Answer:
The unit price is $5.
Answer:
$5.00.
Step-by-step explanation:
This is 22.5 / 4.5
= $5.00
an angle measures 135 degrees through what fraction does the angle turn
Answer:
3/8
Step-by-step explanation:
Since we have given that
Measure of an angle = 135°
As we know that
Total angle formed by a circle = 360°
So, Fraction of a circle when the an angle 135° turn is given by
135/360=
Question
If $500 is borrowed with an interest of 21.0% compounded monthly, what is the total amount of money needed to pay it
back in 1 year? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round
your final answer.
Answer:
$558.68
Step-by-step explanation:
The amount of each monthly payment is given by the amortization formula:
A = P(r/n)/(1 -(1 +r/n)^(-nt)
where P is the principal borrowed, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
We want to find nA where we have n=12, r=0.21, t=1, P=500. Filling in these values, we get ...
nA = Pr/(1 -(1 +r/n)^-n) = $500(0.21)/(1 -1.0175^-12) = $558.68
The total amount needed to repay the loan in 1 year is $558.68.
Answer:
$615.72
Step-by-step explanation:
Use the compound interest formula and substitute the given value: A=$500(1+0.21/12)^12(1)
Simplify using order of operations: A=$500(1.0175)^12=$500(1.231439315)
=$615.72
If m∠A = 87° and m∠B = 32°, find m∠1.
Answer:
m<56. that is all I can help with
Suppose a large consignment of cell phones contained 19% defectives. If a sample of size 399 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 5%
The probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.
To solve this problem, we need to find the probability that the sample proportion of defective cell phones will differ from the population proportion (19%) by more than 5%.
Given information:
- Population proportion of defective cell phones = 0.19 (or 19%)
- Sample size = 399
Calculate the standard error of the proportion.
[tex]\[\text{Standard error of the proportion} = \sqrt{\frac{p \times (1 - p)}{n}}\]Substituting the given values:\[\text{Standard error of the proportion} = \sqrt{\frac{0.19 \times (1 - 0.19)}{399}}\]\[\text{Standard error of the proportion} = \sqrt{\frac{0.19 \times 0.81}{399}}\]\[\text{Standard error of the proportion} = \sqrt{\frac{0.1539}{399}}\]\[\text{Standard error of the proportion} = 0.0196 \text{ or } 1.96\%\][/tex]
Calculate the maximum allowable difference from the population proportion.
Maximum allowable difference = 0.05 (or 5%)
Calculate the z-score for the maximum allowable difference.
z-score = (Maximum allowable difference - Population proportion) / Standard error of the proportion
z-score = (0.05 - 0.19) / 0.0196
z-score = -2.55
Find the probability using the standard normal distribution table or calculator.
The z-score of -2.55 corresponds to a probability of 0.0054 (or 0.54%) in the standard normal distribution table.
Since the question asks for the probability that the sample proportion will differ from the population proportion by more than 5%, we need to find the probability of both tails.
Probability of both tails = 2 × 0.0054 = 0.0108 or 1.08%
Therefore, the probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.
The probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.
To solve this problem, we need to find the probability that the sample proportion of defective cell phones will differ from the population proportion (19%) by more than 5%.
Given information:
- Population proportion of defective cell phones = 0.19 (or 19%)
- Sample size = 399
Calculate the standard error of the proportion.
[tex]\[\text{Standard error of the proportion}[/tex]=[tex]\sqrt{p \times (1 - p))/(n)[/tex]
Substituting the given values:[tex]\[\text{Standard error of the proportion} = \sqrt{(0.19 \times (1 - 0.19))/(399)[/tex]
[tex]\[\text{Standard error of the proportion} = \sqrt{(0.19 \times 0.81)/(399)}\\\text{Standard error of the proportion} = \sqrt{(0.1539)/(399)}\\\text{Standard error of the proportion} = 0.0196 \text{ or } 1.96\%\][/tex]
Calculate the maximum allowable difference from the population proportion.
Maximum allowable difference = 0.05 (or 5%)
Calculate the z-score for the maximum allowable difference.
z-score = (Maximum allowable difference - Population proportion) / Standard error of the proportion
z-score = (0.05 - 0.19) / 0.0196
z-score = -2.55
Find the probability using the standard normal distribution table or calculator.
The z-score of -2.55 corresponds to a probability of 0.0054 (or 0.54%) in the standard normal distribution table.
Since the question asks for the probability that the sample proportion will differ from the population proportion by more than 5%, we need to find the probability of both tails.
Probability of both tails = 2 × 0.0054 = 0.0108 or 1.08%
Therefore, the probability that the sample proportion will differ from the population proportion by more than 5% is 0.0108 or 1.08%.
5. The following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM): 21 16 29 35 42 24 24 25 Calculate a 99% CI for the variance σ 2 , and the standard deviation σ of the coating layer thickness distribution
Answer:
99% CI for the variance [tex]\sigma^{2}[/tex] , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.
Step-by-step explanation:
We are given that the following sample observations on total coating layer thickness (in mm) of eight wire electrodes used for Wire electrical-discharge machining (WEDM) : 21, 16, 29, 35, 42, 24, 24, 25
Firstly, the pivotal quantity for 99% confidence interval for the population variance is given by;
P.Q. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2}__n_-_1[/tex]
where, [tex]s^{2}[/tex] = sample variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 67.43
n = sample of observations = 8
[tex]\sigma^{2}[/tex] = population variance
Here for constructing 99% confidence interval we have used chi-square test statistics.
So, 99% confidence interval for the population variance, [tex]\sigma^{2}[/tex] is ;
P(0.9893 < [tex]\chi^{2}_7[/tex] < 20.28) = 0.99 {As the critical value of chi-square at 7
degree of freedom are 0.9893 & 20.28}
P(0.9893 < [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] < 20.28) = 0.99
P( [tex]\frac{0.9893 }{(n-1)s^{2} }[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{20.28 }{(n-1)s^{2} }[/tex] ) = 0.99
P( [tex]\frac{(n-1)s^{2} }{20.28 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1)s^{2} }{0.9893 }[/tex] ) = 0.99
99% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1)s^{2} }{20.28 }[/tex] , [tex]\frac{(n-1)s^{2} }{0.9893 }[/tex] ]
= [ [tex]\frac{7\times 67.43 }{20.28 }[/tex] , [tex]\frac{7\times 67.43 }{0.9893 }[/tex] ]
= [23.275 , 477.115]
99% confidence interval for [tex]\sigma[/tex] = [ [tex]\sqrt{23.275}[/tex] , [tex]\sqrt{477.115}[/tex] ]
= [4.824 , 21.843]
Therefore, 99% CI for the variance [tex]\sigma^{2}[/tex] , and the standard deviation σ of the coating layer thickness distribution is [23.275 , 477.115] and [4.824 , 21.843] respectively.
An art history professor assigns letter grades on a test according to the following scheme. A: Top 13%13% of scores B: Scores below the top 13%13% and above the bottom 56%56% C: Scores below the top 44%44% and above the bottom 21%21% D: Scores below the top 79%79% and above the bottom 9%9% F: Bottom 9%9% of scores Scores on the test are normally distributed with a mean of 79.779.7 and a standard deviation of 8.48.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B grade is between 81 and 89.
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this problem, we have that:
[tex]\mu = 79.7, \sigma = 8.4[/tex]
B: Scores below the top 13% and above the bottom 56%
Below the top 13%:
Below the 100-13 = 87th percentile. So below the value of X when Z has a pvalue of 0.87. So below X when Z = 1.127. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.127 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 8.4*1.127[/tex]
[tex]X = 89[/tex]
Above the bottom 56:
Above the 56th percentile, so above the value of X when Z has a pvalue of 0.56. So above X when Z = 0.15. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.15 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 8.4*0.15[/tex]
[tex]X = 81[/tex]
The numerical limits for a B grade is between 81 and 89.
A sample of blood pressure measurements is taken from a data set and those values (mm Hg) are listed below. The values are matched so that subjects each have systolic and diastolic measurements. Find the mean and median for each of the two samples and then compare the two sets of results. Are the measures of center the best statistics to use with these data? What else might be better?
Answer:
Step-by-step explanation:
Systolic. Calculate the mean
118+128+158+96+156+122+116+136+126+120+
=1276÷10 = 127.6.
To calculate the median arrange the values from the lowest to the highest.
96,116,118,120,122,126,128,136,156,158.
122+126+2=124.
Disastolic
80+76+74+52+90+88+58+64+72+82= 736÷10=73.6
To calculate the median arrange the values from the lowest to the highest.
52,58,64,72,74,76,80,82,88,90
Median= 74+76=150÷2=75.
Comparison
The Systolic and diastolic blood pressure measures different things, so comparing them is of no use.
It will be good if the relationship between the blood pressure can be investigated because the data are in pairs.
Compute the mean and median for both the systolic and diastolic measurements. Compare the results to identify skewness in the data. The mean and median do not represent data variability, so also consider using the Standard Deviation or Interquartile Range for a broad view.
Explanation:
First, let's begin by calculating the mean or average of both systolic and diastolic data sets. For this, you'll add up all the measurements and divide by the number of measurements.
For the median, you'll arrange the measurements in ascending order. If the total number is odd, the median is the middle number. If it is even, the median will be the average of the two middle numbers.
Comparing the two data sets would involve looking at the calculated mean and median values and determine whether they're close in value or not. If they are close, it indicates a lack of skewness in the data. If they're not, there would appear to be skewness, with the mean being influenced by particularly high or low values.
The mean and median are measures of central tendency that provide some insight into the data, however, they do not show the spread or variability of the data. Therefore, using additional statistics like the Standard Deviation or Interquartile Range might be good options to understand dispersion in the data set.
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Which expression is the result of factoring the expression below by taking out its greatest common factor? 8x^2-24=\,?8x 2 −24=?8, x, squared, minus, 24, equals, question mark Choose 1 answer: Choose 1 answer:
8x² - 24 can be written in factorized form as 8 (x² - 3).
Step-by-step explanation:
Given expression is
8x² - 24
It can be factorized by taking the common factors as,
Since 8 is the common factor for both the terms and the expression can be written as,
8x² - 24
It can be expanded as,
= 8x² - 8×3
Now both the terms has 8, so it can be taken out and the expression can be written as,
= 8 (x² - 3)
So it can be written in factorized form as 8 (x² - 3).
Answer:
carmen winsted
Step-by-step explanation:
Prove that the diagonals of a rectangle bisect each other.
The midpoints are the same point, so the diagonals _____
are parallel to each other.
bisect each other.
have the same slope.
are perpendicular to each other.
Answer:
They Bisect
Step-by-step explanation:
They don't have the same slope.
They aren't instersecting at a right angle (they aren't perpendicular)
They aren't parallel because they touch.
What statements are true about the area of the
parallelogram? Select all that apply.
The area can be found using the formula A=bh.
3.6 m
O The area can be found using the formula A=-bh.
The area can be found using the formula A=52
6.1 m
ER
The area is 9.7 m2
The area is 21.96 m2.
Answer:
The area can be found using the formula A = b h
The area is 21.96 m2.
Step-by-step explanation:
We conclude that the area of the parallelogram is 21.96m², so the correct option is the last one.
How to get the area of a parallelogram?For a parallelogram of base b and height h, the area is:
A = b*h
In this case, we have that the base is 3.6m and the height is 6.1m, replacing that in the area equation we get:
A = 3.6m*6.1m = 21.96m²
Then we conclude that the area of the parallelogram is 21.96m², so the correct option is the last one.
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The polygons below are similar. Find the value of y. (2 points)
Polygons ABCD and EFGH are shown. AB equals 6. BC equals 8. CD equals 10. AD equals x. EF equals y. FG equals 6. GH equals z. HE equals 12.
Group of answer choices
A. 4.5
B. 7.5
C. 12
D. 16
Answer:
the answer is A(4.5)
Step-by-step explanation:
y/6 = 6/8
y=9/2 = 4.5
What is the probability of being dealt a king from a deck of cards
Answer:
4/52
Step-by-step explanation:
4 of each card 52 cards
Joaquin has a $50 gift card from pizza palace . All pizzas at pizza palace cost $7 each . Joaquin wants to give the driver a $5 tip for delivering the pizza . Which inequality could be used to determine the possible number of pizzas,p, he could order with his gift card , including the tip?
Answer:
[tex] 7p + 5 \le 50 [/tex]
Step-by-step explanation:
The number of pizzas is p.
One pizza costs $7.
p number of pizzas cost 7p.
The total cost is the cost of the pizzas plus the $5 tip.
The total cost is 7p + 5
He can spend $50 or less, so the total cost must be less than or equal to $50.
Answer: [tex] 7p + 5 \le 50 [/tex]
Cual conjunto de pares ordenados representa los vértices del triángulo?
Los tres puntos son (-3,0), (3,0), (0,4).
Por lo tanto, la respuesta es A, espero que esto ayude, que tenga un buen día.
ASAP, due soon Please help! I'll mark you brainliest if it's right! Fill in the blanks!
Answer:
(x + 10)^2 + (-186)
Step-by-step explanation:
x^2 + 20x - 86 =
Move the constant term to the right leaving a space between the x-term and the constant term.
= x^2 + 20x - 86
To complete the square, take half of the x-term coefficient and square it.
Half of 20 is 10. 10 squared is 100. This is the number that completes the square. Add it right after the x-term. Now you need to subtract the same amount at the end.
= x^2 + 20x + 100 - 86 - 100
Since 100 was added and subtracted, the expression has the same value. The first three terms are a perfect square trinomial, so we write it as the square of a binomial.
= (x + 10)^2 - 186
Since you have an addition sign, we write -186 as a sum:
= (x + 10)^2 + (-186)
Answer:
Step-by-step explanation:
+10 and -186 is your answer.
Suppose the weights of tight ends in a football league are normally distributed such that σ2=400. A sample of 11 tight ends was randomly selected, and the weights are given below. Calculate the 95% confidence interval for the mean weight of all tight ends in this league. Round your answers to two decimal places and use ascending order.
Answer:
[tex]217.636-1.96\frac{20}{\sqrt{11}}=205.817[/tex]
[tex]217.636+1.96\frac{20}{\sqrt{11}}=229.455[/tex]
So on this case the 95% confidence interval would be given by (205.82;229.46)
Step-by-step explanation:
Assuming the following data: Weight 150 169 170 196 200 218 219 262 269 270 271
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma= \sqrt{400}= 20[/tex] represent the population standard deviation
n=11 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
In order to calculate the mean we can use the following formula:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
The mean calculated for this case is [tex]\bar X=217.636[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]
Now we have everything in order to replace into formula (1):
[tex]217.636-1.96\frac{20}{\sqrt{11}}=205.817[/tex]
[tex]217.636+1.96\frac{20}{\sqrt{11}}=229.455[/tex]
So on this case the 95% confidence interval would be given by (205.82;229.46)
A marketing research company desires to know the mean consumption of meat per week among people over age 30. A sample of 2092 people over age 30 was drawn and the mean meat consumption was 3 pounds. Assume that the population standard deviation is known to be 1.4 pounds. Construct the 95% confidence interval for the mean consumption of meat among people over age 30. Round your answers to one decimal place.
Answer:
95% confidence interval for the mean consumption of meat among people over age 30 is [2.9 pounds , 3.1 pounds].
Step-by-step explanation:
We are given that a sample of 2092 people over age 30 was drawn and the mean meat consumption was 3 pounds. Assume that the population standard deviation is known to be 1.4 pounds.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean meat consumption = 3 pounds
s = population standard deviation = 1.4 pounds
n = sample of people = 2092
[tex]\mu[/tex] = population mean consumption of meat
Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] 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{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]3-1.96 \times {\frac{1.4}{\sqrt{2092} } }[/tex] , [tex]3+1.96 \times {\frac{1.4}{\sqrt{2092} } }[/tex] ]
= [2.9 pounds , 3.1 pounds]
Therefore, 95% confidence interval for the mean consumption of meat among people over age 30 is [2.9 pounds , 3.1 pounds].
At a canning facility, a technician is testing a machine that is supposed to deliver 250 milliliters of product. The technician tests 44 samples and determines the volume of each sample. The 44 samples have a mean volume of 251.6 mL. The machine is out of calibration when the average volume it dispenses differs significantly from 250 mL.
The technician wants to perform a hypothesis test to determine whether the machine is out of calibration. Assume standard deviation = 5.4 is known. Compute the value of the test statistic.
Potential answers are:
4.57
0.30
13.04
0.24
1.97
Answer:
1.97
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 250[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 250[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the hypothesis tested(null hypothesis), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem, we have that:
[tex]X = 251.6, \mu = 250, \sigma = 5.4, n = 44[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{251.6 - 250}{\frac{5.4}{\sqrt{44}}}[/tex]
[tex]t = 1.97[/tex]
Becca bought a shirt that was 25% off and saved $6. What was the original price of the shirt?
Answer:
$24
Step-by-step explanation:
Since 25% is off the price of the shirt, she bought the shirt at 75% of it's cost price. This difference between the full cost and the 75% is what she saved (i.e. 25% was the savings)
So, if the shirt costs x dollars:
$6 = 25% of x
= ( 25/100)*X = 0.25X
X = $6/0.25 = $6x4
X = $24
You are interested in estimating the the mean weight of the local adult population of female white-tailed deer (doe). From past data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 21 pounds. What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 99% confidence level, to within 6 pounds of the actual weight?
Answer:
We need a sample of at least 82 female white-tailed deer
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 99% confidence level, to within 6 pounds of the actual weight?
We need a sample of size at least n.
n is found when [tex]M = 6, \sigma = 21[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 2.575*\frac{21}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 21*2.575[/tex]
[tex]\sqrt{n} = \frac{21*2.575}{6}[/tex]
[tex](\sqrt{n})^{2} = (\frac{21*2.575}{6})^{2}[/tex]
[tex]n = 81.23[/tex]
Rounding up
We need a sample of at least 82 female white-tailed deer
Answer:
[tex]n=(\frac{2.58(21)}{6})^2 =81.54 \approx 82[/tex]
So the answer for this case would be n=82 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=21[/tex] represent the estimation for the population standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =6 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.005;0;1)", and we got [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(21)}{6})^2 =81.54 \approx 82[/tex]
So the answer for this case would be n=82 rounded up to the nearest integer
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), 4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. 9. Find the probability of getting two numbers whose sum is 9. 10.Find the probability of getting two numbers whose sum is 4. 11.Find the probability of getting two numbers whose sum is less than 7. 12.Find the probability of getting two numbers whose sum is greater than 8 13.Find the probability of getting two numbers that are the same (doubles). 14.Find the probability of getting a sum of 7 given that one of the numbers is odd. 15.Find the probability of getting a sum of eight given that both numbers are even numbers. 16.Find the probability of getting two numbers with a sum of 14.
Answer:
(9)[tex]\frac{1}{12}[/tex] (10) [tex]\frac{1}{12}[/tex] (11)[tex]\frac{5}{12}[/tex] (12)[tex]\frac{1}{4}[/tex] (13)[tex]\frac{1}{6}[/tex] 14)[tex]\frac{5}{36}[/tex] (15)[tex]\frac{1}{12}[/tex] (16)0
Step-by-step explanation:
The sample Space of the single die rolled twice is presented below:
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}.
n(S)=36
(9)Probability of getting two numbers whose sum is 9.
The possible outcomes are: (3, 6), (4, 5), (5, 4)
[tex]P(\text{two numbers whose sum})=\frac{3}{36}=\frac{1}{12}[/tex]
10) Probability of getting two numbers whose sum is 4.
The possible outcomes are: (1, 3),(2, 2),(3, 1),
[tex]P(\text{two numbers whose sum})=\frac{3}{36}=\frac{1}{12}[/tex]
11.)Find the probability of getting two numbers whose sum is less than 7.
The possible outcomes are: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)
[tex]P(\text{two numbers whose sum is less than 7})=\frac{15}{36}=\frac{5}{12}[/tex]
12.Probability of getting two numbers whose sum is greater than 8
The possible outcomes are:(4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)
[tex]P(\text{two numbers whose sum is greater than 8})=\frac{9}{36}=\frac{1}{4}[/tex]
(13)Probability of getting two numbers that are the same (doubles).
The possible outcomes are:(1, 1)(2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
[tex]P(\text{two numbers that are the same})=\frac{6}{36}=\frac{1}{6}[/tex]
14.Probability of getting a sum of 7 given that one of the numbers is odd.
The possible outcomes are: (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
[tex]P(\text{getting a sum of 7 given that one of the numbers is odd.})=\frac{5}{36}[/tex]
(15)Probability of getting a sum of eight given that both numbers are even numbers.
The possible outcomes are: (2, 6), (4, 4), (6, 2)
[tex]P(\text{getting a sum of eight given that both numbers are even numbers.})=\frac{3}{36}\\=\frac{1}{12}[/tex]
16.Probability of getting two numbers with a sum of 14.
[tex]P(\text{getting two numbers with a sum of 14.})=\frac{0}{36}=0[/tex]
Vehicle speed on a particular bridge in China can be modeled as normally distributed. (a) If 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.23 m/h, what are the mean and standard deviation of vehicle speed?
Answer:
[tex] -1.64 = \frac{39.18 -\mu}{\sigma}[/tex] (1)
[tex] 1.28 = \frac{73.23 -\mu}{\sigma}[/tex] (2)
From equation (1) and (2) we can solve for [tex]\mu[/tex] and we got:
[tex] \mu = 39.18 + 1.64 \sigma[/tex] (3)
[tex] \mu = 73.23 - 1.28 \sigma[/tex] (4)
And we can set equal equations (3) and (4) and we got:
[tex] 39.18 +1.64 \sigma = 73.23 -1.28 \sigma[/tex]
And solving for the deviation we got:
[tex] 2.92\sigma = 34.05[/tex]
[tex]\sigma = 11.66[/tex]
And the mean would be:
[tex] \mu = 39.18 +1.64 *11.66 = 58.304[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the vehicle speed of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,\sigma)[/tex]
For this case we know the following conditions:
[tex] P(X<39.18) = 0.05 [/tex]
[tex]P(X>73.23) = 0.1[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
We look for a one z value that accumulate 0.05 of the area in the left tail and we got: [tex] z_ 1= -1.64[/tex] and we need another z score that accumulates 0.1 of the area on the right tail and we got [tex] z_2 = 1.28[/tex]
And we have the following equations:
[tex] -1.64 = \frac{39.18 -\mu}{\sigma}[/tex] (1)
[tex] 1.28 = \frac{73.23 -\mu}{\sigma}[/tex] (2)
From equation (1) and (2) we can solve for [tex]\mu[/tex] and we got:
[tex] \mu = 39.18 + 1.64 \sigma[/tex] (3)
[tex] \mu = 73.23 - 1.28 \sigma[/tex] (4)
And we can set equal equations (3) and (4) and we got:
[tex] 39.18 +1.64 \sigma = 73.23 -1.28 \sigma[/tex]
And solving for the deviation we got:
[tex] 2.92\sigma = 34.05[/tex]
[tex]\sigma = 11.66[/tex]
And the mean would be:
[tex] \mu = 39.18 +1.64 *11.66 = 58.304[/tex]
Using the normal distribution, it is found that:
The mean is of 58.33 m/h.The standard deviation is of 11.64 m/h.In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.In this problem, 39.18 m/h is the 5th percentile, hence, when X = 39.18, Z has a p-value of 0.05, so Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{39.18 - \mu}{\sigma}[/tex]
[tex]39.18 - \mu = -1.645\sigma[/tex]
[tex]\mu = 39.18 + 1.645\sigma[/tex]
Additionally, 73.23 m/h is the 100 - 10 = 90th percentile, hence, when X = 73.23, Z has a p-value of 0.9, so Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{73.23 - \mu}{\sigma}[/tex]
[tex]73.23 - \mu = 1.28\sigma[/tex]
[tex]\mu = 73.23 - 1.28\sigma[/tex]
Equaling both equations, we find the standard deviation, hence:
[tex]39.18 + 1.645\sigma = 73.23 - 1.28\sigma[/tex]
[tex]2.925\sigma = 34.05[/tex]
[tex]\sigma = \frac{34.05}{2.925}[/tex]
[tex]\sigma = 11.64[/tex]
Then, we can find the mean:
[tex]\mu = 73.23 - 1.28\sigma = 73.23 - 1.28(11.64) = 58.33[/tex]
A similar problem is given at https://brainly.com/question/24663213
To understand the conditions necessary for static equilibrium. Look around you, and you see a world at rest. The monitor, desk, and chair—and the building that contains them—are in a state described as static equilibrium. Indeed, it is the fundamental objective of many branches of engineering to maintain this state in spite of the presence of obvious forces imposed by gravity and static loads or the more unpredictable forces from wind and earthquakes. The condition of static equilibrium is equivalent to the statement that the bodies involved have neither linear nor angular acceleration. Hence static mechanical equilibrium (as opposed to thermal or electrical equilibrium) requires that the forces acting on a body simultaneously satisfy two conditions: ∑F⃗ =0 and ∑τ⃗ =0; that is, both external forces and torques sum to zero. You have the freedom to choose any point as the origin about which to take torques. Each of these equations is a vector equation, so each represents three independent equations for a total of six. Thus to keep a table static requires not only that it neither slides across the floor nor lifts off from it, but also that it doesn't tilt about either the x or y axis, nor can it rotate about its vertical axis.Frequently, attention in an equilibrium situation is confined to a plane. An example would be a ladder leaning against a wall, which is in danger of slipping only in the plane perpendicular to the ground and wall. By orienting a Cartesian coordinate system so that the x and y axes are in this plane, choose which of the following sets of quantities must be zero to maintain static equilibrium in this plane.Frequently, attention in an equilibrium situation is confined to a plane. An example would be a ladder leaning against a wall, which is in danger of slipping only in the plane perpendicular to the ground and wall. By orienting a Cartesian coordinate system so that the x and y axes are in this plane, choose which of the following sets of quantities must be zero to maintain static equilibrium in this plane.A) ∑Fx and ∑τz and ∑FyB) ∑Fz and ∑τx and ∑τyC) ∑τx and ∑Fx and ∑τy and ∑FyD) ∑τx and ∑Fx and ∑τy and ∑Fy and ∑τz
Answer:
Option A - ∑Fx and ∑τz and ∑Fy
Step-by-step explanation:
All the force will be in x and y plane only
So Torque will be in z plane
These 3 quantities should be 0
∑Fx and ∑τz and ∑Fy
For static equilibrium in a plane, the net forces in the x and y directions, and the net torque about the z-axis, all need to be zero. This is true for a ladder leaning against a wall (a planar equilibrium situation). Hence, the correct set of quantities is ∑Fx, ∑Fy, and ∑τz.
Explanation:To achieve static equilibrium in any system, the sum of all external forces and torques acting on the body must be zero. This is true for both linear and rotational movements. In the case of the ladder against the wall, we're considering a planar equilibrium condition (in the xy-plane), where the spatial extension of the object (ladder) and the effect of z-axis can be disregarded.
Thus, for static equilibrium, the following conditions need to be satisfied: The net force in the x-direction (∑Fx) is zero, the net force in the y-direction (∑Fy) is zero, and the net torque about the z-axis (∑τz) is also zero. This implies that the ladder neither slides along the ground nor falls away from the wall, and does not rotate about its center. Therefore, the correct set of quantities is option A) ∑Fx, ∑Fy, and ∑τz.
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What’s the answer too 76.1*9.6
Answer:
[tex]76.1\times 9.6=730.56[/tex]
Step-by-step explanation:
In this case, we need to find the value of [tex]76.1\times 9.6[/tex]. The numbers are in decimal form. It is understood that the final answer will have decimal point after two places from right.
For an instance, multiply remove decimals from both numbers. Now simply multiply 761 and 96 such that we will get 73056.
Now, keep the decimal point after two places from right. So, we will get 730.56.
Final answer:
The answer to the multiplication of 76.1 and 9.6 is 730 when rounded to two significant figures in accordance with the rules of significant figures in multiplication.
Explanation:
The student asked for the product of 76.1 and 9.6. To compute this, you multiply the two numbers. Since 76.1 has three significant figures and 9.6 has two significant figures, our final answer should be reported with two significant figures, owing to the least number of significant figures in the given numbers.
Now, calculating the product:
76.1 times 9.6 = 730.56
When rounding to two significant figures, the answer is 730.
In calculations involving significant figures, it is important to report your final answer with the correct number of significant figures. In multiplication and division, the number of significant figures in the final answer should be the same as the least number of significant figures in any of the numbers being calculated.
In a normal distribution, which is greater, the mean or the median? Explain.
Choose the correct answer below.
O A. The median; in a normal distribution, the median is always greater than the mean.
OB. The mean; in a normal distribution, the mean is always greater than the median.
OC. Neither; in a normal distribution, the mean and median are equal.
Answer:
Its the neither option
Step-by-step explanation:
In a normal distribution, the mean and median are equal.
Option C is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
In a normal distribution,
The mean and median are both measures of central tendency.
The mean is calculated by adding up all the values in the distribution and dividing by the total number of values.
The median is the value that falls in the middle when the data is arranged in order.
Now,
In a perfectly symmetrical normal distribution, the mean and median are equal and they both fall at the exact center of the distribution.
However, if the distribution is skewed to one side or the other, the mean and median may be different.
Thus,
In a normal distribution, the mean and median are equal.
Learn more about mean here:
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To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 8 numbers, 0 through 7, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively
Final answer:
There are 512 different combinations possible for an 8-number combination lock, as the same number can be reused and each of the three positions has 8 choices.
Explanation:
To calculate the number of different combinations possible for a combination lock with a dial containing 8 numbers (0 through 7), we can use the fundamental counting principle. Since the same number can be reused consecutively, there are no restrictions on the choices for each of the three numbers in the sequence. Therefore, for each position of the sequence (the first, second, and third number), there are 8 possibilities.
The total number of combinations is the product of the number of choices for each position. Thus, the number of combinations for the lock is:
8 (choices for the first number) × 8 (choices for the second number) × 8 (choices for the third number)
Doing the calculation, we get:
8 × 8 × 8 = 512
Therefore, there are 512 different combinations possible for the lock.
Which of these is an example of a non-random sample?
A.
At a school assembly, five students are randomly chosen to receive free admission to a theme park.
B.
Out of all the seventh grade students in a public school district, fifteen are chosen to win a trip to a vacation destination.
C.
Registered voters in Arizona are surveyed to determine if they have relatives in Florida.
D.
Airline passengers to Orlando, Florida, are asked about vacation plans.
Answer:
it is D :)
Step-by-step explanation:
trust me ;)
Final answer:
Option D, which is about asking airline passengers to Orlando about their vacation plans, is an example of a non-random sample, specifically convenience sampling.
Explanation:
An example of a non-random sample is option D: Airline passengers to Orlando, Florida, are asked about vacation plans. This is considered non-random sampling because the passengers already have something in common – they are traveling to a popular vacation destination, which likely influences their vacation plans. This method does not give every individual in the broader population an equal chance of being selected and is thus not a random sample. This type of sampling is referred to as convenience sampling, as it involves selecting individuals who are easily accessible rather than using a process that gives every individual an equal chance of being chosen.
what is the product of -3/8 and -4/12
Answer:
0.125
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
-3/8 * -4/12
We can simplify the second fraction
Divide the top and bottom by 4
4/12 = 1/3
-3/8 * -1/3
The threes in the top and bottom cancel
A negative times a negative cancel
1/8
80. You buy a new car for $24,000. At the end of n years, the value of your car is given by the sequence: an=24000(3/4)n, n=1, 2, 3, ... Find a5 and write a sentence explaining what this value represents. Describe the nth term of the sequence in terms of the value of the car at the end of each year.
The value of the car at the end of the fifth year is approximately $5695.62, determined by the initial value of $24000 and a 25% annual depreciation rate. The nth term formula reflects the cumulative effect of depreciation on the car's value over n years.
Finding the value of the car at the end of the fifth year and how the nth term of the sequence is related to the value of the car at the end of each year.
Finding the value at the end of the fifth year (a₅):
We are given the formula for the value of the car at the end of each year: a_n = 24000 (3/4)^n, where n is the year.
We want to find the value at the end of the fifth year, so we need to substitute n = 5 into the formula: a_5 = 24000 (3/4)^5.
Calculating this expression, we get: a_5 = 24000 * 0.2373 ≈ $5695.62.
Therefore, the value of the car at the end of the fifth year is approximately $5695.62.
Understanding the nth term of the sequence:
The nth term of the sequence, a_n, represents the value of the car at the end of the nth year.
The formula for the nth term shows that the value of the car is determined by two factors:
Initial value: The initial value of the car is represented by 24000 in the formula. This is the value of the car when it is brand new.
Depreciation rate: The depreciation rate is represented by the fraction 3/4. This fraction indicates that the value of the car decreases by 25% each year. The exponent n in the formula tells us how many times this depreciation rate is applied.
Therefore, the nth term of the sequence tells us how much the car's value has depreciated after n years, starting from its initial value of $24000. The higher the value of n, the more the car has depreciated, and hence the lower its value will be.
Given the exponential growth equation y = 50(1.6)^x what is the initial value?
Answer:
50 is the initial value
Step-by-step explanation:
The equation is of the form
y = ab^x where a is the initial value and b is the growth/decay value
b>1 is growth and b<1 means decay
y = 50(1.6)^x
50 is the initial value and 1.6 means growth since it is greater than 1
1.6 -1 = .6 so it has a 60% growth rate