Answer:
True.
Step-by-step explanation:
A probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. Probability distribution is associated with the following characteristics or properties;
1. The outcomes are mutually exclusive.
2. The list of outcomes is exhaustive, which simply means that the sum of all probabilities of the outcomes must equal one (1).
3. The probability for a particular value or outcome must be between 0 and 1.
Since a probability distribution gives the likelihood of an outcome or event, a single random variable is divided into two main categories, namely;
I. Probability density functions for continuous variables.
II. Discrete probability distributions for discrete variables.
For example, when a coin is tossed, you can only have a head or tail (H or T).
Also, when you throw a die, the only possible outcome is 1/6 and the total probability for it all must equal to one (1).
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle. If (3x+3) (5x-9)
Answer:
39 degrees and 51 degrees respectively.
Step-by-step explanation:
Two angles are complementary if their sum adds up to 90 degrees.
Given the pair of complementary angles formed by the three support beams:
3x+3 and 5x-9
Then:
3x+3+5x-9=90 degrees
Collect like terms
3x+5x=90+9-3
8x=96
Divide both sides by 8
x=12
Therefore, the measure of each angle is:
[tex](3x+3)=3(12)+3=36+3=39^\circ\\(5x-9)=5(12)-9=60-9=51^\circ[/tex]
The measure of each angle is 39 degrees and 51 degrees respectively.
Answer:
39 and 51 degrees
Step-by-step explanation:
An automobile manufacturer has given its van a 31.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 140 vans, they found a mean MPG of 31.1. Assume the population standard deviation is known to be 1.3. A level of significance of 0.02 will be used. State the null and alternative hypotheses.
Answer:
[tex]z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z<-1.82)=0.0688[/tex]
For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 31.3 MPG
Step-by-step explanation:
Information given
[tex]\bar X=31.1[/tex] represent the sample mean
[tex]\sigma=1.3[/tex] represent the population standard deviation
[tex]n=140[/tex] sample size
[tex]\mu_o =31.3[/tex] represent the value that we want to test
[tex]\alpha=0.02[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is equal to 31.3 MPG, the system of hypothesis would be:
Null hypothesis:[tex]\mu =31.3[/tex]
Alternative hypothesis:[tex]\mu \neq 31.3[/tex]
Since we know the population deviation, the statistic is given by
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z<-1.82)=0.0688[/tex]
For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 31.3 MPG
Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off (SHOW YOUR WORK)
Answer:
not 100% sure but my answer is 110
Step-by-step explanation:
It is More Affordable and is the better Buy From All the other choices.
Find the slope of the line that goes through the given points.
(6,1) and (9,-1)
Answer:
m = -2/3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
So,
[tex]m = \frac{-1-1}{9-6}[/tex]
m = -2/3
Suppose we want to study the weekly rate of alcohol drinking among USF undergraduate students. Which of the following would be the LEAST preferred method of randomly selecting participants?
A. Selecting a random sample of students from each residence hall
B. Selecting a random sample of students from the list of all undergraduate students from the university's registrar office
C. Selecting a random sample of students who have used the university health services in the past month
D. Selecting a random sample of students from each college
Answer:
Option D
Step-by-step explanation:
I think the least preferred method the researcher would like is to select a random sample of students from each college. This means the researcher would have to go to every college and randomly selects participants which is very exhausting. Thus, this would be the least prefer method over the others...
What is the ratio 28 : 4 in it's simplest form?
Answer:
7:1
Step-by-step explanation:
28:4=
7(4):1(4)=
7:1
Hope this helps!
Answer:
[tex]7:1[/tex]
Step-by-step explanation:
[tex]28:4[/tex]
Common highest factor is 4.
Simplify the ratio.
[tex]28 \div 4 : 4 \div 4[/tex]
[tex]7:1[/tex]
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps. This system of equations models the given information for both stamp types. x – y = 34 x + y = 212 Solve the system of equations. How many foreign stamps does Malik have? foreign stamps How many domestic stamps does Malik have? domestic stamps
Answer:
foreign: 89domestic: 123Step-by-step explanation:
Add the two equations together:
(x -y) +(x +y) = (34) +(212)
2x = 246
x = 123
y = x-34 = 89
Malik has 89 foreign stamps and 123 domestic stamps.
Answer:
89 and 123
Step-by-step explanation:
A marketing consulting group wants to see whether placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales. The average sales of the seasonal cookie for this region was 650 units. A sample of 36 stores that placed the cookie on an end cap showed a sample mean of 671 units sold with a standard deviation of 81. The resulting p-value is 0.1288; thus, the null hypothesis is not rejected. The marketing consulting group concludes that placing the cookies on an end cap does not affect sales. What type of error is possible in this situation
Answer:
Type II error.
Step-by-step explanation:
We have a hypothesis test for the claim that placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales.
The null hypothesis will state that there is no difference, while the alternative hypothesis will state that there is significant positive difference.
The result is a P-value of 0.1288 and the null hypothesis failing to be rejected.
As the null hypothesis failed to be rejected, if an error has been made in the conclusion, is that we erroneusly accept a false null hypothesis.
This is a Type II error, where the null hypothesis is accepted although the alternative hypothesis is true.
Find the range of the function f(x) = -x 2 + 4x if the domain is {-2, 0, 1}.
Answer:
y≤4
Step-by-step explanation:
y≤4
try to graph it on a parabola and u will find the answer above :D hope this helped
plsssssssssssssssss help
Answer:
60
Step-by-step explanation:
x=60 .
The triangle is equilateral and x=60 cause the two lines are ||
a. x=60°
b. Alternate interior angles
Solution,
Given,
All sides of triangle are equal.
AB=BC=AC
<ABC=<ACB=<BAC=y
By angle sum property of triangle,
<ABC+<BCA+<CAB=180
or y+y+y=180
or 3y=180
or y=180/3
y=60
Now,
<ACB=<CAD
<CAD(x)=60( Alternate interior angles)
Hope this helps ..
Good luck on your assignment..
What are the solutions to the system of equations graphed below? Select all
that apply
A. (-6,8)
B. (0,2)
C. (2,0)
D. (-5,0)
E. (0,-10)
Answer:
c and d
Step-by-step explanation:
the x intercepts are the solutions
Answer:
(0,2) and (-5,0)
Step-by-step explanation:
the point where the two graph lines meet would be the answer.
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 48.99 pounds and the sample standard deviation was 3.7 pounds. Conduct the appropriate hypothesis test using a 0.01 level of significance.
a) What is the test statistic? Give your answer to four decimal places.
b) What is the P-value for the test? Give your answer to four decimal places.
Answer:
Step-by-step explanation:
Claim: if the mean amount of garbage per bin is different from 50.
Null hypothesis: u=50
Alternative hypothesis : u =/ 50
Using the z score formular for a one sample z test - z = (x - u ) / (sd/√n)
Where x = 48.99, u = 50 sd =3.7 and n = 36
z = 48.99 - 50 / (3.7/√36)
z = -1.01 / (3.7/6)
z = -1.01/0.6167
z = -1.6377
To find the p value at a 0.01 level of significant from the -1.6377 z score for a two tailed test the p value using the p value calculator is 0.1016. The result is not significant at 0.01 level of significant thus we will fail to reject the null and conclude that the mean amount of garbage per bin is 50.
What is the quoteint of 2/3 in 2/9
Please answer this correctly
Answer:
# of plants # of gardens
10-14 2
15-19 2
20-24 5
25-29 3
30-34 3
35-39 5
40-44 4
Step-by-step explanation:
10-14: 10, 12 (2 numbers)
15-19: 18, 19 (2 numbers)
20-24: 20, 22, 23, 24, 24 (5 numbers)
25-29: 25, 27, 38 (3 numbers)
30-34: 31, 33, 33 (3 numbers)
35-39: 36, 36, 36, 37, 38 (5 numbers)
40-44: 40, 44, 44, 44 (4 numbers)
Answer:
10-14 ⇒ 2
15-19 ⇒ 2
20-24 ⇒ 5
25-29 ⇒ 3
30-34 ⇒ 3
35-39 ⇒ 5
40-44 ⇒ 4
I need help for a grade
Answer:
180
Step-by-step explanation:
2(24)-3=45
24-8=√16=4
45*4=180
Once a fire is reported to a fire insurance company, the company makes an initial estimate, X, of the amount it will pay to the claimant for the fire loss. When the claim is finally settled, the company pays an amount, Y, to the claimant. The comapny has determined that X and Y have the joint density functionf(x,y) = Given that the initial claim estiamted by the comapny is 2, determine the probability that the final settlement amount is between 1 and 3.
Answer:
The probability that the final settlement amount is between 1 and 3 given that the initial claim is 2 = (2/9) = 0.2222
Step-by-step explanation:
The complete question is presented in the attached image to this solution
The joint probability distribution is given as
f(x, y) = {2/[x²(x - 1)} × y^-[(2x-1)/(x-1)] for x>1 And y>1
Given that the initial claim estiamted by the comapny is 2, determine the probability that the final settlement amount is between 1 and 3.
That is, x = 2, and y ranges from 1 to 3
Inserting x = 2 into the expression, we obtain
f(y) = (1/2) × y⁻³ = (y⁻³/2)
The required probability would then be
P(1 < y ≤ 3) = ∫³₁ f(y) dy
= ∫³₁ (y⁻³/2) dy
= [y⁻²/-4]³₁
= [3⁻²/-4] - [1⁻²/-4]
= (-1/36) - (-1/4)
= (1/4) - (1/36)
= (8/36)
= (2/9) = 0.2222
Hope this Helps!!!
Question 1 of 10
2 Points
The standard form of the equation of a parabola is y = 7x2 + 14x + 4.
What is the vertex form of the equation?
A. y = 7(x + 1)2-3
B. y= 7(x + 2)2-3
c. y= 7(x + 1)2 + 3
D. y= 7(x + 2)2 + 3
SUBMIT
Answer:
A. y = 7(x + 1)²-3
Step-by-step explanation:
Parabola:
[tex]y = 7x^{2} + 14x + 4[/tex]
[tex]y = 7(x^{2} + 2x) + 4[/tex]
Putting into vertex form, remember that:
[tex](x + a)^{2} = x^{2} + 2ax + a^{2}[/tex]
In this question:
[tex]x^{2} + 2x[/tex], to put into this format:
[tex]x^{2} + 2x + 1 = (x + 1)^{2}[/tex]
We add one inside the parenthesis to do this. The parenthesis is multiplied by 7, so for the equivalent, we also have to subtract 7. Then
Vertex form:
[tex]y = 7(x^{2} + 2x + 1) + 4 - 7[/tex]
[tex]y = 7(x + 1)^{2} - 3[/tex]
So the correct answer is:
A. y = 7(x + 1)²-3
How do you determine the vertex from the vertex from of a quadratic equation
Answer:
it it the highest or lowest point of a parabola
find the equation of the line that is perpendicular to y= -1/5x-3 and contains the point (1,2) answer all boxes please
Answer:
Y = 5x -3
Step-by-step explanation:
Let's look for the gradient to solve this question for.
We are given y= -1/5x-3
Any line perpendicular to the above line will have a graient of m'.
Where mm'= -1
m = -1/5 from the line equation
So
mm'= -1
-1/5m'= -1
m' =5
For the equation of point (1,2)
(Y-y1)/(x-x1) = m'
(Y-2)/(x-1)= 5
Y-2= 5x -5
Y = 5x -3
In a lottery daily game, a player picks three numbers from 0 to 9 (without repetition). How many different choices does the player have if order does not matter
Answer:
Not sure 3/10?
Step-by-step explanation:
numbers are 0-9...that's 10 choices.
he chooses 3 numbers
I would think 3/10?
The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:______.A. Between 230 and 240 dollars.B. Between 220 and 250 dollars.C. Between 175 and 295 dollars.D. Less than 220 dollars or more than 250 dollars.E. Less than 230 dollars or more than 240 dollars.
Answer:
C. Between 175 and 295 dollars.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 235
Standard deviation = 20
According to the Standard Deviation Rule, almost all (99.7%) of the students spent on textbooks in a semester:
Within 3 standard deviations of the mean.
235 - 3*20 = 175
235 + 3*20 = 295
So the correct answer is C.
Please please help me on this one!
Answer:
3422 x232
Step-by-step explanation:
Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Two circles are shown. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA? (StartFraction pi Over 3 EndFraction)x units (StartFraction 2 pi Over 3 EndFraction)x units 2πx units 6πx units
Answer:
its 2pi/3
Step-by-step explanation:
because the full radian measure of a circle is 2pi radians, the smaller circle is a third of the size of the larger one. Multiply straight across for (2pi/1)(1/3)
The circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].
Given to us,Two similar circles are shown.The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Circumference of the larger circle[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (radius)[/tex]
[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (OB)[/tex]
[tex]\rm{Circumference\ of\ the\ circle = 2\times \pi \times (x)[/tex]
Circumference of the smaller circle,Circumference of the Larger circle = 3 x Circumference of the smaller circle
[tex]2\times \pi \times x = 3\times Circumference\ of\ the\ smaller\ circle\\\\3\times Circumference\ of\ the\ smaller\ circle = 2\times \pi \times x \\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi \times x }{3}\\\\Circumference\ of\ the\ smaller\ circle = \dfrac{2\times \pi}{3}( x )\ units[/tex]
Hence, the circumference of the smaller circle can be given by [tex]\dfrac{2\times \pi}{m}(x)\ units[/tex].
Learn more about similar circles:
https://brainly.com/question/24106562
Can advise on the solution?
Answer:
340
Step-by-step explanation:
If x is the amount of pages in the book we can write:
1/4x + 5 + 3/5(x - (1/4x + 5)) + 10 + 12 + 24 = x
1/4x + 51 + 3/5(3/4x - 5) = x
1/4x + 51 + 9/20x - 3 = x
7/10x + 48 = x
3/10x = 48
x = 160
A sample of 1300 computer chips revealed that 58% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 61% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
There is enough evidence to support the claim that that the actual percentage that do not fail is different from the stated percentage (61%).
Test statistic z = -2.19.
P-value = 0.03.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that that the actual percentage that do not fail is different from the stated percentage (61%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.61\\\\H_a:\pi\neq 0.61[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=1300.
The sample proportion is p=0.58.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.61*0.39}{1300}}\\\\\\ \sigma_p=\sqrt{0.000183}=0.014[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.58-0.61+0.5/1300}{0.014}=\dfrac{-0.03}{0.014}=-2.189[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z<-2.189)=0.03[/tex]
As the P-value (0.03) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that that the actual percentage that do not fail is different from the stated percentage (61%).
The measure of angle O is 600°. The polnt (x, y) corresponding to on the unit circle is?
Answer:
[tex](\frac{-1}{2} , \frac{-\sqrt{3} }{2} )[/tex]
Step-by-step explanation:
Memorize your unit circle.
Step 1: Subtract 360 from 600 degrees to find rotation
600° - 360° = 240°
Step 2: Either find coordinates from unit circle or convert to radians
240° = 4π/3
Step 3: Find coordinates
Approximately 8% of all people have blue eyes. Out of a random sample of 20 people, what is the probability that 2 of them have blue eyes? Round answer to 4 decimal places. Answer:
Answer:
27.11% probability that 2 of them have blue eyes
Step-by-step explanation:
For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. 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.
8% of all people have blue eyes.
This means that [tex]p = 0.08[/tex]
Random sample of 20 people:
This means that [tex]n = 20[/tex]
What is the probability that 2 of them have blue eyes?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]
27.11% probability that 2 of them have blue eyes
The probability that 2 of them have blue eyes is 27.11%.
Given that,
Approximately 8% of all people have blue eyes.
Out of a random sample of 20 people,
We have to determine,
What is the probability that 2 of them have blue eyes?
According to the question,
People having blue eyes p = 8% = 0.08
Sample of people n = 20
For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.
The probability of a person having blue eyes is independent of any other person.
The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]
Therefore,
The probability that 2 of them have blue eyes is,
[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]
Substitute all the values in the formula,
[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]
Hence, The required probability that 2 of them have blue eyes is 27.11%.
For more details refer to the link given below.
https://brainly.com/question/23640563
The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week. Assuming no new donations are made,
how many cans of fruit will remain after 6 weeks?
The solution is
What is the answer for this problem?
Answer:
670 Cans of fruit will be left
Step-by-step explanation:
First you multiply 155 by the 6 weeks.
That equals 930 and then you subtract 930 from 1,600 and that gives you 670.
There are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
The local food pantry has 1, 600 cans of fruit. They give away 155 cans of fruit each week.
First term a = 1600
Common difference d = -155
After 6 weeks means on week 7.
n = 7
a(7) = 1600 + (7-1)(-155)
a(7) = 1600 - 930
a(7) = 670
Thus, there are 670 cans of fruit that will remain after 6 weeks the answer is 670 cans.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ2
Find the point P on the line yequals=33x that is closest to the point (60 comma 0 )(60,0). What is the least distance between P and (60 comma 0 )(60,0)?
Answer:
[tex]18\sqrt{10}$ units[/tex]
Step-by-step explanation:
We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.
We want to find the point on the line y=3x which is closest to Q.
Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.
If x=a, y=3a, so the point P has the coordinates (a,3a).
Distance between point Q and P
[tex]=\sqrt{(60-a)^2+(0-3a)^2}\\D =\sqrt{10a^2-120a+3600}[/tex]
To minimize D, we find its derivative
[tex]\dfrac{dD}{da}=\dfrac{10a-60}{\sqrt{10a^2-120a+3600} }\\$Setting \dfrac{dD}{da}=0\\10a-60=0\\10a=60\\a=6[/tex]
Therefore, the y-coordinate for P is 3*6=18.
The point P=(6,18).
Next, we calculate the distance between P(6,18) and (60,0).
[tex]D =\sqrt{10(6)^2-120(6)+3600}\\=\sqrt{3240}\\=18\sqrt{10}$ units[/tex]
what are the steps (2+2i)(5+3i)??? please help me