Answer:
300'
Step-by-step explanation:
Answer:
1/8 mile
Step-by-step explanation:
Because if you do the math the avarge car is 4.7 feet multiply that by 20 and there is your answer
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that [tex]\mu = 36, \sigma = 5.5[/tex]
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that [tex]n = 9[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{38 - 36}{1.8333}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
Which expression is equivalent to
y
2
Answer:
Hello!
Distributive property: a(b+c)=ab+ac
Minus and plus sign.
Then multiply by the numbers.
Hope this helps!
Thanks!
Have a great day!
Step-by-step explanation:
The Lazy River has a current of 5 miles per hour. A motorboat can travel 20 miles
down the river in and back in 3 hours. What is the speed of the boat in still water?
Please show your work and use table to relate time, speed, distance.
Answer:
5 mph
Step-by-step explanation:
Answer:
15 mph = rate of boat in still water
Step-by-step explanation:
D = RT
Let R = rate of boat in still water
Rate down stream = R + 5
Time down stream = 20/(R + 5)
Rate upstream = R - 5
Time upstream = 20/(R - 5)
Total time = 20/(R + 5) + 20/(R - 5) = 3
20(R - 5) + 20(R + 5) = 3(R + 5)(R - 5)
20R - 100 + 20R + 100 = 3R^2 - 75
3R^2 + 40R - 75 = 0
(3R + 5)(R - 15) = 0
R = -5/3 or 15
Rate cannot be negative, so R = 15 mph = rate of boat in still water
What is the measure of B ?
Answer: if you add then all up you get 75 so it could be A or D I don't know if it want the volume and the volume is 75 hope this helped
Step-by-step explanation:
pleas make brainly
Help answer this question please
Answer:
no and no
Step-by-step explanation:
1. 9+6 = 15 not 17
2. 9 - 3 = 6 not 5
please leave a like if this answers your question
$72 for 7 1/2 hours. Find the unit rate
Answer:
$9.60 for 1 hour
The unit rate is $9.60
Step-by-step explanation:
The vertex of the function is (6, -8)
Answer: I did a screen shot of the answer
Step-by-step explanation:
A bag contains hair ribbons for a spirit rally. The bag contains 18 black ribbons and 2 green ribbons. Lila selects
a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability
that Lila selects a black ribbon and Jessica selects a green ribbon? Express your answer as a fraction in
simplest form
Answer:
9/95
Step-by-step explanation:
just had an exam on it
hope this helps:)
help plssssssssssssssssss
7 2/3 + 8 1/2 + 4 1/6 =
Answer:
20 1/3 or 61/3
Here you go, have a nice day!!
You select a marble without looking and then put it back. If you do this 6 times, what is the
best prediction possible for the number of times you will pick a purple marble?
Answer:
One time
Step-by-step explanation:
The probability of picking a purple marble once is 1/6, so if I pick a marble 6 times, then (1/6)*6=1
Mystery Boxes: Breakout Rooms
The boxes below contain 14 numbers, listed in order, of which 6 have been removed. Your job is
to use the clues given to determine the missing numbers. Write your answers in the boxes.
• The mean is 26
• The median is 22
The interquartile range is 20
The mode is 18
. The range is 60
1
4
15
18
29
30
32
58
Answer:
[tex]\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {[ \ ]} \\ \end{array}[/tex]
Required
Fill in the box
From the question, the range is:
[tex]Range = 60[/tex]
Range is calculated as:
[tex]Range = Highest - Least[/tex]
From the box, we have:
[tex]Least = 1[/tex]
So:
[tex]60 = Highest - 1[/tex]
[tex]Highest = 60 +1[/tex]
[tex]Highest = 61[/tex]
The box, becomes:
[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
From the question:
[tex]IQR = 20[/tex] --- interquartile range
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]Q_3[/tex] is the median of the upper half while [tex]Q_1[/tex] is the median of the lower half.
So, we need to split the given boxes into two equal halves (7 each)
Lower half:
[tex]\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {[ \ ] } & {15} & {18}& {[ \ ] } \\ \end{array}[/tex]
Upper half
[tex]\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
The quartile is calculated by calculating the median for each of the above halves is calculated as:
[tex]Median = \frac{N + 1}{2}th[/tex]
Where N = 7
So, we have:
[tex]Median = \frac{7 + 1}{2}th = \frac{8}{2}th = 4th[/tex]
So,
[tex]Q_3[/tex] = 4th item of the upper halves
[tex]Q_1[/tex]= 4th item of the lower halves
From the upper halves
[tex]\begin{array}{ccccccc}{[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
We have:
[tex]Q_3 = 32[/tex]
[tex]Q_1[/tex] can not be determined from the lower halves because the 4th item is missing.
So, we make use of:
[tex]IQR = Q_3 - Q_1[/tex]
Where [tex]Q_3 = 32[/tex] and [tex]IQR = 20[/tex]
So:
[tex]20 = 32 - Q_1[/tex]
[tex]Q_1 = 32 - 20[/tex]
[tex]Q_1 = 12[/tex]
So, the lower half becomes:
Lower half:
[tex]\begin{array}{ccccccc}{1} & {[ \ ]} & {4} & {12 } & {15} & {18}& {[ \ ] } \\ \end{array}[/tex]
From this, the updated values of the box is:
[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {[ \ ] } & {[ \ ]} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
From the question, the median is:
[tex]Median = 22[/tex] and [tex]N = 14[/tex]
To calculate the median, we make use of:
[tex]Median = \frac{N + 1}{2}th[/tex]
[tex]Median = \frac{14 + 1}{2}th[/tex]
[tex]Median = \frac{15}{2}th[/tex]
[tex]Median = 7.5th[/tex]
This means that, the median is the average of the 7th and 8th items.
The 7th and 8th items are blanks.
However, from the question; the mode is:
[tex]Mode = 18[/tex]
Since the values of the box are in increasing order and the average of 18 and 18 do not equal 22 (i.e. the median), then the 7th item is:
[tex]7th = 18[/tex]
The 8th item is calculated as thus:
[tex]Median = \frac{1}{2}(7th + 8th)[/tex]
[tex]22= \frac{1}{2}(18 + 8th)[/tex]
Multiply through by 2
[tex]44 = 18 + 8th[/tex]
[tex]8th = 44 - 18[/tex]
[tex]8th = 26[/tex]
The updated values of the box is:
[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
From the question.
[tex]Mean = 26[/tex]
Mean is calculated as:
[tex]Mean = \frac{\sum x}{n}[/tex]
So, we have:
[tex]26= \frac{1 + 2nd + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 12th + 58 + 61}{14}[/tex]
Collect like terms
[tex]26= \frac{ 2nd + 12th+1 + 4 + 12 + 15 + 18 + 18 + 26 + 29 + 30 + 32 + 58 + 61}{14}[/tex]
[tex]26= \frac{ 2nd + 12th+304}{14}[/tex]
Multiply through by 14
[tex]14 * 26= 2nd + 12th+304[/tex]
[tex]364= 2nd + 12th+304[/tex]
This gives:
[tex]2nd + 12th = 364 - 304[/tex]
[tex]2nd + 12th = 60[/tex]
From the updated box,
[tex]\begin{array}{ccccccccccccccc}{1} & {[ \ ]} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {[ \ ]} & {58} & {61} \\ \end{array}[/tex]
We know that:
The 2nd value can only be either 2 or 3
The 12th value can take any of the range 33 to 57
Of these values, the only possible values of 2nd and 12th that give a sum of 60 are:
[tex]2nd = 3[/tex]
[tex]12th = 57[/tex]
i.e.
[tex]2nd + 12th = 60[/tex]
[tex]3 + 57 = 60[/tex]
So, the complete box is:
[tex]\begin{array}{ccccccccccccccc}{1} & {3} & {4} & {12} & {15} & {18}& {18 } & {26} & {29} & {30} & {32} & {57} & {58} & {61} \\ \end{array}[/tex]
CAN SOMEONE PLEASE ANSWER THIS QUICKLY I DONT GOT TIME
Answer:
5/20 x 4/15 =1/15
6/7 x 7/6 =1
2 x 7/10 =7/5
Hope this helps!
Quadrilateral PQRS is parallelogram.What is the length of the diagonal SQ?
ST=x^2-8
TQ=3x+2
Answer:
3x+x^2-6
Step-by-step explanation:
Have a great rest of your day.
Bye
Please answer the question in the picture
Answer:
Step-by-step explanation:
use the distance formula
dist = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
where point one ,P1, is A and point 2, P2, is C, so
P1 = (x1,y1) = (-7,3)
P2 =(x2,y2) = (0,6)
then
dist = sqrt[ (0 - (-7))^2 + (6-3)^2 ]
dist = sqrt [ 7^2 + 3^2 ]
dist = sqrt [49 +9 ]
dist = sqrt [58]
dist = 7.6157....
AC = 7.6 ( rounded to nearest tenth)
Again I don’t know this . Plz help me
Answer:
y-2=0(x-3)
Step-by-step explanation:
9. A juice glass holds 180mL. If a client drinks 7/2 glasses , how many milliliters did
the client consume? (5 points)
Answer:
630 ml
Step-by-step explanation:
1 glass contains 180 ml juice
7/2 glasses contains = 180 × 7/2 = 630 ml
Help please thank you
Answer:
In the explanation :)
Step-by-step explanation:
So if we have 1 cup of raisins, then we have 2 1/2 cups of pretzels. Since we doubled the raisins, we double the pretzels as well.
I believe this is right but I'm not sure anymore with today's math
1. The diner sells 4 different sandwiches, 6 different drinks, and 3
different deserts. How many different orders could you place if you
decided to buy a sandwich and a desert?
2. The Downtown Theater has 1 ticket window. In how many ways can 2 people line up to buy tickets?
3. The Downtown Theater has 1 ticket window. In how many ways can 3 people line up to buy tickets?
4. The Downtown Theater has 1 ticket window. In how many ways can 4 people line up to buy tickets?
5. The Downtown Theater has 1 ticket window. In how many ways can 6 people line up to buy tickets?
Answer:
72
Step-by-step explanation:
because you got to multiply to see what you gone get.
Find the domain of the following functions?
Answer:
d. D: (-∞ , ∞) , R: (-10 , ∞)
Step-by-step explanation:
Mathematical logic for this game to make the best
Answer:
Ok tell me which mathematic game
Four people recorded the number of minutes they exercised today. Mackenzie exercised for 3 as many minutes as Brinley. Brinley exercised for 17 fewer minutes than Ariana. Ariana exercised for 3 times as many minutes as Seth Together, Ariana and Mackenzie exercised for 20 more minutes than Brinley and Seth. Let z represent the number of minutes Seth exercised.
Answer:
False
True
True
False
Yw hope this helped yall
Step-by-step explanation:
The equation represents this situation is
3x + 1/2 x (3x + - 17) = x + (3x - 17 ) + 20 — False
x = 40 — True
Brinley and Seth exercised for a combined 95 minutes —-True
Mackenzie exercised for 26 minutes. — False
A tennis ball was thrown from the top of a tall building. The height of the tennis ball above the ground can be found using the function y = -12.5x + 50, where x is the time in seconds the tennis ball has been in the air.
how many seconds did it take the tennis ball to reach the ground?
Answer:
t = 4 seconds
Step-by-step explanation:
Given that,
The height of the tennis ball above the ground can be found using the function y = -12.5x + 50
where x is the time in seconds the tennis ball has been in the air.
We need to find how many seconds did it take the tennis ball to reach the ground.
When it reaches the ground, y = 0
So,
-12.5x + 50 = 0
12.5x = 50
x = 4 seconds
So, it will take 4 seconds for the ball to reach the ground.
120 meals to 52 meals what is the percentage change?
hurry!!
Answer:
56.67
Step-by-step explanation:
I think it is 56.67%
Answer:
The percentage change is 56.67%.
I’ll give brainliest answer to whoever answers first !!!
Answer:
bottom right
Step-by-step explanation:
the bottom right shows the data
Individual gas mileages (in miles per gallon) of Model Extra SS (Extra Super-Sporty) sedans are normally distributed with a population mean of 20 and a population standard deviation of 2. Based on these information, if you bought a Model Extra SS sedan, what is the probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5
Answer: 0.1974
Step-by-step explanation:
Let X be a random variable that denotes the gas mileage (in miles per gallon) of the individual sedan.
Given: Population mean: [tex]\mu=20[/tex]
Standard deviation: [tex]\sigma=2[/tex]
The probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5:
[tex]P(19.5<x<20.5)=P(\dfrac{19.5-20}{2}<\dfrac{x-\mu}{\sigma}<\dfrac{20.5-20}{2})\\\\=P(-0.25<z<0.25)=2P(0.25)-1 [P(-z<Z<z)=2P(Z<z)-1]\\\\=2(0.5987)-1=0.1974[/tex]
The required probability=0.1974
which of the following is written as a rational function
Answer:
f(x)=x-5/3x
Step-by-step explanation:
James bought a new DVD player with a 30% coupon. If James paid $87.00, what was the original price?
A. $113.10
B. $124.29
C. $147.90
D. $290.00
Answer:
$113.1
Step-by-step explanation:
: you add the 30% + the 87 bucks. Hope it helps friend! Please mark the brainliest. A.
A company sells their product in Canada and the United States. They wonder if people in both countries will respond similarly to a new advertisement for the product. They show the ad to a sample of 202020 Canadians and a separate sample of 202020 Americans. Here is a summary of the responses in each sample and the results from a chi-squared test:
Chi-square test: Response vs. country
Canada US
Positive 11 5
Expected 8.0 8.0
Neutral 6 5
Expected 5.5 5.5
Negative 3 10
Expected 6.5 6.5
x = 6.110, DF = 2, P-value = 0.047
Assume that all conditions for inference were met. At the a=0.05 significance level, what is the most appropriate conclusion to draw from this test?
Answer:
This is convincing evidence that the responses differ between these countries.
Step-by-step explanation:
The data in this study came from separate samples, so a test for homogeneity is appropriate. Since the P-value is less than the significance level, we should reject the null hypothesis that the distribution of responses is the same in both countries.
The most appropriate conclusion to draw from the test is an evidence of a significant association between the country of origin and the responses to the new advertisement
What is chi squared statistic?
The chi-squared statistic (often denoted as χ^2) is a measure of the discrepancy between the observed frequencies and the expected frequencies in a categorical data set. It is commonly used in statistical hypothesis tests to assess whether there is a significant association or relationship between categorical variables.
The formula for calculating the chi-squared statistic depends on the type of data and the specific hypothesis being tested. In general, it involves computing the sum of squared differences between the observed and expected frequencies, divided by the expected frequencies.
The chi-squared statistic follows a chi-squared distribution, and its value can be compared to critical values or used to calculate a p-value to determine the statistical significance of the association.
Given data ,
Based on the given summary and the results of the chi-squared test, we can draw the following conclusion:
At the significance level of α = 0.05, we have enough evidence to reject the null hypothesis and conclude that there is a statistically significant difference in the responses to the new advertisement between Canadians and Americans.
The chi-squared statistic (x) of 6.110 with 2 degrees of freedom (DF) produces a p-value of 0.047, which is less than the significance level of 0.05.
This indicates that the observed differences in the responses between the two countries are unlikely to occur by chance alone, and there is evidence of a significant association between the country of origin and the responses to the new advertisement.
Hence , the chi-squared statistic is solved
To learn more about chi-squared statistic click :
https://brainly.com/question/31036349
#SPJ2
5
Find the value of x. Show work to prove your answer.
(3x +
18)
93°
Answer:
x=34.5
Step-by-step explanation:
(3x+18)° and 93° lie along a straight line. The angles in a straight line add up to 180. So:
3x+18+93=`80
2x=180-111
x=69/2
x=34.5
