Answer:
The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.
Step-by-step explanation:
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.
Normally distributed with mean 72 and standard deviation 6.
This means that [tex]\mu = 72, \sigma = 6[/tex]
A random sample of size 36
This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]
The sampling distribution of the sample mean is
By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.
Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra system to confirm your results. (Order your answers from smallest to largest x, then from smallest to largest y.)
f(x, y) = x2 − 4xy + 5
R = {(x, y): 1 ≤ x ≤ 4, 0 ≤ y ≤ 2}
f(x, y) = x ² - 4xy + 5
has critical points where both partial derivatives vanish:
∂f/∂x = 2x - 4y = 0 ==> x = 2y
∂f/∂y = -4x = 0 ==> x = 0 ==> y = 0
The origin does not lie in the region R, so we can ignore this point.
Now check the boundaries:
• x = 1 ==> f (1, y) = 6 - 4y
Then
max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0
max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2
• x = 4 ==> f (4, y) = 12 - 16y
Then
max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0
max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2
• y = 0 ==> f (x, 0) = x ² + 5
Then
max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4
min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1
• y = 2 ==> f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11
Then
max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1
min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4
So to summarize, we found
max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)
min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
Answer:
Area of rectangle = 2H² - 5H
Step-by-step explanation:
Let the length be L.Let the height be H.Translating the word problem into an algebraic expression, we have;
Length =2H - 5
To write the algebraic expression to model the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = L * H
Where;
L is the Length.H is the Height.Substituting the values into the formula, we have;
Area of rectangle = (2H - 5)*H
Area of rectangle = 2H² - 5H
The sum of 3 times a number and 4 is 9.
Answer: x = 5/3
Step-by-step explanation:
Let the number be x
Then
3x + 4 = 9
3x = 9-4
3x = 5
x = 5/3
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HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
Which line segment has the same measure as ST?
RX
TX
SR
XS
Answer:
The answer is Line Segment SR.
A line passes through the point (-4, -6) and has a slop of 5. Write an equation for this line.
a number has 7 at the tens place .there is zero in the thousand place. the number 5 is at the hundreds place .there is number 1at the ten thousand place..what is the number?
Let U be a matrix where u_ij = 0 if i > j, and L be a matrix where l_ij = 0 if i < j.
(a) U is called an upper triangular matrix and L is a lower tri-angular matrix. Explain why.
(b) Prove or disprove: The sum of two upper triangular matrices is an upper triangular matrix.
(c) Prove or disprove: The product of two upper triangular matrices is an upper triangular matrix.
Answer:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 )
B) sum of two upper triangular matrices = upper triangular matrix.
C) product of two upper triangular matrices = upper triangular matrix
Step-by-step explanation:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 ) since Lij = 0 if i < j
B) To prove that sum of two upper triangular matrices
attached below
C) Prove or disprove that product of two upper triangular matrices is an upper triangular matrix
attached below
Mr. E bought 3 drinks and 5 sandwiches for $25.05 and Mr. E bought 4 drinks and 2 sandwiches $13.80. how much does each drink cost?
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Answer:
drink: $1.35sandwich: $4.20Step-by-step explanation:
Let d and s represent the cost of a drink and a sandwich, respectively. The two purchases give rise to the equations ...
3d +5s = 25.05
4d +2s = 13.80
Dividing the second equation by 2 gives ...
2d + s = 6.90
Subtracting the first equation from 5 times this, we get ...
5(2d +s) -(3d +5s) = 5(6.90) -25.05
7d = 34.50 -25.05 = 9.45
d = 1.35
The cost of each drink is $1.35.
__
Additional comment
Using the simplified 2nd equation, we can find the cost of a sandwich.
s = 6.90 -2d = 6.90 -2.70 = 4.20
The cost of each sandwich is $4.20.
A cylinder with a base diameter of x units has a volume of excubic units.
Which statements about the cylinder are true,Select
two options.
1)The radius of the cylinder is 2x units.
2)The area of the cylinder's base is 1/4 piex^2square units.
3)The area of the cylinder's base is 1/2 piex^2 square units.
4)The height of the cylinder is 2x units.
5)The height of the cylinder is 4x units.
Answer:3 and 4
Step-by-step explanation:
[tex]2i+3x=4-ix[/tex]
Show work.
No wrong answers or you will be reported. I will mark Brainliest! Thank you!
Answer:
Step-by-step explanation:
I am assuming i is the imaginary number:
Factor:
(3 + i)x - (4-2i) = 0.
In order for this to equal 0, x must be equal to 1-i.
I don't want to be reported to so take my word for it.
Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.
Using BTS he properties, find the unit's digit of the cube of each of the following numbers
If a ∥ b and b ⊥ y, then _____
Answer:
a ⊥ y
Step-by-step explanation:
since b is parallel to a & perpendicular to y , line y will eventually cut across line a at a 90 degree angle as well
Answer:
a ⊥ y
Step-by-step explanation:
Look at the image given below.
Trisha bought a carton of orange juice. She drank 1/3 of the carton on Monday and 5/12 of the carton on Tuesday. What fraction of the carton did Trisha drink?
Answer:
9/12 or 2/3
Step-by-step explanation:
Make both fractions have the same denominator by finding their least common multiple
1x12 = 12 1x3 = 3
2x6 = 12 3x1 = 3
3x4 = 12
4x3 = 12
6x2 = 12
12x1 = 12
In which case it would be 12.
1/3 would be 4/12
5/12 + 4/12 = 9/12
which is also 2/3 if your teacher wants the simplest answer
Help plz last question
Answer:
224π in^2
Step-by-step explanation:
Just plug in the values,
Surface area=2πr(h+r) [Factoring]
r=7in
h=9in
2πr(h+r)=2π*7(9+7)=14π(16)=224π in^2
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).
Answer:
Point-slope form: y-4=2(x+1)
Slope intercept form: y=2x+6
I hope this helps!
Answer:
[tex]y-4=2(x+1)[/tex]
Step-by-step explanation:
Point-slope form is equal to
[tex]y-y_1=m(x-x_1)[/tex]
where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:
[tex]4-2=m(-1-(-2))[/tex]
We can simplify negative one minus negative two as positive 1.
[tex]4-2=m(1)[/tex]
4 minus 2 is 2, so m times 1 is 2. That means m is 2.
Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:
[tex]y-4=2(x+1)[/tex]
For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. A circle with a radius 7 cm long is centered at Angle A's vertex, and Angle A subtends an arc length of 9.8 cm along this circle. The subtended arc is how many times as long as the circle's radius
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Answer:
1.4
Step-by-step explanation:
We want to find the multiplier n such that ...
arc length = n × radius
n = arc length / radius = (9.8 cm)/(7 cm)
n = 1.4
The subtended arc is 1.4 times as long as the circle's radius.
There are10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, howmany different slates of candidates are possible
Answer:
The answer is "720"
Step-by-step explanation:
The amount of different slates candidates:
[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]
[tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
PLEASE gelp me with this, gelp me please oh please gelp me!
Answer:
V = 2143.57 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
The diameter is 16 so the radius is 1/2 of the diameter or 8
V = 4/3 ( 3.14) (8)^3
V =2143.57333
Rounding to the nearest hundredth
V = 2143.57 cm^3
Answer:
2143.57 cm^3
Step-by-step explanation:
V = 4/3 * 3.14 * r^3
r = 1/2 * 16 = 8
So V = 4/3 * 3.14 * 8^3
= 2143.57 cm^3.
Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2). It’s dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of the resulting quadrilateral A’B’C’D
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Answer:
A'(-2, -4)B'(-2, 6)C'(8, 6)D'(8, -4)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
A' = 2A = 2(-1, -2) = (-2, -4)
B' = 2B = 2(-1, 3) = (-2, 6)
C' = 2C = 2(4, 3) = (8, 6)
D' = 2D = 2(4, -2) = (8, -4)
what is the equationof the line that passes through (0,3) and (7,0)
OLVE
(a) 3^2x+1=9^
2x-1
Answer:
x=2
Step-by-step explanation:
you first have to make the bases the same
3^2x+1=9^2x-1
3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9
3^2x+1=3^4x-2
2x+1=4x-2
2x-4x=-2-1
-2x/-2=-4/-2
x=2
I hope this helps
In the diagram below, circle O has a radius of 10. If the measure of arc AB is 72°, find the area of shaded sector AOB, in terms of π. Show all your work that leads to the final answer.
Answer:
62.8
Step-by-step explanation:
Area of sector=(pi*r^2)*(theta/360)
Area of sector=(pi*100)*(72/360)=62.8
The area of the shaded sector AOB in terms of π is 20π units squared.
How to find area of a sector?
The area of a sector can be described as follows;
area of sector = ∅ / 360 × πr²
where
r = radius of the circleTherefore,
r = 10 units
∅ = 72°
Hence,
area of the sector = 72° / 360° × π10²
area of the sector = 7200 / 360 π
area of the sector = 20π units²
learn more on sector here: https://brainly.com/question/24351015
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please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
A lottery ticket has a grand prize of $30.1 million. The probity of winning the grand prize is .000000038
Deteman the expected value of the lottery ticket
Answer:
$30.1 million * .000000038
$1.14
did the question say how much the ticket cost?
if it was $1 then you would have to subtract $1 so the expected value would be 14 cents
Step-by-step explanation:
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
Find the missing segment in the image below
Answer:
x = 42
Step-by-step explanation:
24+8 = 32
[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]
32x = 24(x+14)
32x = 24x+336
8x = 336
x = 42
what are the factor of pair of number?
a.45 and 60
b.45 and 70
c.40 and 80
d.30 and 50
The measurements of a circular object are given in the ratio table.
a. Find the missing dimensions of other circular objects by completing the ratio table.
b. Graph the pairs of values.
Answer:
answer hajandtb Tj.yfs5bsyb
