Answer:
147/572
Step-by-step explanation:
The number of combinations of n things chosen r at a time is
[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex] (Some writers use the symbol [tex]_nC_r[/tex])
Choose 4 women from the 7:
[tex]\binom{7}{4}=\frac{7!}{4!(7-4)!}=35[/tex] ways
Choose 3 men from 9:
[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=84[/tex] ways
There are 35 x 84 = 2940 ways to choose both, out of
[tex]\binom{16}{7}=\frac{16!}{7!(16-7)!}=11440[/tex] ways to choose any 7 people from the group of 16.
Probability:
[tex]\frac{2940}{11440}=\frac{147}{572}[/tex]
P.S. As an example of how to calculate combinations, here's the calculation (by hand, a calculator is easier!) of [tex]\binom{9}{3}[/tex].
[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=\frac{9!}{3!6!}[/tex]
When you write out the factorials, you can do a bunch of cancellation between the numerator and denominator.
[tex]\frac{9\cdot8\cdot7\cdot\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1}}{(3\cdot2\cdot1)(\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1)}}=\frac{9\cdot8\cdot7}{3\cdot2\cdot1}=84[/tex]
Question: 33 of 39 Lesson 17
Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
tan θ = 0.7536
Hypotenuse = 29 miles
Opposite side = ?
Choice 'A' opp = 13.7 miles
Choice 'B' opp = 15.2 miles
Choice 'C' opp = 12.4 miles
Choice 'D' opp = 17.5 miles
Answer:
17.5 miles
Step-by-step explanation:
right!!
Pls help me I will mark is your right :)
A fitness center is interested in the average amount of time a client exercises in the center each week.
Match the vocabulary word with its corresponding example.
The average amount of exercise time for the 45 clients from the fitness center who
participated in the study
The average amount of time that all clients from the fitness center exercise
All 45 exercise times there were recorded from the participants in the study
All clients at the fitness center
The amount of time that any given client from the fitness center exercises
b The 45 clients from the fitness center who participated in the study
d
a
c
a. Data
b. Sample
c. Population
d. Variable
e. Statistic
f. Parameter
Textbook Pages
Study data: The 45 exercise sessions from study participants were all recorded.
What is meant by data of study?Study Data includes all information created, obtained, or acquired during the conduct of the Study, including Samples 1 through 3 including databases, documents, reports, and other material.
Any information that has been gathered, noticed, produced, or made specifically to support initial study conclusions is referred to as research data. Research data can also be found in non-digital media like diary and lab notebooks, despite being mostly digital.
A. Study data: The 45 exercise sessions from study participants were all recorded.
B. Study parameter: The average weekly exercise time for all participants.
C. Study variable: The length of time that each individual fitness facility patron exercises.
D. Study participants: all patrons of the fitness club.
E. The 45 gym patrons who took part in the survey made up the study's sample.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
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In the figure below, x = 25.
What is the value of y?
65
130
140
Answer:
130
Step-by-step explanation:
25 + 25 = 50
180 degrees on a strait line so 180 - 50 = 130
Answer:
65
Step-by-step explanation:
• x + y = 90• x is given as 25 so replace 25 instead of x then
=> 25 + y =90
=> y = 90-25
=> y = 65
Please help with homework
Solve
2(x+4)=3(-2+x)
Answer:
x = 14
Step-by-step explanation:
2(x + 4) = 3( -2 + x) distribute the 2 and the 3.
2(x) + 2(4) = 3(-2) + 3(x)
2x + 8 = -6 + 3x Subtract 2x from both sides
2x - 2x + 8 = -6 +3x -2x
8 = -6 +x Add 6 to both sides
8 + 6 = 6 - 6 + x
14 = x
8z = 4x - 32
Please explain step by step
The solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It consists of an equals sign and two expressions, one on each side of the equals sign. Equations are used to solve for the value of the unknown expressions, and can be used to solve problems in various fields such as physics, chemistry, engineering, and mathematics.
1. Start by isolating the z variable by subtracting 4x from both sides of the equation. This will give us: 8z = -32.
2. Divide both sides of the equation by 8. This will give us: z = -4.
3. Finally, substitute z = -4 into the original equation and solve for x. This will give us: 4x = 32, so x = 8.
Therefore, the solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
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Complete questions as follows-
8z = 4x - 32
Please explain step by step how to solve 8z = 4x - 32.
Determine if the following is true: if sin^2x cos^2x=1, then sinx+cosx=1
Answer:
true
Step-by-step explanation:
I need help with these 4 problems
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.
Here,
In New York City, a one-bedroom apartment will cost $1600 in 2020.
Y = mx + c is frequently used as the formula for a straight line graph, where;
gradient = m
The vertical intercept is given by c.
With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.
This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.
y = 40(20) + 800 = $1600
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
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WILL MARK BRAINLIEST!
To the nearest tenth, the perimeter of the rhombus is ___ units long.
Answer:
28.84 units
Step-by-step explanation:
using Pythagorean's Theorem, and halving both 8 and 12, we can find the length of the hypotenuse of on of the triangles. Once we find that length. we multiply it by 4 to complete the total perimeter.
How many solutions are on this graph?
Answer:
There are three intersections on the graph, therefore there are three solutions to the system
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
the 3 places the lines cross are solutions
find the suitable rearrangement for 1+2+3+4+896+897+898+899
Answer:
steps below
Step-by-step explanation:
1+2+3+4+896+897+898+899
= (1+899)+(2+898)+(3+897)+(4+896)
= 900 + 900 + 900 + 900
= 3600
What are the coordinates of the image rectangle for a scale factor of 3 if the center of dilation is the origin?
This doesn’t have a rectangle picture btw
I will mark brainlist
Answer: Choice B)
Explanation:
You mentioned there isn't a diagram to go with this, but I'm assuming that this problem is referring to a previous problem you posted. In that problem, it mentions that point W is at (1,-2). If we apply the scale factor 3, then we're tripling each coordinate. That means x = 1 becomes x = 3, and y = -2 becomes y = -6
We can write it like this:
(1,-2) ---> 3*(1, -2) = (3*1, 3*(-2) ) = (3, -6)
Only choice B has W'(3,-6) so this is likely the final answer.
If we apply this dilation to every point, then that effectively makes quadrilateral W'X'Y'Z' to be three times longer and taller than compared to quadrilateral WXYZ. In other words, its side lengths are 3 times longer.
Q:write the equation of the line that is given slope an y-intercept?
Slope=Undefined y-intercept= -4
[tex]y = mx + b[/tex]
Answer:
y = mx - 4
Step-by-step explanation:
m is the slope, while -4 is the y intercept
You have just secured a job at a web development company. You get paid $19.50 an hour and work
35 hours per week. Your take home pay will be 60% of your total income. You are planning to make
a budget and have estimated that your rent will be about 29% of the total budget. How much money
will you need to pay rent? Answer to the nearest cen
PLEASE HELP ASAP AND IF U SEND A LINK = REPORT
39,000 PER YEAR FOR THIS
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the trinomials with their factors.
a2 + a − 20
a2 − 9a + 20
a2 − 8a − 20
a2 − 12a + 20
a2 − 19a − 20
Factors
Trinomials
(a − 4)(a − 5)
arrowRight
(a − 10)(a − 2)
arrowRight
(a − 4)(a + 5)
arrowRight
(a − 10)(a + 2)
arrowRight
Answer:
2with1
4with2
1with3
3wth4
Using the following list of data, which statement is true?
Answer:
Range>Mean
Step-by-step explanation:
Range: find the largest(100) subtract lowest(50)=50
Mean: add all the numbers (790), then divide how many numbers there are(10)= 79
50>79
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Much would be appreciated <3
what is the average of 12 14 and 16
Answer:
15
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
to find the average, add the numbers together, then multiply by the quantity.
12+14+16=42
42/3= 14
14 is the average
hope this helped <3333333333333333
A simple random sample of 32 men from a normally distributed population results in a standard deviation of 12.9 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normalâ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.
Required:
Identify the null and alternative hypotheses.
Answer:
Null Hypothesis, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute
Alternate Hypothesis, H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute
Step-by-step explanation:
The null hypothesis is basically the problem statement i.e
Pulse rates of men have a standard deviation equal to 10 beats per minute
Hence, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute
The alternate hypothesis will contradict or negate the null hypothesis i.e
H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute
If I deposit $100,000 in a retirement account that gives 8 % paid annually, what will be balance after 25 years?
Answer:
$300,000
Step-by-step explanation:
To find 8% of 100,000 all you need to do is multiply 100,000 by .08.
100,000 (.08) = 8,000
The 8,000 accounts for one year, so now you have to multiply 8,000 by 25.
8,000 (25) = 200,000
Now add the initial amount to the additional 200,00 that will be paid to the retirement account.
100,000 + 200,000 = 300,000
The answer is $300,000.
Can someone please help
50% of babies are born female. Olive wants to find the probability that 20 or more of the 50 babies born today were female. If we use a double-sided coin and assign heads as females and tails
15 minutes for 5 songs = minutes per song
Answer:
The average minutes per song would be 3.
What are the requirements for an experiment to be able to show that changes in one variable cause changes in another?
Answer:
A variable is anything that can change or be changed. In other words, it is any factor that can be manipulated, controlled for, or measured in an experiment.
There are three main variables: independent variable, dependent variable and controlled variables.
A relationship between two variables whereby a change in one coincides with a change in the other is referred to as causality.
Step-by-step explanation:
please mark this answer as brainliest
Given parallelogram ABCD Find the area
Answer:
Area = ab sinx
Area = (8)(18) sin32
Area = 144 sin32
Area = 79.41
help thanks !!!!!!!!!!!!!!!
Answer:
ASA
Step-by-step explanation:
The hash marks are telling which sides are congruent and the angle mark is telling us that those angles are congruent.
plz help me well mark brainliest if correct!!...
Answer:
B
Step-by-step explanation:
Henrie plays baseball. He hits 80% of the time he bats. If he is up to bat 20 times this weekend at his baseball tournament, how many times is he expected to hit
Answer:16
Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.
50 POINTS Answer the following questions and draw a rough sketch of the function:
f(x)=-x^4+8x^3+8x^2-96x-144
What is the function’s general shape?
Does the function face up or down?
What is the function’s y-intercept?
If one of the factors is (−6), how would you show that on the graph?
The function's general shape is a downward-opening parabola.
The function faces down The function's y-intercept is -144x - 6 is a factorWhat is the function’s general shape?
From the question, we have the following parameters that can be used in our computation:
f(x)=-x^4+8x^3+8x^2-96x-144
Express properly
So, we have
f(x) = -x⁴ + 8x³ +8x² - 96x - 144
Next, we plot the graph (see attachment)
From the attached graph, we can see that the function opens down
This means that the general shape is a downward-opening parabola.
Does the function face up or down?The function faces down (as shown on the graph)
What is the function’s y-intercept?Here, we set x = 0
So, we have
f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144
Evaluate
f(0) = -144
So, the y-intercept is -144
How to show that one of the factors is (x - 6) on the graph?We start by setting the factor to 0
So, we have
x - 6 = 0
Solve for x
x = 6
From the graph;
When x = 6, y = 0
This means that x - 6 is a factor
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Which relation is the factored form of f(x)=x^2-4x+4
a) f(x)=(x-2)^2
b) f(x)=(x+4)(x-1)
c)f(x)=4(x-1)^2
d)f(x)=(x-2)(x+2)
Answer:
answer is a) f(x)= (x-2)^2
Please answer correctly for brainliest
Answer:
oki! mizuki here to answer and help!
The answer will be 19/10 or 1 9/10
Step-by-step explanation:
Soo... let's simplify 1 2/5 first.
The simplified version of 1 2/5 is 7/5.
and we solve the equation!
since there are two negatives, turn it into a plus!
7/5 + 1/2
5 x 2 = 10 2 x 5 = 10
7 x 2 = 14 1 x 5 = 5
so...
14/10 + 5/10 which will be 19/10, or 1 9/10
The question should be find the answer, not the difference ngl.