Answer:
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
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 establishes 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 48.3 ppm and a standard deviation of 8 ppm.
This means that [tex]\mu = 48.3, \sigma = 8[/tex]
Sample of 40:
This means that [tex]n = 40, s = \frac{8}{\sqrt{40}}[/tex]
Find the probability that the disposal of such capacitors will be regulated.
Sample mean above 48.5, which is 1 subtracted by the p-value of Z when X = 48.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48.5 - 48.3}{\frac{8}{\sqrt{40}}}[/tex]
[tex]Z = 0.16[/tex]
[tex]Z = 0.16[/tex] has a p-value of 0.5636.
1 - 0.5636 = 0.4364
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
Simplify the ratio
6 doctors to 27 patients
Answer:
2 doctors to 9 patients
Step-by-step explanation:
Divide each by 3. They cant be simplified more.
WILL GIVE U BRAINLIEST
True or False: All obtuse triangles are scalene?
Answer:
False
Step-by-step explanation:
an obtuse triangle maybe isosceles or scalene
Which does NOT have a value of 4 when
simplified?
1. 5.6x0.15 + (-3.16)
1. (-7x23) + (-43)
III. -5.6+4(3)
Answer:
3 beause when you dividend it -5.6+4(3) .
Hello can someone answer this question please
1/4 = 0.25 is the largest value..
It is right answer....
how to find the vat on 14% of 1800
Answer:
14/100*1800
25200/100
252
Step-by-step explanation:
therefore vat=252
The area of the base of a cylinder is equivalent to the base of a circle? A) True. B) False
Answer:
Yes
Step-by-step explanation:
The base of both the cylinder and Circle are both circles.
Please answer :D pretty simple for math experts I’m just bad
Answer: 74 inches
Step-by-step explanation:
Since we are given the equation of the regression line for the son's height y to be:
y = 0.5x + 38
where,
x = father's height = 72 inches
Then, we put the value of x into the equation and this will be:
y = 0.5x + 38
y = 0.5(72) + 38
y = 36 + 38
y = 74 inches
Therefore, the son is 74 inches.
if the sum of two consecutive odd number is 20 find the number
Answer:
Step-by-step explanation:
let a number be x
let another number be x+1
x+x+1=20
2x=20-1
x=19/2
x=9.5
therefore one number is 9.5 and another number is x+1=9.5+1=10.5
[tex]\huge{ \mathrm{ \underline{ Answer} \: \: ✓ }}[/tex]
Let the Consecutive odd numbers be x and x+2
[tex]x + x + 2 = 20[/tex][tex]2x = 20 - 2[/tex][tex]2x = 18[/tex][tex]x = 9[/tex]Therefore, the numbers are :
[tex]x = 9[/tex][tex]x + 2 = 11[/tex]______________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
Enter the correct answer in the box.
Simplify the expression (62,4.
Answer:
1679616
Step-by-step explanation:
C. 20 people show up to the party, and Robert decides to give them each the
same amount of pizza. How much pizza does each person get?
Answer:
Step-by-step explanation:3/5 of the pizza
Find the slope of the line tangent to the function y=6-3x at the point (5,0)
Answer:
-3
Step-by-step explanation:
To get the slope of the line tangent to the function y = 6 - 3x
First, we need to differentiate;
dy/dx = 0 -3x^{1-1}
dy/dx = 0 - 3x^0
dy/dx = 0 - 3
dy/dx = -3
Hence the slope of the line tangent to the function at the point is -3
If [×] =5 what is the value of x?
Answer:
x = 5
Step-by-step explanation:
I didn't quite understand what you were asking but x should equal 5
Answer: 1 is the answer because nothing time _ will equal 5 but 1 times anything equal that number So its 1
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
Answer:
a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes
c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
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 establishes 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 8.9 minutes and a standard deviation of 2.9 minutes.
This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]
Sample of 37:
This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
320/37 = 8.64865
Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a p-value of 0.2981
0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
275/37 = 7.4324
Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -3.08[/tex]
[tex]Z = -3.08[/tex] has a p-value of 0.001
1 - 0.001 = 0.999
0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So
0.2981 - 0.0010 = 0.2971
0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
HELP PLISS
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answer:
It's Cos.
Hope this helps
Every morning Ramona misses her bus with probability 1/10, independently of other mornings. What is the probability that next week she catches her bus on Monday, Tuesday, and Thursday, but misses her bus on Wednesday and Friday
Answer:
The probability is [tex]\frac{729}{100000}[/tex].
Step-by-step explanation:
probability of missing the bus = 1/10
Probability of catching the bus = 1 - 1/10 = 9 /10
So, the required probability is
[tex]\frac{9}{10}\times \frac {9}{10}\times \frac {1}{10}\times \frac {9}{10}\times \frac {1}{10}[/tex]
[tex]\frac{729}{100000}[/tex]
Help please worth 57 points
Answer:
Always, always.
Sami made 23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year. What was his hourly pay rate?
Answer:
$15 per hour
Step-by-step explanation:
30 hours per week x 52 weeks in a year = 1560 hours per year
23,400 / 1560 = $15 per hour
A car dealer just took delivery on forty new cars. He plans to put four of these cars on display at the front of the lot. In how many ways can the dealer combine four of the forty cars if order is not important?
A. 1,096,680
B. 91,390
C. 45,695
D. 2,193,360
Answer:
B. 91,390
Step-by-step explanation:
I've had this question before, I don't like'em, but that's the answer.
Answer:
option B
Step-by-step explanation:
[tex]40C_4 = \frac{40\times 39 \times 38 \times 37}{1 \times 2 \times 3 \times 4} = 91,390[/tex]
Find the exact value of tan A in simplest radical form.
PLEASE HELP
Answer:
[tex] \tan(A) = \frac{opp}{adj} \\ \tan(A) = \frac{ \sqrt{72} }{3} \\ \tan(A) = \frac{ \sqrt{36 \times 2} }{3} \\ \tan(A) = \frac{6 \sqrt{2} }{3} \\ \tan(A) = 2 \sqrt{2} [/tex]
Wanda Frey insured her home for $156,400. Her annual insurance rate is $0.83
per $100. What annual premium did she pay?
Answer:
$1,298.12
Step-by-step explanation:
there are 1564 hundreds in 156,400
so 1564 x .83 = 1298.12
A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit
take x from 0 to 7. From the graph find:
a) the area of the rectangle when x = 2.25cm
b) the dimensions of the rectangle when its area is 9cm^2
c) the maximum area of the rectangle
d) the length and width of the rectangle corresponding to the maximum area
e) what shape of the rectangle has the largest area
Answer:
B
Step-by-step explanation:
the dimensions of the rectangle when its area is 9cm^2
i need this done fast
Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd
Step-by-step explanation:
I GIVE BRAINLIEST!!! Derek wants to save up for a new baseball glove. The price of the glove with tax is $385. If he can save $65 per month , how many months will it take him to save up for the glove?
Answer:
6
Step-by-step explanation:
385/65= about 6 but technically its like 5.92307...
Step-by-step explanation:
Price of glove with tax = 385
Money saved per month = 65
Months needed for Derek to save enough money
= 385/65
= 5.923 months
Which ordered pair belongs to the function shown by this mapping diagram?
Answer:
{(7, 3), (8, 1), (9, 1), (10, 2)}
Step-by-step explanation:
Options are missing for this given problem, however, let's find the ordered pairs that should belong to the function shown by the mapping above:
We have the x-values (inputs) on our left while the corresponding y-values (outputs) are on our right.
The ordered pairs (x, y) are as follows:
{(7, 3), (8, 1), (9, 1), (10, 2)}
Solve the system of linear equations by elimination. Show your work
2x-y=-3
4x + 3y = -21
Answer:
x = -3, y = -3
Step-by-step explanation:
Solve the following system:
{-y + 2 x = -3 | (equation 1)
3 y + 4 x = -21 | (equation 2)
Swap equation 1 with equation 2:
{4 x + 3 y = -21 | (equation 1)
2 x - y = -3 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 3 y = -21 | (equation 1)
0 x - (5 y)/2 = 15/2 | (equation 2)
Multiply equation 2 by 2/5:
{4 x + 3 y = -21 | (equation 1)
0 x - y = 3 | (equation 2)
Multiply equation 2 by -1:
{4 x + 3 y = -21 | (equation 1)
0 x+y = -3 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = -12 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 4:
{x+0 y = -3 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: x = -3, y = -3
Which pair of expressions below are equivalent (the same)?
1. 2x + 2y and 4xy
2. 3(x + 4) and 3x + 12
3. 7x + 6x and 42x
4. 5x + x + x and 6x
Please help it’s a test !
Answer:
2.
Step-by-step explanation:
2. because 3(x+4) if we distribute 3 in parenthesis we have 3x+12
Suppose that y varies inversely with x, and y= 3 when x = 10.
(a) Write an inverse variation equation that relates x and y.
Equation:
(b) Find y when x = 5
y =
Answer:
y=6
Step-by-step explanation:
the equation that relates x and y is y=30(1÷x)
Can someone please help?
Answer:
It is closer to 7,000 than 8,000
find the radius of a circle if the circumference is 66cm
Answer:
Approximately 10.5, or 10.5095541.
Step-by-step explanation:
To find the radius given the circumference of a circle, we first have to divide the circumference by pi, or an estimation of 3.14. This will give us the diameter.
Since we know that the radius of a circle is simply half the diameter, we divide the number we got from the problem above by 2. This will give you your answer!
Answer:
r = 10.50
Step-by-step explanation:
Circumference =
[tex]2\pi \: r[/tex]
[tex] 66 = 2\pi \: r[/tex]
[tex] \frac{66}{2\pi} = r[/tex]
r = 10.5
What is the length of x?
Answer:
9.04
Step-by-step explanation:
tan 37 = x/12
0.7536 x 12= x
x = 9.04