A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent. Probability and Fuel Cost by Region Region Probability in Region Fuel Cost per Gallon Southeast 20% $3. 10 Southwest 30% $3. 50 California 50% $4. 05 $3. 53 $3. 55 $3. 68 $3. 70.
Answers
The cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
What does the expectation of a random variable tells about?A random variable is usually taking some numerical information of each elementary event of the sample space . (map from sample space to real numbers). Its expected value is the best prediction value in most of the cases. It is the mean or average value of that random variable.
How to find the mean (expectation) of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\[/tex]
where [tex]x_i; \: \: i = 1,2,.. , n[/tex] is its n data values
and [tex]f(x_i)[/tex] probability of [tex]X = x_i[/tex]
How to convert percent to probability?Percent counts the number compared to 100 whereas probability counts it compare to 1.
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in probability)
If assuming that X = Fuel cost per gallon, then
E(X) = Average fuel cost per gallon that the company should budget (its per gallon, means for a gallon)
Using the tabulated value given in the problem, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\\\\\E(X) = 3.10 \times 0.2 + 3.5 \times 0.3 + 4.05 \times 0.5 = 3.695 \approx 3.70[/tex] (in dollars)
(we converted percentage to probability).
Thus, the cost the company budget on average for a gallon of fuel across its operations is given by: Option D: $3.70
Learn more about expectation of a random variable here:
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Answer:
D is the correct answer! ~Hope this helps!
Step-by-step explanation:
Work:
Related Questions
Which number is an irrational number?
Answers
Answer:
(b) -√3
Step-by-step explanation:
Any fraction or terminating decimal is rational. (a) and (c)
Any repeating decimal is rational.
Any square root of a perfect square is rational. (d)
Any square root of an integer that is not a perfect square is irrational. (c)
The sign of the number is irrelevant.
__
Of these numbers, the irrational one is -√3.
Find [tex]\frac{d^2y}{dx^2}[/tex] if [tex]x^2y^2=1[/tex]
Options:
A. [tex]\frac{2y}{x^2}[/tex]
B. 0
C. [tex]\frac{y}{x}[/tex]
D. [tex]\frac{-y}{x}[/tex]
E. [tex]\frac{-y}{x^2}[/tex]
Answers
Answer:
A) [tex]\frac{d^2y}{dx^2}=\frac{2y}{x^2}[/tex]
Step-by-step explanation:
Use implicit differentiation to find dy/dx
[tex]x^2y^2=1\\\\\frac{d}{dx}(x^2y^2)=\frac{d}{dx}(1)\\ \\x^2(\frac{d}{dx}y^2)+(\frac{d}{dx}(x^2))y^2 =0\\\\2yx^2\frac{dy}{dx}+2xy^2=0\\\\2xy(x\frac{dy}{dx}+y)=0\\ \\x\frac{dy}{dx}+y=0\\ \\x\frac{dy}{dx}=-y\\ \\\frac{dy}{dx}=-\frac{y}{x}[/tex]
Determine d²y/dx² using dy/dx
[tex]\frac{dy}{dx}=\frac{-y}{x}\\ \\ \frac{d^2y}{dx^2}=\frac{(x)[\frac{d}{dx}(-y)]-(-y)[\frac{d}{dx}(x)] }{x^2}\\ \\ \frac{d^2y}{dx^2}=\frac{-x\frac{dy}{dx}+y}{x^2}\\ \\ \frac{d^2y}{dx^2}=\frac{-x(\frac{-y}{x})+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{-(-y)+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{y+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{2y}{x^2}[/tex]
Helpful tips
When doing implicit differentiation, make sure to treat "y" as a constant and write dy/dx next to the y-term because it's differentiated with respect to xThe product rule is [tex]\frac{d}{dx}[f(x)g(x)]=f(x)[\frac{d}{dx}g(x)]+[\frac{d}{dx}f(x)]g(x)[/tex]The quotient rule is [tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{f(x)[\frac{d}{dx}g(x)]-g(x)[\frac{d}{dx}f(x)]}{(g(x))^2}[/tex][tex]\frac{dy}{dx}[/tex] represents the first derivative of y with respect to x and [tex]\frac{d^2y}{dx^2}[/tex] represents the second derivative of y with respect to xLet me know if you have any more questions!
The net for a cube is shown below. Find the lateral surface area of the
cube.
8 m
Answers
Answer:
48 m
Step-by-step explanation:
8 times 6 which is how many sides a square has.
I need help I forgot all about this and I would appreciate it!
Answers
Answer:
$3.75
Step-by-step explanation:
You only have to multiply 3 pounds by the $1.25 to get the cost.
Solve for m by completing the square.
-5m^2 + 5m – 2 = 0
Answers
Answer:
M=5+sr of 15/10, 5-sr of 15/10
A box of candy weighs 340. 23 grams and costs $18. 99. If 1 gram is approximately 0. 03527 ounces, what is the unit price per ounce of the candy? a. $0. 53 b. $0. 67 c. $1. 58 d. $1. 97.
Answers
Unit price per ounce of the candy of 340.23 grams is $1.58
What is ounce and gram ?Ounce and gram are two different unit of mass and relation between them is 1 gram = 0.03527 ounces .
In the question it is given that weight of candy is 340.23 grams
And it costs $18.99
Now we can covert grams to ounces as
[tex]1 \text{gram}= \ 0.03527 \text{ounces}\\[/tex]
Hence
[tex]340.23 \text{gram}= \ 340.23\times 0.03527 \text{ounces}\\\\\\340.23 \text{gram}=11.99 \ \text{ounces}\\[/tex]
Now 11.99 ounces of candy cost $18.99
So 1 ounce of candy cost 18.99/11.99= $1.58
Unit price per ounce of the candy of 340.23 grams is $1.58
To learn more about gram visit: https://brainly.com/question/26161082
75% of what number is 15? make it so clear pls pls
Answers
20 is the answer.
Step-by-step explanation:
Take a look at the given question,
"75% of what number is 15"
Let's substitute this "what number" as "x"
[tex]75[/tex]%[tex] \times x = 15[/tex]
[tex]→x = \frac{15}{75 \: percent} [/tex]
[tex]→x = \frac{15}{ \frac{75}{100} } [/tex]
[tex]→x = \frac{15}{0.75} [/tex]
To make the denominator as positive for making calculations more easy, we get,
[tex]x = \frac{15 \times 100}{0.75 \times 100} [/tex]
[tex]→x = \frac{1500}{75} [/tex]
Now after doing the division, we get,
[tex]x = 20[/tex]
Hence, 75% of 20 is 15.
Which of the following points are
solutions to the equation?
Answers
Answer:
(2;-5) and (0;-4).
Step-by-step explanation:
if the given graph is the same as in the attached picture (y=-0.5x-4), then two points only belong to it.
300 people attended a concert.
5% of the people came from Scotland.
30% of the people came from Wales.
How many more people came from Wales than from Scotland?
Answers
Answer:
75
Step-by-step explanation:
0.3*300=90
0.05*300=15
90-15=75
Answer:
ok so we want to find out 30% of 300 is
so first lets turn it into its decmil form by multiplying by 0.01 so
30*0.01=0.3
then lets multiply that by 300 so
300*0.3=90
90 people were from whales
15 people from scotland
90-15=75
Hope This Helps!!!
Evaluate each expression 4x0x9.17 and 1.8x1x2
Answers
Answer:
0 and 3.6
Step-by-step explanation:
4x0x9.17= 0
1.8x1x2= 3.6
Answer:
0
3.6
Step-by-step explanation:
4x0x9.17=0
1.8x1x2=3.6
What is the value of x in this figure?
x = 22
x = 68
X = 90
Answers
Answer:
2nd Option 68 :)
Step-by-step explanation:
A rectangular vegetable garden will have a width that is 4 feet less than the length, and an area of 140 square feet. If x
represents the length, then the length can be found by solving the equation:
x(x - 4) = 140
What is the length, x, of the garden?
The length is
feet
Answers
Answer:
14
Step-by-step explanation:
x equals 14
14(14-4)=140
(SHOW UR WORK) What is the result of 90.425 subtracted from 48.4?
Answers
Answer
42.025
Step-by-step explanation:
8
90.425
- 48.400
= 42.025
You substitute the 9 to an 8
Hope this helps ._.
What is the solution for the linear system 4x + 2y = 8 and
2x+2y=2
Answers
Answer:
(3,-2)
Step-by-step explanation:
See image
A farmer owns a total of 8 4/5 acres of land. The land is separated into 4
equally sized sections. How many acres are in each section?
Answers
Explanation:
The mixed number 8 & 4/5 consists of the whole part 8 and the fractional part 4/5.
Divide the whole part 8 into 4 equal pieces
8/4 = 2
This means 2 is part of the final answer.
Also, divide the 4/5 into 4 equal pieces as well. This is the same as multiplying by 1/4
(1/4)*(4/5) = 1/5
Overall, the size of each section is 2 & 1/5 acres
A basketball team played six games. In those games, the team won by 7 points, lost by 20, won by 8, won by 11, lost by 3, and won by 9. Which was the mean amount by which the team won or lost over the six games?
A. -3 points
B. 2 points
C. 3 points
D. 6 points
Answers
Evaluate the expression z2 - 6 if z = 4 The solution is:
Answers
Answer:
4 x 2 - 6
= 8 - 6
=2
Step-by-step explanation:
Determine whether the line through (−4, 6) and (−3, −2) intersects the line through (−3, −3) and (−5, 5).
Answers
Answer: No
Step-by-step explanation:
Like all the numbers in are the negative sides of the axis, -3,3 could not possibly go through -3, -2 because one side is horizontal the other is vertical.
What is the solution to this equation -8x - 40 = 8
Answers
The answer is -6 :)
1. Add 40 to both sides of the equation.
-8x-40=8
-8x-40+40=8+40
2. Add the numbers.
-8x=48
3. Divide both sides of the equation by the same term.
-8x=48
[tex]\frac{-8x}{-8}[/tex]=[tex]\frac{48}{-8}[/tex]
4. Cancel terms that are in both the numerator and denominator and divide the numbers.
x=-6
hope this helped! :)
Please help me solve this inequality thank you
Answers
Answer:
x < 4
Step-by-step explanation:
12x - 11 < 37 ( add 11 to both sides )
12x < 48 ( divide both sides by 12 )
x < 4
solve: this equation down below:
7×10n=700
Answers
Answer:
n = 10
Step-by-step explanation:
[tex]7 \times 10n = 700 \\ 10n = \frac{700}{7} \\ 10n = 100 \\ \frac{10n}{10} = \frac{100}{10} \\ n = 10[/tex]
Please name every primary number up to 1000
Answers
Answer:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
Step-by-step explanation:
168 total
Parallelogram ABCD is a rhombus. Side BC= 5 cm and segment AO = 3.8 cm. what is the area of ABCD
Answers
The area of a shape is the amount of space it occupies
The area of the rhombus is 24.7 square inches
How to determine the area of the rhombusStart by calculating the length BO using the following Pythagoras theorem
[tex]BC^2 = AO^2 + BO^2[/tex]
So, we have:
[tex]5^2 = 3.8^2 + BO^2[/tex]
Evaluate the exponents
[tex]25 = 14.44 + BO^2[/tex]
Collect like terms
[tex]BO^2 = 25 - 14.44[/tex]
[tex]BO^2 = 10.56[/tex]
Take the square roots
[tex]BO = 3.25[/tex]
The area of the rhombus is then calculated as:
[tex]Area = \frac{2BO * 2AO}{2}[/tex]
This gives
[tex]Area = \frac{2 * 3.25 * 2 * 3.8}{2}[/tex]
[tex]Area = 24.7[/tex]
Hence, the area of the rhombus is 24.7 square inches
Read more about areas at:
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Can someone tell me if this right or wrong
Answers
Answer:
Yes, it's right
Step-by-step explanation:
serena paid $24.60 for 7 1/2 gal of gasoline
Answers
Answer:
For each gallon, serena payed $3.28.
Step-by-step explanation:
Answer:
Serena paid 3.28 for each gal of gasoline
Step-by-step explanation:
Simply, divide 24.60 by [tex]7\frac{1}{2}[/tex] and you get 3.28 (your answer)
What is the y intercept and slope hurry please
Answers
From the given graph , we see that it passes through the point (0,-1) .
Hence the y intercept is -1 .→ y intercept = -1
For finding slope , take another point as (1,3) . Now using the points (1,3) and (0,-1) we can find out the slope as ,
→ m = y2 - y1 / x2 - x1
Substituting the respective values,
→ m = 3 -(-1)/1-0
→ m = 3+1/1
→ m = 4/1
→ m = 4
Hence the slope of the line is 4 and its y intercept is -1 .
Make X the subject in the following relation. y=2x+3
Answers
Answer:
[tex]x = \frac{y - 3}{2} \\ [/tex]
Step-by-step explanation:
[tex]y = 2x + 3 \\ y - 3 = 2x \\ \frac{y - 3}{2} = x \\ [/tex]
4. What is the solution to the inequality
below?
2x + 10 < 40
A x< 10
CX > 10
B x < 15
D x> 15
Answers
Answer:
the answer I got was B
Step-by-step explanation:
subtact 10 from both sides:
2x + 10 - 10 < 40 - 10
simplify the arithmetic:
2x < 40 - 10
simply again:
2x < 30
divide:
30 / 2 = 15
ASAPPPPPPPPPPPPPP Pls help question in picture
Answers
Answer:
Three ways I experience these benefits is 1, being able to vote in free elections, 2, being able to receive an education, and 3, being able to volunteer for things.
Step-by-step explanation:
A student is about to take a true-false, 5-question quiz, with absolutely no knowledge of the subject. So, the student flips a coin to determine their response to each question. If you let the random variable X = "a number of correct answers on the quiz," what is the correct histogram?
Answers are from 1-4, and they are all in order.
Answers
Using the binomial distribution, considering the probability of each event, the correct histogram is the fourth one.
For each question, there are only two possible outcomes, either the student guesses the correct answer, or not. The probability of guessing the correct answer on a question is independent of any other question, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
There are questions, hence n = 5.They are true-false questions, that is, they have one correct option out of 2, hence p = 0.5.Then, the probabilities are as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]
[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
Hence the fourth histogram is correct.
More can be learned about the binomial distribution at https://brainly.com/question/14424710