Answer:
[tex]\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }[/tex]
Step-by-step explanation:
First, find the magnitude of the vector:
[tex] |v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58} [/tex]
Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:
[tex]unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} } [/tex]
A manufacturer of car batteries claims that the batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries have lifetimes of 1.9, 2.4, 3.0, 3.5, and 4.2 years, construct a 95% confidence interval for σ2 and decide if the manufacturer’s claim that σ2 = 1 is valid. Assume the population of battery lives to be approximately normally distributed.
Answer:
[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]
[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]
And in order to obtain the confidence interval for the deviation we just take the square root and we got:
[tex] 0.541 \leq \sigma \leq 2.595[/tex]
Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim
Step-by-step explanation:
Data provided
1.9, 2.4, 3.0, 3.5, and 4.2
We can calculate the sample mean and deviation from this data with these formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}[/tex]
And we got:
[tex]\bar X= 3[/tex]
s=0.903 represent the sample standard deviation
n=5 the sample size
Confidence=95% or 0.95
Confidence interval
We need to begin finding the confidence interval for the population variance is given by:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
The degrees of freedom given by:
[tex]df=n-1=5-1=4[/tex]
The Confidence level provided is 0.95 or 95%, the significance is then[tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical values for this case are:
[tex]\chi^2_{\alpha/2}=11.143[/tex]
[tex]\chi^2_{1- \alpha/2}=0.484[/tex]
And the confidence interval would be:
[tex]\frac{(4)(0.903)^2}{11.143} \leq \sigma^2 \leq \frac{(4)(0.903)^2}{0.484}[/tex]
[tex] 0.293 \leq \sigma^2 \leq 6.736[/tex]
And in order to obtain the confidence interval for the deviation we just take the square root and we got:
[tex] 0.541 \leq \sigma \leq 2.595[/tex]
Since the confidence interval cointains the 1 we don't have enough evidence to reject the hypothesis given by the claim
Wilbur spends 2/3 of his income, share 1/12, and saves the rest. What part of his income does he save? Give the answer in simplest form.
Answer:
1/4 of his income.
Step-by-step explanation:
If Wilbur spends 2/3 of his income, 1/3 or 4/12 of it is left for other purposes (It is easier if everything has a common denominator of 12). And if he shares 1/12 of that remaining amount, there is 3/12 left. And when we simplify 3/12, we get 1/4.
*Mark me brainliest!*
In 1999 the population of Austria was one-third the population of Nepal. At that time the number of people living in Austria was 8,100,000. How many people were living in Nepal
Combine like terms to create an equivalent expression: -n + (-4) - (-4n) + 6
Answer:
3n + 2
Step-by-step explanation:
-n + 4n -4 + 6
3n + 2
How many moles of H2 would be required to produce 9.0 grams of water? 10
2 H2 + O2 + 2 H20
Answer:
8.1 moles
Step-by-step explanation:
Given parameters: Mass of water to be decomposed = 29.2g Unknown: Number of moles of oxygen. Solution: To solve this problem, we first write the balanced reaction equation : 2H₂O → 2H₂ + O₂ Now convert the given mass of the water to number of moles; Number of moles of water = Molar mass of water = 2(1) + 16 = 18g/mol Number of moles of water = = 16.2moles From the balanced reaction equation: 2 moles of water produced 1 mole of oxygen gas; 16.2 mole of water will produce = 8.1moles of oxygen gas
Hope this helps you :3
Question 1
Convert from parametric to rectangular:
x=t+4, y = t^2
Answer:
y = x^2 +8x +16
Step-by-step explanation:
t can be written in terms of x, then substituted into the equation for y.
x = t -4
x + 4 = t
y = t^2 = (x +4)^2
y = x^2 +8x +16
A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean of $145 for this sample. It is known that the standard deviation of all such textbooks is $35 and the population of such prices is normal.
a. What is the point estimate of the mean price of all such college textbooks?
b. Construct a 90% confidence interval for the mean price of all such college textbooks.
Answer:b
Step-by-step explanation:
a. The point estimate of the mean price of college textbooks is $145. b. A 90% confidence interval for the mean price is ($133.49, $156.52).
Given a sample of 25 comparable textbooks with a mean price of $145 and a known population standard deviation of $35, the following steps will help answer the questions:
a. Point Estimate:
The point estimate of the mean price of all such college textbooks is simply the sample mean, which is $145.
b. 90% Confidence Interval:
To construct a 90% confidence interval for the mean price of college textbooks, we follow these steps:
Identify the sample mean [tex]ar_{x}[/tex] = $145, sample size (n) = 25, and population standard deviation [tex]\sigma[/tex] = $35.Determine the z-score for a 90% confidence level. The z-score corresponding to a 90% confidence level is 1.645.Calculate the standard error (SE) of the mean using the formula: SE = [tex]\sigma[/tex] / [tex]\sqrt{n}[/tex] = $35 / √(25) = $7.Compute the margin of error (ME) using the formula: ME = [tex]z \times SE[/tex] = 1.645 × $7 = $11.515.Determine the confidence interval using the formula: ([tex]\bar{x}[/tex] - ME, [tex]\bar{x}[/tex]} + ME) = ($145 - $11.515, $145 + $11.515) = ($133.485, $156.515).Thus, the 90% confidence interval for the mean price of all college textbooks is ($133.49, $156.52).
Can someone help.....
Answer:
7
Step-by-step explanation:
formula for circumference of a circle is [tex]\pi[/tex]d
7[tex]\pi[/tex] = [tex]\pi[/tex]d
d = 7
PLEASEEEEE HELPPPP MEEE WITHHH NUMBERR 20!!!!!
Answer:
∠3 = ∠4 = 60°
Step-by-step explanation:
Angles 1 and 3 are "remote interior angles" with respect to angle 2, so ...
∠2 = ∠1 + ∠3
120° = 60° + ∠3 . . . fill in known values
60° = ∠3 . . . . . . . . . subtract 60°
__
Since two of the interior angles in the triangle ABC are 60°, the third one is also. The interior angle at B (supplementary to angle 2) is corresponding to ∠4, so has the same measure as angle 4.
∠4 = 60°
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is ?
Answer: 320°
Step-by-step explanation:
This is a circle geometry.
The arc length of the circle is given to be 8πcm and the radius is 4.5cm.
Now the length of an arc of a circle is
Arc length = πr0°/180° or 2πr0°/360°
To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go
πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.
πr0° = 8π × 180
0°. = 8π × 180
-----------
π × r
= 8 × 180. 8 × 180
-------- or ---------
9/2. 4.5
= 8 × 180 × 2
------------
9
= 8 × 20 × 2
= 320°
or 8 × 180/4.5
= 1440/4.5
= 320°
Which type of car had the largest range in monthly sales? Explain how you came up with your answer.
Answer:
Used car have the highest range of 75
Step-by-step explanation:
Yeah the type of car that have the highest range In monthly sales.
we know that
The range is the difference between the highest and the lowest value
First we,
calculate the range in monthly sales for the new car
highest value=51
lowest value=20
range=51-20
range=31
Secondly,we
calculate the range in monthly sales for used car
highest value=87
lowest value=12
range=87-12
range=75
Answer:
My answer: "The car that had the largest range in monthly sales was a used. Through finding the range by subtracting the highest and lowest data points, i was able to find the range for used cars being 75, and for new cars was 31. 75 is larger then 31, so therefore the used cars have the largest monthly range in sales. "
Their sample answer: Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger."
Select all that you included in your explanation.
The range for new cars was 31.
The range for used cars was 75.
Subtract the highest and lowest numbers.
Step-by-step explanation:
edg2020
Lydia drove 441 miles in 6 hours. On average, how fast did she drive in miles per hour? Express your answer in simplest form.
Answer:
She drove [tex]\frac{147}{2} miles/ hour[/tex]
Step-by-step explanation:
We are given that Lydia drove 441 miles in 6 hours.
We are supposed to find how fast did she drive in miles per hour
Distance covered by Lydia in 6 hours = 441 miles
Distance covered by Lydia in 1 hour =[tex]\frac{441}{6}[/tex]
Distance covered by Lydia in 1 hour =[tex]\frac{147}{2} miles/ hour[/tex]
Hence She drove [tex]\frac{147}{2} miles/ hour[/tex]
Since 1936, the Gallup Organization has been asking Americans: "Are you in favor of the death penalty for a person convicted of murder?" The percentage has fluctuated significantly over the years, ranging from a low of 42% in 1966 to a high of 80% in 1994. Here are the results of the most recent survey; in a sample of 3100 females, 62% said that they were in favor of the death penalty for convicted murders. Construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders.
Plugging in the values and calculating, we find that the 98% confidence interval is approximately (0.5847, 0.6553).
Explanation:To construct a 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders, we can use the formula:
CI = p ± z * √(p * (1-p) / n)
Where:
CI is the confidence intervalp is the sample proportion (0.62)z is the z-score corresponding to the desired confidence level (98% or 0.98)n is the sample size (3100)Using a standard normal distribution table or a calculator, we can find that the z-score for a 98% confidence level is approximately 2.33.
Plugging in the values into the formula:
CI = 0.62 ± 2.33 * √(0.62 * (1-0.62) / 3100)
Calculating the values:
CI = 0.62 ± 2.33 * √(0.62 * 0.38 / 3100)
CI = 0.62 ± 2.33 * √(0.235 / 3100)
CI = 0.62 ± 2.33 * 0.01516
CI = 0.62 ± 0.03535
CI ≈ (0.5847, 0.6553)
Therefore, the 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is approximately (0.5847, 0.6553).
Learn more about Confidence interval here:https://brainly.com/question/34700241
#SPJ3
Odessa starts counting the frogs in the small pond that the forest service just set up by her house. She marks the data in this graph. If y equals the number of frogs and x equals the number of months that have passed, the frog population can be described by the mathematical formula y = x.
Answer:
Answer is 2
Step-by-step explanation:
If it shows a graph with Frog Population on top
Fill in the blanks in the following proof, which shows that the sequence defined by the recurrence relation
sk = sk − 1 + 2k, for each integer k ≥ 1
s0 = 3.
satisfies the formula
sn = 3 + n(n + 1) for every integer n ≥ 0.
Proof (by mathematical induction):
To prove that the sequence defined by the recurrence relation satisfies the formula sn = 3 + n(n + 1), we need to show that the base case holds and then prove the inductive step.
Explanation:To prove that the sequence defined by the recurrence relation satisfies the formula , we need to show that the base case holds and then prove the inductive step.
Base case:
When , we have . This matches the formula, so the base case holds.
Inductive step:
Assume that the formula holds for some . We want to show that it holds for .
Using the recurrence relation, we have:
sn+1 = sn + 2(n+1)
Using the induction hypothesis, we can substitute in the expression:
sn+1 = (3 + n(n + 1)) + 2(n+1)
Expanding the expression:
sn+1 = 3 + n(n + 1) + 2n + 2
Combining like terms:
sn+1 = 3 + n(n + 1) + 2(n+1)
sn+1 = 3 + (n+1)((n + 1) + 1)
This matches the formula for , so the inductive step holds. Therefore, the formula holds for all integers .
Chandler has 828 millimeters of fabric.
How many centimeters of fabric does Chandler have?
Use the numbers and symbols on the tiles to enter an equation to show the
828 8.28
182.8
0.828
100 || 1.000
Chandler has
centimeters of fabric.
Answer:
82.8 centimeters
Step-by-step explanation:
Chandler has 828 millimeters of fabric.
1 centimeter =10 millimetersx centimeters = 828 millimetersExpressing as a ratio
[tex]\dfrac{1}{x}= \dfrac{10}{828}\\10x=828\\x=828\div 10\\x=82.8 cm[/tex]
Therefore, Chandler has 82.8 centimeters of fabric.
Answer:
82.8 centimeters of fabric
Step-by-step explanation:
1 centimeters= 10 millimeters;
828mm x 1cm ÷10 mm=82.8cm ;centimeters of fabric
The exercise is performed by conversion factor and a smaller unit is transferred to a larger unit that is centimeters.
What is the mean for the data set?
8 10 6 4
12 6 8 14
Answer:
8.5
Step-by-step explanation:
To find mean, we simply take the average of all the numbers in the data set, and divide in by the amount of values!
[tex]8+10+6+4+12+6+8+14= 68\\[/tex]
68 ÷ 8 = 8.5!
Answer:
[tex]8\frac{1}{2}[/tex]
Step-by-step explanation:
First add up all the numbers:
8+10+6+4+12+6+8+14=68
Now you have to divide the sum by the amount of numbers. There are 8 numbers.
[tex]\frac{68}{8}=\frac{34}{4}=\frac{17}{2}[/tex]
[tex]\frac{17}{2}=8\frac{1}{2}[/tex]
5. The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56, 47, 49, 37, 38, 60, 50, 43, 43, 59, 50, 56, 54, 58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53, 21, 32, 49, 45, 38, 44, 33, 32, 43, 53, 46, 36, 48, 39, 35, 37, 36, 39, 45. (a) Construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings. (b) Can we claim a significant reduction in the rate of intrusion attempts
To construct a 95% confidence interval for the difference between the average number of daily intrusion attempts before and after changing firewall settings, you determine the standard deviation and mean for both periods. Use these in the formula for the confidence interval. If the interval doesn't include zero, it indicates a significant difference in the average number of daily intrusion attempts, and thus, potentially a significant reduction in intrusion attempts.
Explanation:To perform this analysis, we first need to calculate the mean of the numbers of intrusion attempts for both periods - before and after the change of firewall settings. Then, we need to calculate the standard deviation for the numbers of intrusion attempts for both periods. The formula for the confidence interval is Mean Difference ± (Z*Standard Error). Where Z is a standard score value retrieved from the Z distribution table for a particular confidence level, in this case, 95%. The confidence levels you will be working with depend on the number of samples, in this case 14 and 20 respectively.
Once you have the confidence interval, it will give you the range in which the actual difference between the two means lies with 95% certainty. If the interval does not include zero, it indicates a significant difference between the means. By observing whether the values are predominantly positive or negative, we can infer about the significant reduction in the rate of intrusion attempts.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
#SPJ11
What is the side length of a square with a perimeter of 52 meters
Answer:
13 meters
Step-by-step explanation:
The perimeter is the sum of all the sides.
As a square has four identical sides, to calculate the length of one side you would simply divide 52 by 4,which gives you 13.
1) Divide 52 by 4.
[tex]52/4=13meters[/tex]
Answer:
13m
Step-by-step explanation:
52/4 = 13
4. Which of the following points on the number line best represents 5/8?
Answer:
B
Step-by-step explanation:
You can see that the dashes on the number line are going up by 1/4 which is equal to 2/8 (when you multiply 1/4 by 2). At point C your already at 6/8 which is a little larger than 5/8 so when you do a little less than 6/8 you get to point B which is the best answer.
What is mBC?
A.70
B.140
C.28
D.56
What is mBCD
A.168
B.192
C.220
D.82
Answer:
is there more to the question?
Step-by-step explanation:
Answer:
1. is 56
2. is 82
Step-by-step explanation:
Just took the quiz and got it right (Like it please so people know its the correct answer)
Simplify this complex fraction
Answer:
1/4
Step-by-step explanation:
2/4 ÷ 2
Copy dot flip
2/4 * 1/2
We can cancel the 2 in the numerator and denominator
1/4 * 1/1
1/4
A marketing firm wishes to know what proportion of viewers of Impractical Jokers feels that the current season is at least as good as, or better, than previous seasons. A randomly selected group of 200 was polled. 58 responded that they felt that quality standards have been maintained. Please calculate a 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons.
Answer:
The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 200, \pi = \frac{58}{200} = 0.29[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 - 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.2372[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.29 + 1.645\sqrt{\frac{0.29*0.71}{200}} = 0.3428[/tex]
The 90% confidence interval for the true population proportion that feels that the current season is as good as, or better, than previous seasons is (0.2372, 0.3428).
Answer:
[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]
[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]
And the confidence interval for this case would be (0.237; 0.343).
Step-by-step explanation:
We can begin find the proportion estimated of responded that they felt that quality standards have been maintained with the following formula:
[tex]\hat p = \frac{X}{n}[/tex]
And replacing we got:
[tex] \hat p =\frac{58}{200}= 0.29[/tex]
The confidence interval is given by 90%, and the significance level would be [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The confidence interval for the true proportion is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing the values we got:
[tex]0.29 - 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.237[/tex]
[tex]0.29 + 1.64\sqrt{\frac{0.29(1-0.29)}{200}}=0.343[/tex]
And the confidence interval for this case would be (0.237; 0.343).
A sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction. Find the area of the sector to the nearest square foot.
The sprinkler can water ____
square feet.
We have been given that a sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 11 feet. The sprinkler is located in the middle of the circular region. The sprinkler begins malfunctioning and is only able to rotate 225∘ in each direction.
We are asked to find the area of the sector to nearest square foot.
We will use area of sector formula to solve our given problem.
[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where,
[tex]\theta[/tex] = Central angle of sector,
[tex]r[/tex] = Radius.
For our given problem [tex]\theta = 225^{\circ}[/tex] and [tex]r=11[/tex].
[tex]\text{Area of sector}=\frac{225^{\circ}}{360^{\circ}}\times \pi (11)^2[/tex]
[tex]\text{Area of sector}=0.625\times 121\pi[/tex]
[tex]\text{Area of sector}=237.5829444277281137[/tex]
[tex]\text{Area of sector}\approx 238[/tex]
Therefore, the sprinkler can water approximately 238 square feet.
To find the area of the sector, we need to find the central angle, find the fraction of the circle covered by the sector, and then multiply it by the area of the entire circle with a radius of 11 feet.
Explanation:To find the area of the sector, we need to find the central angle first. Since the sprinkler can only rotate 225∘ in each direction, the total angle covered is 225∘+225∘=450∘.
Next, we need to find the fraction of the circle covered by the sector. We can do this by finding the ratio of the central angle to the total angle of a circle, which is 360∘. This can be calculated as (450/360).
Finally, we multiply the fraction by the area of the entire circle with a radius of 11 feet, which is π(11)^2, to find the area of the sector.
1. (a) Show that the polynomial x⁴+ 4x³ + 6x² - 8 is divisible by x+2
Answer:
Step-by-step explanation:
if x= -2
and P(x)=x^4+4x^3+6x^2-8
then P(-2)=(-2)^4+4*(-2)^3+6*(-2)^2-8=16-32+24-8=0
so P(x)=(x+2)* Q(x) and P(x) is divisible by x+2
Associations In Data:Question 10
The list below show test scores for 3rd period on a
recent test. Finding the mean absolute deviation.
62 63 68 72 79 80 83 93 94 95
Select one:
7.8
101.2
78.9
10.12
Answer:
[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]
[tex] |62-78.9| = 16.9[/tex]
[tex] |63-78.9| = 15.9[/tex]
[tex] |68-78.9| = 10.9[/tex]
[tex] |72-78.9| = 6.9[/tex]
[tex] |79-78.9| = 0.1[/tex]
[tex] |80-78.9| = 1.1[/tex]
[tex] |83-78.9| = 4.1[/tex]
[tex] |93-78.9| = 14.1[/tex]
[tex] |94-78.9| = 15.1[/tex]
[tex] |95-78.9| = 16.1[/tex]
[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]
And replacing we got:
[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]
And the best anwer is
10.12
Step-by-step explanation:
We have the following data given:
62 63 68 72 79 80 83 93 94 95
And we need to begin finding the mean with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X = \frac{62+63+68+72+79+80+83+93+94+95}{10}= 78.9[/tex]
Now we can find the mean absolute deviation like this:
[tex] |62-78.9| = 16.9[/tex]
[tex] |63-78.9| = 15.9[/tex]
[tex] |68-78.9| = 10.9[/tex]
[tex] |72-78.9| = 6.9[/tex]
[tex] |79-78.9| = 0.1[/tex]
[tex] |80-78.9| = 1.1[/tex]
[tex] |83-78.9| = 4.1[/tex]
[tex] |93-78.9| = 14.1[/tex]
[tex] |94-78.9| = 15.1[/tex]
[tex] |95-78.9| = 16.1[/tex]
And finally we can find the mean abslute deviation with the following formula:
[tex] MAD = \frac{\sum_{i=1}^n |X_i -\bar X|}{n}[/tex]
And replacing we got:
[tex] MAD =\frac{16.9+15.9+10.9+6.9+0.1+1.1+4.1+14.1+15.1+16.1}{10}= 10.12[/tex]
And the best anwer is
10.12
If a single 12-sided die is tossed once, find the probability of rolling a 2.
What is the probability?
Answer:
1/12
Step-by-step explanation:
hope this helps you
Final answer:
The probability of rolling a 2 on a single 12-sided die is 1/12, which is approximately 8.33%.
Explanation:
If a single 12-sided die is tossed once, the probability of rolling a 2 is calculated by dividing the number of ways to roll a 2 by the total number of possible outcomes on the die. Since there is only one way to roll a 2, and there are 12 different possible outcomes on a 12-sided die, the probability is calculated as follows:
Count the number of favorable outcomes for rolling a 2: There is 1 way to roll a 2.
Count the total number of possible outcomes on a 12-sided die: There are 12 possible outcomes (1, 2, 3, ... 12).
Divide the number of favorable outcomes by the total number of possible outcomes to get the probability: P(rolling a 2) = 1/12.
Therefore, the probability of rolling a 2 on a 12-sided die is 1/12, which can also be expressed as approximately 8.33%.
Suppose you are constructing either a mean chart with known variation or a p-chart to monitor some process. The process will only be stopped if a sample taken falls outside your control limits. If the process is in control, management wants only 12.6% of the samples taken to fall outside of your limits. (The company does not like stopping the process "accidentally.") What Z value should you use for your chart?
Answer:
1.53
Step-by-step explanation:
Find the attachment for explanation
The z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53 and this can be determined by using the given data.
Given :
Suppose you are constructing either a mean chart with a known variation or a p-chart to monitor some process. The process will only be stopped if a sample taken falls outside your control limits.The process is in control, management wants only 12.6% of the samples taken to fall outside of your limits.Assuming that the distribution is normal so the probability for being within the maximum limit is given by:
[tex]\rm P=1-\dfrac{6.3}{100}[/tex]
P = 0.937
Now, the z-value corresponding to the probability of 0.937 using the standard normal distribution table is 1.53.
Therefore, the correct option is D) 1.53.
For more information, refer to the link given below:
https://brainly.com/question/23044118
What is the value of x in the equation x/-4=7?
Answer: -28
Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.
On the left side, the -4's will cancel
and on the right side, 7(-4) is -28.
So x = -28.
Please do not try to do this problem in your head.
Show the work that it takes to get x by itself.
Answer:
x= - 28
Step-by-step explanation:
-4/1[x/-4 = 7]
x = -28
A follow-up study will be conducted with a sample of 20 people from the 300 people who responded yes (support) and no (do not support). Two sampling methods have been proposed: a simple random sample and a stratified random sample with the survey response as strata. (b) If the stratified random sample is used, what is the number of people that will be selected from those who responded yes? Support your answer by showing your work.
Using the concept of stratified sampling, it is found that 10 people will be selected from those who responded yes.
In a stratified sample, the population is divided into groups, and the same number of elements of each group is surveyed.
In this problem:
Two groups, one with those who responded yes and other with those who responded no.Sample of 20 people, thus 10 people who responded yes and 10 people who responded no.A similar problem is given at https://brainly.com/question/24188753
To decide how many participants who answered 'yes' to include in a stratified random sample of 20, use the proportion of 'yes' answers out of 300 to calculate the sample from that stratum.
Explanation:In a stratified random sample, the population is divided into groups, or strata, and a sample is taken from each group to ensure that each subgroup of the population is adequately represented. To determine the number of people that will be selected from those who responded yes in a stratified random sample, we need to find the proportion of 'yes' responses among the 300 respondents and then apply that proportion to the sample size of 20.
Assuming we know the exact number of people who responded 'yes', let's call that number 'Y'. The number of 'yes' responses in the stratified sample would then be (Y/300) * 20. Without the actual number of 'yes' responses, we cannot compute the exact number of people that should be selected from the 'yes' group. However, this formula demonstrates how you would calculate it once the value for 'Y' is known.
Learn more about Stratified Random Sampling here:https://brainly.com/question/29852583
#SPJ3