The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.
In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us
0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16
Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.
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according to an article in a business publication, the average tenure of a u.s. worker is 4.6 years. the most appropriate one-sample test of hypothesis to test this belief is: group of answer choices a two-tailed test. an upper one-tailed test. a lower one-tailed test.
The most appropriate one-sample test of hypothesis to test the belief that the average tenure of a U.S. worker is 4.6 years is option (c) a lower one-tailed test.
The reason for this is that the article states a specific average tenure of U.S. workers (4.6 years), and the hypothesis we want to test is whether this average tenure is lower than this value or not. We are not interested in whether the average tenure is higher than 4.6 years, so a two-tailed test or an upper one-tailed test would not be appropriate.
Therefore, we would use a lower one-tailed test to test the null hypothesis that the average tenure of U.S. workers is 4.6 years or higher, against the alternative hypothesis that the average tenure is lower than 4.6 years. We would then use statistical analysis to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.
Therefore, the correct option is (c) a lower one-tailed test
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Find the probability of exactly 4 successes in 6 trials of a binomial experiment in which the probability of success is 40%
Answer:
0.13824
Step-by-step explanation:
You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.
Binomial probabilityThe probability of k successes in n trials with each having a probability of success of p is given by the formula ...
P(k of n) = nCk·p^k·(1-p)^(n-k)
P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824
The probability of exactly 4 successes is 0.13824.
__
Additional comment
The binomial coefficient nCk is computed as ...
nCk = n!/(k!(n-k)!)
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The exact spread of the t distribution depends on the _________. A. Number of degrees of freedom
b. Standard deviation of the sample
c. Z distribution
d. Sample size n
The exact spread of the t-distribution depends on the number of degrees of freedom. (Option A)
The t distribution is a probability distribution that is used in hypothesis testing and confidence interval estimation when the population standard deviation is unknown. It is similar to the standard normal distribution, but its spread (or variability) depends on the sample size and the number of degrees of freedom (df).
The degree of freedom (df) is a parameter that determines the shape of the t distribution. It is defined as the number of observations in the sample minus one (df = n-1), where n is the sample size. As the sample size increases, the t distribution becomes closer to the normal distribution, which has infinite degrees of freedom.
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Jim and Avery compare the number of points they scored during a game. Explain your answer mathematically
Jim notices that when he doubles his number of points, then subtracts 10 from that number, the result is the same as the number of points Avery scored. Write an expression representing the number of points
Avery scored, in terms of the number of points Jim scored, j. Enter your expression in the response box
The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:
2j - 10 = number of points scored by Avery
To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:
number of points scored by Avery = 2j - 10
Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.
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Karim and Ali look at the following expression and made a comment.
2 - 3 = ( -1 )
Kareem :- Whole numbers are not closed under subtraction
Ali:- integers are closed on the subtractions.
why do they have different? conclusions about the closure property for whole numbers and integers
Karim and Ali have different conclusions about the closure property for whole numbers and integers because when two whole numbers are subtracted, the result may not be a whole number, but when two integers are subtracted, the result is always an integer. Therefore, integers are closed under subtraction, but whole numbers are not.
Karim and Ali, both have different conclusions about the closure property for whole numbers and integers because of their definitions.
Whole numbers are defined as all positive integers, including zero. When two whole numbers are subtracted, the result may not be a whole number because the result may be a negative number.
For example, when 3 is subtracted from 2, the result is -1, which is not a whole number.
Integers, on the other hand, are defined as all positive and negative whole numbers, including zero. When two integers are subtracted, the result is always an integer because the result may be a negative or positive number, but it will always be a whole number.
For example, when 3 is subtracted from 2, the result is -1, which is still an integer.
Therefore, Karim and Ali have different conclusions because whole numbers are not closed under subtraction, but integers are closed under subtraction.
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How to find the perimeter of a composite shape with missing sides(rectangles)
Answer: You have to add up the lengths.
HELP WITH THIIS PLLS
Answer: not compleatly sure but its possibly C
The volume of a triangular pyramid is 756 units3 . If the base and height of the triangle that forms its base are 18 units and 12 units respectively, find the height of the pyramid.
If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.
The formula for the volume of a triangular pyramid is:
V = (1/3) * base area * height
We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:
A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2
Substituting the given values into the formula for the volume of a pyramid, we get:
756 = (1/3) * 108 * h
Multiplying both sides by 3 and dividing by 108, we get:
h = 756 / 36 = 21
Therefore, the height of the pyramid is 21 units.
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PLEASE HELP, NEED IT BY TODAY
Write three equations. Each equation must include the numbers 3 and 30.3 and must be easy to solve by inspection. Solve your equations.
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
We have,
Equation 1:
3x = 30.3
Solving for x, we can divide both sides by 3:
x = 10.1
Equation 2:
30.3 - x = 27.3
Solving for x, we can subtract 27.3 from both sides:
x = 3
Equation 3:
3x + 30.3 = 63.6
Solving for x, we can first subtract 30.3 from both sides:
3x = 33.3
Then, we can divide both sides by 3:
x = 11.1
Thus,
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
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Solve the following equation and check your result (2n)/3 + 1 = (7n)/15 + 3
both sides are equal, we can conclude that n = 150/29 is the correct solution.
What is an Equations?
Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.
(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides
(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions
10n = 3(7n)/5 + 30 // multiply both sides by 3
10n = 21n/5 + 30 // subtract 21n/5 from both sides
50n/5 - 21n/5 = 30 // simplify fractions
29n/5 = 30 // multiply both sides by 5/29
n = 150/29
To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:
(2n)/3 + 1 = (7n)/15 + 3
(2(150/29))/3 + 1 = (7(150/29))/15 + 3
100/29 + 1 = 70/29 + 3
129/29 = 129/29
Since both sides are equal, we can conclude that n = 150/29 is the correct solution.
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g(x)=3x^2+30x+78 minimum and maximum
The minimum value of the given function is 3 at x=-5.
By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).
The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.
In this case, a = 3 and b = 30, so:
x = -b/(2a) = -30/(2*3) = -5
Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:
[tex]G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3[/tex]
Therefore, the minimum value of G(x) is 3 and there is no maximum value.
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lines A and B are parallel lines cut by a transversal find the value of x
The required value of the x is 13 in the measures of the angle.
Given that,
Line A and B are parallel lines and intersect by a transversal line.
Here,
If a pair of parallel lines intersect by the transversal line then their corresponding angles are equal in measure,
Thus, we get;
8x + 2 = 14x - 76
6x = 78
x = 78 / 6
x = 13
Thus, the required value of the x is 13 in the measures of the angle.
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which is the best estimate of 7.21x3.86/10.09
Answer:
7.21x3.86/10.09
7 x 4 / 10
28 / 10
2.8
{3x+4y-z=-7
X-5y+2z=19
5x+y-2z=5
Answer:
x = 2, y = -3 and z = 1.
Step-by-step explanation:
3x+4y-z=-7 ............. A
X-5y+2z=19 ..............B
5x+y-2z=5 ...............C
Adding equations B and C to eliminate z:
6x - 4y + 0 = 24
6x - 4y = 24.............D
Now we multiply Equation A by 2:-
6x + 8y - 2z = -14
Now adding this to equation B, ( again to eliminate z) we get equation E:
7x + 3y = 5 -----------E
Bring down equation D:
6x - 4y = 24.............D
Multiplying E by 4 and D by 3:
28x + 12y = 20
18x - 12y = 72
Adding:
46x = 92
x = 2.
and substituting in equation D
6(2)- 4y = 24
-4y = 12
y = -3.
Finally we find z by substituting in equation A:
3(2) + 4(-3) - z = -7
-z = -7 - 6 + 12
-z = -1
z = 1.
a team of soccer players spend an average of 15 minutes on weight weight training per practice session.how many minutes of weight trainingon an average would they have to complete in 116 practise?
Answer:
The answer to your problem is, 1,740 minutes
Step-by-step explanation:
The time period of 116 trainings solutions;
The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740
Thus the answer to your problem is, 1,740
Answer:1,740 minutes
Step-by-step:
I first saw that I need to take 15 minutes and x it be the 116 Practices.
So 15 x 116 is 1,740.
1,740 minutes is your answer.
Michael has a bag of smarties.He has 6 red smarties 4 blue smarties and 2 pink smarties.What is the probability he will pick 2 blue smarties two times
Answer:
Step-by-step explanation:
If he puts smarty back
because it's an "and" multiply by the 2 possibilities
4/12 *4/12
=1/3 *1/3
=1/9
If does not put smarty back
4/12 *3/11
=1/3*3/11
=3/33
Please help ASAP! NO LINKS OR FILES!!! I WILL REPORT! THANKS! All 4 problems please
Answer:
1. 25.74
2. 13.13
3. 9.31
4. 13.47
Step-by-step explanation:
1. solution: C= (A^2 + B^2 - 2 ab cosy) = C= (10^2 + 19^2 - 2 * 10 * 19 cos (122 degrees) = 25.73654 rounded to the nearest 10 is 25.74
2. Solution: C= (A^2 + B^2 - 2 ab cosy) = C= (14^2 + 8^2 - 2 * 14 * 8 * cos (67 degrees) = 13.13302 rounded to the nearest 10 is 13.13
3. Solution: C=(A^2 + B^2 - 2 ab cosy) = C= (15^2 + 13^2 - 2 * 15 * 13 * cos (38 degrees) = 9.30998 rounded to the nearest 10 is 9.31
4. Solution: C=(A^2 + B^2 - 2 ab cosy) = C= (34^2 + 26^2 - 2 * 34 * 26 * cos (21 degrees) = 13.46959 rounded to the nearest 10 is 13.47
Hope this helped
which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]
The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.
An exponential function is of the form:
[tex]f(x) = a ^x[/tex]
The function represents an exponential decay If b < 1
The function represents an exponential growth If b > 1
From the given data about equations, we have;
Exponential Growth is;
The equation with the values b < 1 is:
[tex]A = 20,000(1.08)^t[/tex]
[tex]A = 40(3)^t[/tex]
[tex]P = 1700(1.07)^t[/tex]
Exponential Decay is;
The equation with the values b > 1 is:
[tex]A = 80(1/2)^t[/tex]
[tex]A = 1600(0.8)^t[/tex]
[tex]P = 1700(0.93)^t[/tex]
Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex] the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]
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The complete question is
Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
Urgently need the answer please help!!
Answer:
A = 81
Step-by-step explanation:
Using the formulas
A=a2
P=4a
Solving forA
A=1
16P2=1
16·362=81
Answer:
[tex]36 {r}^{4} {s}^{5}[/tex]
Perimeter of the square
one side has a length of 9r⁴s⁵
area is equal to 9r⁴s⁵ × 9r⁴s⁵
= 81r⁸s¹⁰
or 81r⁸s¹⁰cm²
9(x-11)=9
Solve this with step by step explanation
Answer:
x=12
Step-by-step explanation:
given: 9(x-11)=9
Distribution: 9x-99=9
Simplify:(common denominator is 9) x-11=1
x=12
Step-by-step explanation:
multiply the 9 in the brackets, so the equation will be 9x-99=9.
next move -99 to the other side and change its sign
making the equation 9x=108
now diveide both sides by 9 to leave x alone.
x=12 is the final answer;)
Chen and Megan have a parcel Chen’s parcel weighs 1 1/2kg Megan’s parcel weighs 1. 2kg how many more grams does Chen’s parcel weigh than Megan’s parcel
Chen’s parcel weighs 0.3 kg more than Megan’s parcel
What is the difference in fraction?When working with fractions and decimals, it is good to use only one unit for ease of solving.
We are given the weights as:
Weight of Chen’s Parcel = 1¹/₂ kg
Weight of Megan's Parcel = 1.2 kg
Now, let us convert the weight of Chen’s Parcel from fraction to decimal to get 1.5 kg
Thus:
Difference in weight = 1.5 kg - 1.2 kg
= 0.3 kg
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a data analyst notices that two variables in their data seem to rise and fall at the same time. they recognize that these variables are related somehow. what is this an example of?1 pointvisualizationcausationtabulationcorrelation
This is an example of a correlation between the two variables, where they tend to change together in a predictable way, but it does not necessarily imply causation.
This is an example of a correlation between the two variables. When two variables are correlated, they tend to change together in a predictable way. In other words, when one variable goes up, the other tends to go up as well, or when one variable goes down, the other tends to go down as well.
It's important to note that correlation does not necessarily imply causation. Just because two variables are correlated, it does not mean that one causes the other. There may be other factors that influence both variables, or the correlation may be coincidental. To establish causation, a more rigorous study design and analysis is required.
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the trainer for a professional soccer team has found that hamstring injuries on their team follow an exponential distribution. on average, their team experiences a pulled hamstring muscle every 342 minutes. if a game lasts 90 minutes, determine the following: what is the probability that the team will pull a hamstring muscle in the next game? round your answer to four decimal places (include zero if necessary). what is the probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game? round your answer to four decimal places (include a zero if necessary).
1)The probability that the team will pull a hamstring muscle = 0.240. 2)The probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game = 0.020.
Given that hamstring injuries on the team follow an exponential distribution with an average time between injuries of 342 minutes, we can use the formula for the exponential distribution to answer the following questions:
1)The time duration of a game is 90 minutes. Therefore, the probability of a hamstring injury occurring during a game can be calculated as follows:
λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)
t = 90 minutes (duration of a game)
P(X ≤ t) = 1 - e^(-λt)
P(X ≤ 90) = 1 - e^(-1/342 * 90) ≈ 0.2399
So the probability that the team will pull a hamstring muscle in the next game is approximately 0.2399 (or 0.240 when rounded to 4 decimal places).
2)The probability of a hamstring injury occurring between the 15th and 25th minute of the game can be calculated as follows:
λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)
t1 = 15 minutes (starting time)
t2 = 25 minutes (ending time)
P(t1 < X ≤ t2) = e^(-λt1) - e^(-λt2)
P(15 < X ≤ 25) = e^(-1/342 * 15) - e^(-1/342 * 25) ≈ 0.0199
So the probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game is approximately 0.0199 (or 0.020 when rounded to 4 decimal places).
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i really need help any answer would be appreciated
Answer:
If 4 units equal 16 ounces, we can find the value of 1 unit by dividing both sides by 4:
4 units = 16 ounces
4 units ÷ 4 = 16 ounces ÷ 4
1 unit = 4 ounces
So, 1/4 x 16 ounces = 4 ounces.
4/1 is the answer in fraction :)
consider the data about the number of blocked intrusions in exercise 8.1, p. 240. (a) construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances). (b) can we claim a significant reduction in the rate of intrusion attempts? the number of intrusion attempts each day has approximately normal distribution. compute pvalues and state your conclusions under the assumption of equal variances and without it. does this assumption make a difference?
The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).
To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.
Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have
x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36
x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95
s₁ = standard deviation of x₁ = 8.23
s₂ = standard deviation of x₂ = 8.98
The pooled standard deviation, sp, is given by
sp = √(((n₁-1)s₁² + (n₂-1)s₂²)/(n₁+n₂-2))
where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:
sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63
The t-statistic for the difference between the means is given by
t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))
Substituting the values, we get
t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28
We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by
(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)
Substituting the values, we get
(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21
= (3.36, 13.78)
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The given question is incomplete, the complete question is:
The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).
Please solve this as soon as possible!
The value of
1. sin(tetha) = 8/√89
2. cos(tetha) = 5/√89
3. sec(tetha) = √89/5
4. cosec(tetha) = √89/8
5. cot( tetha) = 5/8
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
This means that, since tan(tetha) = 8/5 , the adj is 5 and the opp is 8
Using Pythagorean theorem,
hyp = √opp²+adj²
hyp = √8²+5²
hyp = √64+25
hyp = √89
therefore;
sin(tetha) = 8/√89
cos(tetha) = 5/√89
sec(tetha) = 1/cos(tetha) = √89/5
cosec(tetha) = 1/sin(tetha) = √89/8
cot (tetha) = 1/tan(tetha) = 5/8
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Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00.
Total annual cost for Dave's car driving 6,000 miles last year is $2,250.00 with fixed cost of $1,250.00 plus variable cost of $1,000.00.
Based on the given information, we can use the formula for total cost
Total Cost = Fixed Cost + (Variable Cost per unit x Number of units)
In this case, we know the fixed cost is $1,250.00, and the variable cost per mile is $1,000.00 / 6,000 miles = $0.1667/mile. Therefore, we can calculate the total annual cost as
Total Cost = $1,250.00 + ($0.1667/mile x 6,000 miles)
Total Cost = $1,250.00 + $1,000.20
Total Cost = $2,250.20
So, Dave's total annual cost of driving his car for 6,000 miles is $2,250.20.
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--The given question is incomplete, the complete question is given
" Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00. What is the total annual cost?"--
The debate over pipelines and the use of oil sands is far from over. There is likely to be another
application for a pipeline to bring oil from Alberta to Texas or a proposal to pipe oil across Canada
.
to ships that could take it to refineries in Asia. What do you think should be done? Explain your
answer using complete sentences.
The decision of whether or not to build pipelines to transport oil from Alberta to Texas or other parts of Canada is a complex one that involves multiple factors.
From a mathematical perspective, the debate over pipelines and oil sands can be analyzed in terms of supply and demand. On the other hand, opponents of pipelines argue that the supply of oil is finite and that the continued extraction and transportation of oil will have long-term negative consequences for the environment.
In addition to the economic and environmental factors, there are also geopolitical considerations to take into account. For example, some argue that building a pipeline to transport oil from Alberta to Texas would reduce Canada's reliance on foreign oil and would increase our energy independence.
However, others argue that building a pipeline would tie us more closely to the United States and would not necessarily benefit Canada in the long run.
Regardless of the decision that is ultimately made, it is clear that pipelines will continue to play a significant role in our energy infrastructure for many years to come.
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I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)
(a) If we draw 2 letters from a bag containing 26 letters of alphabet, and we return the letters in between the draws, the probability of drawing a "W" both the time is 1/676.
(b) If we toss two-cubes numbered 1 to 6 each time, then probability that we toss a 6 on first cube and a odd number on second cube is 1/12.
Part (a) : The letters in between the draws are returned, which means each draw is independent of the other.
So, the probability of drawing a "W" on any single draw is 1/26.
The probability of drawing a "W" both times is written as :
P(W and W) = P(W) × P(W) = (1/26) × (1/26) = 1/676,
Therefore, the probability of drawing a "W" both times is 1/676.
Part (b) : The probability of getting a 6 on the first-cube is = 1/6, and
The probability of getting an "odd-number" on the second cube is = 3/6, (because there are 3 odd numbers out of a total of 6 numbers).
The probability of 6 on first-cube and odd number on second, cube is written as ;
⇒ P(6 and odd) = P(6) × P(odd) = (1/6) × (3/6) = 1/12,
Therefore, the required probability is 1/12.
Learn more about Probability here
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What are the coordinates of the point on the directed line segment from
(
−
8
,
8
)
(−8,8) to
(
−
2
,
−
10
)
(−2,−10) that partitions the segment into a ratio of 1 to 2?
so let's say A(-3 , -10) and B(9 , 5), so that point C partitions it in a 1 : 2 ratio from A to B
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-3,-10)\qquad B(9,5)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-3,-10)=1(9,5)[/tex]
[tex](\stackrel{x}{-6}~~,~~ \stackrel{y}{-20})=(\stackrel{x}{9}~~,~~ \stackrel{y}{5}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-6 +9}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-20 +5}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ 3 }{ 3 }~~,~~\cfrac{ -15}{ 3 } \right)\implies C=(1~~,~-5)[/tex]
