Answer:
The approximate value of [tex]P(0.45<\bar X<0.50)[/tex] is 0.3686.
Step-by-step explanation:
The pdf of X is:
[tex]f(x) = 6x(1-x), 0 < x < 1[/tex]
Compute the mean as follows:
[tex]\mu=\int\limits^{1}_{0} {x\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{2}-6x^{3}} \, dx\\\\=[\frac{6x^{3}}{3}]-[\frac{6x^{4}}{4}]|^{1}_{0}\\\\=2-\frac{3}{2}\\\\=0.50[/tex]
Compute the variance as follows:
[tex]\sigma^{2}=E(X^{2})-(\mu)^{2}[/tex]
[tex]E(X^{2})=\int\limits^{1}_{0} {x^{2}\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{3}-6x^{4}} \, dx\\\\=[\frac{6x^{4}}{4}]-[\frac{6x^{5}}{5}]|^{1}_{0}\\\\=\frac{3}{2}-\frac{6}{5}\\\\=0.30[/tex]
[tex]\sigma^{2}=E(X^{2})-(\mu)^{2}\\\\\sigma=\sqrt{E(X^{2})-(\mu)^{2}}\\\\=\sqrt{0.30-(0.50)^{2}}\\\\=0.2236[/tex]
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The sample selected is of size n = 64 > 30. Thus a central limit theorem can be applied to approximate the sampling distribution of sample mean.
Compute the value of [tex]P(0.45<\bar X<0.50)[/tex] as follows:
[tex]P(0.45<\bar X<0.50)=P(\frac{0.45-0.50}{0.2236/\sqrt{64}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.50-0.50}{0.2236/\sqrt{64}})[/tex]
[tex]=P(-1.12<Z<0)\\\\=P(Z<0)-P(Z<-1.12)\\\\=0.50-0.13136\\\\=0.36864\\\\\approx 0.3686[/tex]
Thus, the approximate value of [tex]P(0.45<\bar X<0.50)[/tex] is 0.3686.
Using the order of operations, what should be done first to evaluate 6 + StartFraction (negative 5 minus 7) over 2 EndFraction minus 8 (3)
9514 1404 393
Answer:
evaluate inside parentheses
Step-by-step explanation:
It looks like you want the value of ...
[tex]6+\dfrac{(-5-7)}{2}-8(3)[/tex]
The operations inside parentheses (-5-7) are performed first. Then the division and multiplication in order left to right. Finally, the subtractions are done left to right.
[tex]6+\dfrac{-12}{2}-8(3)=6-6-8(3)=6-6-24=0-24=-24[/tex]
Answer:
subtract 7 from -5
Write an inequality using < ». or = that compares one of the fractions to one of the decimals. Then explain how a number line could help you decide which number is greater.
ok it would be moment if something is happening again and again it kl and I have a lot of the complex number of 3333rd graders in the us and I have a 33 year
solve for x
x+11+x+13=22
Answer:
x=-1
Step-by-step explanation:
x+11+x+13=22
2x+24=22
2x=-2
x=-1
Who won more games 7/10 or 2/5
Answer:
7/10
Step-by-step explanation:
Packs of soda are on sale at the supermarket this week. The sign says that it cost $13 for 4 packs. How much do 3 packs of soda cost?
Answer:
9.75 dollars
Step-by-step explanation:
13/4=3.25x3=9.75
Answer:
The answer is $9.75
Step-by-step explanation:
take $13 and divide by 4 to get the unit price, then you multiply by 3 to get what you want to know..
= $9.75
HELP!!!
what is 4.23 divided by 0.012 ??????????
Answer:
352.5
or
705/2
Step-by-step explanation:
4.23 ÷ 0.012 = 352.5
352.5 × 0.012 = 4.23
When 4.23 is divided by 0.012, we get 352.5.
What is Division? What is division algorithm?Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. The division algorithm says when a number [a] is divided by [b], it will give quotient as [q] and remainder [r], then the following relation exist between a, b, q and r as -
a = bq + r
Given are two decimal numbers 4.23 and 0.012 such that → 4.23 divided by 0.012.
Assume that the number -
A = 4.23
B = 0.012
We have to find A/B, therefore, we can write -
A/B = 4.23/0.012A/B = 423000/1200 = 4230/12 = 352.5
Therefore, when 4.23 is divided by 0.012, we get 352.5 as the result.
To solve more questions on division of decimals, visit the link below-
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12/11 - (-2/3)= what is the answer
Answer:
58/33 or 1.75
Step-by-step explanation:
The equation of line Q is y = -8/9x + 1/6 line r is parallel to line q what is the slope of line r
Hello.
Parallel lines have the same slope.
If the given line has a slope of [tex]\displaystyle-\frac{8}{9}[/tex], then the line parallel to it has the same slope.
Thus, line r has a slope of [tex]\displaystyle-\frac{8}{9}[/tex].
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]
What is the measure of F
Answer:
degrees
Step-by-step explanation:
right for ap-ex
In monopoly, what is the difference in price between the least expensive property + the most expensive property
Answer:
The least amont property and the most amount property
Step-by-step explanation:
one has lest revenue and one you get more revenue
Answer:
$340
Step-by-step explanation:
most expensive property and cost: Boardwalk- $400
least expensive property and cost: Old Kent or Whitechapel Road- $60
equation: $400-$60=?
answer: $340
Department A had a beginning inventory balance of 25 units which were 40% complete. During the accounting period, the department started an additional 275 units and had an ending balance of 50 units which were 20% complete. Using FIFO, the equivalent units of production is units.
Answer:
250
Step-by-step explanation:
The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to:_______
a. 2
b. 3
c. 6
d. 9
e.12
Answer: a. 2
Step-by-step explanation:
According to the Empirical rule, when data is normally distributed then 95% of the lies within 2 standard deviations from mean.
Given: The distribution of the heights of students in a large class is roughly bell-shaped ( i.e. Normally distributed).
The average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches.
Then, by Empirical rule, 68 -2(standard deviations) =62 [lower limit]
⇒ 2(standard deviations)= 68-62 = 4
⇒ standard deviations=2
Hence, correct option is a. 2
Answer:
B-3
Step-by-step explanation:
According to the empirical rule, roughly 95% of the distribution is within 2 standard deviations of the mean.
The mean is 68. The distance from 62 to 68 is 6 inches
68-62=6
Cut that in half to get 6/2 = 3
So the standard deviation is 3
Sarah began the school week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for lunch. what equation was the balance in her lunch account on the end of the day on Friday?
Answer:
17.85
Step-by-step explanation:
2.60+20= 22.60
22.60-4.75= 17.85
Equations are used to find the unknown quantity.
The equation which represents the total balance in Sarah lunch account on the end of the day on Friday i[tex]x=22.6-19\\x=3.6[/tex]
Thus the total balance in her lunch account on the end of the day on Friday is 3.6.What is equality equation?
The equation which represents the equality between the two expressions. Equations are used to find the unknown numbers.
Given information-
Sarah began the school week with $2.60 in her lunch account.
The amount deposited by the Sarah is $20 on Monday,
The amount spent by the Sarah each day from Thursday to Friday is $4.75.
Suppose the total balance in her lunch account on the end of the day on Friday is [tex]x[/tex].
As the amount in her account was $2.60, when she began the school. The $20 was then deposited. Thus,
[tex]x=2.60+20[/tex]
Now she spent $4.75 each day for the next four days. Thus,
[tex]x=2.60+20-4(4.75)[/tex]
Hence this is the equation which represents the total balance in her lunch account on the end of the day on Friday.
Solve the equation,
[tex]x=22.6-19\\x=3.6[/tex]
Thus the total balance in her lunch account on the end of the day on Friday is 3.6.
Hence,
The equation which represents the total balance in her lunch account on the end of the day on Friday i[tex]x=22.6-19\\x=3.6[/tex]
Thus the total balance in her lunch account on the end of the day on Friday is 3.6.Learn more about the equality equation here;
https://brainly.com/question/860971
7n - 5 = 6n + 8
answers plss
Answer:
n=13
Step-by-step explanation:
7n-5=6n+8
-6n -6n
n-5=8
+5 +5
n=13
What is the slope of the graph? (If your answer is not a whole number enter as a fraction rounded to the nearest tenth)
Answer:
3/2
Step-by-step explanation:
rise/run
3/2
its not going down so its positive
Determine the resulting polynomial:
f(x) = -9x + 4
g(x) =
-22
10x - 7
Find: f(x) · g(x)
I have rewritten the expression for g(x) as shown below.
Answer:
[tex]f(x)*g(x)=18x^3-98x^2+103x-28[/tex]
Step-by-step explanation:
Product of polynomials
Given
[tex]f(x)=-9x+4[/tex]
[tex]g(x)=-2x^2+10x-7[/tex]
Note: This function has been rewritten to make it a correct polynomial expression.
Find f(x)*g(x)
We'll apply the distributive property:
[tex]f(x)*g(x)=(-9x+4)*(-2x^2+10x-7)[/tex]
[tex]=18x^3-8x^2-90x^2+40x+63x-28[/tex]
Simplifying:
[tex]\boxed{f(x)*g(x)=18x^3-98x^2+103x-28}[/tex]
If I simplify 3/7 to 1/7 and multiply to 2/9 what did I do wrong
Answer:
Read the explanation
Step-by-step explanation:
You cannot simplify 3/7 to 1/7. 3/7 is 3/7 and cannot be changed unless added, subtracted, divided, or multiplied. 1/7 x 2/9 is 2/63
3/7 x 2/9 is 6/63
in a juice mixture, 750ml of water are mixed with 250ml of juice concentrate. What is the ratio of concentrate to water
Answer:
1:3
Step-by-step explanation:
What you want to do is solve for how much water will be for one fraction of juice concentrate.
To do that you can divide 750 by 250 to get 3. That means that 3 portions of water to one portion of concentrate would be the ratio.
Hope that helps and have a great day!
The table shows the cost of taking a rideshare trip. Which description correctly reflects the way the charges are calculated?
where is the table and the descriptions
solve the square root of 245 please
it can't be in no decimal.
Answer: About 16
Step-by-step explanation: Since the answer is a decimal 15.652... I rounded up to the nearest whole number which is 16.
Road
James has9 cups of blueberries. He uses 5 cups to make a pie. He uses another 2 cups to make muffins.
How many cups of blueberries does James have left?
Enter your answer as a mixed number in simplest form by filling in the boxes.
8
1
cups
8
1
2
3
4
6
Answer:
he has 2 cups left
Step-by-step explanation:
(9) 5+2=7(9-7=2)
star wars fans unite!
Answer:
WASSUP!
Step-by-step explanation:
BABY YODA ADORABLE!
Answer: Luke sky walker
Step-by-step explanation:
... The square below represents one whole. What percent is represented by the shaded area?
Answer:
The percentage is 85%.
Step-by-step explanation:
You can count the shaded squares individually, but I count the rows that are shaded, and then subtract by the squares that aren't shaded in.
A line has a slope of -2 and goes through the point (-1, -6). What is the equation of the line, written in point-slope form?
Answer:
The answer is
[tex] \huge y + 6 = - 2(x + 1) \\ [/tex]
Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question we have the final answer as
[tex]y + 6 = - 2(x + 1)[/tex]
Hope this helps you
A 30oz bottle of a particular juice contains 18oz of water. What percent of this drink is water?
Answer:
my name is jeff
Step-by-step explanation:
Which is the best estimate of the percent? 49% of 598
Answer:
300
Step-by-step explanation:
The dimensions of a rectangular flower bed on a sketch are 4 cm by 6 cm. In real life, the shorter side of the flower bed is 5 m. Find the length of the longer side.
Answer:
125.15
Step-by-step explanation:
Just do it!
The cost of spare parts per machine are normally distributed with a population standard deviation of 158 dollars and an unknown population mean. If a random sample of 23 machines is taken and results in a sample mean of 1790 dollars, find the error bound (EBM) of the confidence interval with a 98% confidence level
Answer:
The 98% confidence interval is [tex] 1713.23 < \mu < 1866.76 [/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = 158[/tex]
The sample size is n = 23
The sample mean is [tex]\= x = 1790 \ dollars[/tex]
From the question we are told the confidence level is 98% , hence the level of significance is
[tex]\alpha = (100 - 98 ) \%[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.33 * \frac{158 }{\sqrt{23} }[/tex]
[tex]E =76.76 [/tex]
Generally 98% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
[tex]1790 -76.76 < \mu < 1790 +76.76 [/tex]
[tex] 1713.23 < \mu < 1866.76 [/tex]
PLEASE HELP!!!
Thanks so much
Answer:
I didn't wrote on the paper but
6 and 18 are corresponding angles. Im sorry i forgot about it.
What is the distance between the top of the fishing pole 8 1/2 feet and the fish 4 1/2 feet
Answer:
4 feet
Step-by-step explanation:
Why? because we can simply just type it and look at it in a more simple way
[tex]8\frac{1}{2}[/tex] - [tex]4\frac{1}{2}[/tex]= 4
Because 4 is the difference.
4 is the difference between [tex]8\frac{1}{2}[/tex] and [tex]4\frac{1}{2}[/tex].
Hope this helps!
Have a nice day!
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
A fraction is a way to describe a part of a whole. The distance between the top of the fishing pole and the fish is 13 feet.
What is a Mixed Fraction?A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,
2 1/2
= (2×2 + 1)/2
= 5/2
= 2.5
Given that the distance between the surface of the water and the top of the fishing pole is 8 1/2 feet, while the distance between the surface of the water and the fish is 4 1/2 feet.
Therefore, the distance between the top of the fishing pole and the fish is the sum of the distance between the surface of the water and the top of the fishing pole and the distance between the surface of the water and the fish.
Now, the distance between the top and the fish is,
Distance = (8 1/2) feet + (4 1/2) feet
Converting Mixed fractions to fractions,
= (8×2 + 1)/2 + (4×2 + 1)/2
= 17/2 + 9/2
= (17+9)/2
= 26/2
= 13 feets
Hence, the distance between the top of the fishing pole and the fish is 13 feet.
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