Answer:
a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.
b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours
Step-by-step explanation:
To solve this question, we need to understand the normal and the binomial probability distributions.
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.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Proportion repaired below 6 hours:
Mean 5 hours and standard deviation 1 hour, which means that [tex]\mu = 5, \sigma = 1[/tex]
This proportion is the p-value of Z when X = 6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6 - 5}{1}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.8413 repaired below 6 hours.
For the binomial distribution, this means that [tex]p = 0.8413[/tex]
5 are chosen:
This means that [tex]n = 5[/tex]
a) Probability that all are repaired in less than 6 hours
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.8413)^{5}.(0.1587)^{0} = 0.4215[/tex]
0.4215 = 42.15% probability that all are repaired in less than 6 hours.
b) Probability that exactly 3 of them repaired below 6 hours
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.8413)^{3}.(0.1587)^{2} = 0.15[/tex]
0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours
Please help first correct will get brianliest. Find the value of x that makes DEF XYZ
Answer:
x = 7
Step-by-step explanation:
The larger triangle is twice as big as the smaller triangle. Therefore, the length of the side EF is twice as large as the side YZ.
I multiplied 4.5 (the length of YZ) and 2 to get 9. The value of side EF is 3x-12 and should be equivalent to 9.
3x - 12 = 9
I solved this equation by adding 12 to both sides and dividing 3 on both sides.
The value of x is 7.
Is it a function yes or no. 1,2,3,4,5,6.
PLZ HELP: Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
Answer:
see explanation
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{1}{2}[/tex] x + 4 ( multiply through by 2 to clear the fraction )
2y = x + 8 ( subtract 8 from both sides )
2y - 8 = x
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex](x ) = 2x - 8
[tex]f^{-1}[/tex](4) = 2(4) - 8 = 8 - 8 = 0
What is the solution set of the equation x2 + 2x – 15 = 0?
Answer:
( x − 3 ) ( x + 5 )
Step-by-step explanation:
HAVE A NICE DAY
Answer:
B
Step-by-step explanation:
; factor the left side of the equation
; (x−3) (x+5) = 0
set factors equal to 0
x − 3 = 0
or
x + 5 = 0
; so, x = 3 or x = −5
Easy
1/6 x 1/2x 1/3
help me (￣▽￣)╭
======================================================
Explanation:
The numbers up top are 1,1,1. They multiply to 1*1*1 = 1. So that means 1 is the numerator of the answer.
The numbers down below are 6,2,3. They multiply to 6*2*3 = 36. This is in the denominator for the answer.
That means (1/6)*(1/2)*(1/3) = 1/36
The rule I used is (a/b)*(c/d) = (a*c)/(b*d)
Answer:
1/36
Step-by-step explanation:
Step 1:
1/6 · 1/2 · 1/3 Equation
Step 2:
1/6 · 1/6 Multiply
Answer:
1/36
Hope This Helps :)
What is the exponent when you convert 71,100,000 into scientific notation?
Answer:
7
Step-by-step explanation:
7.11 × 10^7
The number 71,100,000 can be written in scientific notation as 7.11×10⁷ after using the concept of the scientific form of a number.
What is the number?
A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.
It is given that:
The number is 71,100,000
After converting it into the scientific notation:
7.11×10⁷
Which is equal to 71,100,000
Thus, the number 71,100,000 can be written in scientific notation as 7.11×10⁷ after using the concept of the scientific form of a number.
Learn more about the number here:
brainly.com/question/17429689
#SPJ2
Explica qué significan las variables "m" y "b" en la ecuación y = mx +b*
Answer:
La M representa la pendiente de la recta y la b representa la intersección con el eje y
Step-by-step explanation:
Que tengas un excelente verano :)
Respuesta: En la ecuación y= mx + b, “m” representa la pendiente y “b” representa el y-intercept.
Espero que esto ayude, buena suerte! :D
What are the dimensions of the rectangle shown on the coordinate plane?
The base is 5 units and the height is 4 units.
Hope this helps! :)
A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x+2x+6<50, where xrepresents the smaller number.
From the set (13, 14, 15, 16, 17), the values of x for which the inequality holds true are
Answer:
13, 14
Step-by-step explanation:
The parameters of the numbers are;
A whole number value = 2 × Another number + 6
The sum of the two numbers is less than 50
Given that the first number is equal to more than twice the second number, we have that the first number is the larger number, while the second number is the smaller number
Where 'x' represents the second number, we get;
x + 2·x + 6 < 50
Simplifying gives;
3·x + 6 < 50
x < (50 - 6)/3 = 14.[tex]\overline 6[/tex]
x < 14.[tex]\overline 6[/tex]
Therefore, the numbers for which the inequality holds true are numbers less than 14.[tex]\overline 6[/tex]. From the given option, the numbers are 13, and 14.
Find the missing lengths of the sides.
Answer: x = 8, y = 8
Step-by-step explanation: If 8 is already on the exterior of the triangle then this means that every angle should also be 8. But, if this were an equilateral triangle, a triangle with equal sides, then ALL sides would HAVE to be 8. But since I don't have this information (if it's equilateral or not), then I can't be positive about this. Really hope this helps you!
Please help!! I have a test tomorrow and I'm struggling to answer this question
A periodic function f(x) has a period of 11. The values of f(3) and f(11) are 12 and 27, respectively. What is the value of f(14)?
Answer:
12
Step-by-step explanation:
f(14)= f (3 + 11)
= f(3) = 12
Therefore the value of f(14) is 12.
What are all numbers that equal to 30 in multiplication
Answer:
2 X 15 =30
3 X 10 = 30
5 X 6 = 30
6 X 4 = 30
10 X 3 = 30
Step-by-step explanation:
Question 2 of 10 The diagonals of a square are A perpendicular B. paralle C. sometimes equal D. never congruen:
B parallel yourwelcome
Answer:
b
Step-by-step explanation:
there aren't diagonals in a square there are in a rhombus learn the difference in the future it can really help you try this out please give brainlest I'm trying to rank up
HELP ME WITH MATH PLEASEEEEE PLEASE ILL MARK
Answer:6
Step-by-step explanation:
Answer:
Your answer is right!
-130
Step-by-step explanation:
What are the domain and range of the function represented by the table?
Answer:
Doman is always the x-intercept.
And Range is always the y-intercept.
Domain = {-5, 0, 5, 10, 15}
Range = {-1, 0, 1, 2, 3}
So the answer is C.
pls help!!!!!!!!!!!!!!!!!!
Answer:
32 degrees.
Step-by-step explanation:
A triangle is 180 degrees.
180 - 85 - 63 = 32 degrees.
Answer:
x = 32
Step-by-step explanation:
All interior angles in a triangle equal to 180
use this to solve for x
180 = 85 + 63 + x
180 - 85 - 63 = x
32 = x
A shoe store sends an email survey to all customers who pay with a debit card. The previous month, 34,000 people made debit card purchases. Surveys were sent to 2,000 of these people, chosen at random, and 256 people responded to the survey. Identify the population and the sample. The population is 34,000. The sample is 2,000. The population is 2,000. The sample is 256. The population is 256. The sample is 34,000. The population is 2,000. The sample is 34,000. The population is 34,000. The sample is 256.
Answer:
The population is 34,000. The sample is 2,000
Step-by-step explanation:
Population in statistics can be explained as the group or set of all elements which are of particular interest to a researcher or a study. In the scenario above, the research interest concerns customers who pay with a debit card, whose number amounts to 34,000, this value refers to the population. The sample is referred to as the subset of the population or larger sample, the sample from the study corresponds to number of debit card users who were selected at random to participate in the survey. This value is 2000.
Select all the solutions to the quadratic equation x2-4x-12=0
Answer:
x1= -2
x2= 6
Step-by-step explanation:
x^2-4x-12=0
x^2+2x-6x-12=0
x(x+2)-6(x+2)
(x+2)*(x-6)
one solution
x+2=0
x=-2
other solution
x-6=0
x=6
solver for x, trigonometric ratios
PLEASE PLEASE HELP ME! thank you so so much
explaining your answer = brainliest/five stars
The radius of a circle is 4 kilometers. What is the area of a sector bounded by a 135° arc?
give the exact answer in simplest form
Answer:
6π
Step-by-step explanation:
(135/360)×π×4²
(135/360)×π×16
=6π
Find the volume of the triangular prism
Answer:
72 yd³
Step-by-step explanation:
Volume = Area triangle * height
Area triangle = 1/2( 8 x 3 ) = 1/2( 24 ) = 12
Volume = 12 * 6 = 72
Units = yd³
72 yd³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
After leaving her house, Shelley drove 14.47 kilometers to the gas station and then another 5.8 kilometers to work. How many total kilometers did Shelley drive to get to work after she left her house? Show your work on paper. Then, enter your answer in decimal form in the box
Answer:
20.27 km
Step-by-step explanation:
14.47
+ 5.8
20.27
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
Answer:
y-y1=m(x-x1)
y-2=1/3(x-3)
y=1/3x+1
Need some assistance please
Answer:I hope this could help !ut the answer is 4
Step-by-step explanation:
2 of them left so there are 4 left
¿Cómo expresarías la siguiente cantidad 1149,8x1018, en su equivalencia a notación científica?
I need help to find the value please
Answer:
13.928
Step-by-step explanation:
Pythagorean theorem. 13^2 + 5^2 = x^2
Answer:
this is easy
Step-by-step explanation:
valve of x is 30 add 13 into 30 = 43÷5 5/8
Anthony and Joan have $10 to buy apples and oranges at the market. They will buy a total
of 25 pieces of fruit. Apples cost 50 cents each and oranges cost 25 cents each. Which of
these systems best represents this situation?
Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
Volume of a sphere = 4πr³/3
r=10
V = 4πx10³/3
=4000π/3
V= 1333.33π (in terms of pi)
or
V= 4188.79(Nearest Hundredth).
In a right triangle, the ratio of the length of the side opposite acute angle to the length of the side adjacent to angle is called the tangent of angle .
Answer:
The given statement is "True"
Step-by-step explanation:
The right angle triangle is shown below:
The tangent value of an angle is given by the expression as shown below:
[tex]tan\alpha =\frac{a}{b}[/tex]
describe fully the single transformation that maps A onto c
Answer:
They are different because they are not similar and they have different answer at the end