At a fast food restaurant, customers are asked if they want to “round up” their bill to the next highest dollar and donate the additional money to charity. The cashier is instructed to tell the customer that their bill is X dollars and Y cents. Assume that the values of Y are equally likely to be any value from 0 to 99 cents and that customers are equally likely to “round up” regardless of the amount of their bill. The density curve below models Y, the donation amount. (a) What is the shape of the distribution of donations? (b) What proportion of donations are at least 85 cents? (c) What percent of donations are between 30 and 40 cents?
Answers
Answer:
(a) 0.1414
(b) 0.1010
Step-by-step explanation:
(a)
The density curve is rectangular in shape.
This implies that the distribution of donations is Uniform.
(b)
Compute the probability of donations at least 85 cents as follows:
[tex]P(X\geq 85)=\int\limits^{99}_{85} {\frac{1}{99-0} \, dx[/tex]
[tex]=\frac{1}{99}\times [x]^{99}_{85}\\\\=\frac{99-85}{99}\\\\=0.1414\\\\[/tex]
Thus, the proportion of donations that are at least 85 cents is 0.1414.
(b)
Compute the probability of donations between 30 and 40 cents as follows:
[tex]P(30\leq X\leq 40)=\int\limits^{40}_{30} {\frac{1}{99-0}} \, dx[/tex]
[tex]=\frac{1}{99}\times [x]^{40}_{30}\\\\=\frac{40-30}{99}\\\\=0.1010[/tex]
Thus, the probability of donations between 30 and 40 cents is 0.1010.
Related Questions
help me pls
1) Mrs.Galicia sells online math and reading games. His revenue for each game (in dollars) is modeled by the given equations, where x is the number of days since the games went on sale.
Math Game: M(d)=x^2-9x-10
Reading Game: R(d)=2x+10
Solve the system algebraically. After how many days is the revenue for each game the same? Show your work and explain your answer.
Graph this system to show the solutions. Label each axis appropriately
2) Mrs.Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-2t+36.
The height of Antonio's rocket after t seconds can be represented by the linear function: p(t)=-2t+20.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
Answers
Answer:
a) after 12.59 days the revenue will be equal
b) u just have to graph it
the second one is
a) the two solutions are x=4 and x=-4
b) x=-4 is not reasonable because time can’t be negative
c) after four seconds, the heights will be equal
Step-by-step explanation:
After 12.59 days the revenue for each game is the same. The two solutions of the system equation b(t) and p(t) are 4 and -4, and -4 is not a reasonable solution because time never be negative and after 4 seconds the rocket and the ball reach the same height.
1)
Given :
Math Game -- [tex]\rm M(d) = x^2-9x-10[/tex]
Reading Game -- R(d) = 2x + 10
It is given that after 'x' number of days the revenue for each game is the same, that is:
[tex]\rm x^2 -9x-10=2x+10[/tex]
[tex]\rm x^2 -11x-20=0[/tex]
Simplify the above quadratic equation.
[tex]\rm x = \dfrac{11\pm \sqrt{11^2-(4\times -20)} }{2}[/tex]
[tex]\rm x = \dfrac{11\pm \sqrt{201} }{2}[/tex]
x = 12.59 days
So, after 12.59 days the revenue for each game is the same.
The graph of both the revenue function is attached below.
2)
Given :
[tex]\rm b(t) =- t^2-2t+36[/tex]
p(t) = -2t + 20
The solution of this system can be determined by equating both the above function.
[tex]\rm -t^2 - 2t +36 = -2t +20[/tex]
Simplify the above equation.
[tex]\rm t^2 =16[/tex]
t = 4 and -4
a) The two solutions of the system are 4 and -4.
b) -4 is the solution is not a reasonable solution because time never be negative.
c) After 4 seconds the rocket and the ball reach the same height.
For more information, refer to the link given below:
https://brainly.com/question/2263981
Explain how you would solve for the value of x when you are given the solution to a function.
Answers
Answer:
Substitute
Step-by-step explanation:
Substitute the values given in the function
and you will get the answer.
P.s. It depends on the question
What is the greatest common factor of 72 and 2?
Answers
Answer:
the Greatest Common Factor (GCF) of 2 and 72 is 2
plz mark brainliest
Answer: the greatest Common Factor (GCF) is: 2
Step-by-step explanation:
To get the Greatest Common Factor (GCF) of 2 and 72 we need to factor each value first and then we choose all the copies of factors and multiply them:
*NOTE CAN PLEASE MARK ME AS BRAINLISST PLEASSE
It takes Caroline 1/5 of an hour to walk a mile. Four of Caroline's friends time themselves on their own walk of different lengths. Which friend is walking at the same rate as Caroline? *
0/1
Captionless Image
Answers
Answer:
Please comment the image, it won't load.
Step-by-step explanation:
The large rectangle below represents one whole. A large rectangle with 25 equal sections, 11 of which are shaded What percent is represented by the shaded area?
Answers
fourty four percent hope this helps !
Endpoint: (-8, -10), midpoint: (10,-7)
Answers
Answer:
(28,-4)
Step-by-step explanation:
I can add fractions with unlike denominators. 2/5 + 3/10 =
Answers
Answer:
7/10
Step-by-step explanation:
2/5 multiply the denominator by 2 which will make it 10. Then multiply the numerator by 2 which will make it 4. So it will be 4/10. Then add 4/10 to 3/0 which makes 7/10.
Stephanie has $250 in her account. She withdraws $50 on October 1st to pay the electric bill. Then she withdraws $125 on October 10th to pay the internet. What is the total amount of money she withdraws from her account?
Answers
I need help my mom is going to kill me
Answers
Answer:
x=8
m<FGH=32
m<HGI=32
m<FGI=64
Step-by-step explanation:
The first thing you're going to do is form an equation using 5x-8 and 6x-16. The reason for this is because the two angles FGH and HGI are congruent. You form an equation by setting the two equal to each other. LIke this:
5x-8=6x-16
Then you will find x which is 8. After you find x just plug in x for one of the equations like so:
5(8)-8=_ or 6(8)-16=_
You only need to plug in x for one of the angles because they are congruent so you will get the same answer.
To find the measurment of FGI you add the values from FGH and HGI together (32+32) and you'll get 64.
You need to find two numbers where one number is 4 times as large as the other and where the difference is
the two numbers are 39. What are the numbers?
equation
Answers
4x = y
y - x = 39
Substitute the value of y in
4x - x = 39
3x = 39
x = 13
4x = y
Y = 52
x = 13 and y = 52. Your welcome and a Brainliest would be much appreciated
Some one help me please..?
Answers
Answer:
x = -18
Step-by-step explanation:
3 + -18 = -15
Answer:
the answer is d
Step-by-step explanation:
collect the like terms
PLEASE HELP ASAP!!!!!!!!!! YOU WILL GET BRAINLEST!!!!!!!!!!!!!!!!
The model represents an equation. What value of x makes the equation true?
A) 3/4
B) 9/2
C) −3/4
D) −9/2
Answers
Answer:
I am not completely sure I think it is A im not positive but I think
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
On the left, we have 7 -Xs and 7 1s. So, the left can be represented by the expression:
[tex]-7x+7[/tex]
On the right, we have 5 (positive) Xs and 16 1s. So, the right can be represented by the expression:
[tex]5x+16[/tex]
They are equal to each other. So:
[tex]-7x+7=5x+16[/tex]
Solve for x. Add 7x to both sides:
[tex]7=12x+16[/tex]
Subtract 16 from both sides:
[tex]-9=12x[/tex]
Divide both sides by 12:
[tex]x=-9/12[/tex]
Reduce:
[tex]x=-3/4[/tex]
So, our answer is C.
Which of the following types of numbers is irrational?
A.) a whole number
B.) fractions
C.) the number pi
D.) a decimal that terminates
Answers
Answer:
C
Step-by-step explanation:
the definition of an irrational number is an infinite decimal that has no repeating pattern. rational numbers can be converted into fractions.
A is incorrect because a whole number can be converted into a fraction.
ex: 1 is also 3/3
B is incorrect because the definition of a rational number is that it can be converted into a fraction.
D is incorrect because a terminating decimal can be made into a fraction.
ex: 4.5 is also 9/2
D)
Step-by-step explanation:A Irrational number is a decimal that terminates. I hope this helps! Please rate Brainiest!
-Aslina
Write a positive or negative integer that represents the situation.
The temperature rises 17 degrees.
Answers
Answer:
+17
Step-by-step explanation:
A right triangle is drawn on the coordinate plane.
Apply a dilation with a scale factor of 1 to this triangle and draw the new triangle on the coordinate plane.
Answers
A box Jelly fish travels at a rate of 6.5 feet per second. What is the distance after 5 seconds?
Answers
Answer:
32.5ft
Step-by-step explanation:
Answer:
32.5 feet per 5 seconds
Step-by-step explanation:
multiply 5 by 6.5 you get 32.5
Help please! I’m confused
Answers
Answer:
28 degrees
Step-by-step explanation:
hi! since m<ABC is 175 degrees and m<YBC is 147 degrees, we can subtract these to find m<ABY.
175-147= 28 degrees
if two lines lie in the same plane and are perpendicular to the same line they are perpendicular true or false?
Answers
If two lines lie in the same plane and are perpendicular to the same line they are perpendicular is TRUE.
What are parallel lines?Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines.
Parallel lines are those lines in which slopes are the same and the distance between them remains constant.
If a line is perpendicular to another then they will make 90 degrees at the intersection.
So if another line is also making 90 degrees it means both lines must be in the same direction so they will be parallel as given in the image below.
Hence "If two lines lie in the same plane and are perpendicular to the same line they are perpendicular is TRUE".
To learn more about parallel lines;
https://brainly.com/question/16701300
#SPJ6
A plumber earns $50 for a repair job, plus an additional $75 per hour he works. On Tuesday, he completed 3 repair jobs and earned a total of more than $600. Part A: Write an inequality that can be used to determine h, the number of hours the plumber worked Tuesday.
Answers
Answer:
[tex]150 + 75h > 600[/tex]
Step-by-step explanation:
The inequality that can be used to determine h is shown below:-
As per the given situation, it is mentioned that a plumber could earns $50 for a repair job, so for three jobs he earned $150 as a total amount
Now
We presume h be the number of hours
Also he earns additional $75 per hour worked so $75
Total amount is $150 + $75h)
The total amount is more than $600
So, the inequality equation is as given below:
[tex]150 + 75h > 600[/tex]
Help me with algebra 1 core if its the right answer i'll make you the brainliest! Help me ASAP please i'll give some extra points.
Answers
Answer:
y=3x
Step-by-step explanation:
y=3x
the line passes through the origin so when x=0, y=0
Write the nature of roots of the quadratic equation 9x^2 -6x+2
Answers
Answer:
roots are not real
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 (a ≠ 0 )
Then the nature of the roots can be found using the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
Given
9x² - 6x + 2 = 0
with a = 9, b = - 6, c = 2 , then
b² - 4ac = (- 6)² - (4× 9 × 2) = 36 - 72 = - 36
Since b² - 4ac < 0 then the roots are not real
A grocery store owner is planning a display by stacking cans of soup in a pyramid. The top row of the stack will have 1 can, the row underneath it will have 3 cans, the row underneath it will have 5 cans, and so on. If the owner wants the display to have a total of 12 rows, then how many cans will he need?
Answers
Answer:
144?
Step-by-step explanation:
1+3+5+7+9+11 blah blah blah...
1+3+5+7+9+11+13+15+17+19+21+23 which gives 144.
what is the answer for 2(5/3+3/4)-4/3s
Answers
10/3 + 3/4 - 4/3s
Change the denominator of 10/3 and 3/4 so they are equal. Multiply 10/3 by 4, 3/4 by 3, and 4/3 by 4 to get:
40/12 + 9/12 - 16/12s
49/12 - 16/12s
Solve 5x-8y=19 for y.
Answers
Answer:
-19/8+5x/8
Step-by-step explanation:
Answer:
912
Step-by-step explanation:
8x19= 152
152x5= 760
760+152=
what is the distance from 8 to 0?
Answers
Answer:
8, because |8|=-8
Step-by-step explanation:
Absolute value is always positive, hence the answer.
Please help, I'm stuck and really need this.
Answers
Answer:
r = 8
Step-by-step explanation:
To find the radius with only the area you do r = [tex]\sqrt{A/\pi }[/tex]
Since your area 64[tex]\pi[/tex] = 201.0619298 then 201.0619298/[tex]\pi[/tex] = 64
[tex]\sqrt{64}[/tex] = 8
Hope this helps!!
can you help? 6+(−4 3/4)+(−2 1/8)
Answers
Answer:
I believe it's -7/8
you have to make the fractions improper first with a common denominator and since -4 3/4 and -2 1/8 are negative and 6 is positive, you come out with -7/8
A number problem states, “–5 times a number, minus 22 gives a result of 23.” What is the number?
Answers
Answer:
im pretty sure its -9
Step-by-step explanation:
the equation explained would look something like this...
-5x-22=23
so you would isolate the variable by first adding 22 to both sides and the dividing by -5 on both sides
-5x-22=23
+22 +22
-5x/-5=45/-5
x=-9
+22 +22
-5x = 45
—————
-5x -5x
X=-9
Please help me it would mean a lot
Answers
42.5 i think
The whole angle is 127 minus the angle we know (32) this leaves us with 85 for the rest of the angle but we still have to deal with the angle bisector so we divide it by 2 leaving us with 42.5 I'm pretty sure.
Please help it would be great
Answers
Answer:
120
Step-by-step explanation:
jUts bEcAusE