Answer:
C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year.
Step-by-step explanation:
[tex]U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)[/tex]
[tex]q_1[/tex] is a vector in the set of real numbers [tex]R^2[/tex] that lists the output (measured in dollars) of products B and C manufactured during the first quarter of the year.
Therefore:
[tex]UQ=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)[/tex]
[tex]=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)[/tex]Therefore, UQ has 4 columns and 3 rows.
The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.
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
What is the midpoint of the segment shown below?
Answer:
option a (-1,-1/2)
Step-by-step explanation:
apply mid point formula
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
i dont understand, help?
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
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.
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!!!
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%.
One solution to the problem below is 10. what is the other solution?
b^2-100=0
Answer:
the same
Step-by-step explanation:
Answer:
The two solutions can be +10 and -10
Step-by-step explanation:
b^2 - 100 = 0
b^2 = 100
Take the root of both sides
b = +- 10
b = +10 , b = -10
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.
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°.
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.
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:
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
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
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
how many categories are shown in the rows?
Answer:
4 categories are shown in rows.
2 categories are shown in columns.
12 14 year olds.
82 people were polled.
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.
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
There are two sides of a coin, therefor you have 1/2 a chance of getting heads or tails. 1/2=50%
Answer:
50%
Step-by-step explanation:
There are 2 sides of a coin which have an equal chance of landing on the visible side. In other words, they each have half of the chance, or 50%.
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
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.
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
Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration.
Answer:
The population of interest is all the students at the University, to find their parking times.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
Here, the population of interest is all New York state residents.
An administrator inconspicuously followed 250 students and carefully recorded their parking times.
Sample of 250 students at the University.
So the population of interest is all the students at the University, to find their parking times.
In the interval 0° < x < 360°, find the values of x for which tan x = 2.7475
Give your answers to the nearest degree,
1
Answer:
[tex]70^\circ, 250^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]tan x= 2.7475[/tex]
and [tex]0^\circ < x < 360^\circ[/tex] i.e. [tex]x[/tex] lies in the interval [tex]0^\circ[/tex] to [tex]360^\circ[/tex] or [tex]0\ to\ 2\pi[/tex].
To find: The possible values for x in the interval [tex]0^\circ[/tex] to [tex]360^\circ[/tex] = ?
First of all, let us learn something about [tex]tan\theta[/tex].
In a right angled triangle the value of [tex]tan\theta[/tex] can be calculated as follows:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
i.e. [tex]tan\theta[/tex] is equal to the ratio of Perpendicular to Base in a right angled triangle.
We are given that:
[tex]tan x= 2.7475[/tex]
[tex]\Rightarrow x = tan^{-1}(2.7475)\\\Rightarrow x = 70^\circ[/tex]
So, the value of x in first quadrant is [tex]70^\circ[/tex].
It is also known that value of tangent is positive in the first and third quadrant.
We are given a positive value of tangent here,
So, another value of [tex]x = 180^\circ+70^\circ = 250^\circ[/tex]
Hence, the correct answers are: [tex]x=70^\circ, 250^\circ[/tex]
According to an airline, flights on a certain route are on time 85% of the time. Suppose 20 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment
(b) Find and interpret the probabdity that exadly 15 flights are on time.
(c) Find and interpret the probability that fewer than 15 flights are on time.
(d) Find and interpret the probability that at least 15 flights are on time.
(e) Find and interpret the probability that between 13 and 15 flights, inclusive, are on time.
(a) Identify the statements that explain why this is a binomial experiment. Select all that apply.
A. Each trial depends on the previous trial
B. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late.
C. The experiment is performed unti a desired number of successes is reached
D. The trials are independent.
E. The probability of success is the same for each trial of the experiment.
F. There are two mutually exclusive outcomes, success or failure.
G. The experiment is performed a fixed number of times.
Answer:
See the answers below. Thanks!
Step-by-step explanation:
(a). Option F is the correct choice. "There are two mutually exclusive outcomes, success or failure."
(b). P(X=15) = 0.1702
(c). P(X<15) = 0.0673
(d). P(X>=15) = 1 - P(X<15) = 0.9327
(e). P(13<=X<=15) = 0.1482
Best Regards!
The number of hits on a certain website during a one-minute interval follows a Poisson distribution with a mean rate of four hits per minute. What is the probability that there is at least one hit in a 30-second period (that is the probability of one or more hits)
Answer:
86.47% probability that there is at least one hit in a 30-second period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean rate of four hits per minute.
This means that [tex]\mu = 4n[/tex], in which n is the number of minutes.
What is the probability that there is at least one hit in a 30-second period
30 seconds is 0.5 minutes, so [tex]\mu = 4*0.5 = 2[/tex]
Either the site doesn't get a hit during this period, or it does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1353 = 0.8647[/tex]
86.47% probability that there is at least one hit in a 30-second period
Error Analysis A problem on a test says that 70% of people enjoy the beach. The students are
asked to use the simulation numbers below to estimate the probability that exactly one person says
he or she enjoys the beach. Let the numbers 0-6 represent a person who enjoys going to the beach
and let 7-9 represent a person who does not. One student says that the probability is about 100%.
Estimate the probability that exactly one person enjoys the beach. What error might the student have
made?
(5,8) (2,7) (0,9) (0,2) (9,0) (1,9) (4,7) (0,3) (6,7) (7,5)
Use the simulation to estimate the experimental probability that exactly one person enjoys the beach
is 40%
Enter your answer in the answer box and then click Check Answer
pan
rema
Answer:
Probability that exactly one person says he or she enjoys the beach = 80%
Check Explanation for how to get this and which error the studemt that made the 100% claim must have made.
Step-by-step explanation:
The simulation presented is that for a series of two people sample.
Numbers 0 to 6 represents that the beach-goer enjoys going to the beach and numbers 7 to 9 represents that the beach-goer doesn't enjoy going to the beach.
So, the simulation is then obtained to be
(5,8) (2,7) (0,9) (0,2) (9,0) (1,9) (4,7) (0,3) (6,7) (7,5)
Using the simulation, estimate the probability that exactly one person says he or she enjoys the beach
From the simulation, the ones with exactly one of the two numbers ranging from 0 to 6 to indicate enjoying going to the beach include
(5,8) (2,7) (0,9) (9,0) (1,9) (4,7) (6,7) (7,5)
The probability of an event is defined and expressed as the number of elements in that event divided by the total number of elements in the sample space.
Probabilty that exactly one person says he or she enjoys the beach = (8/10) = 0.80 = 80%
The student claims that this probability is 100%, but the other two simulations that did not satisfy the condition of exactly one person saying that he or she enjoys the beach include
(0,2) and (0,3), which show that in the two cases, the two participants both expressed enjoying going to the beach.
The student's error must have been in counting these two simulations as part of 'exactly one person saying he or she enjoys the beach' which is indeed an error.
Hope this Helps!!!
describe this diagram help please
Answer:
U are finding the slope. so the vertical line is ur rise(x value) and the horizontal line is ur y value. Hopefully that helped
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