Answer:
a. 10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.
b. 0.2457 = 24.57% probability 10 of the problems can be resolved today
c. 0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today
d. 0.5017 = 50.17% probability more than 10 of the problems can be resolved today
Step-by-step explanation:
For each case, there are only two possible outcomes. Either they are solved, or they are not. Cases are independent of each other. So 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 expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
It can resolve customer problems the same day they are reported in 80% of the cases.
This means that [tex]p = 0.8[/tex]
Sample of 13 cases:
This means that [tex]n = 13[/tex]
a. How many of the problems would you expect to be resolved today? What is the standard deviation?
Expected:
[tex]E(X) = np = 13*0.8 = 10.4[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{13*0.8*0.2} = 1.44[/tex]
10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.
b. What is the probability 10 of the problems can be resolved today?
This is [tex]P(X = 10)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]
0.2457 = 24.57% probability 10 of the problems can be resolved today.
c. What is the probability 10 or 11 of the problems can be resolved today?
This is [tex]p = P(X = 10) + P(X = 11)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457[/tex]
[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]
[tex]p = P(X = 10) + P(X = 11) = 0.2457 + 0.2680 = 0.5137[/tex]
0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today.
d. What is the probability more than 10 of the problems can be resolved today?
This is
[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680[/tex]
[tex]P(X = 12) = C_{13,12}.(0.8)^{12}.(0.2)^{1} = 0.1787[/tex]
[tex]P(X = 13) = C_{13,13}.(0.8)^{13}.(0.2)^{0} = 0.0550[/tex]
[tex]P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) = 0.2680 + 0.1787 + 0.0550 = 0.5017[/tex]
0.5017 = 50.17% probability more than 10 of the problems can be resolved today
Marie about six books for total $360 math books cost 80 and science books cost 50 how many science books did she buy
Answer:
4 books are science
2 are math
:)
Which expression is equivalent to this expression (x-1)-(1-x)+x
Answer:
ihkjl; yfcuhbkn mguv7g8inngvui vuiihj n.
Step-by-step explanation:
a. 160 is what percentage of 40?
Answer:400%
Step-by-step explanation:
20+20=40 because if u add ten again then it would be 10+10 and that. Would be 20 then 20+10 is 30 then 30+10 then that would be 40 so then 20+20= cause 2+2=4 then add the zero to get 40
Answer:
Yes Good Job Now Mark Me Brainliest PLEASE
Step-by-step explanation:
Don’t get it help me !
Answer:
a > 12
Step-by-step explanation:
To ride the go karts you need to be OVER 12 years old. We are going to use < and > because you can't be 12 and younger. The hint is OVER because this essentially means that the variable a HAS to be bigger than 12. Thus is why the ineuality is a > 12.
Best of Luck!
What is the midpoint of the line segment with the equation y=12x+3 between x=−4 and x=8?
(2,−2)
(2,2)
(2,4)
(6,6)
Answer:
2, -2
Step-by-step explanation:
what i answered probs not right lol
Point A, located at (-11, - 7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C. What are the coordinates of points B and C?
Answer:
Answer: B(-11,7) C(11,7)
Step-by-step explanation:
Reflections In The Coordinate Plane
Reflect over the x-axis:When we reflect a point over the x-axis, the x-coordinate remains the same, but the y-coordinate is mapped to its opposite.
The reflection of the point (x,y) over the x-axis is the point (x,-y).
Reflect over the y-axis:When reflecting a point over the y-axis, the y-coordinate remains the same, but the x-coordinate is mapped to its opposite (its sign is changed).
The reflection of the point (x,y) across the y-axis is the point (-x,y).
Point A is at (-11,-7). When reflected over the x-axis, it maps to Point B located at B(-11,7).
Point B is now reflected over the y-axis and maps to C(11,7).
Answer: B(-11,7) C(11,7)
Please help :) Thanks!
Answer:
Answer: A
Step-by-step explanation:
Given 10 is a leg of a right triangle and 11 is the hypotenuse, what is the length of the other leg of the right triangle? Round
Vou answer to the nearest hundredi derinals
Answer:
The length of other leg is 4.58
Step-by-step explanation:
It is given that:
One leg of triangle = 10
Hypotenuse = 11
Using Pythagorean theorem,
[tex]a^2+b^2=c^2\\(10)^2 + b^2 = (11)^2\\100+b^2 = 121 \\b^2 = 121-100 \\b^2 = 21[/tex]
Taking square root on both sides
[tex]\sqrt{b^2}=\sqrt{21}\\b=4.58[/tex]
Therefore,
The length of other leg is 4.58
Help!!!!!!!! Pls?????
Answer:
220 newtons
Step-by-step explanation:
just to make sure what is 9 x 2/3
Answer:
6
Step-by-step explanation:
1. If your local library allows you to check out up to 10 books every month, what is the
maximum number of books you can check out in 2 years and 5 months?
Answer:
290 books
Step-by-step explanation:
10 × 12= 120
120×2= 240
10×5=50
50+240= 290 books in 2 years and 5 months. hope this helps!
What is the lowest form of 32:28?
Answer:
to lowest terms of 32:28 is 8/7 or 8:7
Step-by-step explanation:
Find an equation of the line with the given y-intercept and slope m.
10, m= 5
The equation of the line is
(Type your answer in slope-intercept form.)
Answer:
y = 5x + 10
Step-by-step explanation:
Use formula: y = mx + b
1. Since m = 5, plug it into where m is
2. 10 has no variable so it's b ( the y-intercept)
3x + 2y = 5
5x + 2y = 7
Based on the given system of equations, which of the following is not true?
8x=12
4y=4
2x=2
Answer:
I am guessing the 1st one.
Step-by-step explanation:
8x does NOT equal 12 I believe. I am sorry if I am incorrect
Dan buys a car for £1700.
It depreciates at a rate of 4% per year.
How much will it be worth in 4 years?
Answer:
Step-by-step explanation:
100%-4%=96%
96/100=0.96
£1700*0.96^4=£1443.89
Answer:
1143.89Step-by-step explanation:
I HOPE it's help you
What is the diameter of the inscribe circle of the triangle?
============================================
Work Shown:
The two angle bisectors intersect to form the incenter. The incenter is the center of the inscribed circle (aka "incircle"). This circle is the largest possible, but is completely inside the triangle. No portions of the circle spill outside the triangle.
The two segments marked with lengths x+8 and 2x-5 are two radii of the incircle. This is because the sides of the triangle are tangent to the incircle.
Since all radii are the same length, we can set those expressions equal to one another and solve for x
x+8 = 2x-5
x-2x = -5-8
-x = -13
x = 13
This x value then leads to
x+8 = 13+8 = 212x-5 = 2*13-5 = 26-5 = 21Both radii are 21 units long, which helps confirm we have the proper x value. We double the length of the radius ot get the diameter.
So the diameter of the incircle is 2*21 = 42 units long.
The relationship between the elapsed time t, in days, since the mass of the sample was initially measured, and its mass, M(t), in grams, is modeled by the following function:
M(t)=900⋅(8/27)^t
Complete the following sentence about the rate of change of the sample. Round your answer to two decimal places.
The sample loses 1/3 of its mass every ___ days.
Answer:
The sample Loses .33 mass every day
Step-by-step explanation:
How wide is a pool that has a length of 25/2 feet and area of 225/2 square feet?
Answer:
16 feet for pool and 12 for square feet
Step-by-step explanation:
Identify the first step when evaluating the expression 11 – 10 ÷ 2 + 6 × 1
Answer: 6.5
Step-by-step explanation: You first substract 11-10 that would be 1 so, you divide it by 2, that tyhe answer of that is 0.5 so we add 6, the total owuld be 6.5, times 1, it would be the samen cantity because each number multiple by 1 give the same answer.
PLEASE HELP 10 BRAINLY POINTS
Find SA for this triangular prism: DON'T FORGET TO SHOW ALL WORK
Answer: 872
10 times 16 = 160
12vtimes 10 = 120
20 times 20 = 400
12 times 16 = 192
*with the area of triangles, you have to divide your number by 2, but there is 2 triangles, so 192, instead of 96*
Step-by-step explanation:
63 is 11% of what number?
Answer:
572.7272
572.73 (rounded)
Step-by-step explanation:
used calc
Consider an example of an apartment: The number of bedrooms, bathrooms, and the floor of an apartment determines its price. Which is the dependent variable in this example
Answer: The price of the apartment.
Step-by-step explanation:
We know that for a given apartment, the number of bedrooms, bathrooms, and floor determines the price.
Then we could define the variables:
x = number of bedrooms.
y = number of bathrooms
z = floor.
And define the price of the apartment as a function of these variables:
p(x, y, z) = price
Then the independent variables are x, y, and z.
And the dependent variable (this is, the variable that changes in response to the changes in the independent variables) will be the price of the apartment.
Using function concepts, it is found that the dependent variable in this example is the price.
The standard format of a function is: [tex]y = f(x)[/tex].In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.In this problem, price depends of the number of bedrooms, bathrooms, and the floor of an apartment, hence, the function is:
[tex]p = f(be, ba, fl)[/tex]
Which means that the dependent variable is the price.
You can learn more about dependent and independent variables at https://brainly.com/question/1429012
Convert 0.245 into a percent and choose the appropriate result.
А
24.5%
B
2.45%
245%
D) 0.245%
Answer:
A. 24.5
Step-by-step explanation:
HOPE THIS HELPS!!!!
Can I have Brainliest???
Answer:
Its A, 24.5%
Step-by-step explanation:
I remember doing this before
When the supplies are endless, prices tend to O A. fluctuate O B. stay the same O C. decrease O D. increase
the answer is c. decrease
what is 2 + 2 - 90 + 40
Answer:
-46
Step-by-step explanation:
hope this helps ;)
Answer:
Pemdas makes it -46
Step-by-step explanation:
since this is only addition and subtraction it doesn't matter really what order you do it in
2+2=4
-90+40=-50
4+-50=-46
this is thanks to the Commutative property of addition which states that "Changing the order of addends does not change the sum."
PLEASE HELP!!!!!
Solve, showing and explaining all steps in the process. 7(y + 2) – (2y – 5) = 41
Answer:
Step-by-step explanation:
Remove parentheses.
7(y+2)-2y+5=41
2 Expand.
7y+14-2y+5=41
3 Simplify 7y+14-2y+5 to 5y+19.
5y+19=41
4 Subtract 19 from both sides.
5y=41-19
5 Simplify 41-19 to 22
5y=22
6 Divide both sides by 5.
y= 22/5
Answer:
y=6.4
Step-by-step explanation:
distribute:
7y+14-2y-5=41
then combine like terms:
5y+9=41
subtract 9 from both sides:
5y=32
divide 5 by both sides:
y=6.4
Identify the first step when evaluating the expression 11 – 10 ÷ 2 + 6 × 1
9) Martin was jogging to school at a speed of 10 mph. Unfortunately,
when he was halfway there, he sprained his ankle and his mom had
to give him a ride the rest of the way at 40 mph. After school Martin
rode the bus home at an average speed of 20 mph. What was
Martin's average speed on his round trip to school and back?
23.33mph
Step-by-step explanation:
You add all the speed and divide it by 3
An environmental club is raising money to preserve habitat for local owls. They are keeping track of their progress using the “thermometer” shown. Which is the best estimate of the progress they have made in reaching their goal?
what's the answer
A
30%
B
14
C
12
D
0.95
Answer:
is there an image?
Step-by-step explanation:
if no then i guess B