Answer:
The velocity is v(t) = 2*t + a
a) we want to find the average velocity betwen t = 0 and t = 1.
We can do this as:
Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a
b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.
For this we can see the integral:
[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]
A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.
They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.
The point estimate for this problem is: (report your answer to 3 decimal places)
Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
C) Yes, the population standard deviation is known.
D) No, the population mean is unknown.
Answer:
Step-by-step explanation:
The point estimate is the sample proportion.
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 137
n = number of samples = 200
p = 137/200 = 0.685
From the information given,
Population proportion = 62% = 62/100 = 0.62
The correct options are
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)
Answer:
(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.
(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.
(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.
Step-by-step explanation:
We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.
Suppose five 25- to 30-year-olds are selected at random.
The above situation can be represented through the binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = Five 25- to 30-year-olds
r = number of success
p = probability of success which in our question is probability that
people used a computer while under the influence of alcohol,
i.e. p = 29%.
Let X = Number of people who used computer while under the influence of alcohol.
So, X ~ Binom(n = 5, p = 0.29)
(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)
P(X = 5) = [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]
= [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]
= 0.0021
(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71
SO, now X ~ Binom(n = 5, p = 0.71)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]
= 1 - 0.0021 = 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)
P(X = 0) = [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 \times 1 \times 0.71^{5}[/tex]
= 0.1804
(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]
= 1 - 0.1804 = 0.8196
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively. Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f. 514 541 302 400 507 406 369
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively.
514 541 302 400 507 406 369
Find the
a. mean,
b. median,
c. midrange,
d. mode for the data.
Also complete parts e. and f.
e. Which car appears to be the safest?
f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
Answer:
a) Mean = 434.14
b) Median = 406
c) Midrange = 421.5
d) Mode = 0
e) Car C appears to be the safest
f) The small cars does not appear to have about the same risk of head injury in a crash.
Step-by-step explanation:
We are given the head injury measurements from small cars that were tested in crashes.
The measurements are in "hic," which is a measurement of a standard "head injury criterion.
The listed values are;
A = 514
B = 541
C = 302
D = 400
E = 507
F = 406
G = 369
a) Mean
The mean of the measurements is given by
Mean = Sum of measurements/ Number of measurements
Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7
Mean = 3039/7
Mean = 434.14
b) Median
Arrange the measurements in ascending order (low to high)
302, 369, 400, 406, 507, 514, 541
The median is given by
Median = (n + 1)/2
Median = (7 + 1)/2
Median = 8/2
Median = 4th
Therefore, the 4th measurement is the median that is 406
Median = 406
c) Mid-range
The midrange is given by
Midrange = (Max + Min)/2
The maximum measurement in the data set is 541
The minimum measurement in the data set is 302
Midrange = (541 + 302)/2
Midrange = 843/2
Midrange = 421.5
d) Mode for the data
The mode of the data set is the most repeated measurement.
302, 369, 400, 406, 507, 514, 541
In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.
Mode = 0
e) Which car appears to be the safest?
Since we are given that the measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars)
The lowest hic value corresponds to car C that is 302
Therefore, car C appears to be the safest among other cars.
f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?
302, 369, 400, 406, 507, 514, 541
As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.
Can you please help me with this
Answer:
-The total area of a Rectangular Prism:
[tex]A = 366[/tex] [tex]in^{2}[/tex]
Step-by-step explanation:
-To find the total area of a rectangular prism, you need this formula:
[tex]A = 2(l \cdot w + l \cdot h + w \cdot h)[/tex]
[tex]l =[/tex] Length
[tex]w =[/tex] Width
[tex]h =[/tex] Height
-Apply the length, width and height for the formula:
[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]
[tex]l =[/tex] 11 in
[tex]w =[/tex] 8 in
[tex]h =[/tex] 5 in
-Then, solve for the area:
[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]
[tex]A = 2(88 + 55 + 40)[/tex]
[tex]A = 2(143 + 40)[/tex]
[tex]A = 2 \times 183[/tex]
[tex]A = 366[/tex]
So, the total area would be [tex]366[/tex] [tex]in ^{2}[/tex].
The following data summarizes results from 1000 pre-employment drug screening tests. If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.
Positive Test Result Negative Test Result
Subject Uses Drugs 76 6
Subject Is Not a Drug User 95 823
P (subject had a positive test result or a negative test result)= simplify your answer.
Answer:
P (subject had a positive test result or a negative test result) = 1
Step-by-step explanation:
Given
The table above
Required
P (subject had a positive test result or a negative test result)
This is calculated as follows;
P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result)
Calculating P (subject had a positive test result)
This can be calculated by number of subjects with positive results divided by 1000
Only data from the column of subjects with positive results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 76 + 95
Number of Subjects = 171
P (Subject had a positive test Result) = 171/1000
Calculating P (subject had a negative test result)
This can be calculated by number of subjects with negative results divided by 1000
Only data from the column of subjects with negative results will be considered.
Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs
Number of subjects = 6 + 823
Number of Subjects = 829
P (Subject had a negative test Result) = 829/1000
Hence, P (subject had a positive test result or a negative test result) =
P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000
P (subject had a positive test result or a negative test result) = (171 + 829)/1000
P (subject had a positive test result or a negative test result) = 1000/1000
P (subject had a positive test result or a negative test result) = 1
There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?,
Answer:
16.67% probability of getting 2 blues
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[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]
What is the probability of getting 2 blues?
Desired outcomes:
Two blue marbles, from a set of 4.
[tex]D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6[/tex]
Total outcomes:
Two marbles, from a set of 9.
[tex]T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{6}{36} = 0.1667[/tex]
16.67% probability of getting 2 blues
The sum of two numbers is odd. Can the quotient of the two numbers be an odd number?
Answer: No.
Step-by-step explanation:
I guess that here we have the statement:
If the sum of two numbers is odd----> can their quotient be an odd number?
first, for n an integer number, we have that:
an odd number can be written as 2n + 1
an even number can be written as 2n.
The sum of two numbers is only odd if one of them is odd and the other even.
Then we have a number that is 2n and other that is 2k + 1, for n and k integer numbers.
Now, let's see if the quotient can also be an odd number.
One way to think this is:
There is an odd number such that when we multiply it by another odd number, the result is an even number?
no, and i can prove it as:
let 2k + 1 be an odd number, and 2j + 1 other.
the product is:
(2k + 1)*(2j + 1) = 2*(2*k*j + k + j) + 1
and as k and j are integers, also does 2*k*j + k + j, so:
2*(2*k*j + k + j) + 1 is an odd number.
This says that the product of two odd numbers is always odd, then we never can have that the quotient between an even number and an odd number is odd.
A rectangular fish tank is 50 cm long, 40 cm wide, and 20 cm high. a) How many cubic centimeters of water will the tank hold? b) How many milliliters of water will the tank hold? c) How many liters of water will the tank hold?
Answer:
40 litres
Step-by-step explanation:
V = l x w x h
50 x 40 x 20 = 40000
40000 cm^3
1cm^3 = 1ml
40000 cm^3/ 1cm^3 = 40000ml
40000 x 10^-3 = 40 litres
what is the output from the following machine when the input is 4
Answer:
4 - 7 = -3
-3 / 3 = -1
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
A consultant built an Einstein Analytics dashboard for a shipping company. The dashboard displays data from several data sources. The consultant enabled data sync (replication) to increase the speed of data refreshing from these sources. What is the maximum number of dataflow definitions available in this situation?
A. 30
B. 45
C. 25
D. 35
Answer: A (30)
Step-by-step explanation:
By defaults, data will be enabled in tens. And it increases by replicating the initial value.
There is no way the maximum number of dataflow definitions available in this situation will be 45, 25 or 35
The only possible replicant that can be available is 30
45 units and is centered at
A circle has a radius of
(-2.4, -4.8).
What is the equation of this circle?
The correct question is:
A circle has a radius of 45 units and is centered at (-2.4, -4.8).
What is the equation of this circle?
Answer:
Equation of the circle is;
(x + 2.4)² + (y + 4.8)² = 2304
Step-by-step explanation:
The standard equation of a circle is;
(x - a)² + (y - b)² = r²
where;
(a,b) is the center of the circle and r is the radius of the circle
Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45
Thus, plugging those values into the standard form of equation of a circle, we have;
(x - (-2.4))² + (y - (-4.8))² = 48²
This gives;
(x + 2.4)² + (y + 4.8)² = 2304
URGERNT!!!PLS AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESSS!! AND BLESS YOUR GRADES!
1. What could you prove about the following diagram, using the Hinge Theorem?
PIC BELOW
A) IJ>jk
B) HJ>HK
C) HK>HI
D) HI>HJ
2. Which theorem would explain why m∠CBD > m∠ADB? SECOND PICTURE
A) Hinge Theorem
B) Converse of Hinge Theorem
C) Pythagorean Theorem
Answer:
Dear Laura Ramirez
Answer to your query is provided below
1) option A is correct
2) option B is correct
Step-by-step explanation:
Explanation for the first question attached in image
Also note - The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.
Answer:
1) option A is correct2) option B is correct
Step-by-step explanation:
Someone claims that the average amount of time that a freshman at TAMU studies is 7 hours. We think it’s higher than that and decide to test, using a random sample of 49 freshmen. The sample mean is 8.5 hours with a sample variance of 4 hours. What are the test statistic and p-value in this case?
Answer:
Test statistic t = 5.25
P-value = 0.000002 (one-tailed test)
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=7\\\\H_a:\mu> 7[/tex]
The significance level is 0.05.
The sample has a size n=49.
The sample mean is M=8.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√s^2=√4=2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{49}}=0.29[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8.5-7}{0.29}=\dfrac{1.5}{0.29}=5.25[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
This test is a right-tailed test, with 48 degrees of freedom and t=5.25, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>5.25)=0.000002[/tex]
As the P-value (0.000002) 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 the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.
In ΔEFG, ∠E \cong≅∠G, GE = 7 and FG = 15. Find the length of EF.
Answer: EF = 15
Step-by-step explanation:
The given description is that of an isosceles triangle. The base angles are congruent, therefore the sides opposite of those angles are also congruent.
The base angles are ∠E and ∠G and the vertex angle is ∠F.
The sides opposite to the base angles are EF and FG.
Thus, EF ≡ FG.
Since FG = 15 and FG = EF, then 15 = EF.
Based on the definition of an isosceles triangle, the length of EF in the triangle is: 15 units.
What is an Isosceles Triangle?An isosceles triangle has two sides that are congruent. The angles opposite these congruent sides are also congruent.
ΔEFG is an isosceles triangle. The congruent sides are, FG and EF.
Therefore, EF = FG = 15 units.
Learn more about isosceles triangle on:
https://brainly.com/question/11884412
I need some help please
Answer:
ofn
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since there are 44 average people out of 80. We can do this,
Total students : 600
Checked: 80
Average: 44
Number of averaged throughout the school: 600/80 * 44
l: 7.5 * 44
Thus it is: 330 average students
which shows the equation below written in the form ax^2 + BX + C=0
x+10=3(x - 1)^2
Answer:
C
Step-by-step explanation:
Given
x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL
x + 10 = 3(x² - 2x + 1) ← distribute
x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides
0 = 3x² - 7x - 7 → C
Answer:
Step-by-step explanation:
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a seven or king. (b) Compute the probability of randomly selecting a seven or king or jack. (c) Compute the probability of randomly selecting a queen or spade.
Answer:
(a)[tex]\dfrac{2}{13}[/tex]
(b)[tex]\dfrac{3}{13}[/tex]
(c)[tex]\dfrac{4}{13}[/tex]
Step-by-step explanation:
In a standard deck, there are 52 cards which are divided into 4 suits.
(a)
Number of Seven Cards =4
Number of King cards =4
Probability of randomly selecting a seven or king
=P(Seven)+P(King)
[tex]=\dfrac{4}{52} +\dfrac{4}{52} \\=\dfrac{8}{52}\\=\dfrac{2}{13}[/tex]
(b)
Number of Seven Cards =4
Number of King cards =4
Number of Jack(J) cards =4
Probability of randomly selecting a seven or king
=P(Seven)+P(King)+P(Jack)
[tex]=\dfrac{4}{52} +\dfrac{4}{52}+\dfrac{4}{52} \\=\dfrac{12}{52}\\=\dfrac{3}{13}[/tex]
(c)
Number of Queen Cards =4
Number of Spade cards =13
Number of Queen and Spade cards =1
Probability of randomly selecting a seven or king
[tex]=P$(Queen)+P(Spade)-P(Queen and Spade Card)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]
In a class of 30 students, there are four more girls than boys. a)Using x as the number of boys, write down an equation b)Solve the equation and find the number of girls in the class.
easy claps!!
Answer: 30=2x+4 and there are 17 girls in the class.
Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.
It's BASIC prealgebra so you should probably practice bit more with linear equations!
A triangle has two sides of length 10 and 19. What is the smallest possible whole-number length for the third side?
Answer:
answer for the question is 130 length
Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matrix consistent? A. Yes, because the rightmost column of the augmented matrix is a pivot column. B. Yes, because the rightmost column of the augmented matrix is not a pivot column. C. No, because the rightmost column of the augmented matrix is a pivot column. D. No, because the rightmost column of the augmented matrix is not a pivot column.
Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Angelina read 30% of her book containing 360 pages. How many pages has she read so far
Answer:
108 pages
Step-by-step explanation:
Angelina read 30% of the book that contains 360 pages.
30% of 360 pages
"of" also means multiply, so we must multiply 30% and 360.
30% * 360
Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.
30/100=0.30
or
30.0---> 3.0---> 0.30
Plug the decimal in for the percent.
0.30*360
Multiply the 2 numbers together
108
Angelina has read 108 pages so far.
On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three times the number of hamburger sold. How many hamburger were sold on Sunday
What’s the correct answer for this?
Answer:
(2,-2)
Step-by-step explanation:
In the attached file
The market and Stock J have the following probability distributions:
Probability rM rJ
0.3 14% 22%
0.4 10 4
0.3 19 12
1. Calculate the expected rate of return for the market. Round your answer to two decimal places.%
2. Calculate the expected rate of return for Stock J. Round your answer to two decimal places.%
3. Calculate the standard deviation for the market. Round your answer to two decimal places.%
4. Calculate the standard deviation for Stock J. Round your answer to two decimal places.%
Answer:
1) [tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]
2) [tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]
3) [tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]
And the variance would be given by:
[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]
4) [tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]
And the variance would be given by:
[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]
Step-by-step explanation:
For this case we have the following distributions given:
Probability M J
0.3 14% 22%
0.4 10% 4%
0.3 19% 12%
Part 1
The expected value is given by this formula:
[tex] E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]
Part 2
[tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]
Part 3
We can calculate the second moment first with the following formula:
[tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]
And the variance would be given by:
[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]
Part 4
We can calculate the second moment first with the following formula:
[tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]
And the variance would be given by:
[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]
And the deviation would be:
[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean salary of city 1 librarians
x2 = sample mean salary of city 2 librarians
s1 = sample standard deviation for city 1
s2 = sample standard deviation for city 2
n1 = number of soles for city 1
n1 = number of soles for city 2
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28
z = 2.048
x1 - x2 = 28,900 - 30,300 = - 1400
Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)
= 1647
The upper boundary for the confidence interval is
- 1400 + 1647 = 247
The lower boundary for the confidence interval is
- 1400 - 1647 = - 3047
A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?
Given Information:
sample mean time = 72.7
sample standard deviation = 0.92
Sampling size = n = 150
Confidence level = 95%
Required Information:
95% confidence interval = ?
Answer:
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.
The t-score corresponding to 95% confidence level is
Significance level = 1 - 0.95 = 0.05/2 = 0.025
Degree of freedom = n - 1 = 150 - 1 = 149
From the t-table at α = 0.025 and DoF = 149
t-score = 1.975
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]
So the required 95% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]
Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)
Please answer this correctly
Answer:
2
Step-by-step explanation:
Set the height of the bar to 2 since there are 2 numbers between 21-40.
Answer:
2 people.
Step-by-step explanation:
34 minutes and 40 minutes were recorded.
Therefore, 2 people.
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Solve the inequality for y.
-4y ≤ -12
Divide both sides by -4:
y ≤ 3
Because both sides were divided by a negative value you need to reverse the inequality sign:
y ≥ 3
Answer:
y = 3
Step-by-step explanation:
it says -4y ≤ -12 sooooooo 4 x 3 = 12!!!! so y = 3
