The variance of a discrete random variable calculation involves working out (x-µ)^2 * p(x) for each x value and summing them up. Using given data and mean as 20.59, variance ≈ 27.89 (options a and b).
Explanation:To calculate the variance of a discrete random variable, we use the formula: Variance = Σ[(x-µ)^2 * p(x)] where 'x' is each value of the variable, 'µ' is the mean and 'p(x)' is the probability of 'x'
Given that the mean µ is 20.59 we perform the calculation, (x-µ)^2 * p(x) for each value of 'x' and sum them all up:
(13-20.59)^2 * .07 = 14.08(16-20.59)^2 * .21 = 4.38Continuing this process for all given values of 'x' and summing them up, we find that the variance ≈ 27.89.So, the correct answer is 27.89, which corresponds to option a and b.
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Han has 410,000 in a retirement accounts that earns 15,785 each year find the simple interest rate for this investment
The simple interest rate on this investment is.0385 or 3.85%:
What is Simple Interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Given:
Han has 410,000 in a retirement accounts that earns 15,785 each year.
Using Simple Interest
Interest = principle x rate x time / 100
Rate = Interest / ( principle x time )
Rate = 15785/(410,000x1)
Rate = 0.0385
Rate= 3.85 %
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Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt. Which quadratic equation can be used to find s, the side length of the square quilt?
s^2 =(1/2s) (s + 6)
s^2 = (s)(s + 6)
s^2 =(1/2s) (6s)
s^2 = (s)(6s)
Answer:
Option 1 - [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Step-by-step explanation:
Given : Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.
To find : Which quadratic equation can be used to find s, the side length of the square quilt?
Solution :
The first quilt will be square,
Let the side of square be s
The area of the square is [tex]A=s\times s[/tex]
The second quilt will be a rectangle,
A width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.
Width of the rectangle = [tex]\frac{1}{2}s[/tex]
Length of the rectangle = s+6
Area of the rectangle is [tex]A=(\frac{1}{2}s) \times (s+6)[/tex]
According to question,
Area of square and rectangle are equal,
So, [tex]s\times s=(\frac{1}{2}s) \times (s+6)[/tex]
[tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Therefore, Option 1 is correct.
The required equation is [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
What is the quotient when 0.75 is divided by 5?
If there are 4 math courses, 3 psychology courses, and 5 english courses offered in non-overlapping times so that you could select one of each for your schedule, how many different schedules would be possible?
Answer:
there are many different answers that is because there are four different ways to answer this one question.
Step-by-step explanation:
4*3*5=60
4-+5+3=12
1) 435 2) 435 3) 435
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. –2y2 + 6y = –2
–0.61, 6.61
–0.3, 3.3
–3.3, 0.3
–11.5, 14.5
In a string of 100 christmas lights, there is
a.015 chance that a given bulb will fail within the first year of use (if one bulb fails, it does not affect the others). find the approximate probability that six or more bulbs will fail within the first year. (round your answer to 4 decimal places.) probability
The approximate probability that six or more bulbs will fail within the first year is approximately 0.1461, rounded to four decimal places.
To find the approximate probability that six or more bulbs will fail within the first year, we can use the binomial probability formula:
P(X ≥ k) = 1 - P(X < k)
where:
P(X ≥ k) is the probability of getting "k" or more successes (bulbs failing).
P(X < k) is the probability of getting less than "k" successes (bulbs failing).
In this case, "k" is 6 (six or more bulbs failing), and the probability of a bulb failing in the first year is 0.015.
Now, let's calculate the probability of getting less than six failures (k < 6):
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial probability formula:
P(X = k) = C(n, k) *[tex]p^k * (1 - p)^{n - k}[/tex]
where:
C(n, k) is the binomial coefficient (n choose k).
n is the number of trials (total bulbs, which is 100 in this case).
p is the probability of success (a bulb failing, which is 0.015).
k is the number of successes (bulbs failing).
Now, calculate P(X < 6):
P(X = 0) = C(100, 0) * 0.015⁰ * (1 - 0.015)^(100 - 0)
P(X = 1) = C(100, 1) * 0.015¹ * (1 - 0.015)^(100 - 1)
P(X = 2) = C(100, 2) * 0.015² * (1 - 0.015)^(100 - 2)
P(X = 3) = C(100, 3) * 0.015³ * (1 - 0.015)^(100 - 3)
P(X = 4) = C(100, 4) * 0.015⁴ * (1 - 0.015)^(100 - 4)
P(X = 5) = C(100, 5) * 0.015⁵ * (1 - 0.015)^(100 - 5)
After calculating each term, add them up:
P(X < 6) ≈ 0.8539
Now, find the probability of getting six or more failures:
P(X ≥ 6) = 1 - P(X < 6)
P(X ≥ 6) ≈ 1 - 0.8539 ≈ 0.1461
So, the approximate probability that six or more bulbs will fail within the first year is approximately 0.1461, rounded to four decimal places.
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ABC Bookstore sells new books according to the demand function P = -Q + 25, where P is the price and Q is the quantity. If the bookstore charges $18 for a new book, how many new books can the store expect to sell?
Answer:
P = -Q + 2518 = -Q + 2518-25 = -Q-7 = -Q-7/-1 = -Q/-1Q = 7
Therefore, the store can expect to sell 7 new books if they will charge $18 for the new books.
9.
Leola Hain purchases 220 shares of Circuit City stock at $42.75 per share.
Find the annual dividend if the dividend per share is $0.0625.
$43
$55
$9,460
$9,405
1. Assume you buy 100 shares of stock at a price of $63.75 per share and incur brokerage fees of $200. You own the stock for 5 years and receive dividends of 50 cents per share at the end of each quarter. Immediately after receiving the 20th quarterly dividend, you sell the stock at a price of $48.63 per share and incur brokerage fees of $200. Calculate your rate of return. (IRR)
2. You own a thriving restaurant but want to change careers. Your brother offers to buy the business with the following monthly payments: $2,750 at the end of each month for 4 years, followed by $3,000 at the end of each month for 3 years. Assuming that you can earn 9% compounded monthly, what is the equivalent cash price of your brother’s offer? (NPV)
A bag of rice weights 3.18 lbs find its mass in kilograms
The radius of a cone can be found using the formula r=3Vπh , where V stands for the volume of the cone and h stands for the height. If r=3 , h=8 , and π is 3.14, find the volume (V). Round the answer to the nearest hundredths place.
Using the formula for the radius of a cone and the given values of r = 3, h = 8, and [tex]\pi[/tex] = 3.14, the volume of the cone is calculated to be approximately 25.12 [tex]cm^3[/tex].
To find the volume V of a cone, we need to solve for V in the given formula [tex]\( r = \frac{3V}{\pi h} \). With \( r = 3 \),[/tex] h = 8, and [tex]\pi = 3.14[/tex], let's proceed as follows:
Rearrange the Formula
1. Given that [tex]\( r = \frac{3V}{\pi h} \)[/tex], isolate V to get:
[tex]\[ V = \frac{r \cdot \pi \cdot h}{3} \][/tex]
2. Using r=3, h=8, and [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[ V = \frac{3 \cdot 3.14 \cdot 8}{3} \][/tex]
3. Simplify and solve:
[tex]\[ V = 3.14 \cdot 8 \approx 25.12 \][/tex]
Rounding to the nearest hundredths place, the value for the volume V is approximately 25.12 cubic units.
Hey can you please help me posted picture of question
If a body moves in a straight line according to the law s = 24t + 3t2 - t3 , where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body's velocity as a function of time. A. V = 30t - t2 B. V = 24 + 6t - 3t2 C. V = 24 + 3t - t2 D. V = 30t - 3t2
what is the positive solution to the equation 0=⅓x²-3
The scale factor of the dilation of figure ABCD is
James bought $175 in accessories for his video game console. He spent $15 on a new power cord and the rest of his money on 5 new video games. Each video game cost the same amount. Write two equations you could use to find the cost of each video game.
The solution is, two equations are: (175-15)/5 and, 5x+15=175
the cost of each video game is 32.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here, we have,
two equations we can make to represent the question are...
(175-15)/5
and
5x+15=175
The first equation, (175-15)/5, makes you subtract 15 from 175 to get 160. You'll then divide 160 by 5 to get 32.
The second equation, 5x+15=175, makes you subtract 15 from 15 and 175, so you'll equation will look like this...
5x=160
You'll then divide 5x and 160 by 5 to get x=32.
So for both equations, we'll get an answer of 32.
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draw 8 lines that are between 1inch and 3 inches long
A survey was conducted at Springdale High to find the number of hours students sleep at night. The histogram shows the data collected in this survey. Which statement about the number of hours students sleep is true? Seventeen students sleep between 6 and 8 hours at night. Seventeen students sleep for 6 hours at night. Ten students sleep for 4 hours at night. Six students sleep between 2 and 4 hours at night. Four students sleep for 10 hours at night.
What is the value of x, if 105% of 90 is equal to 200% of x?
From the given equation
105% * 90 = 200% * x
105/100 * 90 = 200/100 * x
105*90 = 200*x
x = 105*90/200
X = 21*9/4
X = 189/4
x = 47.25
Value of x = 47.25 or 47 1/4
two cylindrical candles have a scale factor of 3:5. The larger candle has a volume of 40(3.14) cubic inches. Fund the volume of thel the smaller candle. Write your answer in term of (3.14)
The volume of the smaller candle is 8.64π cubic inches.
How to find the volume
The volume of a cylinder is given by the formula
V = π r² h,
where
r is the radius and
h is the height.
The scale factor is given as 3:5, which means the ratio of the volumes is (3³ : 5³)
Using the ratio, let volume of the the smaller candle. be x
3³ : 5³
x : 40π
cross multiply
x = 40π * 3³ / 5³
x = 40π * 27 / 125
x = 8.64π cubic inches.
circle the fraction in the set with the least value 4/3 5/5 4/4 1/2 1/1
a hiker walks 12 miles north. then she walks 9 miles west. What is the shortest distance the hiker can travel to return tonher starting point
In general, the y-intercept of the function F(x)=a•b^x is the point what????
which expression defines the given series for seven terms? -13 + (-16) + (-19) +...
Answer:
[tex]a_n =-3n-10[/tex]
Step-by-step explanation:
-13 + (-16) + (-19) +...
Difference between two terms = -3
-16 -(-13)= -3
-19 -(-16)= -3
Common difference is a constant so it is arithmatic
[tex]a_n = a_1+(n-1)d[/tex]
where 'd' is the difference = -3
a1 is the first term that is -13
[tex]a_n = -13+(n-1)(-3)[/tex]
[tex]a_n = -13-3n+3[/tex]
Combine like terms
[tex]a_n =-3n-10[/tex]
if you change the sign of a point’s x -coordinate from positive to negative, how will the location of the point change?
Answer:
The point will cross over the y-axis
Step-by-step explanation:
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Adair had 6 1/2 cups of tomato juice. He used 4/5 of the juice to make soup. How many cups of tomato juice did Adair use to make soup?
To find how many cups of tomato juice Adair used to make soup, we multiply the fraction representing the portion of tomato juice used (4/5) by the total amount of tomato juice Adair had (6 1/2 cups). The answer is 5 1/5 cups.
Explanation:To find how many cups of tomato juice Adair used to make soup, we need to multiply the fraction representing the portion of tomato juice used (4/5) by the total amount of tomato juice Adair had (6 1/2 cups). First, we can convert 6 1/2 cups to an improper fraction: 6 1/2 = 13/2 cups. Next, we multiply the fractions: 4/5 * 13/2 = 52/10 = 5 2/10 = 5 1/5 cups.
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Complete the equation of the line whose slope is − 2 and y-intercept is ( 0 , 3 )
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas? (Approximate to the nearest hundredth inch.)
10.62 inches
10.63 inches
10.64 inches
10.65 inches
Answer:
The approximate length of one side of the canvas is 10.63 inches
Step-by-step explanation:
Given :The area of an artist's square canvas can hold 113 square inches of paint.
To Find :What is the approximate length of one side of the canvas?
Solution:
Canvas is in the shape of square
Area of square = [tex]Side^2[/tex]
Let the side of the canvas be x
Area of canvas = [tex]x^2[/tex]
Since we are given that The area of an artist's square canvas can hold 113 square inches
So, [tex]113=x^2[/tex]
[tex]\sqrt{113}=x[/tex]
[tex]10.630=x[/tex]
So, the approximate length of one side of the canvas is 10.63 inches
Hence Option B is correct.
Get Brainliest if you answer What was Hammurabi's most important achievement as the ruler of Babylon? A. He built extensive canals, which carried water to many parts of his kingdom. B. He established permanent armies, which he used to control his empire. C. He appointed governors to rule over conquered cities. D. He was responsible for a codification of laws that influenced later societies.
Answer:
Its D
Step-by-step explanation:
I did the quiz
During the first stages of an epidemic, the number of sick people increases exponentially with time. Suppose that at = 0 days there are 2 people sick. By the time = 3, 40 people are sick. a) Let be the number of sick people at time . Find an exponential equation = expressing in terms of .
b) How many people will be sick by the time = 6?