Six stand up comics A,B,C ,D ,E and F are to perform on a single evening at a comedy club. The order of phrases of performance is determined by random selection.
a. Comic D wall perform fourth.
b. Comic F will perform first and Comic C will perform fourth.
e. The connections will perform in the following order, D, F, C, E, A, B.
d. Comic A or Comic B will perform third.
a.
b.
c.
d.
Answers
A) The Probability that comic D will perform fourth is; 1/6
B) The Probability that Comic F will perform first and Comic C will perform fourth is; 1/30
C) Probability that the comedians will perform in the following order, D, F, C, E, A, B is; 1/720
D) Probability that Comic A or Comic B will perform third is; 1/15
How to solve permutation and combination?A) Probability that comic D will perform fourth;
Number of ways that this will succeed = 1 * 5!
Number of possible outcomes normally = 6!
Thus;
P(D is 4th) = 5!/6! = 1/6
B) Probability that Comic F will perform first and Comic C will perform fourth.
Number of ways that this will succeed = 1 * 1 * 4!
Number of possible outcomes normally = 6!
Thus;
P(F is 1st and C is 4th) = 4!/6! = 1/30
C) Probability that the comedians will perform in the following order, D, F, C, E, A, B;
There is only 1 way and as such the probability = 1/6! = 1/720
D) Probability that Comic A or Comic B will perform third;
(2!*4!)/6! = 1/15
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Related Questions
I MEED HELPP WITH THIS PAGE PLSSS
Answers
9. The value of x is 7
10. In the figure x = 10
11. The relationship is that their sum is 180 degrees
This relationship is known as the Same-Side Interior Angles Theorem.
12. The statement is true.
Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal
14 < 3 = 94 degrees
How to find the value of x9. The value of x is solved using the knowledge of corresponding angles are equal
< A = < B
4x = 3x + 7
x = 7
10. In the figure < 3 and < 6 are alternate internal angles which is equal
7x - 10 = 5x + 10
7x - 5x = 10 + 10
2x = 20
x = 10
11. The relationship between the interior angles on the same side is that their sum is 180 degrees
This relationship is known as the Same-Side Interior Angles Theorem. It is a fundamental concept in geometry and is used to solve problems involving parallel lines and transversals.
12. The statement is true.
Supporting statement: If the two lines are parallel, then the alternate exterior angles created by the transversal line are equal
13. The measure of w is solved using the idea of vertical angels
w + 85 = 148
w = 148 - 85
w = 63
14. The mistake is that < 5 is not corresponding angle to < 2
The correct solution is < 3 = < 5 alternate internal angles
< 3 + 86 = 180 supplementary angles
< 3 = 180 - 86
< 3 = 94 degrees
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In a large university, 70% of the students live in the dormitories. A random sample of 110 students is selected for a particular study.The probability that the sample proportion of students living in the dormitories falls in between 0.6 and 0.8 equals a.0.9780 b.0.9318 c.0.9365 d.1.6450
Answers
Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
\(\mu_{\hat p}=p\)
The standard deviation of this sampling distribution of sample proportion is:
\(\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\)
As the sample selected is quite large, i.e. n = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
\(\mu_{\hat p}=p=0.70\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.70(1-0.70)}{110}}=0.044\)
Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:
\(P(0.60<\hat p<0.80)=P(\frac{0.60-0.70}{0.044}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.80-0.70}{0.044})\)
\(=P(-2.27<Z<2.27)\\\\=P(Z<2.27)-P(Z<-2.27)\\\\=0.98840-0.01160\\\\=0.9768\\\\\approx0.9780\)
*Use a z-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
8. What is the slope of the line?
A. 0
B. 1
C. Infinity
D. Undefined
Answers
Because y=2 is a horizontal line, there is no rise
Answer:
0.
Step-by-step explanation:
The slope of the line is defined as the change of elevation of the line (\(\frac{rise}{run}\)).
In this case, there is no change in the slope as the line continues across (0 , 2), meaning that the slope of the line is 0.
If the slope of the line is 1, then the line will have (rise 1/run 1), meaning that it will have a linear slope. (See attached image).
Vertical lines have infinite slope, and so can also be called undefined as it moves neither left or right, giving it no run.
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State the name of the property illustrated. (x + 7) + [-(x + 7)] = 0
Answers
Answer:
addittional property
Step-by-step explanation:
Which did you include in your response? Check all that apply? Use ten StartFraction 1 Over 12 EndFraction bars. Circle groups of StartFraction 4 Over 6 EndFraction. There is one group of StartFraction 4 Over 6 EndFraction, with StartFraction 1 Over 6 EndFraction remaining. The quotient is 11 and one-fourth.
Answers
The simplified expression of the fraction expression is (b) One group of 4/6, with 1/6 remaining.
How to evaluate the fraction?
The fraction expression is given as
ten StartFraction 1 Over 12 EndFraction bars.
Rewrite the fraction properly
So, we have
Ten 1/12 bars
This can be represented as
10 * 1/12
Rewrite 10 as 10/1
So, we have the following equation
10 * 1/12 = 10/1 * 1/12
Evaluate the products of the numerator
So, we have the following equation
10 * 1/12 = 1/1 * 10/12
Evaluate the products of the denominator
So, we have the following equation
10 * 1/12 = 10/12
Simplify the fraction
10 * 1/12 = 5/6
Split the fraction
10 * 1/12 = 4/6 + 1/6
This means that, the result is
Quotient = 4/6 and remainder = 1/6
Hence, the true statement about the fraction is (b)
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Complete question
Which did you include in your response? Check all that apply?
Use ten 1/12 bars.
4/6One group of 4/6, with 1/6 remaining. The quotient is 11 and one-fourthSuppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
Answers
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
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Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
Answers
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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A right triangle has a hypotenuse of 12 feet and a leg of length 6 feet.
A triangle has hypotenuse of 12 feet and a leg of length 6 feet. What is the length of the other leg?
A. 6 feet
B. 6V 3 feet
C. 65 feet
D. S4 feet
Answers
Answer:6
Step-by-step explanation:
What transformations take place by graphing the function below in respect to its parent function? Check all that apply.
Answers
Answer:
y = x² is the parent
y = 3/2(x+7)²+2 shifts 7 u left, up 2 u, and has vertical compression
Answer:
Right 7 unitsUp 2 unitsVertical StretchStep-by-step explanation:
Given the function, f(x) = 3/2(x + 7)² + 2,
where:
a = 3/2
vertex (h, k ) = (7, 2)
The value of a determines whether the graph opens up or down. The value of a also makes the parent function wider or narrower (vertical stretch by a factor of a ). If a > 1, the graph is narrower than the parent function. The value of h determines how far left or right the parent function is translated. If h is positive, the function is translated h units to the right. The value of k determines how far up or down the parent function is translated. If k is positive, the function is translated k units up.
Given these descriptions, we can assume that:
The function is vertically translated by 2 units upward. The function is horizontally translated by 7 units to the right.Vertical stretch by a factor of 3/2 (or 1.5).Please mark my answers as the Brainliest, if you find my explanations helpful :)
Solve for x: 3(x + 1) = −2(x − 1) + 6. (1 point)
1
4
5
25
Answers
Answer: 1
Step-by-step explanation:
You are welcome :)
my math grade currently is a 96%. i get a 55% on a math test. the weight of the test is 50% of my grade. what would my grade be?
Answers
Answer:
h
Step-by-step explanation:
g
Simplify 5 √ 24 ⋅ 4 √ 24
Answers
Answer:
480 - don't need to simplify
Step-by-step explanation:
\(5 \sqrt{24} \: \times 4 \sqrt{24} \)
\(5 \times 4 \times \sqrt{24 } \: \times \sqrt{24} \)
=
\(20 \times 24\)
\( = 480\)
Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Answers
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
(a) Find the initial population. P(0) = 80 )ãbacteria
(b) Find an expression for the population after t hours. r(t) = 180( 125(6 Plt) =180(125(2))-
(c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7)=72.358- bacteria
(d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P(7) 2x bacteria/hour
(e) When will the population reach 200,000? (Round your answer to one decimal place.) hours
Answers
Answer:
a) P(0) = 80
b) \(P(t) = 80(2.2361)^t\)
c) 22,363 cells.
d) The rate of growth after 7 hours is of 18,000 bacteria per hour.
e) 9.7 hours.
Step-by-step explanation:
A bacteria culture grows with a constant relative growth rate.
This means that the population is given by:
\(P(t) = P(0)(1+r)^t\)
In which P(0) is the initial population and r is the growth rate, as a decimal.
After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So
\(50000 = 400(1+r)^6\)
\((1+r)^6 = \frac{50000}{400}\)
\((1+r)^6 = 125\)
\(\sqrt[6]{(1+r)^6} = \sqrt[6]{125}\)
\(1 + r = 125^{\frac{1}{6}}\)
\(1 + r = 2.2361\)
So
\(P(t) = P(0)(2.2361)^t\)
(a) Find the initial population. P(0)
We have that P(2) = 400. We use this to find P(0). So
\(P(t) = P(0)(2.2361)^t\)
\(400 = P(0)(2.2361)^2\)
\(P(0) = \frac{400}{(2.2361)^2}\)
\(P(0) = 80\)
So
\(P(t) = 80(2.2361)^t\)
(b) Find an expression for the population after t hours.
\(P(t) = 80(2.2361)^t\)
(c) Find the number of cells after 7 hours.
This is P(7). So
\(P(7) = 80(2.2361)^7 = 22363\)
22,363 cells.
(d) Find the rate of growth after 7 hours.
We have to find the derivative when t = 7. So
\(P(t) = 80(2.2361)^t\)
\(P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t\)
\(P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000\)
The rate of growth after 7 hours is of 18,000 bacteria per hour.
(e) When will the population reach 200,000?
This is t for which \(P(t) = 200000\). So
\(P(t) = 80(2.2361)^t\)
\(200000 = 80(2.2361)^t\)
\((2.2361)^t = \frac{200000}{80}\)
\((2.2361)^t = 2500\)
\(\log{(2.2361)^t} = \log{2500}\)
\(t\log{2.2361} = \log{2500}\)
\(t = \frac{\log{2500}}{\log{2.2361}}\)
\(t = 9.7\)
So 9.7 hours.
A car travels a distance of 112km at an average Speed of 70km/h. It then Travells Further for 60km at an average Speed of 50 km/hr. Calculate for the entire Journey of the total time taken.
Answers
The total time taken for the entire journey is 2.8 hours.
To calculate the total time taken for the entire journey, we can use the formula:
Time = Distance / Speed
For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:
Time1 = 112 km / 70 km/h = 1.6 hours
For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:
Time2 = 60 km / 50 km/h = 1.2 hours
To find the total time for the entire journey, we sum up the times for both parts:
Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours
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A pension fund manager is considering three mutual funds The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.3%. The probability distributions of the risky funds are:Expected Return Standard DeviationStock fund (S) 14% 43%Bond fund (B) 7% 37%The correlation between the fund returns is .0459What is the reward-to-volatility ratio of the best feasible CAL?
Answers
For the correlation between the fund returns is .0459, the reward-to-volatility ratio of the best feasible CAL is equals to 0.1621 or 16.21%.
A probability distribution is helps to determine the future what frequency distribution is to the past. Standard deviation is used in the concept of risk of portfolio of investment. Risk refer to the dispersion of a probability distribution.
Stock fund (S) Bond fund (B)
Expected Return 14% 7%
Standard Deviation 43% 37%
Risk-free returns , Rf = 5.3%
Correlation coefficient = 0.459
Covariance : 0.459 = COV(s,b)/0.43×0.37
Covariance = 0.073
Stock Fund =( (σB)²− σS× σB× correationco, SandB)/((σS)²(σB)² - 2 × σS× σB× correationco, SandB)
= ((0.37)²− 0.43× 0.37× 0.0459) /((0.43)²(0.37)² −2× 0.43× 0.37× 0.0459)
Weight of S = 42.18%
Weight of B = 1 - 42.18 = 57.82%
Expected Return of the portfolio (Rp) = WS× E(RS) + WB × E(RB) = 42.18 × 14% + 57.82 × 7%
= 5.90 + 4.05 = 9.95
Standard Deviation of the portfolio (SDp)
= (WS²SD² + WB²× lSD²+ 2WS WBCov(S,B))1/2
= 28.68
Reward to volatility = (Expected return - Rf) / SD of Portfolio
= (9.95- 5.3) / 28.68
=0.1621
Hence, the required volatility is 0.1621 or 16.21%.
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Which statement represents the expression?
24−8÷4
A.24 minus 8 divided by 4
B.the difference of 24 and 8 divided by 4
C.24 minus the quotient of 8 divided by 4
D.24 minus 4 divided by 8
Answers
Answer:
Which statement represents the expression?
24−8÷4
A. 24 minus 8 divided by 4
B. the difference of 24 and 8 divided by 4
C. 24 minus the quotient of 8 divided by 4
D. 24 minus 4 divided by 8
The answer is a. 24 minus 8 divided by 4
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Hope it is useful...y = 9x - 17
y = -5x + 11
Solve each system of equations by substitution
Answers
Answer:
\(y=1,\:x=2\)
Step-by-step explanation:
\(\begin{bmatrix}y=9x-17\\ y=-5x+11\end{bmatrix}\)
\(\mathrm{Substitute\:}y=-5x+11\)
\(\begin{bmatrix}-5x+11=9x-17\end{bmatrix}\)
\(x=2\)
\(\mathrm{For\:}y=-5x+11\)
\(\mathrm{Substitute\:}x=2\)
\(y=-5\cdot \:2+11\)
\(\mathrm{Simplify}\)
\(y=1\)
\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)
\(y=1,\:x=2\)
Pls help me do you know the answer let me know
Answers
Answer:
Are you telling us to answer it all?
Step-by-step explanation:
Answer:
I'm so sorry I have no idea seems so so complicated
Step-by-step explanation:
But I think you would need a specific equation for it and substitute numbers in it.
The product of two fractions is 2/1/2 if one of the fraction is 7/1/2 find the other
Answers
Then, we have:
7/ 1/2 . x
= 2 / 1/2
Simplifying the left-hand side, we get:
7x = 4
Dividing both sides by 7, we get:
x = 4/7
Therefore, the other fraction is
4/7
Out of 340 racers who started the marathon, 311 completed the race, 25 gave up, and 4 were disqualified. What percentage did not complete the marathon?
Answers
25+4 = 29
340-311 also = 29 that didn’t complete it
So we do 29/340 = 0.0852
0.0852 x 100 = 8.529 = 8.5%
PLSSS HELP ME 14 POINTS
Answers
The transformation of f(x) to g(x) is :
Vertically compressed by a factor of 9Shifted down by 2 Describing the transformation of the functionsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = x
g(x) = 1/9x - 2
The graph of the functions f(x) and g(x) are added as an attachment
And we have the transformations to be:
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A bag contains 10 red, 5 yellow, and 6 blue marbles. What is the probability of pulling out one blue marble and then one red marble without replacing the first blue marble?
Answers
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
How to determine the probability?The given parameters are
Red = 10
Yellow = 5
Blue = 6
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is
P = P(Blue) * P(Red Having selected Blue)
So, we have
P = 6/21 * 10/20
Evaluate
P = 1/7
Hence, the probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
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Can u help me please
Answers
Answer:
Step-by-step explanation:
2 more tiles are added in the next figure so in figure 30 the tiles will be 61
Answer:
9 tiles
Step-by-step explanation:
So figure 3 is literally figure 2 but added 1 to each corner. If the pattern is to contiue there should be 9 for figure 4.
Work out percentage change 20 from 50
Answers
Answer:
Therefore, the percentage change from 20 to 50 is an increase of 150%.
Step-by-step explanation:
To work out the percentage change from 20 to 50, we can use the following formula:
((New Value - Old Value) / Old Value) x 100%
Plugging in the numbers, we get:
((50 - 20) / 20) x 100%
= (30 / 20) x 100%
= 1.5 x 100%
= 150%
fraction that is equivalent to 3/9 and has a denominator of 3."
Answers
, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: The fraction 3/9
Now we can simplify the fraction further by dividing both the numerator and denominator by 3
let p=3/9
then p=3/3 / 9/3
p= 1/3
Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
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Jeremiah will give all of his sports cards to a number of friends what is the greatest number of friends he can give his cards to so that each friend will receive an equal number of baseball cards and football cards? 4 8 12 or 16 32 baseball 24 football
Answers
Answer:
6 is the greatest answer
Step-by-step explanation:
24÷4=6
The greatest number of friends he can give his cards to so that each friend will receive an equal number of baseball cards and football cards is 6
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jeremiah will give all of his sports cards to a number of friends. the greater number will be calculated as,
Number = 24÷4=6
Therefore, the value of the greatest number will be 6.
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an ice cream truck operator tracks total daily sales rounded to nearest dollar for 14 days as shown in the following 1: 201 2:249 3: 285 4:297 5:288 6:262 7:256 8:240 9:210 10:199 11:192 12:215 13:237 14:290 based on a cubic model of the data what is the predicted number of sales on the 15th day
Answers
The required predicted sales n the 15th day is given as 244 ice creams.
Given that,
an ice cream truck operator tracks total daily sales rounded to the nearest dollar for 14 days as shown in the following 1: 201 2:249 3: 285 4:297 5:288 6:262 7:256 8:240 9:210 10:199 11:192 12:215 13:237 14:290.
The average of the values is the ratio of the total sum of values to the number of values.
Here,
calculate average sales,
= [201 +249 + 285 + 297 + 288 + 262 + 256 + 240 + 210 + 199 + 192 + 215 + 237 + 290] / 14
= 244
So on the 15 day the sale can be predicted as 244.
Thus, the required predicted sales n the 15th day is given as 244 ice creams.
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Answer: $371
Step-by-step explanation:
use the cubic equation
Larry fills his bathtub at a constant rate. The amount of water in his tub is proportional to the amount of time he spends filling it. This relationship is described in the following graph:
Answers
Answer:
7 but im not sure
Step-by-step explanation:
Answer:
its A and B
Step-by-step explanation:
Do NOT hit none of the above, that's wrong
David saves money from his teaching job to buy a new boat when he retires in 20 years. The boat will cost $30,000. He has $12,000 in his simple interest savings account. To reach his goal by retirement, David should
Answer: move his money to a compound interest account
Answers
David ought to keep saving money in his simple interest account regardless of his current age.
He will be able to purchase his 30,000 USD boat at that rate each year. David would need to put at least 5 to 10 percent of his income into a savings account with simple interest.
Your initial investment as well as any interest that has already been accrued will earn interest in a compound interest account. The "compounding" factor is the appreciation of interest based on interest that occurs over time. On the other hand, simple interest accounts only pay interest on the initial principal.
Can a compound interest account result in a loss of funds?Both guaranteed and non-guaranteed substances benefit from compounding. You might lose all of your money or some of it. Stocks, income trusts, real estate, mutual funds, and gold are all examples.
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