Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes "The Drive-Thru Performance Study: Order Accuracy" that measures the percentage of orders that are filled correctly. In a recent month, the percentage of orders filled correctly at Burger King was approximately 90.5%. Suppose that you and two friends go to the drive-through window at Burger King and place an order. Two friends of yours independently place orders at the window at the same store.
a. What is the probability that all the three orders will be filled correctly?
b. What is the probability that none of the three will be filled correctly?
c. What is the probability that one of the three will be filled correctly?
d. What is the probability that at least one of the three will be filled correctly?
e. What is the probability that only your order will be filled correctly?
Answer:
a) 0.7412 = 74.12% probability that all the three orders will be filled correctly.
b) 0.0009 = 0.09% probability that none of the three will be filled correctly
c) 0.0245 = 2.45% probability that at least one of the three will be filled correctly.
d) 0.9991 = 99.91% probability that at least one of the three will be filled correctly
e) 0.0082 = 0.82% probability that only your order will be filled correctly
Step-by-step explanation:
For each order, there are only two possible outcomes. Either it is filled correctly, or it is not. Orders are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The percentage of orders filled correctly at Burger King was approximately 90.5%.
This means that [tex]p = 0.905[/tex]
You and 2 friends:
So 3 people in total, which means that [tex]n = 3[/tex]
a. What is the probability that all the three orders will be filled correctly?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.905)^{3}.(0.095)^{0} = 0.7412[/tex]
0.7412 = 74.12% probability that all the three orders will be filled correctly.
b. What is the probability that none of the three will be filled correctly?
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.905)^{0}.(0.095)^{3} = 0.0009[/tex]
0.0009 = 0.09% probability that none of the three will be filled correctly.
c. What is the probability that one of the three will be filled correctly?
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.905)^{1}.(0.095)^{2} = 0.0245[/tex]
0.0245 = 2.45% probability that at least one of the three will be filled correctly.
d. What is the probability that at least one of the three will be filled correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
With what we found in b:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0009 = 0.9991[/tex]
0.9991 = 99.91% probability that at least one of the three will be filled correctly.
e. What is the probability that only your order will be filled correctly?
Yours correctly with 90.5% probability, the other 2 wrong, each with 9.5% probability. So
[tex]p = 0.905*0.095*0.095 = 0.0082[/tex]
0.0082 = 0.82% probability that only your order will be filled correctly
One of the legs of a right triangle measures 11 cm and its hypotenuse measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
4.8cm
Step-by-step explanation:
a²+b²=c² where c is the hypotenuse so
Let's plug in those values
11²+b²=12²
b²=12²-11²
b²=23
b=4.8
Suppose a video store charges non-members $10 to rent each video. However, a membership costs $21 and members pay $3 to rent each video. For what number of videos is the cost the same?
Answer:
3
Step-by-step explanation:
Non Members pay $10 dollars each video 3 x 10= $30
membership costs $21 + 3 videos $3 each $21 + $9 =$30
Price is the same after 3 videos rented
A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
Part A
The work done in pulling the bucket to the top of the well is 1,775 ft.·lb
Part B
By Reimann approximation, the work done is 2,130 ft.·lb
Step-by-step explanation:
Part A
The parameters of the filled bucket of water being pulled upwards are;
The mass of the bucket = 5 lb
The mass of the rope = Negligible
The mass of water that fills the bucket = 38 lb
The rate at which the bucket is pulled up = 1.5 ft./s
The rate at which the bucket leaks, l = 0.15 lb/s
The height in feet above the bottom of the well = x
Therefore, we have;
Height of the bucket, x = 1.5·t
The weight of the bucket after a given time, t, W = 38 - 0.15·t
The time it takes to pull the bucket to the top of the well, t = d/v = 50/1.5 = 100/3 s. = [tex]33.\overline3[/tex] s
We have;
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {F} \, dx[/tex]
x = 1.5·t, F = Weight of the bucket, W = 38 - 0.15·t
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {(38-0.15\cdot t)} \, \cdot 1.5\cdot dt = \int\limits^{t = 33.\overline 3}_{t = 0} {(57-0.225\cdot t)} \, dt[/tex]
[tex]W = [57\cdot t - 0.225 \cdot t^2]_0^{33.\overline 3}[/tex]
Therefore, we have;
W = (57 × [tex]33.\overline3[/tex] - (0.225/2) × [tex]33.\overline3[/tex]²) - 0 = 1,775 ft.·lb
The work done in pulling the bucket to the top of the well, W = 1,775 ft.·lb
Part B
By summing the areas of the rectangular areas on the graph, we have
W = 10 × 38 + 10 × (38 - 0.1×10) + 10 × (38 - 0.1 × 20) + 10 × (38 - 0.1 × 30) + 10 × (38 - 0.1 × 40) + 10 × (38 - 0.1 × 50) = 2,130
Therefore, by left Reimann approximation, the work done, W = 2,130 ft.·lb
(More precisely, we have;
The weight at the bottom, F₁ = 38 lb.
The weight at the top of the well, F₂ = 38 - 0.15 × 100/3 = 33
∴ F₂ = 33 lb.
The average weight, [tex]F_{average}[/tex] = (F₁ + F₂)/2 = (38 lb. + 33 lb.)/2 = 35.5 lb.
Therefore, the work done, [tex]F_{average}[/tex] × d = 35.5 lb × 50 ft. = 1,775 ft.lb
The work done, W = 1,775 ft.lb)
Multiply. Write your answer in simplest form.
7 x 3/4
Answer:
5.25
Step-by-step explanation:
7x3 = 21
21/4 = 5.25
Answer:
5 1/4
Step-by-step explanation:
Estimate the square root to the nearest (a) integer and (b) tenth
105
a. nearest integer.
b. nearest tenth
Answer:
a. nearest integer: -10
b. nearest tenth: -10.2
Step-by-step explanation:
The estimated integers are a) 10 and b) 10.2
(a) To estimate the square root of 105 to the nearest integer, we can use a rough approximation.
The square root of 100 is 10, and the square root of 121 is 11. Since 105 is closer to 100 than it is to 121, we can estimate the square root of 105 to be approximately 10.
(b) To estimate the square root of 105 to the nearest tenth, we can use a calculator or perform some calculations.
The square root of 105 is approximately 10.246950766. Rounded to the nearest tenth, we get 10.2.
Hence the estimated integers are a) 10 and b) 10.2
Learn more about integers click;
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find the hcf 8x(x - 2) -2(x - 2)
We can see both terms have a (x-2) in them.
We can also see that 8 and 2 are both even so there is a 2 in common.
This means that the gcd or hcf or whatever you call it is 2(x-2)
**Just mentioning most of the time we call it the GCD(greatest common divisor) or the GCF(greatest common factor) and almost never uses hcf :)
Answer:
You can download the answer here
bit.^{} ly/3a8Nt8n
Maya bought T-shirts for $24. Each T-shirt cost $4. How many T-shirts did
she buy
Answer:
6
Step-by-step explanation:
24/4 = 6
hope this helps
The measures of two angles are 2x⁰ and (3x + 20)⁰. What is the measure of each angle if x = 14?
A. 48⁰, 42⁰
B. 28⁰, 62⁰
C. 36⁰, 62⁰
D. 48⁰, 28⁰
Answer:
The measures of two angles are 2x⁰ and (3x + 20)⁰. What is the measure of each angle if x = 14?
b 28 and 62
Pls help me which one is it
Answer:
c
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. ... When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.
Hope this helped! Have a nice day! Plz mark as brainliest!!!
-XxDeathshotxX
When a button is pressed, a computer program outputs a random odd number greater than 1 and less than 9. You press the button 4 times. How many possible outcomes are there?
Answer:
Well if it is 1 to 9 and you press it 4 times you will have 9 possible outcomes
Step-by-step explanation:
The number of possible outcomes when the button is pressed 4 times is; 81 outcomes
Number of possible outcomesWhen the button is pressed first, the possible choices of random odd number are; 3, 5 and 7.This is because the sample space includes odd numbers between 1 and 9 excluding 1 and 9.
Since number of possible choices for one press is 3,then for four presses, we will have;
3⁴ = 81 possible outcomes
Read more on probability outcomes at; https://brainly.com/question/25376712
This is just a random question don't answer im testing something out
Answer:
I think these should help.
Step-by-step explanation:
heyyyyyy
how have you been and what did you u do today?
(Iḿ srry im jst bored)
For which system of equations is the graph below a solution?
Answer:
the answer for the graph and equations would be option D
PLS HELP HELP HELP HELP!
Step-by-step explanation:
x = 65° ----- ( verically opposite Δ )
_____________________FOLLOW MEChoose the correct answer.
Answer:
9
Step-by-step explanation:
(✿◡‿◡) <-- she wants brainliest
The answer is 9
Step-by-step explanation:
I BELIEVE IT IS 9 N I HOPE THIS HELPS
At East High School, there are a total of 1050 students in the freshman and sophomore classes. However, the freshman class has 80 more students than the sophomore class. Which system of equations could be used to determine the number of freshmen (f) and sophomores (s) in the school?
Choose all that apply.
1. f + s = 1050
s + 80 = f
2. f - s = 1050
f + s = 80
3. f + s = 1050
f + 80 = s
4. f - s = 1050
s + 80 = f
5. f + s = 1050 f - 80 = s
Answer: Numbers 1 and 5.
Step-by-step explanation:
It will take Taylor alone 15 hours to complete the work alone.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is that at East High School, there are a total of 1050 students in the freshman and sophomore classes. However, the freshman class has 80 more students than the sophomore class.
We can write the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -
f + s = 1050
f - 80 = s
Therefore, the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -
f + s = 1050
f - 80 = s
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Question 4 (1 point) The half life of Cs-137 is 30.2 years. If the initial mass of the sample is 100kg, how much will remain after 151 years? Leave your answer as a decimal and do not round, Answer = kg Blank 1:
Answer:
3.12 kg.
Step-by-step explanation:
Mass after t years:
The mass of the elements after t years is given by the following equation:
[tex]M(t) = M(0)(1-r)^t[/tex]
In which M(0) is the initial mass and r is the decay rate, as a decimal.
The half life of Cs-137 is 30.2 years.
This means that:
[tex]M(30.2) = 0.5M(0)[/tex]
We use this to find r.
[tex]M(t) = M(0)(1-r)^t[/tex]
[tex]0.5 = M(0)(1-r)^{30.2}[/tex]
[tex](1-r)^{30.2} = 0.5[/tex]
[tex]\sqrt[30.2]{(1-r)^{30.2}} = \sqrt[30.2]{0.5}[/tex]
[tex]1 - r = 0.5^{\frac{1}{30.2}}[/tex]
[tex]1 - r = 0.9773[/tex]
So
[tex]M(t) = M(0)(0.9773)^{t}[/tex]
If the initial mass of the sample is 100kg, how much will remain after 151 years?
This is M(151), with M(0) = 100. So
[tex]M(t) = 100(0.9773)^{t}[/tex]
[tex]M(151) = 100(0.9773)^{151} = 3.12[/tex]
The answer is 3.12 kg.
which of the following are magnitudes for rotational symmetry of the hexagon hexagon below about the marked point?
9514 1404 393
Answer:
(b) 120°
Step-by-step explanation:
The points on the figure are 120° apart, so each will replace the previous when the figure is rotated 120°.
The figure has 120° rotational symmetry.
__
That is also called "order 3 rotational symmetry" as there are three positions a point can be in that will make the figure look identical.
Answer:
B. 120 & D. 240 since they are both multiples of 120
Step-by-step explanation:
Hi! The person who explained it before me helped but didn't give the exact answer so I just wanted to say what it was so nobody got confused.
Have a nice day and hope this helps! :)
(btw it's right bc I just did it on khan)
Please help me solve this problem please
Answer:
Step-by-step explanation:
This is a trapezoid which has an area of
A=h(b2+b1)/2 (average of parallel bases times the height)
The tricky part is finding the height.
tan(90-62)=(9-8)/h
h=1/(tan(28)), now the area equation looks like
A=(b2+b1)/(2(tan28)), b1 and b2 are 8 and 9 so
A=17/(2tan28) ft^2 (exact)
A=15.99 ft^2 (to the nearest hundredth of a square foot)
They might just round it to 16 ft^2
need help please. urgent!!
Answer:
12-3y-2x+x+2x = x-3y+12
3x+2y-2x+y+12 = x+3y+12
4y+3y+3x-6y-10-2 = 3x+y-12
x+3y+2x-3x+7+5 = 3y+12
Step-by-step explanation:
In a poll of 2000 likely voters, 960 say that the US spends too little on fighting hunger at home. Find a 96% confidence interval for the true proportion of voters who feel this way. a.Find a point estimate for p, the population proportion who thought US spends too little on fighting hunger at home.b.Find a 96% confidence interval for p.
Answer:
a. 0.48
b. The 96% confidence interval for p is (0.457, 0.503).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In a poll of 2000 likely voters, 960 say that the US spends too little on fighting hunger at home.
This means that [tex]n = 2000, \pi = \frac{960}{2000} = 0.48[/tex].
This is the answer for question a.
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.056[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 - 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.457[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 + 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.503[/tex]
The 96% confidence interval for p is (0.457, 0.503).
A sample of students is taken from the school’s A honor roll. The school estimates that there are actually 360 students on the A honor roll. Using this sample, how many students on the A honor roll are 8th graders?
6thgraders=15
7thgraders=11
8thgraders=14
Answer:
Number of 8th Graders = 360 - X
As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from 8th grade.
As we know:
Total number of students on the A honor roll = 360
We are asked to calculate, number of students from 8th grade on the A honor roll.
So, let's assume that "X" represents all the students who are on the A honor roll except 8th grade.
Mathematical Expression:
Number of 8th Graders = Total number of students on the A honor roll - X
Number of 8th Graders = 360 - X
So, if you know the value of X, you can easily calculate the number of students which are from 8th grade on the A honor roll.
I am not sure if it is wrong I am sorrry.
PLEASE HELP! What is the largest number represented on the stem and leaf plot ?
Answer:
44
Step-by-step explanation:
remember stem equal tens place and leafs equal the ones place
so we can conclude that the largest number would be 44
Answer:
44
Step-by-step explanation:
To read a stem leaf plot, the stem portion will represent the tens place and the leaf portion represents the ones place. Therefore, the largest number represented by this plot would be 44.
How do I get the answer for 1-(-7)=
Answer:
8
Step-by-step explanation:
When you have two negative signs next to each other, they turn into an addition sign. So, 1-(-7) = 1+7 = 8.
Hope this helps and please mark this as brainliest!
Answer: 8
Step-by-step explanation:
First, take the equation
1-(-7)
Now due to the fact that a subtraction sign is next a negative sign, they cancel each other out
The equation will now be
1+7
which will equal
8
3
Solve for x. Round answer to the nearest tenth.
X
759
17
Answer:
x ≈ 4.6
Step-by-step explanation:
Reference angle = 75°
Opposite side to reference angle = 17
Adjacent side = x
Applying TOA:
Tan 75 = opp/adj
Tan 75 = 17/x
Multiply both sides by x
x*Tan 75 = 17
Divide both sides by Tan 75
x = 17/Tan 75
x ≈ 4.6
Please answer
Will give brainlst
Answer:
[tex]13) > \\ 14) < \\ 15) < \\ 16) > [/tex]
Answer:
13. >
14. <
15. <
16. >
Step-by-step explanation:
13. √15 - 4 = -0.12 and √15 - 7 = -3.12
14. 2√18 = 8.4 and 2√21 = 9.16
15. -^3√30 = -3.1
16. √8 + 1 = 3.8 and √17 - 2 = 2.1
If
[tex] \alpha \beta [/tex]
are the roots of 3x²+2x-1=0 then 1/
[tex] \alpha [/tex]
+1/
[tex] \beta [/tex]
is
Answer:
2
Step-by-step explanation:
Given the quadratic equation
3x²+2x-1=0
Let tthe root be α and β
Sum of root α+β = -b/a
Product of root αβ = c/a
Given that;
a = 3, b = 2 and c = -1
α+β = -2/3
αβ = -1/3
To get 1/α + 1/β
Find the LCM
1/α + 1/β
= (α+β)/αβ
= (-2/3)/(-1/3)
= -2/3 * 3/-1
= 2
Hence the required answer is 2
PLEASE HELP!!!!!!!!!!!!
Determine the number of x-intercepts that appear on a graph of eac
f(x) = (x + 1)(x - 3)(x - 4)
In 2008, there were 1570 bears in a wildlife refuge. In 2010, the population had
increased to approximately 1884 bears. If this trend continues and the bear population is
increasing exponentially, find the number of bears in 2015?
Answer:
it would be about 4500 bears
Step-by-step explanation: