If you take a sample of 9 pacemakers from the company, what is the probability that the mean lifetime of components in this sample will be longer than 99 months
Using the normal distribution and the central limit theorem, it is found that there is a 0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
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. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 9 years, hence, in months, [tex]\mu = 9(12) = 108[/tex]The standard deviation is of 1 year, hence, in months, [tex]\sigma = 12[/tex].Sample of 9 pacemakers, hence [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].The probability is 1 subtracted by the p-value of Z when X = 99, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{99 - 108}{4}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
1 - 0.0122 = 0.9878.
0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
A similar problem is given at https://brainly.com/question/24663213
A line passing through the point(-10,-5) and has a slope of -1/2
Which inequality represents this graph?
A) y ≤ 1/3x - 1
B) y > 1/3x - 1
C) y ≥ 1/3x - 1
D) y < 1/3x - 1
Answer:
D) y < 1/3x - 1
Step-by-step explanation:
the equation of the line is y= 1/3x-1, then the dark part represents all the values that less than the values of y. The broken line means 'strongly', then the sign should be '<'.
Match the expression to its simplified form
Answer:
2 exponent 5 = 32
5 exponent 3 = 125
2 - exponent 4 = 1/16
5 - exponent 2 = 1/25
Step-by-step explanation:
An average clementine is shaped like a sphere and has a diameter of 3.5 inches. What is the volume of the fruit? Use 3.14 for pi. Round your answer to the nearest hundredth. (4 points)
a
20.45 cubic inches
b
21.34 cubic inches
c
22.44 cubic inches
d
23.78 cubic inches
Answer:
Calculate the average rate of change for the graphed sequence from n = 1 to n = 3.
graphed sequence showing point 1, 2, point 2, 4, point 3, 8, point 4, 16, point 5, 32, and point 6, 64
1
2
3
6
Step-by-step explanation:
Answer:
c
Step-by-step explanation
First you have to find the radius.
3.5 divide by 2 = 1.75
v= 4/3 pi r ^3
v = 4/3 (3.14) (1.75)^3
v= 4/3 (3.14) (5.36)
v= 4/3 (16.83)
v= 4/3 (16.83) = (4/3) (16.83/1)
v= (4/3) (16.83/1) = 67.32/3 = 22.44
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box
Quick please!!!! 50 points!!
Answer:
2,1
Step-by-step explanation:
is this 8th grade class too
Answer:
I think so..I'm not really sure though, u know?
Which of the following is NOT a solution to this system of inequalities?
with examples
Nonsense = report
Answer: Choice D. (0,-2)
Note how this point is in the blue region, but it is not in the red region. The solution must satisfy all of the shaded regions of the system of inequalities. The red and blue regions overlap to form the darker shaded region on the right side (the somewhat grayish purple triangular region). Points in this darkest shaded region are solutions to the system. The points (5,2), (0,3) and (4,0) are all located in this region so they are solutions.
find the gcf and the distributive property to each sum.19,22
Answer:
50 is sum of gcf its couldn't of 19 is 20
In a fruit basket there are 9 bananas, 4 apples, and 3 plums.
The ratio of bananas to apples is
Answer
The ratio of bananas to apples is 3 to 4
Step-by-step explanation:
Find the quotient. Use a model to help you divide
6
.
15
÷
5
=
A.
1.03
B.
1.23
C.
1.3
D.
1.2
Answer:
Step-by-step explanation:
6.15/5=1.23
The answer is B.
percent of change original:8 new :12
Answer:
?????????
Step-by-step explanation:
What are u asking
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test.
B. No, because it is not a straight line.
C. Yes, because it is a curved line.
D. Yes, because it passes the vertical line test.
Answer:
A. No, because it fails the vertical line test.
Step-by-step explanation:
A because is dosent pass the vertical line test
How many arrangements can be made from the letters in the word PICCOLO
Answer:
1260Step-by-step explanation:
This is a permutation of 7 letters with double O and double C:
7!/2!2! = 5040/4 = 1260P = 1
I = 1
C = 2
O = 2
L = 1
--------
Total (n) = 7(k) = 2(C), 2(O)p = N! ÷ k!
p = 7! ÷ 2!2!
p = 5,040 ÷ 4
P = 1,260
what is 5000000000000 divided by 11
Answer:
45.454
Step-by-step explanation:
2 tbsp. of peanut butter have 0.25 of total carbohydrate a day what fraction is that?
0.25 is 1/4 if that's what youre asking, i'm not sure,
b) Now, let’s try “what if”. What if you had medical bills for $10,000 for a minor surgery? What would each of the insurance policies pay if you had not yet paid any deductible? Remember that 20% is your part (coinsurance) so the insurer’s percent is 80% for the first formula. Show how you are getting the answer.
Formulas:
Insurer’s part of Medical Bill = (Bill – deductible) (80%)
Your part of medical bill = Total bill – Insurers part
• AAA+
Insurer’s Part of bill =
Your part of bill =
• Health Today
Insurer’s Part of bill =
Your part of bill =
• Best Insurance
Insurer’s Part of bill =
Your part of bill =
The insurer's part of the medical bill is 80 percent of the medical bill after deductible
The insurer would cover 80 percent of the insured's claims on the medical bill based on coinsurance agreement. However, the insured would have to pay deductible prior to coinsurance(80,20 share of bill)
Example: if insured's annual deductible is $2000 and coinsurance is 80:20, a medical bill of $10000, assuming the insured has not paid any deductibles, would amount to 80% of $8000(after subtracting deductibles) for the insurer"s cover and the rest for the insured.
Insurance deductibles are paid before your health plan covers its part of the medical bill, usually 80 percent.
Depending on your agreement with the insurer there could also be a copay on the insurance policy.
Learn more here: https://brainly.com/question/13564874
which of the following has factor of (× - 4) (× - 3)?
Answer:
Hello!
After reading your question I have come up with the correct way to factor (x-4) and (x-3) together:
x²-7x+12
Step-by-step explanation:
This is my work:
solve pls brainliest
Answer:
$6.75
Step-by-step explanation:
try try serving it's ok glad to help
12. The square root of a number is a whole number between 50 and 100. What do you know about the number?
13. Could the square root of a whole number ever be greater than the number is? Explain.
no links please thanks
Answer:The radical symbol √ is used to indicate the square root. For example, √16 = 4. The radical symbol is also called a root symbol or surds. If a number is a perfect square, we can easily find the squar
Step-by-step explanation:
Answer:
See belowStep-by-step explanation:
#12The square root of a number is a whole number between 50 and 100.
Let the number be n, given:
50 < √n < 100Square both sides:
50² < n < 100²2500 < n < 10000The number is a perfect square between 2500 and 10000.
#13Let the number is n:
√n > nSquare both sides:
n > n²n² - n < 0n(n - 1) < 0Solution is:
0 < n < 1The answer is yes, the number must be between 0 and 1.
SOMEONE PLEASE HELP IM FAILING HS
2-20. Evaluate each expression for x=-2 and y=-5.
a. 1-2x + 3y
b. -|x-y|
c. √x^2 + ^3√x^3
d. 1/2x+1/3y
Answer:
a. 1-2(-2) + 3(-5) = 1-4 -15 = -18
b. -|-2--5| = |3| = -3
d. 1/2x+1/3y = 1/2 (-2) + 1/3(-5) = -1 - 5/3 = -8/3
Hope it works
Which expression is equivalent to (-x-16)
-x-16?
X-+16
-X+16
X-16
Answer:
- x - 16
Step-by-step explanation:
What annual rate of interest compounded annually is required to double an investment in 6 years?
Answer:
Approximately 12.25%
Step-by-step explanation:
The compound interest formula is:
Final balance = Principal * (1 + interest rate/number of times interest compounded per year)^(number of times interest compounded per year * years elapsed)
If we want our final balance to be twice our principal, our formula looks like:
[tex]2P = P * (1 + \frac{r}{1})^{1*6}[/tex]
We can divide our principal from both sides to get the following equation:
[tex]2 = (1 + \frac{r}{1})^{6}[/tex]
Since anything divided by 1 is itself, we can simplify a little further to:
[tex]2 = (1 + r)^{6}[/tex]
Now, we need to solve for r. We can start by taking the sixth root of both sides.
[tex]\sqrt[6]{2} = 1 + r[/tex]
Then subtract 1 from both sides:
[tex]\sqrt[6]{2} -1 = r[/tex]
Finally, we can use a calculator to get a decimal approximation:
0.1225 ≅ r
What is dehydrogenation ?
Answer:
Dehydrogenation is the a chemical reaction that involves the removal of hydrogen, usually from an organic molecule. It is the reverse of hydrogenation. Dehydrogenation is important, both as a useful reaction and a serious problem.
Elizabeth writes down: One multiple of 13; and Two different factors of 77. Elizabeth adds up her three numbers. Her answer is greater than fifty but less than sixty. What three numbers could Elizabeth have written down?
Answer:
7, 11, 39 OR -26, 1, 77;
Step-by-step explanation:
Mumble. Let's call the first number 13k, which is obviously a multiple of 13.
The factor of 77 are easy to find. It's either 77 and 1, or 11 and 7.
Now two cases. If we consider negative multiples of 13 (ie, -39 is -3 times 13) we can use the first pair (77 and 1, who sum up to 78, and start taking 13 from it as many times as we need to get to our interval.
1st pass: 78-13 = 65 out
2nd pass: 65-13 = 52 in
3rd pass : 52 - 13 = 39 out
So a possible triplet is 77, 1 and -26.
Case two: we aren't allowed to take negative numbers, and 77 and 1 will bring out of our range already. Let's stick to 11 and 7, who sum up to 18. Again, let's keep adding 13 as many times as we need
1st pass: 18+13 = 31, no good
2nd pass: 31+13 = 44, out again
3rd pass: 44+13= 57, we're good!
4th pass: 57+13 = 70, too far.
So another possible triplet is 7, 11, 39.
The moment you allow the product of the second and third number to be rationals will open a whole new can of worm that isn't any close to be interesting or fun to explore.
Please help me what dos this mean? Giving brainliest
Answer:
Draw a picture of FOUR calculators and TWELVE pencils
Step-by-step explanation:
just double what you see in the picture
Mary can swim 3 laps in 6
minutes. Use an equivalent ratio
to determine how many laps
Mary can swim in 18 minutes.
How many laps?
Answer:
9 laps
Step-by-step explanation:
Set up a proportion
3 laps / 6 minutes = x [which represents laps]/18 minutes Cross multiply
6*x = 3 * 18 Combine
6x = 54 Divide by 6
6x/6 = 54/6
x = 9
plsssssssssssssssssssssssssssssssssssssss
FACTORISATION
i) Factorise:
4a(a-b)+3b(b-a)
4a(a - b) + 3b(b - a)
= 4a² - 4ab + 3b² - 3ab
= 4a² - 4ab - 3ab + 3b²
= 4a² - 7ab + 3b²
= (a - b) (4a - 3b)
________
Hope it helps ⚜
what is the answer help
Answer:
1
Step-by-step explanation:
y=-x-1
when it is perpendicular, it is the opposite then flip the fractions so 1 and if you flip 1 it is still 1