(a) To find the number of committees of six that contain three men and three women, we can use the concept of combinations.
The number of ways to choose three men out of five is given by the combination formula:
[tex]\({{5}\choose{3}} = \frac{5!}{3!(5-3)!} = 10\)[/tex]
Similarly, the number of ways to choose three women out of seven is given by:
[tex]\({{7}\choose{3}} = \frac{7!}{3!(7-3)!} = 35\)[/tex]
Since the choices for men and women are independent, we can multiply these two values to get the total number of committees with three men and three women:
[tex]\(10 \times 35 = 350\)[/tex]
(b) To find the number of committees of six that contain at least two men, we can consider two cases:
1. Committees with exactly two men:
The number of ways to choose two men out of five is [tex]\({{5}\choose{2}} = 10\)[/tex].
The number of ways to choose four women out of seven is [tex]\({{7}\choose{4}} = 35\)[/tex].
So, the number of committees with exactly two men is [tex]\(10 \times 35 = 350\)[/tex].
2. Committees with three men or more:
We have already calculated the number of committees with exactly three men and three women in part (a), which is 350.
To get the total number of committees with at least two men, we sum the results from the two cases: .
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Given the following data: 46, 47, 110, 56, 71, 109, 63,91, 111,93, 125,78,85, 108,73, 118,70,89,99, 45,73.
Compute the five-number summary and draw the boxplot.
The five-number summary for the given data is as follows: Minimum = 45, First Quartile (Q1) = 71, Median (Q2) = 89, Third Quartile (Q3) = 108, Maximum = 125.
The five-number summary provides key descriptive statistics that summarize the distribution of the data. It consists of the minimum value, the first quartile (Q1), which represents the lower 25% of the data, the median (Q2), which represents the middle value or the 50th percentile, the third quartile (Q3), which represents the upper 25% of the data, and the maximum value.
To draw a boxplot based on this five-number summary, a box is drawn from Q1 to Q3, with a line indicating the median (Q2). Whiskers extend from the box to the minimum and maximum values. Outliers, if present, are represented as individual data points beyond the whiskers.
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The circle radius is 12 cm. Then the circle content is
PLEASE HEEEELP
verify that the following function is a cumulative distribution function. f(x)={0x<10.51≤x<313≤x round your answers to 1 decimal place (e.g. 98.7).
The probability distribution of X is as follows:P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31.
Given function: f(x)={0x<10.51≤x<313≤xTo verify that the given function is a cumulative distribution function, we have to check the following conditions:1. f(x) is non-negative for all x.2. f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1. Now, let's verify these conditions one by one.1. f(x) is non-negative for all x. This condition is satisfied, as the given function f(x) is defined only for x ≥ 1, and is non-negative for all x in this domain. Therefore, f(x) is non-negative for all x.2. f(x) is continuous from the right for all x. This condition is also satisfied, as the given function f(x) is defined piecewise as a continuous function for all x. Therefore, f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x. This condition is satisfied, as the given function f(x) is non-decreasing for all x in its domain.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1.
Using the definition of f(x) for x < 10, we have f(x) = 0 for x < 10. Therefore, lim{x → -∞} f(x) = 0. Using the definition of f(x) for x ≥ 31, we have f(x) = 1 for x ≥ 31. Therefore, lim{x → ∞} f(x) = 1. Hence, all four conditions are satisfied. Therefore, the given function is a cumulative distribution function. To find the probabilities of the intervals, we use the formula: P(a ≤ X ≤ b) = F(b) - F(a)where P(a ≤ X ≤ b) is the probability that X lies between a and b, and F(x) is the cumulative distribution function of X. Furthermore, the probability of the interval (a, b] is: P(a < X ≤ b) = F(b) - F(a)Therefore, the probabilities of the intervals are: P(1 < X ≤ 10.5) = F(10.5) - F(1) = 0 - 0 = 0P(10.5 < X ≤ 31) = F(31) - F(10.5) = 1 - 0 = 1P(X > 31) = F(∞) - F(31) = 1 - 1 = 0Therefore, we have: P(1 < X ≤ 10.5) = 0P(10.5 < X ≤ 31) = 1P(X > 31) = 0
Hence, the probability distribution of X is as follows: P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31. Therefore, the given function is a cumulative distribution function, and the probability distribution of X is as above.
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HELP ASAP PLEASE!!!!
Answer:
Q' = (1, -5)
R' = (3, 1)
S' = (0, 0)
T' = (-2, -3)
Step-by-step explanation:
Look at the numbers of the current vertices and then change the signs of the y-coordinates around. For example, the original Q-coordinate was (1,5) so I changed the 5 to a -5 to reflect across the axis. Changing the y-coordinate sign reflects across the x-axis, while changing the x-coordinate sign reflects across the y-axis.
HELP ASAP!! In the problem below there is an error in the math. Find the error and write what the error is in complete sentences. You will then work out the problem correctly.
Please help me.
Please simplify it and group it in like terms.
3a+6+2a-4+a-2=
Answer:
6a
Step-by-step explanation:
Answer:
6a
Step-by-step explanation:
3a+2a+a= 6a
6-4-2=0
6a+0=6a
statistics are used to: a. ask questions b. make estimates of population parameters c. form a basis for analysis d. theoretically specify grouping of study elements
Statistics are used to make estimates of population parameters. Therefore, the correct option is B.
Statistics are used for various purposes in data analysis. One important application of statistics is to make estimates of population parameters. Population parameters are characteristics or measures that describe an entire population. However, it is often impractical or impossible to collect data from the entire population, so statistics provide methods for estimating these parameters based on a sample of the population.
By collecting and analyzing data from a sample, statisticians can make inferences and draw conclusions about the larger population. These estimates help researchers understand the characteristics, patterns, and relationships within the population.
Additionally, statistics form the basis for analysis in many fields, including scientific research, business, social sciences, and more. They provide tools and techniques to summarize, interpret, and draw meaningful insights from data, enabling researchers and decision-makers to make informed choices and draw valid conclusions from their observations and experiments.
Therefore, the correct choice is option b. Statistics play a crucial role in estimating population parameters and providing insights for analysis and decision-making.
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Find the total surface area of this triangular prism.
Answer:
28 i think
Step-by-step explanation:
The following data sets are the math and science test scores, out of 100, for a group of twelve seventh grade students
The interquartile range (IQR) of both the data sets is 8. Create a box plot for each data set Which statement correctly compares
the two data sets?
A. The majority of the math scores are greater than the median of the science scores
B. The majority of the science scores are greater than the median of the math scores
C. The medians of both data sets are equal
D. There is not enough information given to compare the data and medians of the math and science scores
Answer:
The answer and work are in the pdf
Step-by-step explanation:
Answer: A. The majority of the math scores are greater than the median of the science scores
Step-by-step explanation:
I took the test!
A dartboard has 20 equally divided wedges, and you are awarded the number of points in the section your dart lands in. If you are equally likely to land in any wedge, what is the probability you will score 10, 11, or 12 points?
Answer: 10 points
Step-by-step explanation:
Can the following angle measures be the interior angles of a triangle: 29°, 29°, and 29° ? Justify your answer.
Answer:
No
Step-by-step explanation:
Angle measures of a triangle must add up to 180 and this only adds up to 87
Can someone help me with this. Will Mark brainliest.
Answer:
B ( -1, -8)
Step-by-step explanation:
A ( -7, -6)
midpt (-4, -7)
Equation:
(x + 3, y - 1)
Solve for B:
(-4, -7)
(x + 3, y - 1)
( -1, -8)
A. 5 cartoons/toy
B. 12 toys/ cartoon
C. 5 toys/ cartoon
Answer:
c
Step-by-step explanation:
15% of $9.00 is $
I need help!!
Answer:
$ 1.35
Step-by-step explanation:
9 times 0.15 is 1.35
Kim's fish is 10 inches long.
Sam's fish is 3 inches long.
How many inches shorter is Sam's fish?
Answer:
7
Step-by-step explanation:
Answer:
Sam's is 7in shorter
Step-by-step explanation:
[tex]10-3=7[/tex]
Approximately what percentage of hardcover books sold were nonfiction?
Answer:
B
Step-by-step explanation:
What is the answer for these this question
does anyone know the answer
Answer:
I think it is A.
Step-by-step explanation:
I hope this helps.
You are creating a 4-digit pin code. How many choices are there in the following cases? a. With no restriction, b. No digit is repeated, c. No digit is repeated, 2 and 5 must be present.
the number of choices in each case is:
a. With no restriction: 10,000 choices.
b. No digit is repeated: 5,040 choices.
c. No digit is repeated, 2 and 5 must be present: 56 choices.
Let's calculate the number of choices in each case:
a. With no restriction:
For each digit in a 4-digit pin code, we have 10 choices (0-9). Since there are 4 digits in total, the number of choices is 10⁴ = 10,000.
b. No digit is repeated:
For the first digit, we have 10 choices (0-9).
For the second digit, we have 9 choices (any digit except the one chosen for the first digit).
For the third digit, we have 8 choices (any digit except the two chosen for the first and second digits).
For the fourth digit, we have 7 choices (any digit except the three chosen for the first, second, and third digits).
The total number of choices is 10 * 9 * 8 * 7 = 5,040.
c. No digit is repeated, and 2 and 5 must be present:
We have two fixed digits (2 and 5) that must be present in the pin code.
For the first fixed digit (2), we have only 1 choice.
For the second fixed digit (5), we have only 1 choice.
For the remaining two digits, we have 8 choices each (any digit except 2 and 5).
The total number of choices is 1 * 1 * 8 * 7 = 56
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I need help figuring out this question
Answer:
no picture
Step-by-step explanation:
identifying the coefficients and constant of a quadratic function consider the quadratic function f(x) = x2 – 5x 6. what are the values of the coefficients and constant in the function? a = b = c =
For the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:
a = 1
b = -5
c = 6.
To identify the coefficients and constant in the quadratic function f(x) = x^2 - 5x + 6, let's examine the standard form of a quadratic equation:
f(x) = ax^2 + bx + c
Comparing this with the given quadratic function, we can determine the values of the coefficients and constant:
a = 1 (coefficient of x^2 term)
b = -5 (coefficient of x term)
c = 6 (constant term)
Therefore, for the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:
a = 1
b = -5
c = 6.
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solve the system using elimination. 4x+5y=2 -2x+2y=8 ( ? , ? )
Answer:
(-2,2)
Step-by-step explanation:
Hi,
4x + 5y = 2
-2x + 2y = 8
To solve using elimination, we can multiply the second equation by 2 to try and get rid of the x. So...
4x + 5y = 2
-4x + 4y = 16
Now, add...
9y = 18
Divide by 9...
y = 2
Now, let's solve for x...
4x + 5(2) = 2
4x + 10 = 2
4x = -8
x = -2
Your solution is, (-2,2)
I hope this helps :)
A local pet groomer accepts walk-in customers. From experience, the groomer has determined that the probability that a walk-in customer will get a full-service grooming, which includes a bath and nail trimming, is 0.71. The probability that a walk-in customer will get a haircut for their pet is 0.42. The probability that customers who get the full-service grooming will also ask for a haircut is 0.28. What is the probability that a walk-in customer will ask for both a full-service grooming and a haircut?
0.12
0.20
0.28
0.30
Answer:
0.28
Step-by-step explanation:
Answer:
0.20
Step-by-step explanation:
i got it right on edge 2022
ABCD is a quadrilateral that has a four right angle What is the most accurate way to classify this quadrilateral
Answer:
A rectangle
Step-by-step explanation:
A square can be a rectangle but a rectangle can't always be a square.
Does anyone know how to do 3 & 4
Answer:
2.True
3. HGK
4. 17°
hope it helps
A student is required to solve the initial-value problem as follows:
y ' + 1x+3 y= x2 y-1 , y0= -4.
It is assumed here that x is positive. Then he/she has to find the numerical value of y 2.0, round it off to THREE figures and present the result. A student solved the problem and found that y 2.0 rounded-off to three figures was as follows :
Main Answer: The numerical value of y(2.0) rounded off to three figures is 1.279.
Supporting Explanation:
The student solved the initial-value problem and found that y(2.0) = 1.27977. The question asks to round off the value to three figures. Therefore, we have to keep only the first three digits after the decimal point, which are 279. The next digit after 9 is 7, which means we have to round up the last digit. Thus, the rounded off value of y(2.0) is 1.279.
The initial-value problem is a differential equation that has an initial condition given for a specific value of the independent variable. In this case, the initial condition is y(1) = 2. The solution of the initial-value problem gives the value of y for other values of x. Here, we are required to find the value of y for x = 2.0.
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A rabbit is carrying a dominant allele for brown hair (B) and a recessive allele for white hair (b). What is the rabbit's phenotype?
Answer:
B
Step-by-step explanation:
Its dominant because its brown hair.
Help help help! This is 40% of my grade and i am stuck.
FIND THE MEASURES OF THE INTERIOR ANGLES
Answer:
Angle A=68
Step-by-step explanation:
68+x+(x-24)=180
68+x+x-24=180
2x+44=180
2x=136
x=68
PLEASE HELP FOR BRAINLIEST! The sum of two numbers is 4 and the difference of their squares is 64. Find the two numbers.
10 and -6
.....................................................
(a) Find ged(18675, 20112340) (b) Factor both numbers from (b) above. (c) Find the lem of the two numbers from (b) above.
The lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
(a) To find the greatest common divisor (GCD) of 18675 and 20112340, we can use the Euclidean algorithm. The algorithm involves repeatedly dividing the larger number by the smaller number until the remainder becomes zero.
Using the Euclidean algorithm:
20112340 = 1074 * 18675 + 12590
18675 = 1 * 12590 + 6095
12590 = 2 * 6095 + 4000
6095 = 1 * 4000 + 2095
4000 = 1 * 2095 + 1905
2095 = 1 * 1905 + 190
1905 = 10 * 190 + 15
190 = 12 * 15 + 10
15 = 1 * 10 + 5
10 = 2 * 5 + 0
Since the remainder is now zero, the GCD is the last non-zero remainder, which is 5.
Therefore, ged(18675, 20112340) = 5.
(b) To factor the numbers 18675 and 20112340, we can find their prime factorizations.
Prime factorization of 18675:
18675 = 3^2 * 5^2 * 83
Prime factorization of 20112340:
20112340 = 2^2 * 5 * 7 * 143659
(c) To find the least common multiple (LCM) of 18675 and 20112340, we can use the prime factorizations obtained in the previous step.
The LCM is the product of the highest powers of all the prime factors involved.
Prime factors in the LCM:
2^2 * 3^2 * 5^2 * 7 * 83 * 143659
Therefore, the lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
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