Answer:
a) 75%.
b) 84%
c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Chebyshev Theorem:
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean: 6.3 hours
Standard deviation: 1.6 hours
(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.
3.1 = 6.3 - 2*1.6
9.5 = 6.3 + 2*1.6
Within 2 standard deviations, so the minimum percentage is 75%.
(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.
How many standard deviations from the mean?
One standard deviation is 1.6
These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which
[tex]k = \frac{4}{1.6} = 2.5[/tex]
The minimum percentage is:
[tex]100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%[/tex]
So 84%.
(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.
Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.
Consider a savings account earning annual compound interest with no additional deposits or withdrawals made after the initial deposit. The balance in the account after x years can be modeled by the function s(x) = 2.000(1.045) Which statement is the best interpretation of one of the values in this function? A) The initial balance of the account is $2,000. B) The balance in the account at the end of one year is $2,000. The initial balance of the account increases at a rate of 104.5% each year. D) The initial balance of the account decreases at a rate of 4 5% each year.
Answer:
The initial balance of the account is $2,000.
Step-by-step explanation:
I took the test on usa test prep
Answer:The initial balance of the account is $2,000.
f(x) = abx, where a = initial value, b = change factor, and x = time period.
What is the value of x in the figure above? Assume ↔B and ↔C are parallel.
Answer:
x=4
Step-by-step explanation:
180-58=26x+18
122=26x+18
122-18=26x
104=26x
4=x
25 divided by 12 PLEASE answer quick
24 divided by 12 equals 2,083
The division of 25 by 12 gives the quotient 2 and remainder is 1.
What is Division?One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
Given:
We have to divide 25 by 12.
The division is as follow:
12| 25 | 2
24
______
1
Thus the Quotient is 2 and remainder is 1.
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a gain of five meters
1.A gain of five meters:5
Because gain＝+
Let y = x² In(x).
dy/dx the lesson is differentiate products
Answer:
dy/dx = x(1+2lnx)
Step-by-step explanation:
Given y = x² In(x).
dy/dx = Udv/dx + Vdu/dx
Let U = x², V = lnx
du/dx = 2x
dv/dx = 1/x
Substitute into the formula;
dy/dx = x²(1/x) + lnx(2x)
dy/dx = x + 2xlnx
dy/dx = x(1+2lnx)
24j - 9 Factor the following expression using GCF
Answer:
See it and do it
Follow please
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense?
Answer:
It is by contract the same amount every month.
Step-by-step explanation:
what is the slope of (4,7) (9,7)?! please help i tried omni and it didn't give me an answer
Answer:
0
Step-by-step explanation:
The sector of a circle has an area of 104pi/9 square inches and a central angle with measure 65 degrees. What is the radius of the circle in inches? Show work. a. 5.7 b. 8 c. 64 d. 104
The radius of the circle is 8 inches when the sector of a circle has an area of 104pi/9 square inches.
What is a sector of a circle?A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
Which is the radius of a circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference.
Area of a sector = [tex]\frac{\theta}{360} \pi r^2[/tex]
[tex]\text{Given area = }\frac{104\times \pi}{9}=\frac{65}{360}\times \pi r^2\\\\\frac{104}{9}=\frac{65}{360} \times r^2\\\\r^2=\frac{37440}{585}\\\\r=8.001[/tex]
Hence, option b is correct, that is the radius of the circle is 8 inches.
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The arrow shown is on a sign. What is the area of the arrow? Plz
Answer:
61 inches squared
Step-by-step explanation:
find the area of the rectangle then the area of the triangle and add.
Answer:
61 in²
Step-by-step explanation:
first u work out the rectangle. so u do 4 times 10 which is 40 . then u do 1.5 plus 1.5 plus 4 which equals 7 . then u do 7 times 6 which is 42 . 42 two divide by 2 = 21 . 21 plus 40 equals 61. answer 61.
area of triangle: base times height divide by 2 .
to work out area of rectangle : 4×10=40 in²
1.5+1.5+4= 7 in
area of triangle: 7×6=42 then divide by 2 = 21 in²
plus them to get the area of arrow : 21+40=61 in²
hope this helps. give brainliest and like this . rate it and follow me . amd I will follow u back and help u more
5 tons of compost cost $6,300.00. What is the price per pound?
Answer:
300 , is the answer
Step-by-step explanation:
find the area? need help guys!!
help asap i will get yelled at =( this is going to give yoyu 42 points
Answer:
24+24=48
Step-by-step
24+24=48
Answer: first pic: true. second pic: is D. third pic: false. forth pic: C.
Step-by-step explanation:
How many notebooks do you think it would take to make a stack that is 5 feet high?
Answer:
There are total 30 books in the 5 feet high stack of books.
Step-by-step explanation:
The complete question is
Given, Each note book is 2 inches thick, How many notebooks do you think it would take to make a stack that is 5 feet high
Solution
Thickness of each book [tex]= \frac{2}{12} = \frac{1}{6}[/tex]
The total height of the book stack is [tex]5[/tex] feet.
The number of books in the stack is equal to total height of the stack divided by the thickness of one book
Number of books in five feet high stack is
[tex]\frac{5}{\frac{1}{6} } \\5 * \frac{6}{1} \\30[/tex]
Hence, there are total 30 books in the 5 feet high stack of books.
what is the following sum
Answer:
2nd option is the correct answer
[tex] 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Step-by-step explanation:
[tex]3 {b}^{2} \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^{6} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{27 \times 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^{2} )}^{3} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{ {3}^{3} \times 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^{2} )}^{3}2a} } \bigg) \\ \\ = 3 {b}^{2} \times 3 \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 9 {b}^{2} \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Answer:
second option: 12b²(∛2a)
Step-by-step explanation:
you can break [tex]\sqrt[3]{54a}[/tex] into [tex]\sqrt[3]{3^3(2a)}[/tex] which equals 3[tex]\sqrt[3]{2a}[/tex]
you can break [tex]\sqrt[3]{2ab^6}[/tex] into [tex]\sqrt[3]{2ab^3b^3}[/tex] which equals b²[tex]\sqrt[3]{2a}[/tex]
now we can simplify: (3b² · 3[tex]\sqrt[3]{2a}[/tex]) + 3b²[tex]\sqrt[3]{2a}[/tex] = 9b²[tex]\sqrt[3]{2a}[/tex] + 3b²[tex]\sqrt[3]{2a}[/tex]
this equals 12b²[tex]\sqrt[3]{2a}[/tex]
If f (x) = x – 1 and g(x) = 5x – 2 , then (f/g) (x) help me plz
Answer:
[tex](f/g)x = \frac{x-1}{5x - 2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 1[/tex]
[tex]g(x) = 5x - 2[/tex]
Required
(f/g)x
In functions:
[tex](f/g)x = \frac{f(x)}{g(x)}\ \ \ g(x)\ne 0[/tex]
So:
[tex](f/g)x = \frac{x - 1}{5x - 2}[/tex]
Help pls!! I need help!!
Answer:
what u need help wt?
Step-by-step explanation:
Find the factors of following:
(i) 8x^2 yy
Answer:
i•8xy^2yz
Step-by-step explanation:
Remove unnecessary parentheses
Answer:
i) 8x^2 yz=2×2×2×x×x×y×z
write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. y=a(x-h)^2+k
vertex:(4,-1) point:(2,3)
Answer:
y = ( x − 2 ) ^ 2 + 3
y = x^2 − 4x + 7
Step-by-step explanation:
y = a ( x − h ) ^ 2 + k
where vertex is (h,k) = (4,-1)
h=4, k=-1
y = a ( x − 4 ) ^ 2 - 1
sub ( 2,3 )
3 = a (2 - 4)^2 - 1
a=1
y = 1 ( x − 2 ) ^ 2 + 3
y = ( x^2 − 4x + 4 ) + 3
y = x^2 − 4x + 7
Please help... picture is below
Answer
x=29
Step-by-step explanation:
Okay we know that the sum of all angles in a triangle is 180, so all we have to do is add them up first
(x+17)+(2x+5)=3x+22
(3x+22)+(3x-16)=6x+6
okay so we now know that 6x+6=180
subtract 6 on both sides 6x=174
then divide by 6 to get x=29
hope this helps!
please help me with this math wuestion
Answer:
A) 3 1/4
Step-by-step explanation:
x+1/2 = 3 3/4
x = 3 3/4 - 2/4 = 3 1/4
I WILL MARK BRANLIEST IF U ARE RIGHT!!
Answer:
Perimeter=100 area=688.19
Step-by-step explanation:
There's a big formula for area of pentagon and I pretty tired, so unless you want me to show my work I wont
Could someone help me with this
Answer:
try to do this formula
XYZ
= X times Y times Z
The slope of a linear function is 1/5. For every rise of 5 units, what is the run?
Answer:
for every rise of 1 the run would be 25
Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey(NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium (mg). They found in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Using these values for the mean and standard deviation for the U.S. population, find and interpret the probability that a random sample of size 50 will a mean:
Complete question :
Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.
Answer:
0.10935
0.3718
0.9778
0.606
Step-by-step explanation:
μ = 721 ; σ = 454 ; n = 50
P(x > 800)
Zscore = (x - μ) / σ/sqrt(n)
P(x > 800) = (800 - 721) ÷ 454/sqrt(50)
P(x > 800) = 79 / 64.205295
P(x > 800) = 1.23
P(Z > 1.23) = 0.10935
2.)
Less than 700
P(x < 700) = (700 - 721) ÷ 454/sqrt(50)
P(x < 700) = - 21/ 64.205295
P(x < 700) = - 0.327
P(Z < - 0.327) = 0.3718
Between 700 and 850
P(x < 850) = (850 - 721) ÷ 454/sqrt(50)
P(x < 850) = 129/ 64.205295
P(x < 700) = 2.01
P(Z < 2.01) = 0.9778
P(x < 850) - P(x < 700) =
P(Z < 2.01) - P(Z < - 0.327)
0.9778 - 0.3718
= 0.606
The table shows the average distance in yards of the tee shots of several professional golfers and their accuracy as percentages of landing golf ball in the fairway. what does the correlation coefficient for the data indicate about the strength of the linear association between the average distance of a tee shots in the accuracy of the golf ball landing in the fairway ?
Answer: strong negative correlation
Step-by-step explanation:
Taking the test
Sylvester spends a total of $1725 for Common and preferred shares. He has purchased $975 worth of preferred.
Answer:
750
Step-by-step explanation:
A piece of land in north county is a parallelogram with a base that is four more meters than eight times the height, h. Which of the
following represents the area of the land?
A. A(n) = 8h2 + 32
B.
A(h) = 8h2 + 4
C. A(h) = 4h2 + 8h
D.
A(n) = 8h2 + 4h
Answer:
D
Step-by-step explanation:
The probability of getting a red gumball from a gumball machine is 1/8. The probability of getting a red piece of candy from a candy machine is 1/6. If both a gumball and a piece of candy are purchased, what is the probability that both are red?
Answer: 1/48
Step-by-step explanation: equation: 1/8x1/6
you have to multiply both numerators together (1x1)=1 then you multiply the denominators together (8x6)=48. you can't simplify it so your answer is 1/48
What is the area enclosed by the curves???