Answer:
[tex]c = \frac{1}{12}[/tex]
The mean of the distribution is 0.25.
The variance of the distribution is of 0.6875.
Step-by-step explanation:
Probability density function:
For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:
[tex]3c + 3c + 6c = 1[/tex]
[tex]12c = 1[/tex]
[tex]c = \frac{1}{12}[/tex]
So the probability distribution is:
[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]
Mean:
Sum of each outcome multiplied by its probability. So
[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]
The mean of the distribution is 0.25.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probability. So
[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]
The variance of the distribution is of 0.6875.
Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the (population) standard deviation of the data
Answer:
[tex]\sigma = 121.53[/tex]
Step-by-step explanation:
Required
The population standard deviation
First, calculate the population mean
[tex]\mu = \frac{\sum x}{n}[/tex]
This gives:
[tex]\mu = \frac{148+ 329+ 491 +167+ 228+285+ 441}{7}[/tex]
[tex]\mu = \frac{2089}{7}[/tex]
[tex]\mu = 298.43[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(148 - 298.43)^2 + ..........+ (441- 298.43)^2}{7}}[/tex]
[tex]\sigma = \sqrt{\frac{103387.7143}{7}}[/tex]
[tex]\sigma = \sqrt{14769.6734714}[/tex]
[tex]\sigma = 121.53[/tex]
Help me with moth of these questions please
Answer:
10. CD + DE = CE
11. BC + CE = BE
Step-by-step explanation:
10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.
11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.
You bought a car that was $25500 and the value depreciates by 4.5% each year.
How much will the car be worth after 5 years?
How much after 8 years?
Answer:
(a) 20256.15625
(b) 17642.78546
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
So, in 5 years the car will be worth, 25500(1-4.5%)^5 or 20256.15625 dollars
(b) And after 8 years the car will be worth 25500(1-4.5%)^8 or 17642.78546 dollars.
The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits.
Answer:
79.5, 110.5, 141.5, 172.5, 203.5, 234.5
Step-by-step explanation:
Given
The attached distribution
Required
The lower class limits
To do this, we simply subtract 0.5 from the lower interval
From the attached distribution, the lower intervals are:
80.0, 111.0, 142.0, 173,0 .......
So, the lower class limits are:
[tex]80.0-0.5 = 79.5[/tex]
[tex]111.0-0.5 = 110.5[/tex]
[tex]142.0-0.5 = 141.5[/tex]
[tex]173.0-0.5 = 172.5[/tex]
[tex]204.0-0.5 = 203.5[/tex]
[tex]235.0-0.5 = 234.5[/tex]
The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is
Answer:
-1
Step-by-step explanation:
1-2=-1
y=mx+b
b= y intercept
Answer:
-1
Step-by-step explanation:
Can someone do eight nine one and two ?
Answer: hello there here are your answers:
8) B multiplication property of zero
9) C additive identify
1) 8
2) -2a-7
Step-by-step explanation:
1) [tex]\frac{3+u}8^{2} \\u=5 \\so\\ \frac{3+5}8^{2} \\3+5=8^{2} \\8^{2} =\\64 \\\\ 64/8=\\\\\\8 \\there.\\\\\\[/tex]
2)[tex]-2(a-7)\\\\-2(a)(-7)\\\\=-2a+14\\\\\\there[/tex]
Three more than twice a number is 35.
Answer:
x = 16, or if you didn't want the value for x,
2x + 3 = 35
Step-by-step explanation:
Three more: +3
Twice a number: 2x
Combined:
2x + 3 = 35.
Get rid of the 3 by subtracting it from both sides:
2x = 32
Get rid of the 2 by dividing it from both sides:
x = 16
Answer:
The number is 16.
Step-by-step explanation:
Let the unknown number be x.
Now we translate the sentence into an equation piece by piece.
Three more than twice a number is 35.
2x
Three more than twice a number is 35.
2x + 3
Three more than twice a number is 35.
2x + 3 = 35
Now we solve the equation.
Subtract 3 from both sides.
2x = 32
Divide both sides by 2.
x = 16
Answer: The number is 16.
P.S. Notice that x was a variable that was introduced solely to solve the problem. The original problem is a word problem, not an equation, and has no x in it. The correct answer makes no reference to x since x was used to solve the equation but is not part of the given problem. The person asking the question has no idea what x is. He just wants a number as an answer.
For any real number √a²
a
- |al
lal.
-a
Answer:
|a|
Step-by-step explanation:
For any positive or negative a, when you square it, the answer is positive.
The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.
Answer: |a|
The total mass of 8 identical dictionaries is 9.92 kilograms. What is the mass, in kilograms, of one dictionary? Enter your answer in the space provided
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
To learn more on Division click:
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Answer pls:) I would really appreciate it
Answer:
1. C
2. B
3 A
4. A
Step-by-step explanation:
#1
Brady starts off with 12 coins
And buys 6 more coins every year
So add 6 to find number of coins he will have the next year until we've done it five times ( because we want to find how many he will have after 5 years )
12 ( 1st year )
Add 6
12 + 6 = 18 ( 2nd year )
Add 6
18 + 6 = 24 ( 3rd year )
Add 6
24 + 6 = 30 ( 4th year )
Add 6
30 + 6 = 36 ( 5th year )
By the fifth year he will have 36 coins and the sequence would be
12, 18, 24, 30, 36
Which corresponds with answer choice C
2
15, 19, 23, 27, ?
We want to find the next term
To do so we must find the common difference
We can do this by subtracting the last given term by the term before it
27 - 23 = 4
Just to clarify we can do the terms before those
19 - 15 = 4
So the common difference is 4
Now to find the next term we simply add 4 to the last given term
27 + 4 = 31
The next term would be 31
3. Cumulative property of addition states that you can add any 3 numbers in a different order and they will be the same
a + b + 2 = 2 + a + b
Same variables and numbers just different order
Therefore this is an example of cumulative property of addition
4. The GCF ( greatest common factor ) is the greatest number that the two numbers can be divided by
18a and 24ab
Factors of 18
2 , 9 , 6, 3 , 1 and 18
Factors of 24
24, 1, 2, 12, 6, 4, 3 and 8
The greatest factor that both 18 and 24 have is 6
The GCF would be 6a ( not 6 ) because both numbers share a common variable (a) ( 18a , 24ab )
suppose y varies inversely with X, and y = 48 when x = 3. What is the value of x when y = 24?
NO LINKS OR ANSWERING YOU DON'T KNOW.
a. 3
b. 12
c. 6
d. 24
Answer:
C. 6
Step-by-step explanation:
Recall that inverse variation is given by:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We know that y = 48 when x = 3. Substitute:
[tex]\displaystyle (48)=\frac{k}{(3)}[/tex]
Solve for k:
[tex]k=3(48)=144[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{144}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{144}{x}[/tex]
Cross-multiply:
[tex]24x=144[/tex]
Divide both sides by 24. Hence:
[tex]x=6[/tex]
Our answer is C.
The time that it takes to fold 1,000 origami cranes varies inversely with the number of people folding the cranes. If a class of 25 students work together to fold the 1,000 cranes, it will take 3 hours. Write an equation to show the relationship between time (t) and the number of people (n) folding cranes.
ASAP!!!!
Answer:
t = [tex]\frac{75}{n}[/tex]
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Replace y with t, and replace x with n, since those are the variables in this situation:
t = [tex]\frac{k}{n}[/tex]
Plug in 3 as t and 25 as n, and solve for k:
3 = [tex]\frac{k}{25}[/tex]
75 = k
Create the equation by plugging in 75 as k:
t = [tex]\frac{75}{n}[/tex]
So, the equation is t = [tex]\frac{75}{n}[/tex]
Find the area of the following figure with the indicated dimensions.use pi.
Answer:
The answer is "47.5354".
Step-by-step explanation:
In the given graph it is a half-circle and a triangle.
So, the diameter of the circle is 6.2 so the radius is 3.1
[tex]\text{Area of a circle}= \pi r^2\\\\\text{Area of a triangle}= \frac{1}{2} b h\\\\[/tex]
Calculating the total area of the shape:
[tex]= \pi r^2+\frac{1}{2} \times b\times h\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\= 30.1754+17.36\\\\=47.5354\\\\[/tex]
If P = (2,-1), find the image
of P under the following rotation.
270° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.
9514 1404 393
Answer:
P'(-1, -2)
Step-by-step explanation:
The transformation for 270° CCW rotation is ...
(x, y) ⇒ (y, -x)
Then the image of the given point is ...
P(2, -1) ⇒ P'(-1, -2)
Cai wants to buy cherries and apples to make a fruit tart. Cherries cost $3.75 per
pound and apples cost $2.25 per pound. How much does he spend if he buys 2
pounds of cherries and 1.5 pounds of apples? How much does he spend if he buys x
pounds of cherries and y pounds of apples?
The mean age of 5 people in a room is 27 years.
A person enters the room.
The mean age is now 35.
What is the age of the person who entered the room?
Answer:
main age = total age/total people
if Main age is = 27
[tex]27 = \frac{ \times }{5} [/tex]
and x = 135
Total age is = 135
then main age is 35
[tex][35 = \frac{y}{6} [/tex]
and y = 210
first main age - second main age = age of the person participating
210 - 135 = 75
the age is = 75HAVE A NİCE DAY
Step-by-step explanation:
GREETINGS FROM TURKEY
How to solve this problem what do I do
=================================================
Explanation:
We undo the "minus 6" by adding 6 to both sides.
Also, we undo the "+s" by subtracting s from both sides
-----------
So we have these steps
P = r+s-6
P+6 = r+s-6+6 .... adding 6 to both sides
P+6 = r+s
r+s = P+6
r+s-s = P+6-s ..... subtracting s from both sides
r = P + 6 - s
Answer:
P+6-s=r
Step-by-step explanation:
Hi there!
We are given the equation P=r+s-6 and we need to solve for r
To do that, we need to isolate r onto one side, and have everything else on the other.
Here is the equation:
P=r+s-6
start by adding 6 to both sides to clear it from the right side
P+6=r+s
now subtract s from both sides to clear it from the right side
P+6-s=r
now everything that isn't r is on the left side, and r is by itself on the right side. P+6-s=r is the answer.
Hope this helps!
Plz help. I’m finding surface area. I need the answer in units. Thank you.
Answer:
C. 17 units
Step-by-step explanation:
Surface area of rectangular prism is given as:
A = 2lw + 2lh + 2wh
A = 930 square units
l = 12 units
h = 9 units
w = ? (We're to find the width)
Plug in the value into the formula
930 = 2*12*w + 2*12*9 + 2*w*9
930 = 24w + 216 + 18w
Add like terms
930 - 216 = 42w
714 = 42w
Divide both sides by 42
714/42 = 42w/42
17 = w
w = 17 units
5/6 ÷ 1/3 - 2/3 (2/5)
Answer:
[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]
Step-by-step explanation:
5/6 ÷ 1/3 - 2/3 (2/5)
= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30Hope it helps you! ＼(^ᴥ^)／
PLEASE HELP ASAP! So the answer I got for this problem is 50.26. Can someone make sure that is the correct answer? Please let me know how to solve this problem if it is wrong.
Answer:
Step-by-step explanation:
every thing looks good, except the question says "round" and soooooo, if you are rounding to the 2nd decimal place, then the next two decimal places are 54, or 50.2654 so, to round that, round up , so your final answer would look like 50.27 :) see?
9514 1404 393
Answer:
50.24 inches (or 50.2 inches)
Step-by-step explanation:
The formula for circumference in terms of radius is ...
C = 2πr
Using the given values for radius and for pi, the circumference is ...
C = 2(3.14)(8 in) = 50.24 in
__
Additional comment
If you use a more accurate value of pi, the rounded value is 50.27 in. That is not the value requested by this problem. It helps to follow directions.
If you like, you can round to 50.2, since only one decimal place is required in the result.
(x-5)(X+12)=-70
[tex](x - 5)(x + 12) = - 70[/tex]
Answer:
[tex]x = - 2[/tex]
[tex]x = - 5[/tex]
Step-by-step explanation:
Give
[tex](x - 5)(x + 12)[/tex]
Apply FOIL Method
[tex]x {}^{2} + 7x - 60 = - 70[/tex]
Add 70 on both sides
[tex] {x}^{2} + 7x + 10[/tex]
Factor
[tex](x + 2)(x + 5)[/tex]
So our roots are
x=-2
x=-5
Answer:
dtet
Step-by-step explanation:
dgbyn
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta.
A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.
In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Step-by-step explanation:
how many layers of bricks are used ?
also, I assume, the thickness of bricks means actually their height when laid.
but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...
From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)
Answer:
the answer is 32.8in.
Step-by-step explanation:
(sin 22)/42 = (sin 24)/x
x = 45.60
sin 46 = x/45.60
x = 32.80
32.8in.
hope it helped :)
mark me brainliest!
Given that m∠abc=70° and m∠bcd=110°. Is it possible (consider all cases): Line AB intersects line CD?
The line AB and CD are parallel. Then it is impossible that the line AB intersects the line CD.
What are parallel lines?When the distance between the lines is constant, then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.
Given that ∠ABC = 70° and ∠BCD = 110°.
Then the line AB and the line CD makes the same angle with the line BC.
Hence, the line AB and CD are parallel.
Then it is impossible that the line AB intersects the line CD.
More about the parallel lines link is given below.
https://brainly.com/question/16701300
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If someone can pls give me the answer the would be greatly appreciated :)
Step-by-step explanation:
The Answer Is Provided Below ➳
(2²)² = 2⁴/2⁴ = 2⁰ × 2⁰ = 2⁰/2⁰
when 5 is added to 2 times a number , the results is 45. find the number
Answer:i think its 20
Step-by-step explanation: 20 x 2 is 40 plus 5 is 45
Answer:
✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20
Step-by-step explanation: Algebra.com
What is the general form of the equation for the given circle centered at [0, 0)?
Answer:
x^2+y^2=r^2 is quation of circle whose centre is (0,0)
Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
