given as 2 minutes.
Calculate the 95th percentile: Mean + 2(Standard Deviation) = 35 + 2(2) = 39 minutes.
So, on 95% of occasions the mailing preparation takes less than 39 minutes. None of the options (a, b, c, and d) provided are correct based on the calculations.
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The diagram below shows the measurements of two identical rectangular prisms joined together. Austin says the combined volume of the prisms is 225 cubic meters. Explain Austin’s error and give the correct volume.
Answer:
450 cubic meters
Step-by-step explanation:
( 15 X 5 X 3) + ( 15 x 5 x 3)225 + 225 450 cubic metersAustin didn't add the 2 prisms, he multiplied the 1st prism and kept it as the answer.
Austin is not correct as the combined volume of the prisms is 1100 cubic meter.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
From the figure the dimension of prism is 5 x 11 x 10.
Austin says the combined volume of the prisms is 225 cubic meters.
So, Volume of combined prism
= 2 x 5 x 11 x 10
= 2 x 55 x 10
= 110 x 10
= 1100 cubic meter.
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Simplify to create equivalent to 19-6(-k+4)
Answer: don’t use k for the other numbers
Step-by-step explanation:
Answer:
6k -5
Step-by-step explanation:
19-6(-k+4)
Distribute
19 -6*-k -6*4
19 +6k -24
Combine like terms
6k +19-24
6k -5
You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Answer:
a. 20
b. -5
c. 5
Step-by-step explanation:
Please see attachment
The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.3 15.3 15.7 15.7 15.3 15.9 15.3 15.9 Construct a 98% confidence interval for the mean amount of juice in all such bottles
Answer:
[tex]15.55-2.997\frac{0.278}{\sqrt{8}}=15.26[/tex]
[tex]15.55+2.997\frac{0.278}{\sqrt{8}}=15.84[/tex]
The 98% confidence interval would be given by (15.26;15.84)
Step-by-step explanation:
Notation
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We can calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=15.55[/tex]
The sample deviation calculated [tex]s=0.278[/tex]
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=8-1=7[/tex]
Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,7)".And we see that [tex]t_{\alpha/2}=2.997[/tex]
And the confidence interval is given by:
[tex]15.55-2.997\frac{0.278}{\sqrt{8}}=15.26[/tex]
[tex]15.55+2.997\frac{0.278}{\sqrt{8}}=15.84[/tex]
The 98% confidence interval would be given by (15.26;15.84)
A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the proportion who have health insurance and the mean dollar amount that Americans spent on health care this past year. a. Identify the population parameters that this study will estimate. b. Identify the statistics that can be used to estimate these parameters.
Answer:
Step-by-step explanation:
(a) A parameter of a population measures the characteristics of the population, In the question the proportion of all the persons who have health insurance and the mean of the entire dollar amount that Americans spent on health care in the past year measure the population.
Invariably, the proportion of persons having health insurance, and the mean dollars spent on health care for all Americans are the population parameter
(b) A statistics measure the characteristics of the sample.
In the question, the sample of 1500 Americans are considered to estimate the proportion of all Americans, proportion of all the persons who have health insurance among 1500 and the sample mean of all the dollar amounts that the selected Americans spent on healthy care in the past year describe the sample.
Invariably, the sample proportion of persons having health insurance, and the mean dollars spent on health care for 1500 selected Americans are sample statistics
Find the value of g(-1)
Answer:
g(-1) = -3
Step-by-step explanation:
g(-1) is the y value of the graph when x = -1
when x=-1 y=-3
g(-1) = -3
Help meeeeeewwww :):):)):
Answer: Top Right, A rectangle has all the properties of a square.
Step-by-step explanation: Nobody how hard you try to make a rectangle a square, it won't work. A rectangle cannot have 4 equal slides.
What is the median of this set of data?
1,2,5, 6, 9
Answer:
5
Step-by-step explanation:
It be 5 because its in the middle
3,4,7,8
Step-by-step explanation:
1 2 3 4 5 6 7 8 9
3 4 7 8
6. The Brinson family is going camping. Their tent is shaped like a rectangular pyramid. The volume
of the tent is 6,000 cubic inches. The area of the base of the tent is 1,200 cubic inches. What is
the height of the tent? *
(1 Point)
Given:
Given that Brinson's family is going camping. Their tent is shaped like a rectangular pyramid.
The volume of the tent is 6000 cubic inches.
The area of the base of the tent is 1200 square inches.
We need to determine the height of the tent.
Height of the tent:
The height of the tent can be determined using the formula,
[tex]V=\frac{1}{3}Bh[/tex]
where B is the area of the base and h is the height of the pyramid.
Substituting V = 6000 and B = 1200, we get;
[tex]6000=\frac{1}{3}(1200)h[/tex]
[tex]6000=400h[/tex]
[tex]15=h[/tex]
Thus, the height of the tent is 15 inches.
The surface area of the cube is 150in squared. What is the length of the side of the cube?
Answer:
Cube surface area = 6 * side^2
150 square inches = 6 * side^2
sq root (side) = 25
side = 5 inches
Step-by-step explanation:
What is y={-\dfrac{1}{3}}x-9y=− 3 1 x−9y, equals, minus, start fraction, 1, divided by, 3, end fraction, x, minus, 9 written in standard form?
Answer:
[tex]x+3y=-27[/tex]
Step-by-step explanation:
We are given that
[tex]y=(-\frac{1}{3})x-9[/tex]
We have to find the standard form of given equation
[tex]y=\frac{-x-27}{3}[/tex]
[tex]3y=-x-27[/tex]
By using multiplication property of equality
[tex]x+3y=-27[/tex]
We know that
Standard form of equation
[tex]ax+by=c[/tex]
Therefore, the standard form of given equation is given by
[tex]x+3y=-27[/tex]
The equation y = -1/3x - 9 can be converted to standard form by eliminating fractions and rearranging. The final equation in standard form is x - 3y = 27.
Explanation:The equation you provided is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, you're asked to convert this equation into standard form, which is Ax + By = C, with A, B, and C being integers, and A and B not both equal to zero.
To convert the given equation y = -1/3x - 9 into standard form, we first need to eliminate the fractions. We can achieve this by multiplying every term by -3, giving us 3y = x + 27. To make it fit the standard form, we can rearrange as -x + 3y = -27.
Remember, standard form shouldn't have any negatives in front of the x term, so we multiply everything by -1. The final equation in standard form is x - 3y = 27.
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Make COS the subject of the formula
c^2 = a^2 + b^2 - 2(ab)(cos C)
c^2 + 2(ab)(cos C) = a^2 + b^2
2(ab)(cos C) = a^2 + b^2 - c^2
cos C = (a^2 + b^2 - c^2) / 2ab - Answer choice E
Hope this helps! :)
To make COS the subject of a formula, the equation is rearranged such that COS is isolated. An example can be in the equation a = b cos(x) which can be rearranged as cos(x) = a/b. A complete formula is necessary for an accurate step-by-step guide.
Explanation:To make COS the subject of a formula, it typically involves other known quantities represented by variables and constants. For example, in the equation a = b cos(x), we can make cos(x) the subject of the equation by rearranging it to: cos(x) = a/b. However, to provide a more accurate step-by-step guide, the complete formula is necessary. This principle can be applied to various trigonometric formulas so that COS becomes the main focus.
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A consumer group selected 100 different airplanes at random from each of two large airlines. The mean seat width for the 100 airplanes was calculated for each airline, and the difference in the sample mean widths was calculated. The group used the sample results to construct a 95 percent confidence interval for the difference in population mean widths of seats between the two airlines. Suppose the consumer group used a sample size of 50 instead of 100 for each airline. When all other things remain the same, what effect would the decrease in sample size have on the interval
Answer: B The width of the interval would increase
Step-by-step explanation:
i just took this and go the answers back
Decreasing the sample size from 100 to 50 would widen the 95 percent confidence interval for the difference in mean seat widths between two airlines. This is because smaller samples have more variability, requiring a larger interval to capture the population mean with the same level of certainty.
Explanation:If the consumer group used a sample size of 50 instead of 100 for each airline, that would increase the width of the 95 percent confidence interval for the difference in population mean widths of seats between the two airlines. This is because smaller sample sizes result in more variability, requiring a wider interval to capture the true population mean with the same level of certainty.
As with the unoccupied seats example, where the sample mean of 11.6 and standard deviation of 4.1 were used to form a confidence interval, the size of the interval is dependent on the variability within the sample, and smaller samples generally have higher variability. Similarly in the case of exam scores, with a lower confidence level of 90 percent, a narrower interval is needed compared to a higher confidence level of 95 percent.
Therefore, in effect, decreasing the sample size from 100 to 50 would make the confidence interval wider, as more variability is expected and a larger interval is needed to capture the true population mean with a 95 percent confidence level.
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what would be the value of $150 after eight years if you earn 12 %interest per year
Answer:
$371.39
Step-by-step explanation:
150 * .12+150 = 168
168 * .12+168 = 188.16
188.16 * .12+188.16 = 210.7392
210.7392 * .12+210.7392 = 236.027904
264.3512525 * .12+264.3512525 = 296.0734028
296.0734028 * .12+296.0734028 = 331.6022111
331.6022111 * .12+331.6022111 = 371.3944764
you multiply your current number by 12% and add that to the number, the last number i rounded for the answer as you can see
Let z denote a random variable that has a standard normal distribution. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 2.36) = (b) P(z 2.36) = (c) P(z < -1.22) = (d) P(1.13 < z < 3.35) = (e) P(-0.77 z -0.55) = (f) P(z > 3) = (g) P(z -3.28) = (h) P(z < 4.98) =
Answer:
(a) P (Z < 2.36) = 0.9909 (b) P (Z > 2.36) = 0.0091
(c) P (Z < -1.22) = 0.1112 (d) P (1.13 < Z > 3.35) = 0.1288
(e) P (-0.77< Z > -0.55) = 0.0705 (f) P (Z > 3) = 0.0014
(g) P (Z > -3.28) = 0.9995 (h) P (Z < 4.98) = 0.9999.
Step-by-step explanation:
Let us consider a random variable, [tex]X \sim N (\mu, \sigma^{2})[/tex], then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, [tex]Z \sim N (0, 1)[/tex].
In statistics, a standardized score is the number of standard deviations an observation or data point is above the mean. The z-scores are standardized scores.
The distribution of these z-scores is known as the standard normal distribution.
(a)
Compute the value of P (Z < 2.36) as follows:
P (Z < 2.36) = 0.99086
≈ 0.9909
Thus, the value of P (Z < 2.36) is 0.9909.
(b)
Compute the value of P (Z > 2.36) as follows:
P (Z > 2.36) = 1 - P (Z < 2.36)
= 1 - 0.99086
= 0.00914
≈ 0.0091
Thus, the value of P (Z > 2.36) is 0.0091.
(c)
Compute the value of P (Z < -1.22) as follows:
P (Z < -1.22) = 0.11123
≈ 0.1112
Thus, the value of P (Z < -1.22) is 0.1112.
(d)
Compute the value of P (1.13 < Z > 3.35) as follows:
P (1.13 < Z > 3.35) = P (Z < 3.35) - P (Z < 1.13)
= 0.99960 - 0.87076
= 0.12884
≈ 0.1288
Thus, the value of P (1.13 < Z > 3.35) is 0.1288.
(e)
Compute the value of P (-0.77< Z > -0.55) as follows:
P (-0.77< Z > -0.55) = P (Z < -0.55) - P (Z < -0.77)
= 0.29116 - 0.22065
= 0.07051
≈ 0.0705
Thus, the value of P (-0.77< Z > -0.55) is 0.0705.
(f)
Compute the value of P (Z > 3) as follows:
P (Z > 3) = 1 - P (Z < 3)
= 1 - 0.99865
= 0.00135
≈ 0.0014
Thus, the value of P (Z > 3) is 0.0014.
(g)
Compute the value of P (Z > -3.28) as follows:
P (Z > -3.28) = P (Z < 3.28)
= 0.99948
≈ 0.9995
Thus, the value of P (Z > -3.28) is 0.9995.
(h)
Compute the value of P (Z < 4.98) as follows:
P (Z < 4.98) = 0.99999
≈ 0.9999
Thus, the value of P (Z < 4.98) is 0.9999.
**Use the z-table for the probabilities.
To find the probabilities, we use the standard normal distribution table or a calculator to calculate probabilities for a standard normal distribution. We calculate each probability step by step and round the answers to four decimal places.
Explanation:To determine the probabilities, we will use the standard normal distribution table or a calculator that can calculate probabilities for a standard normal distribution.
(a) P(z < 2.36) = 0.9900
(b) P(z > 2.36) = 1 - P(z < 2.36) = 1 - 0.9900 = 0.0100
(c) P(z < -1.22) = 0.1103
(d) P(1.13 < z < 3.35) = P(z < 3.35) - P(z < 1.13) = 0.9993 - 0.8708 = 0.1285
(e) P(-0.77 < z < -0.55) = P(z < -0.55) - P(z < -0.77) = 0.2896 - 0.2823 = 0.0073
(f) P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013
(g) P(z > -3.28) = 1 - P(z < -3.28) = 1 - 0.0005 = 0.9995
(h) P(z < 4.98) = 1 - P(z > 4.98) = 1 - 0.0000 = 1.0000
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A teacher wants to see if a new unit on fractions is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Suppose that you are about to compute a confidence interval for \mu_dμ d, how do you check for normality?
Answer:
Find the difference between the two scores for a number of sample distributions. Make a plot of the differences and check for outliers.
Step-by-step explanation:
Checking for Normality means basically checking if one's data distribution approximates a normal distribution.
A normal distribution is represented by a bell-shaped curve, peaking around the mean, indicating that all of the data spreads out from the mean.
Th original aim of the teacher is to check the effects of the particular added unit on the performance of students in the subject.
The teacher goes about this by testing the students before and after learning the unit.
The best way to compare of course, is to take a difference of the test scores for different samples. This first gives the idea of whether the newly introduced unit affects performance.
This set of differences is then checked for normality.
So, the best manner to make a plot of these differences. Like we mentioned earlier, a normal distribution is bell shaped. So, the plot of these differences would be a bell shaped curve if the distribution was normal and we wouldn't get a bell shaped curve if the distribution wasn't normal.
Checking for outliers help to eliminate part of data that can totally scatter the regular behaviour of the data distribution.
So, the best way for the teacher to check for normality is to find the difference between the two scores for a number of sample distributions. Make a plot of the differences and check for outliers.
Hope this Helps!!!
Since the data include the pretest and post test scores of each student or subject, then, it is approached as a paired t test. Hence, checking for normality would require obtaining the difference between the two scores for each subject, then make a plot of the differences and check for outliers.
Working on a paired sample involves taking the difference between the scores. Which is called the paired difference. The plot of the paired difference is made, and outliers are checked in the plot made. As outlier values are more associated with skewed distributions.Hence, the most appropriate check for normality in this scenario is to check for outliers in the plot made from the score difference.
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Suppose you are working in an insurance company as a statistician. Your manager asked you to check police records of car accidents and out of 576 accidents you selected randomly, teenagers were at the wheel in 120 of them. (a) Construct a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. (b) Explain your findings to your manager. (c) Before you were hired in the company, the percentage of teenagers who where involved in car accidents was 18%. Your manager wants you to see if the percentage of teenagers has changed since you join the company. Perform an appropriate hypothesis test using α = 0.05 and Interpret your results to your manager. (d) Use α = 0.1 and repeat part (c).
Answer:
(a) 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].
(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.
(c) We conclude that the the percentage of teenagers has not changed since you join the company.
(d) We conclude that the the percentage of teenagers has changed since you join the company.
Step-by-step explanation:
We are given that your manager asked you to check police records of car accidents and out of 576 accidents you selected randomly, teenagers were at the wheel in 120 of them.
(a) Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion teenage drivers = [tex]\frac{120}{576}[/tex] = 0.21
n = sample of accidents = 576
p = population percentage of all car accidents
Here for constructing 95% confidence interval we have used One-sample z proportion statistics.
So, 95% confidence interval for the population population, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] ) = 0.95
95% confidence interval for p = [[tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex]]
= [ [tex]0.21-1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}[/tex] , [tex]0.21+1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}[/tex] ]
= [0.177 , 0.243]
Therefore, 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].
(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.
(c) We are also provided that before you were hired in the company, the percentage of teenagers who where involved in car accidents was 18%.
The manager wants to see if the percentage of teenagers has changed since you join the company.
Let p = percentage of teenagers who where involved in car accidents
So, Null Hypothesis, [tex]H_0[/tex] : p = 18% {means that the percentage of teenagers has not changed since you join the company}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 18% {means that the percentage of teenagers has changed since you join the company}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion teenage drivers = [tex]\frac{120}{576}[/tex] = 0.21
n = sample of accidents = 576
So, test statistics = [tex]\frac{0.21-0.18}{\sqrt{\frac{0.21(1-0.21)}{576} }}[/tex]
= 1.768
The value of the sample test statistics is 1.768.
Now at 0.05 significance level, the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the the percentage of teenagers has not changed since you join the company.
(d) Now at 0.1 significance level, the z table gives critical value of -1.6449 and 1.6449 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the the percentage of teenagers has changed since you join the company.
Mismatch went to a store spent half of her money and then $10 more she went to the second store spend half the money she has left and then $10 more then she had no money left how much money did mismatch have when she started our
Answer: I had a stroke trying to read and understand this sorry
Step-by-step explanation:
Answer:
$60.
Step-by-step explanation:
x / 2 - 10 = 0
x / 2 = 10
x = 20
Before she spent her money:
x / 2 - 10 = 20
x / 2 = 30
x = 60
She had $60 before she went shopping.
Feel free to let me know if you need more help. :)
When a certain prescription drug is taken orally by an adult, the amount of the drug (in mg/L) in the bloodstream at t hours is given by the function y=f(t)
1. What is the concentration of the drug in the bloodstream at t= 8 hours?
2. During what time interval is the drug level in the bloodstream increasing? Decreasing?
Answer:
1. y = f(8)
2. So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.
Step-by-step explanation:
The concentration of the drug in the bloodstream at t hours is:
y = f(t)
1. What is the concentration of the drug in the bloodstream at t= 8 hours?
At t hours, y = f(t)
So at 8 hours, y = f(8)
2. During what time interval is the drug level in the bloodstream increasing? Decreasing?
A function f(t) is increasing when
f'(t) > 0
And is decreasing when
f'(t) < 0
So for t which f'(t) > 0, the drug level in the bloodstream is increasing. And for t which f'(t) < 0, it is decreasing.
(1) The concentration of drug in the bloodstream in 8 hours is given by
[tex]\rm \bold{y = f (8)}[/tex]
(2) The time interval for which [tex]\rm y'=f'(t)>0[/tex] the drug level of the bloodstream is increasing.
The time interval for which [tex]\rm y' = f'(t) <0[/tex] the drug level of the bloodstream is decreasing.
When a certain prescription drug is taken orally by an adult.
the amount of the drug (in mg/L) in the bloodstream at t hours is given by the function y=f(t)
To be determined
(1) The concentration of the drug in the bloodstream at t= 8 hours
(2) During what time interval is the drug level in the bloodstream increasing or deceasing
The amount of the drug (in mg/L) in the bloodstream at t hours is given by the function
y=f(t).......(1)
(1) The concentration of drug in the bloodstream in 8 hours is given by putting t= 8 in the equation (1) which can be formulated as below
[tex]\rm y = f (8)[/tex]
(2) From the definition of increasing and decreasing function we can write that
[tex]\rm y = f(x) \; is \; increasing \; when \; f' (x)>0 \\and\; y = f(x) ; is \; decreasing \; when \; f' (x)<0 \\\\\\\\[/tex]
By the definition of increasing and decreasing function we can say that
The time interval for which [tex]\rm y'=f'(t)>0[/tex] the drug level of the bloodstream is increasing.
The time interval for which [tex]\rm y'=f'(t) <0[/tex] the drug level of the blood stream is decreasing.
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5 of 5
It is worked out that if 5 ladles full of soup are given to
each person,
140 people can be fed.
The customers have complained in the past that the
portions are too small.
The cook decides to give 7 ladles full of soup to each
person.
How many people can now be fed soup?
Answer:100 people
Step-by-step explanation:
140 people x 5 ladle/1 person = 700 ladles full
700 ladles x 1 person/7 ladles = 100 people fed
At Denver International Airport, 86% of recent flights have arrived on time. A sample of 11 flights is studied. What is the variance in a sample of 11 flights? Round your answer to 2 decimal places if needed.
Answer:
[tex]s^2=1.32[/tex]
Step-by-step explanation:
-This is a binomial probability distribution problem.
-Given that p=0.86 and n=11, the sample variance can be calculated using the formula:
[tex]\sigma^2=np(1-p)[/tex]
#We substitute the given parameters in the formula to solve for variance:
[tex]\sigma^2=np(1-p)\\\\\\=11\times 0.86(1-0.86)\\\\=1.324\approx1.32[/tex]
Hence, the sample variance is 1.32
Final answer:
The variance in a sample of 11 flights that have arrived on time at Denver International Airport, where 86% of flights are on time, is calculated using a binomial distribution with the formula variance = np(1-p), resulting in a variance of 1.33 after rounding to two decimal places.
Explanation:
The subject of this question is about finding the variance in a sample of flights that have arrived on time at Denver International Airport, given that 86% of recent flights have arrived on time and that a sample of 11 flights is studied. To calculate the variance for a binomial distribution, which is applicable in this context because each flight can either be on time or not, we use the formula:
Variance = np(1-p).
Where 'n' is the number of trials (or flights, in this case), which is 11, and 'p' is the probability of success on each trial (a flight arriving on time), which is 0.86. Thus, the variance for the 11 flights can be calculated as follows:
Variance = 11 × 0.86 × (1 - 0.86) = 11 × 0.86 × 0.14 = 1.3284.
After rounding to two decimal places, the variance for a sample of 11 flights is 1.33.
A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,684 firms, 715 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%? Use alpha equals0.05 to make your decision.
Calculate the value of the z-statistic for this test.
Answer:
z = 1.960
Step-by-step explanation:
The sample proportion is:
p = 715 / 2684 = 0.2664
The standard error is:
σ = √(pq/n)
σ = √(0.266 × 0.734 / 2684)
σ = 0.0085
For α = 0.05, the confidence level is 95%. The z-statistic at 95% confidence is 1.960.
The margin of error is 1.960 × 0.0085 = 0.0167.
The confidence interval is 0.2664 ± 0.0167 = (0.2497, 0.2831).
The upper limit is 28.3%, so the journal can conclude with 95% confidence that the true percentage is less than 29%.
Yes, the considered sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%.
The z-test statistic came out to be -2.69What is the z test statistic for one sample proportion?Suppose that we have:
n = sample size[tex]\hat{p}[/tex] = sample proportionp = population proportion (hypothesised)Then, the z test statistic for one sample proportion is:
[tex]Z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
For this case, we're provided that:
Size of sample = n = 2684Sample proportion of those who announced one or more acquisitions during year 2000 is: [tex]\hat{p}[/tex] = 715/n = 715/2684 Level of significance = 0.05We want to determine if true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29% = 0.29 (converted percent to decimal).
Hypotheses:
Null hypothesis: [tex]H_0: p \geq p_0 = 0.29\\[/tex] (it nullifies what we want to test for, thus assumes that true mean of the population proportion is not less than 0.29).Alternate hypothesis: [tex]H_A: p < p_0 = 0.29[/tex] Assumes that the true population mean is less than 0.29Thus, the test is left tailed test.
where [tex]p_0[/tex] = 29% = 0.29 is the hypothesized mean value of population proportion.
The test statistic is:
[tex]Z = \dfrac{\hat{p} - p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\ Z = \dfrac{715/2684 - 0.29}{\sqrt{\dfrac{0.29(1-0.29)}{2684}}} \approx -2.69[/tex]
The critical value of Z at level of significance 0.05 is -1.6449
Since the test statistic = -2.69 < critical value = -1.6449, so the test statistic lies in the rejection region (the rejection region for the left tailed test is all the values below critical value).
Thus, we reject the null hypothesis and accept the alternative hypothesis that the true population mean is less than 0.29.
Thus, the considered sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%.
The z-test statistic came out to be -2.69
Learn more about one-sample z-test for population proportion mean here:
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Given that €1 =£0.72 a) how much is €410
Answer: £569.40p
Step-by-step explanation:
410÷£0.72=£569.40p
Answer:
£295.20
Step-by-step explanation:
€410 x 0.72 = £295.20
Two candidates ran for class president. The candidate that won received 80% of the 290 total votes. How many votes did the winning candidate receive?
Answer:
232 votes
Step-by-step explanation:
This question is just asking what 80% of 290 is. In order to find this, you convert 80% into a decimal, then multiply by 290.
Converting percentages into decimals is just moving the decimal left twice.
0.8 x 290 = 232
You can check this by doing 232/290, and making sure it's 80%.
I hope this helps!
Convert 2.575 into a mixed number in simplest form
Step-by-step explanation:
(2575÷25)(1000÷25) = 10340 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 25751000 is also equal to 22340 when expressed as a mixed number.
Her fee is 5 hours of work is $350
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 and a multiple of 2?
Answer:
6.67% probability that the result is a multiple of 5 and a multiple of 2
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Multiples of 2 AND 5
Between 1 and 15, the multiples of 2 are: 2,4,6,8,10,12,14
Between 1 and 15, the multiples of 5 are: 5,10,15
So only 10 is a multiply of both 2 and 5, so only one desired outcome, which means that [tex]D = 1[/tex]
Total outcomes:
Any number between 1 and 15, there are 15, so [tex]T = 15[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1}{15} = 0.0667[/tex]
6.67% probability that the result is a multiple of 5 and a multiple of 2
Answer:
Step-by-step explanation:
3/5 or 9/15
use the unit circle to find the value of sin(3pi/2) and cos(3pi/2). hurry I need help ASAP!
Answer:
Step-by-step explanation:
Final answer:
The value of sin(3π/2) is -1, and the value of cos(3π/2) is 0, as determined by their positions on the unit circle at an angle of 3π/2 radians.
Explanation:
To find the values of sin(3π/2) and cos(3π/2) using the unit circle, we need to understand the positions on the circle.
At 3π/2 radians, which is the same as 270°, the point on the unit circle is directly below the center of the circle, at coordinates (0, -1).
This position corresponds to a cosine value of 0 (since the x-coordinate is 0) and a sine value of -1 (since the y-coordinate is -1).
A study is run to estimate the mean total cholesterol level in children 2 to 6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows. 180 220 240 196 175 183 195 140 200 What is the sample mean?A)196B)200C)192.11D)180
Answer:
C) 192.11
Step-by-step explanation:
To find the mean of any group of numbers, you simply add up all the numbers and then divide by how many numbers there are.
Using a calculator or a pencil, add the following:
180 + 220 + 240 + 196 + 175 + 183 + 195 + 140 + 200
= 1,729
The last step is to divide 1,729 by 9:
1,729 ÷ 9 = 192.11
Which conversion factors can be used to multiply 4 kilometers/min to get meters per hour
Answer:
(1000 m)/(1 km) and (60 min)/(1 h)
Step-by-step explanation:
Put the unit you don't want in a position to cancel the unit in the given number. Write the fraction so that the equivalent amount of the unit you do want is on the other side of the fraction bar.
Here we have km/min with km in the numerator. To cancel that, we need a fraction with km in the denominator. We want meters (m) in the numerator, so we need a fraction that has a number of meters equivalent to 1 km. That will be ...
(1000 m)/(1 km)
This is one of the conversion factors we will need to multiply by.
__
We also have "min" in the denominator. To cancel that, we need a conversion factor with min in the numerator. The unit we want in the denominator is h (hours), so we need an equivalent for hours and minutes. That would be 60 min = 1 h, so we write the conversion factor as ...
(60 min)/(1 h)
So, our conversion factors are ...
(1000 m)/(1 km) and (60 min)/(1 h)
_____
The converted number is ...
(4 km/min)(1000 m/km)(60 min/h) = 240,000 m/h
__
Comment on conversion factors
As you can see, we write the fraction so equal amounts are in numerator and denominator. Since the amounts are equal, the value of the fraction is 1. Multiplying by 1 in this form doesn't change the original value, it only changes the units.