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
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:
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.
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.
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
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:
Do not answer or report What is -6 plus -6
Answer:
-12Step-by-step explanation:
it is -12 because -6 plus -6 is also like 6 plus 6
and then you have to add the negative Sign.
pls brainliest me
-6 - 6 = - 12
Happy to help! Please mark as the brainliest!
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).
Wisconsin Public Radio wants to duplicate a survey conducted in 2011 that found that 68% of adults living in Wisconsin felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%? Be sure to show all your work and round appropriately
Answer:
655 people would need to be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In this question, we have that:
[tex]\pi = 0.68[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%?
We need to survey n adults.
n is found when M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.68*0.32}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.68*0.32}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.68*0.32}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645\sqrt{0.68*0.32}}{0.03})^{2}[/tex]
[tex]n = 654.3[/tex]
Rounding up
655 people would need to be surveyed.
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].
Q‒4. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,b)R(c,d) means that a+d=b+c.
Prove that R is an equivalence relation.
Find [(2,4)].
Answer:
Step-by-step explanation:
REcall that given a set A, * is a equivalence relation over A if
- for a in A, then a*a.
- for a,b in A. If a*b, then b*a.
- for a,b,c in A. If a*b and b*c then a*c.
Consider A the set of all ordered pairs of positive integers.
- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).
- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).
- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then
a+d = b+c, c+f = d+e. We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).
So R is an equivalence relation.
[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).
Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.
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]
what is the output from the following machine when the input is 4
Answer:
4 - 7 = -3
-3 / 3 = -1
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
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
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
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]
Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5)______.
If necessary, round to three decimal places.
Suppose Isabella scores 187 points in the game on Sunday. The z-score when x=187 is ___ The mean is _________
This z-score tells you that x = 187 is _________ standard deviations.
Answer:
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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.
In this question:
[tex]\mu = 152, \sigma = 14.5[/tex]
The z-score when x=187 is ...
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{187 - 152}{14.5}[/tex]
[tex]Z = 2.41[/tex]
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
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.
Consider the polynomial 9x2 – 16.
Answer: 2
Step-by-step explanation:
9 × 2 - 16
18 - 16
2
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
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
Please answer this correctly
Answer:
Car: 60%
Motorcycle: 30%
Truck: 10%
Step-by-step explanation:
Car: [tex]\frac{12}{12+6+2} =\frac{12}{20} =\frac{60}{100}[/tex] or 60%
Motorcycle: [tex]\frac{6}{12+6+2} =\frac{6}{20} =\frac{30}{100}[/tex] or 30%
Truck: [tex]\frac{2}{12+6+2} =\frac{2}{20} =\frac{10}{100}[/tex] or 10%
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
Solve for x.
6(x - 2) = 4
Answer:
8/3
Step-by-step explanation:
6(x-2)=4
x-2=4/6
x= 8/3
Answer:
x = 8/3
Step-by-step explanation:
Use Distributive Property
6(x-2) = 4
6x -12 = 4
add 12 on both sides
6x = 16
Divide by 6
x = 8/3
In decimal form: 2.667
ASAPPPPP
PICTURE BELOW
WILL HAVE MORE OF THESE
Answer: -6m-n+3
Step-by-step explanation:
The answer is -6m-n+3 because -3
times 2m is -6m and -n stays the same its outside of the parenthesis
and lastly -3 times -1 is positive 3
so answer maches up with the last one
the answer is -6m-n+3
Hope this helps :)
Answer:
-6m-n+3
Step-by-step explanation:
-3 x 2 is -6m (n stays same)
-3 x -1 is whole or positive 3
put it together and u get -6m-n+3
hope this helps
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.
A bank wants to attract new customers for its credit card. The bank tries two different approaches in the marketing campaign. The first promises a cash back reward; the second promises low interest rates. A sample of 500 people is called the first brochure; of these, 100 get the credit card. A separate sample of 500 people is called the second brochure; 125 get the credit card. The bank wants to know if the two campaigns are equally attractive to customers. What is a 95% confidence interval for the difference in the two proportions
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the first brochure,
x = 100
n1 = 500
p1 = 100/500 = 0.2
For the second brochure
x = 125
n2 = 500
p2 = 125/500 = 0.25
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.2(1 - 0.2)/500 + 0.25(1 - 0.25)/500]
= 1.96 × √0.000695
= 0.052
Confidence interval = (0.2 - 0.25) ± 0.052
= - 0.05 ± 0.052
