Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let X represent the number of customers on a randomly chosen trip.
Based on previous data, here is the probability distribution of X along with summary statistics:
X = # of customers 0 1 2 3
P(X) 0.10 0.20 0.30 0.40
Mean: μx = 2
Standard deviation: σx = 1
Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10. Let Y represent Marcos' net gain from a randomly chosen trip. What are the mean and standard deviation of Y?
Answer:
Mean y = 19 ; SD y = 10
Step-by-step explanation:
Given that:
No of customers : __ 0 ____ 1 _____ 2 ___ 3
P(x) : ___________0.10 __ 0.20 __0.30 _0.40
Fuel cost =$1 (constant)
Amount paid per customer =$10
Number of customers = x
σx = 1 ; μx = 2
σ^2 = 1^2 = 1
Mean of Y
μy = E(Y)
= E(10x - 1)
= 10(Ex) - 1
E(x) = 2
= 10(2) - 1
= 20 - 1
= 19
σY = SD(y)
SD(10x - 1)
10*SD(x) - 1
SD(x) = 1
10(1) - 0
Note : SD of a constant = 0
10 - 0
= 10
The mean of Y is 19 and the standard deviation of Y is 10 and this can be determined by using the given data.
Given :
Marcos owns and operates a shuttle service that runs every hour and transports customers between their hotels and the city's downtown area. Let X represent the number of customers on a randomly chosen trip.Standard deviation: σx = 1 Suppose that each trip costs Marcos $1 in fuel regardless of how many customers he has, and each customer on a trip pays him $10. Let Y represent Marcos' net gain from a randomly chosen trip.The mean of Y can be calculated as given below:
[tex]\rm \mu(Y)=E(Y)[/tex]
[tex]\rm \mu(Y)=E(10x - 1)[/tex]
[tex]\rm \mu(Y) = 10E(x) - 1[/tex]
According to the given data, the value of E(x) is 2. Substitute the value of E(x) in the above expression.
[tex]\rm \mu(Y) = 10(2) - 1[/tex]
[tex]\rm \mu(Y) = 19[/tex]
Now, the standard deviation of Y can be calculated as:
[tex]\rm \sigma_Y=SD(Y)[/tex]
[tex]\rm \sigma_Y=SD(10x-1)[/tex]
[tex]\rm \sigma_Y=10SD(x)-SD(1)[/tex]
The value of SD for a constant is zero.
[tex]\rm \sigma_Y=10(1)-0[/tex]
[tex]\rm \sigma_Y = 10[/tex]
For more information, refer to the link given below:
https://brainly.com/question/12402189
HELP ASAP
What is the area of the shaded region?
(2571 - 48) cm
O (2517 - 30) cm
(2517 - 24) cm
(257-12) cm
Answer:
Step-by-step explanation:
We are given a circle with a partially shaded region. First, we need to determine the area of the whole circle. To do this, we need the measurement of the radius of the circle:
Use the Pythagorean theorem to solve for the other leg of the right triangle inside the circle:
5^2 = 3^2 + x^2
x = 4
The radius is 4 + 1 cm = 5 cm
So the area of the circle is A = pi*r^2
A = 3.14 * (5)^2
A = 25pi cm^2
To solve for the area of the shaded region:
Ashaded = Acircle - Atriangles
we need to solve for the area of the triangles:
A = 1/2 *b*h
A = 1/2 *6 * 5
A = 15 cm^2
Atriangles = 2 * 15
Atriangles = 30 cm^2
Ashaded = 25pi - 30
U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutions will be a useful integration technique. Then, you are to compute the antiderivative with that specific n. (E.g., if n = 5 makes u-subs work, then solve the integral with a 5 in place of n).
(a) [ zºeke*+1 "'de
(b) /co cos(1/2) dr
(c) / r+n dr 22 + 8x - 4
Answer:
Step-by-step explanation:
(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]
Suppose [tex]5x^4 + 1 = f[/tex]
by differentiation;
[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]
Suppose n = 3
Then, the integral
[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]
[tex]= \int e^f \ \dfrac{df}{20}[/tex]
[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]
[tex]= \dfrac{1}{20} e^f + C[/tex]
recall that [tex]f = 5x^4 + 1[/tex]
Then;
[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]
(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]
suppose; [tex]\dfrac{1}{x^3} = f[/tex]
[tex]x^3 = f[/tex]
[tex]\implies -3x^{-4} \ dx = df[/tex]
[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]
If n = u, then the integration is:
[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]
[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]
Since; [tex]x^3 = f[/tex]
Then;
[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]
(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]
Suppose [tex]x^2 + 8x - 4 = f[/tex]
Then, by differentiation of both sides
[tex](2x + 8) \ dx = df[/tex]
[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]
Suppose n = 4 in integration, then:
[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]
By substitution;
[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]
[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]
[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]
The suitable substitutions of n are 3,4,4 respectively.
What is integration?The process of finding integrals is called integration.
a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
Suppose
[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]
So, we need n=3 for easy integration.
[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]
[tex]I=\frac{e^{t} }{20}[/tex]
[tex]I = e^{5x^{4}+1 }/20 +c[/tex]
b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]
n=4 is needed for easy integration.
I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]
c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]
n=4 is needed for easy integration.
[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]
Hence, the suitable substitutions of n are 3,4,4 respectively.
To get more about integration visit:
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I will give a brainlist if someone could answer this problem with a explanation:)
Answer:
Step-by-step explanation:
The two base angles in each triangle are equal. (The triangle is isoceles and the property used is angles opposite equal sides are equal).
Now the tricky part. The peak angles are also equal. That's because both peak angles are made equal by Peak angle + 2*base angle = 180
Peak angle = 180 - 2*base angle
Therefore the triangles are congruent by SAS.
I suppose you could get them equal by taking one of the base angles (all 4 are equal to each other) and the peak angles and claim equality by ASA, but it seems a little bit tortuous to me.
Solve the equation.
7(1 – 8x) – 6 = 169
Answer:
x=-3
Step-by-step explanation:
rearrange terms
distribute
subtract the numbers
subtract 1 from both sides of the equation
simplify
Answer:
Step-by-step explanation:
Here you go mate
Step 1
7(1-8x)-6=169 Equation/Question
Step 2
7(1-8x)-6=169 Simplify
-56x+1=169
Step 3
-56x+1=169 Subtract 1
-56x=168
Step 4
-56x=168 Divide both sides
Answer
x=-3
Suppose potato chips cost 22.5 cents per ounce. What would a bag of chips cost if it contained 12 oz? Round your answer to the nearest cent, if necessary
Answer:
the anser is 22.10
Step-by-step explanation:
you have to round to the nearest ten. here is a tip 4 or down round down 5 or up round up now you are good to go! and also to find me if you need help
Find two consecutive whole numbers that 34 lies between.
Answer:
34 lies in between 5 and 6
5^2=25, 6^2=36, so sqrt(34) lies between 5 and 6
How many different 3-digit numbers can be made using the digits 6, 7, and 8 if no digit is reapeated? One digit is repeated?
Answer:
You can make infinite 3-digit number using the digits 6,7 and 8. Hope it helps :)
Which is the hidden question in this problem?
Jason bought 6 season tickets to the theatre. Each ticket cost $120.
A season parking pass cost $30. How much did Jason spend for the tickets and the parking pass?
A Will the tickets cost more than $1,500?
B. How much more is the cost of the tickets than the cost of the parking pass?
How much do six season tickets cost?
D
How much will two parking passes cost?
Answer
how much more is the cost of tickets than the cost of parking pass
Step-by-step explanation:\
i think, sorry if im wrong but its kinda hard to understand what you typed.
Answer:
A: No the tickets won't cost more than $1500.
B: 90 more dollars.
6 season tickets cost $720
D: 2 parking tickets will cost $60
39) Solve the inequality: 4(x+5)≤116
A. x≤−51
B. x≤−40
C. x≤24
D. x≥24
Answer:
x≤24
Step-by-step explanation:
4(x+5)≤116
x+5≤29
x≤29-5
x≤24
Write an expression to represent each problem. Then, draw a model to solve.
1.
How many fourths are in 3 fourths?
A TV that usually sells for $171.38 is on sale for 15% off. If sales tax on the TV is 9%, what is the price of the TV, including tax?
Answer:
171.38 - 15% plus tax= 171.23
Hope this helped!
Pls help I don’t know what to do and it’s due today
Answer:
it's easier if you use the scan & solve. that brainly provided for you
Step-by-step explanation:
Ryan's garden=1.3 yards wides
We know that,
1 yard=0.914 meters
so,
1.3 yards=0.914×1.3=1.1882=1.9
So,
Ryan's garden is 1.9 meters wide.
Answer this question
(Factors of 36)
1,36
_,_
_,_
4,9
_,_
*please answer asap!*
Answer:
1,36 2,18 3,12 4,9 and 6,6
Step-by-step explanation:
If you multiply them, they equal 36
True or false
$24 fir 6 ft of chain represents a rate of $4 per foot of chain
Answer:
I think its true but im not sure
Step-by-step explanation:
Please help me! (12 points)
Answer:
4
Step-by-step explanation:
25÷2= 12.50
So it would be 4 because you are trying to find the price (p) for the boots (b)
Answer:
c is correct answer is yes then please
Will mark brainliest!!!Solve for each variable
Answer:
n=5, m = 4
Step-by-step explanation:
It is a parallelogram so m+8 = 3m and 2n-1 = 9
This question has 2 parts.
Part A: Matt has 2/3 yard of fishing line. He uses 3/8 of the line to make fishing knots. How much fishing line does he use to make fishing knots?
Part B: Kara says Matt uses 25/24 of the line to make knots. Explain Kara’s error and tell how to use an equation to find the amount of line Matt uses.
Answer:
um well i can do part A
Step-by-step explanation:
its 6/24 which equals 1/4 yards
Will mark brainliest!!! Plz solve for each variable
Step-by-step explanation:
parallel
8g - 3 = 25
8g = 25 + 3
8g = 28
g = 28/8
g = 14/4
f + 30 + 72 = 180 (straight angle = 180°)
f = 180 - 30 - 72
= 78
.12 divided by 7.15 please put step by step thank you
Answer:
59.58333
Step-by-step explanation:
715/12
write in long division format ( which u did )
divide 71 by 12 to get 5
multiply 71 by 12 = 5
subtract 60 by 71
bring down the next number
115/12 =9
multiply 12 by 9
subtract 180 by 115
add a decimal on the top and bring down zero
divide 70 by 12 = 5
multiply 5 by 12
subtract 60 - 70
bring down a zero
divide 100 by 12 = 8
multiply 12 by 8
subtract 96 by 100
bring down zero
divide 40 by 12 = 3
anddd u get the point
sorry it took so long
The econ motel charges $260 for four nights at this rate how much would seven nights cost
Answer:
$455 for seven nights
Step-by-step explanation:
260/4= 65
65 is the cost for 1 night
65*7=455
Answer:
$455
Step-by-step explanation:
260 divided by 4 will give you how much for one night so then multiply that answer by 7 and you have your answer.
A convex polygon has 6 sides what is the sum of its interior angles 1980°.
Step-by-step explanation:
Sum of interior angles in a polygon
= 180°(n - 2), where n is the number of sides.
Hence a convex polygon with 6 sides
=> 180°(6 - 2) = 720°.
I need help please if you can
Answer:
i really dont know
Step-by-step explanation:
i just dont
Find all real zeros of the function y= -5x - 7.
Brian has reduced his cholesterol level by 14% after his last check up. If his original level was 180, what is his approximate cholesterol level now?
Answer:
154.8 is you answer
Step-by-step explanation:
Are they the same or not
Answer:
yes they are Similar
The population of London is currently estimated at 8.156 million.
What is the value of the 5?
Answer:
50 , or , 10 ...................
Answer: Hundredth- thousandths
Step-by-step explanation:
Expand 8.156 million
8.156 = 8,156, 000
As you can see 5 is at the hundredth- thousands place
Consider following situation, which involves two options. Determine which option is less expensive. Are there unstated factors that might affect your decision?
You currently drive 325 miles per week in a car that gets 14 miles per gallon of gas. You are considering buying a new fuel-efficient car for S16,000 (after trade-in on your current car that gets 47 miles per gallon
premiums for the new and old car are $1000 and $600 per year, respectively. You anticipate spending $1500 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 pen
ive-year period, is it less expensive to keep your old car or buy the new car?
a five-year period, the cost of the old car iss) and the cost of the new car issThus, over a five-year period, it is less expensive to
and to the nearest dollar as needed
9514 1404 393
Answer:
it is less expensive to purchase a new car
Step-by-step explanation:
The expected cost of gas, insurance, and repairs for the old car are ...
Total miles in 5 years = (325 mi/wk)(52 wk/yr)(5 yr) = 84,500 mi
Old car
Gas cost in 5 years = (84,500 mi)/(14 mi/gal)($3.50/gal) = $21,125
Insurance cost in 5 years = (5 yr)($600/yr) = $3,000
Repair cost in 5 years = ($1500/yr)(5 yr) = $7,500
Total operating cost in 5 years = $21125 +3000 +7500 = $31,625
__
New Car
Gas cost in 5 years = (84,500 mi)/(47 mi/gal)($3.50/gal) ≈ $6,293
Insurance cost in 5 years = (5 yr)($1000/yr) = $5,000
Repair cost in 5 years = (0)(5 yr) = 0
Total operating cost in 5 years = $6293 +5000 = 11,293
__
Difference in operating costs is $31,625 -11,293 = $20,332.
It is less expensive to purchase a new car for any price less than $20,300. If the new car costs only $16,000, it is the less-expensive option.
Purchase of a new car is the least-expensive option.
__
Additional comments
The cost of financing, annual license fees, and resale value of the new car may also come into play. In addition, the relative non-economic values of consumption of new materials, adding old materials to the scrap heap, and environmental pollution may figure in the decision. While the car dealer may pay for maintenance costs of a new car, it seems likely that at least one set of tires will be required in 5 years (85000 miles). (Assuming wheel alignment is not an issue for tire wear, that cost may balance out for the two cars.)
what is the equation for the line of reflection
a. x= 3
b. y = 3
c. y = x
d. x = 6
Answer:
The answer to that question is c. y = x
Part2
Please help I’ll make u brainly
Answer:
someone game me that same question but sadly i wasn't able to get the answer sorry for the inconvience
Step-by-step explanation:
Answer:
3. 2nd degree. Leading term:
[tex] {3x}^{2} [/tex]
Leading coefficient: 3x
Part 1:
[tex] {2x}^{2} + 11x + 15[/tex]
Part 2:
[tex] {3x}^{2} - x - 2[/tex]
Part 3:
[tex] - {x}^{2} + 12x + 17[/tex]
(Part 3 should be correct, double check it, I think it cancels out the minuses in the part 2 equation?)
P.S. I forgot to solve the equations on this and the first page, don't forget that and I can leave another answer for those if you need!