To find the probability that exactly two of the five will take the same test, we use combinations. The probability is 2/3 or 0.667. To find the probability that the two women will take the same test, we use combinations. The probability is 1/2 or 0.500.
To find the probability that exactly two of the five will take the same test, we can use the concept of combinations. There are six different tests, and we need to choose two of them to be taken by two people. The total number of ways to select two tests out of six is given by the combination formula C(6,2) = 6!/(2!(6-2)!) = 15. Now, for each of these two selected tests, there are two people (either two men or two women) who can take the test, resulting in a total of two possibilities. Therefore, the number of favorable outcomes is 2 * 15 = 30. Finally, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 6!/(2!3!) = 15. So the probability is 30/15 = 2/3 or 0.667 (rounded to three decimal places).
To find the probability that the two women will take the same test, we can use similar reasoning. There are six different tests, and we need to choose one of them to be taken by both women. The total number of ways to choose one test out of six is given by the combination formula C(6,1) = 6!/1!(6-1)! = 6. Now, for the chosen test, there are three possible ways both women can take it, since they can be the first two applicants, the last two applicants, or the middle two applicants. Therefore, the number of favorable outcomes is 3. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is also 6. So the probability is 3/6 = 1/2 or 0.500 (rounded to three decimal places).
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Final answer:
The probability that exactly two of the five will take the same test is 0.00463. The probability that the two women will take the same test is 1.167.
Explanation:
To find the probability that exactly two of the five will take the same test, we can use combinations. There are 6 different tests and we want to select 2 of them for the same test. Since order doesn't matter, we can use combinations. The number of ways to choose 2 tests out of 6 is 6 choose 2 = 15.
Now, for each pair of tests, we have 5 people who can take those tests. The probability that exactly 2 of the five will take the same test is the probability that exactly 2 people are randomly assigned to the same test out of the 5 people. The total number of possible outcomes is 6^5 since each person has 6 choices for which test to take, and there are 5 people.
So, the probability that exactly two of the five will take the same test is 15/6^5, which is approximately 0.00463.
To find the probability that the two women will take the same test, we consider the different possibilities. The two women can take the same test out of the 6 tests, or they can take different tests.
If they take the same test, there are 5 possible tests for them to choose from. The probability of this happening is 5/6.
If they take different tests, there are 5 possible tests for each of them to choose from. The probability of this happening is (5/6) * (4/5) = 2/3.
Therefore, the probability that the two women will take the same test is (5/6) + (2/3) = 7/6, which is approximately 1.167.
A student reads 3/5 of a book in 30 minutes. if the student is reading at the same speed in 40 minute how much of the book will the student read
Express this amount in dozens. (Use decimal form.) 7.5 cupcakes
...?
Suppose the first term of a geometric sequence is multiplied by a nonzero constant, c. What happens to the following terms in the sequence? What happens to the sum of this geometric sequence? (This question has one right answer.) Give an example of a geometric sequence to illustrate your reasoning. (Many answers are possible.)
The reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?
If total Revenue is $3000, Cost of Goods is $1500, and total Selling Expense is $500; what is the Profit for the business?
A boat, whose speed in still water is 1.96 m/s, must cross a W = 217 m wide river and arrive at a point D = 111 m upstream from where it starts, as shown in figure below.
To do so, the pilot must head the boat at a 42.9° upstream angle. What is the speed of the river's current?
Deshaun went for a drive in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. For how many hours did he drive?
Deshaun drove at a speed of 62 miles per hour for 99.2 miles. To calculate the time spent driving, use the formula Time = Distance / Speed. The time taken for his drive is approximately 1.6 hours.
The question pertains to calculating the driving time given the speed and distance traveled by Deshaun in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. To find out how many hours he drove, we use the formula for time which is:
Time (t) = Distance (d) / Speed (v)Here, the distance d is 99.2 miles and the speed v is 62 miles per hour.
So we calculate the time t as follows:
t = 99.2 miles / 62 miles per hourThe time taken by Deshaun for his drive is approximately 1.6 hours.
Choose what the expressions below best represent within the context of the word problem.
The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?
x best represents .
x + 12 best represents .
$9.00 for 3 pairs of socks
what is the product of 3x4 y2 and 2xy3?
what is the GCF of 9, 27,and 63
eremy is working at 2 jobs to save money for his college education. He makes $8 per hours working for his uncle at Pizza Pie busing tables and $10 per hour tutoring peers after school in math. His goal is to make $160 per week. Part c- After researching the costs of colleges, Jeremy decides he needs to make more than $160 each week. Write an inequality in two variables to represent the amount of money Jeremy needs to make. Then graph.
Final answer:
Jeremy needs to create an inequality to represent his new earning goal higher than $160 a week, leading to the inequality 8x + 10y > 160. This can be graphed by first converting to intercept form, plotting the intercept and slope, drawing a dashed boundary line, and shading the region above this line.
Explanation:
Jeremy is working two jobs to save for his college education and needs to create an inequality to represent the amount he needs to make each week, now more than $160. Let's denote the number of hours Jeremy works busing tables as x and the number of hours he spends tutoring as y. He makes $8 per hour busing tables and $10 per hour tutoring.
To express Jeremy's goal of making more than $160 a week, we can write the following inequality:
8x + 10y > 160
To graph this inequality:
First, rewrite the inequality as y > (-4/5)x + 16 to get the intercept form.
Plot the y-intercept at (0, 16) on the graph.
Use the slope of -4/5 to determine another point. From (0, 16), move 5 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point.
Draw a dashed line through the two points to represent the boundary of the inequality (dashed because the inequality is strict and does not include the line itself).
Shade above the line to indicate that all solutions to the inequality lie in this area, where Jeremy would be earning more than $160.
What describes each face on a dodecahedron?
A. equilateral triangle B. equilateral pentagon C. circle D. square ...?
Which of the following are true statements?
Check all that apply.
A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
B. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it horizontally by a factor of 1/2.
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
D. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will shrink it vertically by a factor of 1/2.
...?
Answer:
A
C
Step-by-step explanation:
Here we must compare a function and its transformation, we will see that the correct options are A and C.
First, we must define the transformations that we will be using here.
Reflection about the x-axis:
For a function f(x) a reflection about the x-axis is written as:
g(x) = -f(x)
Vertical contraction.
For a function f(x) a vertical contraction of scale factor k is written as:
g(x) = k*f(x)
So here we start with:
ƒ(x)=√x
Then we reflect it about the x-axis to get:
ƒ(x)=-√x
Then we shrink it by a scale factor k = 1/2
ƒ(x) = (-1/2)*√x
From this, we can see that the correct options are:
A. The graph of ƒ(x)=-1/2√x will look like the graph of ƒ(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.
And C is also true, because we have a reflection about the x-axis, the range changed from positive values to negative values, so:
C. ƒ(x)=-1/2√x has the same domain but a different range as ƒ(x)=√x.
Is also a correct option.
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what is the highest common factor of 630 and 1560
A group of 483 students is taking a field trip. one bus is needed for every 50 students. how many buses are needed?
6 times the sum of 3 consecutive odd intergers is -18
solve the equation for y 2x+6y=13
What is the multiplicative rate of change for the exponential function f(x) = 2(5/2)–x(to the negative X)?
A.0.4
B.0.6
C.1.5
D.2.5
Answer:
A. 0.4
Step-by-step explanation:
Benny has saved 42 quarters from washing cars how many cents does Benny have
A test for the presence of a certain disease has probability 0.2 of giving a false-positive result (indicating that an individual has the disease when this is not the case) and probability 0.1 of giving a false-negative result. Suppose that 10 individuals are tested, 5 of whom have the disease and 5 whom do not. Let X be the number of positive readings that result.
a. Explain why X does not have a binomial distribution.
b. Find the probability that exactly 3 of the 10 test results is positive?
Devil has 39 toy blocks what is the value of the digit nine in this number
triangle PQR is similar to Triangle TUV. the perimeter of triangle PQR is 60 inches. what is the perimeter of triangle TUV?
whats the anserr becuse i got this wrong on a home work sheet
Which number sentence should be used to solve this problem? Ethan collected 30.4 pounds of recycling in June. He collected 35.5 pounds in July.
How many more pounds of recycling did Ethan collect in July than June?
A.
30.4 + 35.5 = ?
B.
35.5 - 30.4 = ?
C.
30.4 - 35.5 = ?
D.
35.5 + 30.4 = ?
Rewrite the fraction as a decimal 57/5
HELLPP MEE PLEAASSEEE!!????
Is ABC DEF?
If so, name the postulate that applies.
A. congruent - SAS
B. congruent - ASA
C. congruent - SSS
D. might not be congruent
AB is tangent to O. If AO = 24 and BC = 27, what is AB?
Choices:
45
69
54
51
The measure of the side AB will be 45. The correct option is A.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Use the Pythagorean theorem to calculate the length of AB as below,
OB² = AB² + OA²
(BC + OC)² = AB² + OA²
(27 + 24)² = AB² + 24²
AB² = 51² - 24²
AB = 45 units
Therefore, the correct option is A. The value of length AB is 45.
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.
Which of the following is the correctly abbreviated SI unit describing the amount of a substance?
M
kg
mol
g
If a 100(degree) arc of a circle has a length of 8 inches, to the nearest inch, what is the radius of the circle?