Answer:
(a) P(Millennial | Read a Book) = 0.3086
(b) P( Not Millennial | Did Not Read a Book) = 0.8421
(c)
P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)
0.25 = 0.81 × 0.28
0.25 ≠ 0.2268
Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.
Step-by-step explanation:
The probability a person has read a book in the past year is 0.81.
P(Read a Book) = 0.81
The probability a person is considered a millennial is 0.28.
P(Millennial) = 0.28
The probability a person has read a book in the past year and is considered a millennial is 0.25.
P(Millennial and Read a Book) = 0.25
(a) Find P(Millennial | Read a Book)
Recall that Multiplicative law of probability is given by
P(A ∩ B) = P(B | A) × P(A)
P(B | A) = P(A ∩ B) / P(A)
For the given case,
P(Millennial | Read a Book) = P(Millennial and Read a Book) / P(Read a Book)
P(Millennial | Read a Book) = 0.25 / 0.81
P(Millennial | Read a Book) = 0.3086
(b) Find P(Not Millennial | Did Not Read a Book)
P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)
Where
∵ P(A' and B') = 1 - P(A or B)
P(Not Millennial and Did Not Read a Book) = 1 - P(Millennial or Read a Book)
∵ P(A or B) = P(A) + P(B) - P(A and B)
P(Millennial or Read a Book) = P(Read a Book) + P(Millennial) - P(Millennial and Read a Book)
P(Millennial or Read a Book) = 0.81 + 0.28 - 0.25
P(Millennial or Read a Book) = 0.84
So,
P(Not Millennial and Did Not Read a Book) = 1 - 0.84
P(Not Millennial and Did Not Read a Book) = 0.16
Also,
∵ P(A') = 1 - P(A)
P(Did Not Read a Book) = 1 - P(Read a Book)
P(Did Not Read a Book) = 1 - 0.81
P(Did Not Read a Book) = 0.19
Finally,
P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)
P( Not Millennial | Did Not Read a Book) = 0.16/0.19
P( Not Millennial | Did Not Read a Book) = 0.8421
(c) Are being considered a millennial and having read a book in the past year independent events? Justify your answer mathematically.
Mathematically, two events are considered to be independent if the following relation holds true,
P(A and B) = P(A) × P(B)
For the given case,
P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)
0.25 = 0.81 × 0.28
0.25 ≠ 0.2268
Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.
If the legs of a right triangle are 10 and 24, then the
hypotenuse is
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using
function notation?
Fly) = -
f(x) = - 3x + 4
f(x) =
FCV) = -3y+ 4
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Step 1: Write it in slope-intercept form
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
Step 2: Replace y with f(x)
f(x) = -3x + 4
In math, function f(x) is equal to the variable y.
A problem requires finding the distance traveled in miles. Which would not be a reasonable answer? Justify your response. A. minus10 B. 1.8 C. 10 and one half D. 50
Answer:
A. minus 10,
Step-by-step explanation:
The distance travelled must be positive.
Therefore minus 10 would not be a reasonable answer.
What is the midpoint of the segment shown below?
Answer:
option a (-1,-1/2)
Step-by-step explanation:
apply mid point formula
Does the equation Axequalsb have a solution for each b in set of real numbers RSuperscript 4? A. No, because A has a pivot position in every row. B. Yes, because the columns of A span set of real numbers RSuperscript 4. C. Yes, because A does not have a pivot position in every row. D. No, because the columns of A do not span set of real numbers R
Answer:
C. Yes, because A does not have a pivot position in every row.
Step-by-step explanation:
The pivot position in the matrix is determined by entries in non zero rows. The pivot position may be in the row or a column. By Invertible Matrix Theorem the equation Axequalsb has non trivial solution. A has fewer pivot positions therefore A is not invertible. Ax will map RSuperscript into real numbers for n times. A has pivot position if left parenthesis bold x right parenthesis.
A perfect square number can never have the digit ….. at the units place.
a :1
b :9
c :8
please tell me the answer as soon as possible
Answer:
the answer is the last option, c :8.
20 Find the area of the rectangle given that
the perimeter is 50 cm.
3m + 2
m - 5
F 32
G 7
H 46
J 9
Answer: H - 46
Step-by-step explanation:
Primeter = 2(l + w)
50 = 2{(3m+2) + (m-5)}
25 = 3m+2 +m -5
25 = 4m -3
m = 28/4 = 7
l = 3m+2 = 23 cm
w = m-5 = 2 cm
Area = l x b
= 23 x 2 = 46 sq. cm.
The measure of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.
Answer:
21°
Step-by-step explanation:
All angles in a triangle add up to 180°.
180 - 31 - 128
= 21
The measure of the third angle is 21°.
Translate to an algebraic expression.
28 more than d
Answer: d + 28
Step-by-step explanation:
Answer:
d+28
Step-by-step explanation:
it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
Help me please thank u
Answer:
160cm
74mm
3.6km is 3600m
Step-by-step explanation:
1. 6 x 100= 160cm
7.4cm x 10 =74mm
3.6 x 1000= 3600m
find the mean of x,2x,3x,4x,5
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{TotalNumberOfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
Three solid shapes, A B and C are similar. The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to shape C is 27:125 Work out the ratio of the height of shape A to shape B Give your answer in its simplest form.
Answer:
9:20
Step-by-step explanation:
The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.
If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².
Therefore, (A/B )² = 9/16
square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4
The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.
Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5
To make the ratio equivalent A:B:C = 9:12:20
A:C = 9:20
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola
Answer:
The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Step-by-step explanation:
Complete Question
A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.
Solution
For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.
Each skier is expected to exceed 333.333 lb weight.
Probability of one skier exceeding this limit = P(x > 333.333)
This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb
We first standardize 333.333 lbs
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (333.333 - 200)/40 = 3.33
To determine the required probability
P(x > 333.333) = P(z > 3.33)
We'll use data from the normal distribution table for these probabilities
P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)
= 1 - 0.99957
= 0.00043
So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵
= (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Hope this Helps!!!
Which best compares the slope and y-intercepts of the linear functions f and g where f= 1/3 x + 3 and g is shown in the table? X =0,1,2,3 and g(x) =3,6,9,12
Answer:
different slope same intercept
Step-by-step explanation:
g(x)= 3x+3
this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for
PLZ I NEED THIS BY THE END OF THE DAY What are at least 5 examples of math that we often do in everyday life?
Answer:
cooking ( mesurments )
gardening ( landscape )
designing ( art )
shopping for the best price ( aka money counting )
car rides ( figuring out distance and time )
sewing.
hope this helped :)
Step-by-step explanation:
What two numbers is the square root of 74 between?
Answer:
8 and 9
Step-by-step explanation:
√64 = 8
√81 = 9
√74 falls inbetween those 2
3. Students arrive at an ATM machine in a random pattern with an average inter-arrival time of 3 minutes. The length of transactions at the ATM machine is exponentially distributed with an average of 2 minutes. (a) What is the probability that a student arriving at the ATM will have to wait
Answer:
The probability that a student arriving at the ATM will have to wait is 67%.
Step-by-step explanation:
This can be solved using the queueing theory models.
We have a mean rate of arrival of:
[tex]\lambda=1/3\,min^{-1}[/tex]
We have a service rate of:
[tex]\mu=1/2\,min^{-1}[/tex]
The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).
Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.
The last can be calculated as:
[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]
Then, the probability that a student arriving at the ATM will have to wait is 67%.
The two figures are similar. Write a proportion to find the missing measure. Then find the value of x.
Answer:
First option is the right choice.
Step-by-step explanation:
x/95 = 15/19
x = 75
Best Regards!
Answer:
Option A
Step-by-step explanation:
Triangle ABC and DEF are similar.
Taking proportion of their sides to find the value of the unknown.
=> x/15 = 95/19
Cross Multiplying
=> 19x = 1425
Dividing both sides by 9
=> x = 75
Prove your work what is 1/12 of a dozen Branliest
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
Order the numbers from least to greatest: -5, 6, and 9.
Answer: -5, 6, and 9
Step-by-step explanation:
Step-by-step explanation:
least to greatest
-5 6 9
The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places)
Answer:
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 0.5, \mu = \frac{1}{0.5} = 2[/tex]
What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)[/tex]
In which
[tex]P(X \leq 1) = 1 - e^{-2} = 0.8647[/tex]
[tex]P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507[/tex]
So
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314[/tex]
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
i dont understand, help?
Please answer this correctly without making mistakes as my work is due today
Answer:
2
Step-by-step explanation:
Arranging them in ascending order we have the scores as;
[tex]2, 3, 3, 4, 4, 6, 8, 9, 9, 9[/tex]
The median is the average of the 5th and 6th scores.
[tex] \frac{4 + 6}{2} \\ \frac{10}{2} \\ 5[/tex]
The new set of scores become
[tex]2,3,3,4,6,8,9,9,9,9[/tex]
The median is;
[tex] \frac{6 + 8}{2} \\ \frac{14}{2} \\ 7[/tex]
The difference is
[tex]7 - 5 = 2[/tex]
Hope it helps! Vote for brainliest!
Please help me with this problem, I can't figure it out
Answer: 44
Step-by-step explanation:
This is a confusing problem to look at, so use PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction).
5 * (-4) + (1 - (-3)^2)^2 simplify inside the parenthesis
5 * (-4) + (1 - 9)^2
5 * (-4) + (-8)^2 simplify exponents
5 * (-4) + 64 multiply
-20 + 64 finally, addition
44
Compare and contrast the following piecewise
defined functions.
(-x+ 2 x<0
X+2, x<0
f(x) =
x? + 1, x>0 X + 2, x>0
g(x)=
Answer:
Both piecewise functions have a linear portion and a quadratic portion. The y-intercepts of both linear pieces are the same, 2. The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2). The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.
Step-by-step explanation:
Comparing and contrast of the functions are shown in below.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given piecewise functions are;
⇒ f (x) = { - x + 2 ; x < 0
= { x² + 1 ; x > 0
Now, Comparison and contrast of the above piecewise functions are,
The similarities are;
1) Both piecewise functions are linear when x < 0.
2) Both piecewise functions are quadratic when x > 0.
3) The magnitude the slope of the linear part both function are equal.
4) The leading coefficient of the quadratic function are the same.
5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.
6) The domain of the linear and quadratic functions are the same.
The contrasts (differences) in the function are;
1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.
2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.
3) The quadratic function in f(x) and g(x) have graphs that do not intersect.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water? Answer: (round to 4 decimal places)
Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Kinda been stuck on this one, someone pls let me know
Answer:
255
Step-by-step explanation:
use calculator
Answer:
255
Step-by-step explanation:
∑ᵢ₌₁⁸ 2ⁱ⁻¹
Using brute force method:
S = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷
S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
S = 255
Using formula:
S = a₁ (1 − rⁿ) / (1 − r)
S = 1 (1 − 2⁸) / (1 − 2)
S = 255
In right triangle PQR, What is tan P
Answer:
c. 3/4
Step-by-step explanation:
tan is opposite over adjacent and based off of the included information its 3/4
78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0