A gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed
Answer:
C=78.5
Step-by-step explanation:
C=πr²
r=1/2 of diameter
π=3.14
C=π5²
C=78.5
The circumference and the area of the circular flower bed are 31.4 feet and 78.5 square feet respectively.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A gardener makes a new circular flower bed. The bed is ten feet in diameter.
D = 10 feet
The radius r = D/2 = 10/2 = 5 feet
A = πr²
π = 3.14
A = π(5)²
A = 78.5 square feet
The circumference:
C = 2πr
C = 2(3.14)(5)
C = 31.4 feet
Thus, the circumference and the area of the circular flower bed are 31.4 feet and 78.5 square feet respectively.
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A continuous random variable X has probability density function X. Show how its
moment generating function can be used to determine the variance of this random
variable.
The moment generating function is defined by
[tex]M_X(t) = \mathbb E[e^{tX}][/tex]
Recall the power series expansion for the exponential function:
[tex]\displaystyle \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}2 + \frac{x^3}6 + \cdots[/tex]
Then by extension, the MGF could be similarly written as
[tex]\displaystyle M_X(t) = \mathbb E \left[1 + Xt + \frac{(Xt)^2}2 + \frac{(Xt)^3}6 + \cdots\right][/tex]
There's a certain theorem (due to Fubini, in case you're interested in learning more about it) that let's us exchange the order of integration (recall the definition of expectation for continuous random variables) and summation, so that
[tex]\displaystyle M_X(t) = \mathbb E[1] + \mathbb E[Xt] + \mathbb E\left[\frac{X^2t^2}2\right] + \mathbb E\left[\frac{X^3t^3}6\right] + \cdots[/tex]
and by the linearity of expectation,
[tex]\displaystyle M_X(t) = 1 + \mathbb E[X] t + \frac12 \mathbb E\left[X^2\right] t^2 + \frac16 \mathbb E\left[X^3\right] t^3 + \cdots[/tex]
and here we see where the name MGF comes from: the coefficient of the n-th order term in the series expansion "generates" the n-th moment, which is defined as E[Xⁿ].
Now, recall the definition of variance:
[tex]\mathrm{Var}(X) = \mathbb E\left[\left(X - \mathbb E[X]\right)^2\right][/tex]
[tex]\mathrm{Var}(X) = \mathbb E\left[X^2\right] - \mathbb E[X]^2[/tex]
and this is exactly the difference between the second moment and the square of the first moment.
So if you know the MGF, then you essentially get the variance for free with little effort. By differentiating the MGF, we get
[tex]\displaystyle M_X''(t) = \mathbb E[X] + \mathbb E\left[X^2\right] t + \frac12 \mathbb E\left[X^3\right] t^2 + \cdots[/tex]
and setting t = 0 lets us recover the first moment, E[X].
Differentiating again gives
[tex]\displaystyle M_X'(t) = \mathbb E\left[X^2\right] + \mathbb E\left[X^3\right] t + \cdots[/tex]
and setting t = 0 once again recovers the second moment.
Then in terms of the MGF, we have
[tex]\boxed{\mathrm{Var}(X) = M_X''(0) - M_X'(0)^2}[/tex]
HELPLPLPLPLPPkkkki need help
Answer:
2 is the variable
Step-by-step explanation:
8(2) = 16
16-27 = -11
Need help I got 23,294 as the answer but it’s not an option please explain how you got the answer.
Answer:
A
Step-by-step explanation:
Calculation seems correct to me, with d the distance and h the height of the plane, and i got the same value. Closest value is A tho, so i'd stick with it.
If you want to be pedantic about it, you can always divide the heigth by each value, and get the inverse tangent of each value. With A you get 17.995 which seems the best value you get
If you spent 24 weeks working on a project for your job and are rewarded with 3 days of vacation write the ratio of time on vacation to time working as a fraction in lowest terms
10x-6x-4-1=7-12+2x+2x
Any value of
x
makes the equation true.
Always true
Interval Notation:
(−∞,∞)
A company makes a profit of $y (in thousand dollars) when it produces x computers,
where y is given by the formula y = a(x - 100)(x - 200) for x 20 If 120
computers are produced, the profit will be $3,200,000.
a) Find the value of a.
b) What is the maximum profit the company can make? At this profit, how many
computers should be produced?
c) If the company targets to make at least $4,800,000, what is the range of the
number of computers to be produced?
The solutions to the questions if y is represented by the formula y = a(x - 100)(x - 200) are:
a) The value of a = -2000
b) The maximum profit the company can make = $5,000,000
To make maximum profit, 150 computers must be produced
c) The company must produce between 140 and 160 computers to make at least $4,800,000
The equation representing the company's profit is:
y = a(x - 100)(x - 200) for x > 20
If 120 computers are produced, the profit will be $3,200,000
That is, y = 3,200,000 if x = 120
a) Find the value of a
3,200,000 = a(120 - 100)(120 - 200)
3200000 = -16000a
a = -3200000/1600
a = -2000
b) Maximum profit the company can make
The equation becomes:
y = -2000(x - 100)(x - 200)
y = -2000(x² - 200x - 100x + 20000)
y = -2000(x² - 300x + 20000)
y = -2000x² + 600000x - 40000000
dy/dx = -4000x + 600000
dy/dx = 0 at maximum value
-4000x + 600000 = 0
4000x = 600000
x = 600000/4000
x = 150
To make maximum profit, 150 computers must be produced
Substitute x = 150 into y = -2000x² + 600000x - 40000000 to find the maximum profit
y = -2000(150²) + 600000(150) - 40000000
y = 5000000
The maximum profit the company can make = $5,000,000
c) Calculate the range of the number of computers to be produced If the company targets to make at least $4,800,000
-2000x² + 600000x - 40000000 ≥ 4800000
-2000x² + 600000x - 40000000 - 4800000 ≥ 0
-2000x² + 600000x - 44800000 ≥ 0
Divide through by -2000
x² - 300x +22400 ≤ 0
(x - 140)(x - 160) ≤ 0
140 ≤ x ≤ 160
The company must produce between 140 and 160 computers to make at least $4,800,000
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Mr. Janak ordered packages of hamburger buns, cheese slices, and patties for 3 cafes. He listed
the number of packages needed per store in matrix Mand the cost per package in matriz N.
H. C. P. Cost
Cafe 1 [15 10 12]. H. [2.50]
M=cafe2 [20. 13. 15]. N=c[4.25]
Cafe 3. [18. 14. 14]. P [3.15]
What does the stuff down below mean?
Which of the following could be the number shown on the number line?
A. V66
B. V60
C. V63
D. V65
Answer:
A
Step-by-step explanation:
v666
describe using their angles please
Answer:
equilateral triangle is a triangle in which all 3 sides have the same length
Mr. Solomon, the art teacher, has 49.6 pounds of clay. If he gives every student 1.6 pounds of clay and has none left, how many students are in his class?
Answer:
He has 31 students
Step-by-step explanation:
You know this because 49.6 ÷ 1.6 = 31
The difference of a number and six is negative four
Answer:
(2) is the possible missing number substitute for (n)Step-by-step explanation:
Let the number word be (n)And number 6 remain (6)The possible answer will be (-4)Here we go: n-6=(-4)Try to add six and negative four: 6+-4=2Therefore u got two 2+-6=-4
If the map distance is 20 cm and the scale is 4 cm = 60 km, what is the actual distance?
Answer:
300
Step-by-step explanation:
1. 60/4=15
2. 15x20=300
Write a function that has the following characteristics:
-Exponential decay
-Asymptote is y = -2
-Shifted left 3 units from the parent function
9514 1404 393
Answer:
y = 0.4^(x+3) -2
Step-by-step explanation:
I have chosen the decay function y=0.4^x as the parent function.
Shifting any function f(x) left 3 and down 2 will transform it to ...
y = f(x+3) -2
So, the shifted parent function is ...
y = 0.4^(x+3) -2
I NEED THIS ANSWERED ASAP
Answer:
X = 3
Bc = 6
AC = 12
Step-by-step explanation:
Hope it helped
Find the value of y for the given value of I.
y=x/2 + 9;x = -12
9514 1404 393
Answer:
y = 3
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
[tex]y=\dfrac{x}{2}+9\\\\y=\dfrac{-12}{2}+9=-6+9\\\\\boxed{y=3}[/tex]
If the Mac and cheese is 7.50 for 3 lbs how much can you get for 29 dollars?
Answer:
6lbs
Step-by-step explanation:
7.50 can only go into 20, two times
7.50
× 2
-------
15.00
Find atleast four equivalent fractions for each fraction 8/18
16/36, 24/54, 32/72 and 40/90.
these are the equivalent fractions of 8/18
PLEASE MARK MY ANSWER AS BRAINLIEST
Answer:
16/36, 4/9, 24/54, 32/72
PLEASE HELP WILL GIVE 40 POINTS
Amy is planning the seating arrangement for her wedding reception. Each round table can sit 8 guests. The head table can sit the bride and groom with the 6 wedding attendants. If Amy expects 158 to 174 guests to attend her wedding, including the attendants, what is the range for the number of round tables she will need for her reception?
A. 20 to 22
B. 25 to 27
C. 19 to 21
D. 21 to 23
Answer:
19 to 21
Step-by-step explanation:
Head table is for 6 attendants
158 to 174 - 6 attendants
152 to 168 people for round tables
each round table can sit 8 guests
so, 152/8 168/8
19 to 21
Answer:
D. 21 to 23
Step-by-step explanation:
1. First, you use the biggest number of guests just to be safe. Since there will be about 174 guests attending
2. you divide 174 by the number of seats a round table can hold. Since the number is 8, you 174/8 which is 21.75.
3. You round up to the biggest number of tables that has the number 21 in it.
4. Your answer is D. 21 to 23
Solve all of them please u get 30 points
Step-by-step explanation:
from which text book please
What is the equation of the line in slope-intercept form?
6
5
4
3
2
1
-5 -4
1
2
3
4
43 -2 -1
-1
-2
-3
-4
Enter your answer in the boxes.
y = IX +
Answer:
y = 4/3x + 4
Step-by-step explanation:
The y intercept is 4. So if we look the 2 points are (-3,0) and (0,4)
So the run is 3 and rise 4
so 4/3 is the slope
3. A train set costs $120.00. Find the discount if it is on sale for
30% off.
Answer:
36
Step-by-step explanation:
To find the discount, you will need to find 30% of $120, so you will need to do:
120*0.3=36
Also, if you were asking for the COST if it was 30% off, it would be 84 as 120-36=84.
(I hope this helps!)
READ No link or bot and answer the question 15 points I give Brainliest to the best answer
Answer:
1. 46
2. 307.3
3. 40
4. 0
5. 4
6. 0
7.
8. 400
9. -1000
10. 10582
expand: Evaluate:
11. -216 21. 0.015625
12. 81 22. -216
13. 0.03125 23. 2¹.⁹²
14. -81 24. 729
15. 25. 64
16. 343
simplify.
17. 68526
18. 262144
19. 5.960464 x 10¹⁶
20. 0.003906
Step-by-step explanation:
sana maka tulong to sayo
A tin contains 425g baked beans in sauce. The tin itself weighs 60g. How much will a pack of 6 tins weigh in kilograms
Answer:
2.91 Kg
Step-by-step explanation:
Tin weighs 60g, it contains 425g of baked beans, add that together to get a full tin of baked beans
= 485.
Multiply by 6 to get the total amount in grams
= 2910g.
Turn that into Kg.
2.91 kg.
The weight of 6 tins will be 2.19 Kg,
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Tin weighs 60g, it contains 425g of baked beans,
So, the total weight along with tin
= 425 + 60
= 485 g
Now, the weight of 6 tins
= 485 x 6
= 2190 g
= 2190/1000 Kg
= 2.19 Kg
Hence, the weight is 2.19 Kg.
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3. Round the numbers to the nearest given place
value
a. Round 63 to the nearest ten.
b. Round 56 to the nearest hundred.
Cound 56 to the nearest ten.
Answer:
a) 60
Step-by-step explanation:
sorry I know only of one
. The sum of infinity of G.S is 15, 1st term is 3 then the common ratio is.
Step-by-step explanation:
We know ,
=> Sum = a / 1 - r
=> 15 = 3/1-r
=> 15 - 15r = 3
=> 15r = 18
=> r = 18/15
=> r = 6/5
Round 1.04to the tenths place.
Dear, the answer is 1.0
Hope this helps~ ^^
Please answer the question in the picture
Answer:
2x² + 2x - 24
Step-by-step explanation:
We can use the FOIL method to multiply the terms together and then find the values in our trinomial. First, the F in FOIL. It stands for first, and we need to multiply the first terms in the two expressions. These terms are 2x and x. Multiplying 2x by x gives us 2x², so that's our first term.
Next, the O in FOIL. It stands for outside, and we need to multiply the terms on the very left and the very right. These are 2x and -3, and multiplying 2x by -3 gives us -6x. That's our second term.
Now, the I in FOIL. It stands for inside, so we need to multiply the terms in the middle of the expressions. Those are 8 and x, and we multiply those together to get 8x. That's our third term.
Finally, the L in FOIL. This stands for last; we need to multiply the last terms of each expression. Those are 8 and -3, and we can multiply those to get -24. Now we can get all our terms added together and simplify as needed.
2x² - 6x + 8x - 24
We can simplify -6x and 8x since they are like terms.
2x² + 2x - 24
And there is our trinomial. Hopefully that's helpful! :)
A file that is 249 megabytes is being downloaded. If the download is 15.7% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth ?
Answer:
39.1 megabytes
Step-by-step explanation:
Percentages are out of a hundred, so 15.7% is 15.7 out of 100, aka 15.7/100, which is 0.157.
Now, you just need to multiple this number by 249 megabytes to get 0.157 * 249 = 39.093 which rounds to 39.1
Which is a property of an angle?
A-has two sides that each extend forever in both directions
B-has two endpoints
C-has two center points
D-has two rays that share a common endpoint
