The expected daily loss of the company due to blackouts, E(Y), can be calculated by multiplying each possible loss (which is the number of blackouts times 500) by the probability of that loss occurring, and summing these products. The variance, Var(Y), is found by first finding the expected value of the square of the loss, E(Y^2), which is done in a similar way to finding E(Y), but by squaring each loss before multiplying by its probability. The variance is then given by E(Y^2) - [E(Y)]^2, resulting in a variance of $110,000.
Explanation:The expectation (or mean) of a random variable Y can be computed by multiplying each outcome by its probability and summing all these products. The random variable Y here is the daily loss corresponding to x blackouts, which is given by 500*x, where x is the number of blackouts. Hence to find the expected daily loss, E(Y), you need to calculate:
E(Y) = 0*0.7 + 1*500*0.2 + 2*500*0.1 = $200
The variance of a random variable is found by taking the expected value of the squared variation of that variable from its mean. In this case, you'll calculate:
Var(Y) = E(Y^2) - [E(Y)]^2.
To find E(Y^2), you'll calculate:
E(Y^2) = 0*0.7 + (1*500)^2*0.2 + (2*500)^2*0.1
Substitute E(Y) and E(Y^2) into the variance formulas to get Var(Y) = 110,000.
So, the expectation and variance of the company's daily loss due to blackouts are $200 and $110,000 respectively.
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Which statement is true about the line segments below
What is the measure of angle 4?
Kris forwards an e-mail to 5 people. each of those people forward that e-mail to 5 more people. if this happens two more times, which expression shows the total number of people who have received the e-mail, not including Kris?
A) 4 x 5
B) 1+5+5^2
C)5+5^2+5^3
D) 5+5^2+5^3+5^4
The total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3.
Explanation:The expression that shows the total number of people who have received the e-mail, not including Kris, after it has been forwarded 2 more times is 5 + 5^2 + 5^3 (option C).
Kris forwards the e-mail to 5 people, so there are initially 5 recipients.Each of those 5 people forwards the e-mail to 5 more people, resulting in 5 x 5 = 25 additional recipients.After the second round of forwarding, each of the 25 people forwards the e-mail to 5 more people, resulting in 25 x 5 = 125 additional recipients.To find the total number of people who have received the e-mail, you sum up the number of recipients at each stage: 5 + 25 + 125 = 155. Therefore, the expression 5 + 5^2 + 5^3 represents the total number of people who have received the e-mail, not including Kris.
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what is the y-intercept of y=4x?
Find the area of the following figure. The base angles are right angles.
143 in.2
137.5 in.2
121 in.2
113 in.2
area of the bottom square = 11*9 =99 squre inches
for the triangular top the area = 1/2 x b x h
you have hypotenuse and height so need to calculate the base dimension
4^2 +x^2 = 7^2
16 +x^2 = 49
x^2 = 33 x = sqrt(33) = 5.7
area = 1/2 4*5.7 = 11.489
there are two similar triangles so 11.489*2 = 22.97
99+22.97 = 121.97
looks like they rounded the numbers slightly different
so 121 in2 is their answer
Answer:
121 in^2
Step-by-step explanation:
What is the result of converting 3560 meters into kilometers?
A mobile phone carrier charges an extra fee if a customer uses more than 500 minutes each month. Tom has already used 230 minutes this month. Which inequality can be used to determine how many more minutes Tom can use this month without going over the 500-minute limit?
Answer:
230+m_<500 the line is meant to be under the sighn btw
Step-by-step explanation:i got it right on edge 2021
To determine how many more minutes Tom can use without exceeding his limit, we use the inequality X ≤ 270, which indicates that Tom can use up to 270 additional minutes.
To determine how many more minutes Tom can use this month without exceeding a 500-minute limit, given that he has already used 230 minutes. To solve this, we let X represent the additional minutes Tom can use. Since he has already used 230 minutes, we form the inequality 230 + X ≤ 500 to ensure that the total does not surpass the 500-minute limit. Simplifying this inequality, we subtract 230 from both sides to get X ≤ 270. Therefore, Tom can use up to 270 more minutes without incurring extra charges.
Help me pleas win really stuck!!!
what is a1 of the arithmetic sequence for which a3=126 and a64=3,725
Answer: The required value of the first term is 8.
Step-by-step explanation: We are given to find the first term of the arithmetic sequence for which the third term is 126 and sixty fourth term is 3725.
We know that
the nth term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
According to the given information, we have
[tex]a_{3}=126\\\\\Rightarrow a+(3-1)d=126\\\\\Rightarrow a+2d=126~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]a_{64}=3725\\\\\Rightarrow a+(64-1)d=3725\\\\\Rightarrow a+63d=3725~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Subtracting equation (i) from equation (ii), we get
[tex](a+63d)-(a+2d)=3725-126\\\\\Rightarrow 61d=3599\\\\\Rightarrow d=59.[/tex]
From equation (i), we get
[tex]a+2\times59=126\\\\\Rightarrow a=126-118\\\\\Rightarrow a=8[/tex]
Thus, the required value of the first term is 8.
six more than five times a number X is at least 21
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. Which is the slant height of the pyramid if Helen uses all the clay? 3 inches 4 inches 5 inches 6 inches
Answer: 5 inches
Step-by-step explanation:
Given: Volume of clay = 48 cubic inches
If we make a solid square right pyramid with a base edge a= 6 inches.
Then its base area = [tex]a^2=6^2=36\ inches^2[/tex]
we know that volume of square right pyramid=[tex]\frac{1}{3}\times\ a^2h[/tex]
Therefore, volume of square right pyramid made by all of clay=[tex]\frac{1}{3}\times\ a^2h[/tex]=48 cubic inches
[tex]\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}[/tex]
Now, slant height [tex]l=\sqrt{(\frac{a}{2})^2+h^2}[/tex]
[tex]\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5[/tex]
The slant height of the pyramid if Helen uses all the clay=5 inches
Answer:
The correct answer would be 5 inches.
Step-by-step explanation:
write an expression with an exponent that has a value between 0 and 1
Okay, so first, we find a number that is between 0 and 1.
A number that qualifies for that condition would be ½.
A property of exponents is x^(n/m) = √x m sqrt(x^n), so x^(1/2) = √x
Therefore, such expression is:
x^(1/2) = 4
Where you now solve for x.
Exponential notation is a common language that is
needed in order to communicate mathematical ideas efficiently and clearly.
Efficiently written repeated multiplication was the reason that this notation was
developed.
An example of this is the division of cells that causes growth to occur in
living organisms. A single type of cell is divided 2 times in an hour,
therefore in 12 hours, the cell will divide into 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
• 2 • 2 • 2 • 2 time, or as efficiently written, 2^12.
Sam rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 75 cents for each mile driven. Sam had to pay $159.49 when he returned the truck. For how many miles did he drive the truck?
Final answer:
Sam drove 186 miles with the truck he rented. To calculate this, the total paid was subtracted by the base fee, and the result was then divided by the per-mile charge.
Explanation:
The student is asked to calculate the number of miles driven by Sam based on the total cost of truck rental and the additional charge per mile. We use a linear equation to represent the total cost (C) as the sum of the base fee (F) and the product of the number of miles (m) and the charge per mile (P).
The equation for this problem is:
C = F + (P × m)
We are given:
The total cost of rental (C) = $159.49
The base fee (F) = $19.99
The charge per mile (P) = $0.75/mile
Substituting the values we have into the equation gives us:
$159.49 = $19.99 + ($0.75 × m)
To find the number of miles (m), we need to isolate the variable m. We do this by subtracting the base fee from the total cost:
$159.49 - $19.99 = $0.75 × m
$139.50 = $0.75 × m
Now, divide both sides by the charge per mile to get:
m = $139.50 / $0.75
m = 186 miles
Therefore, Sam drove 186 miles.
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m – 1/2= 2 + 1/4m
Answer:
4.
Step-by-step explanation:
We are given that an equation
[tex]\frac{-3}{4}m-\frac{1}{2}=2+\frac{1}{4}m[/tex]
We have to find a number by which each term multiply and eliminate the fractions before solving
We can see that in the given expression
Denominator of first term is 4 and denominator of second term is 2 on left side.
Denominator of second term is 4 on right side
Therefore ,the lcm of 2,4,4
2=[tex]2\times1[/tex]
4=[tex]2\times2\times1[/tex]
LCM of 2 and 4 =[tex]2\times2\times1= 4 [/tex]
Therefore, the number is 4 by which each term is multiplied to eliminate the fractions before solving.
Hence, the answer is 4.
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. If x represents the length, then the length can be found by solving the equation: x(x−3)=54x(x-3)=54 What is the length, x, of the garden?
I can't remember the steps to solving this.
Determine the zeros of f(x) = x3 + 7x2 + 10x − 6
in a right triangle the sum of the squares of the leg lengths is equal to the square of the hypotenuse length what does this describe ?
Given quadrilateral ABCD with sides, 3, 3, 5, 5 respectively, identify the type of quadrilateral
Number four please and please explain how to find perimeter only using vertices
How can the Distance and Midpoint Formulas be used to identify specfic polygons? For example, how could you show that a quadrilateral is a rectangle?
What is the mean and mode of the data set shown below? {2, 4, 5, 6, 8, 2, 5, 6}
The mean and mode of the data set shown would be 4.75 and 2, 5 and 6 are modes.
How to find mean of a data?Mean is the ratio of sum of the observations to the total number of observations.
The given set of data is follows as;
{2, 4, 5, 6, 8, 2, 5, 6}
The mean can be calculated by adding all numbers and dividing by the count:
(2+4+5+6+8+2+5+6)/8
= 38/8
= 4.75
The mode is the number that occurs most often.
this is the case for 2, 5, and 6.
A data set can have multiple modes. 2, 5 and 6 are modes.
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If b = 5, then 4 1 · 4 b is equal to?
A water cooler holds 1,284 ounces of water. How many more 6 ounce glasses than 12-ounce glasses can be filled from the cooler
What is the length of the shortest side of a triangle that has vertices at (-2, 5), (-2, -7), and (-6, -4)?
The shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4) is 5 units. The lengths were calculated using the distance formula derived from the Pythagorean theorem.
Explanation:The subject matter of the given question pertains to the discipline of Geometry, specifically, the calculation of the length of the sides of a triangle. To find the length of the shortest side of a triangle having vertices at (-2, 5), (-2, -7), and (-6, -4), we can use the distance formula, which is derived from Pythagoras' theorem.
The formula for calculating the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:
√((x₂ - x₁)² + (y₂ - y₁)²)
The distance between the points (-2,5) and (-2,-7) is: √((-2 - (-2))² + (-7 - 5)²) = √(0 + 144) = √144 = 12 unitsThe distance between the points (-2,5) and (-6,-4) is: √((-6 - (-2))² + (-4 - 5)²) = √(16 + 81) = √97 units [approx. 9.85 units]The distance between the points (-2,-7) and (-6,-4) is: √((-6 - (-2))² + (-4 - (-7))²) = √((16 + 9) = √25 = 5 unitsThus, the shortest side of the triangle is the one with length 5 units.
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The length of the shortest side of the triangle is 5.
To find the shortest side of the triangle with vertices at (-2, 5), (-2, -7), and (-6, -4), use the distance formula [tex]\( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)[/tex]:
1. Between (-2, 5) and (-2, -7):
[tex]\[ \sqrt{( -2 - (-2) )^2 + ( -7 - 5 )^2} = \sqrt{0 + 144} = 12 \][/tex]
2. Between (-2, 5) and (-6, -4):
[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - 5 )^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.85 \][/tex]
3. Between (-2, -7) and (-6, -4):
[tex]\[ \sqrt{( -6 - (-2) )^2 + ( -4 - (-7) )^2} = \sqrt{16 + 9} = 5 \][/tex]
Thus, the shortest side is 5 units.
Please help!!!
Which of the following best describes interval C on the graph shown?
Linear constant
Linear decreasing
Linear increasing
Nonlinear increasing
why are people down voting the answer above me? Anyways, the answer is A. linear constant
This is because of the fact that a linear constant is a straight horizontal line that stays, as it says, constant, that is until you go to the next interval.
The median salary for the Dallas Cowboys was $441,300 in 2000 and $1,326,720 in 2008. Write a linear equation giving the median salary y in terms of the year x. Then use the equation and predict the median salary in 2016.
The linear equation that is asked from the problem takes the form of:
y = m x + b
where,
y = the median salary
x = the number of years
m = the slope of equation
b = y-intercept
The slope of the equation (m) can be calculated using the formula:
m = (y2 – y1) / (x2 – x1)
m = (1326720 – 441300) / (2008 – 2000)
m = 110,677.5
The y-intercept is then obtained by using any of the data pair:
441300 = 110677.5 (2000) + b
b = -220913700
Therefore the complete equation is:
y = 110677.5 x – 220913700
The median salary in 2016 is therefore:
y = 110677.5 (2016) – 220913700
y = $2,212,140
Answer:
$2,212,140
How many tens are in 1,000
Peter went to his local zoo where 50% of its exhibits featured lions. If the zoo features 24 exhibits in total, then how many of the zoos exhibits featured lions?
What is three ratios that are equivalent to 18:4
The probability that you will get grounded if you have a bad grade is 85%. The probability that you will get grounded and have extra chores is 50%. What is the probability that you will have extra chores given that you are already grounded?