Answer:
21 / 143
Step-by-step explanation:
Given that:
Number of Eastern conference reps = 8
Number of western conference rep = 7
Probability of selecting 3 from Eastern reps and 2 from western reps
Probability = required outcome / Total possible outcomes
Total possible outcomes:
selection to be made = 3+ 2 = 5
Total Number of players = 8 +7 = 15
Total possible outcomes
Using combination formula :
nCr = n! / (n-r)!r!
15C5 = 15! / 10!5! = (15 * 14 * 13 * 12 * 11) / (5*4'3*2*1) = 360360 / 120 = 3003
Total possible outcomes = 3003
Required outcome :
8C3 * 7C2
8C3 = 56 ; 7C2 = 21
8C3 * 7C2 = 56 * 21 = 1176
required outcome / Total possible outcomes
= 1176 / 3003
= 21 / 143
Using the hypergeometric distribution, it is found that the probability is:
c. 56/143
The players are selected from the sample without replacement, hence, the hypergeometric distribution is used.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 15 representatives, hence [tex]N = 15[/tex]8 are from the Eastern Conference, hence [tex]k = 8[/tex]Sample of 5, hence [tex]n = 5[/tex].The probability is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,15,5,8) = \frac{C_{8,3}C_{7,2}}{C_{15,5}} = 0.3916[/tex]
For which the equivalent fraction is option c.
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Dots sells T-shirts ($7) and shorts ($9). In April, total sales were $572. People bought 5 times as many T-shirts as shorts. How many T-shirts and shorts did Dots sell?
Dots sold 65 T-shirts and 13 shorts
How to calculate the number T-shirts and shorts ?let the x represent the number of T-shirts and y and shorts
7x + 9y= 572.......equation 1
x= 5y........equation 2
substitute 4y for x in the equation
7(5y) + 9y = 572
35y + 9y= 572
44y= 572
y= 572/44
y= 13
substitute 13 for y in equation 2
x= 5(13)
x= 65
Hence there 65 T-shirts and 13 shorts
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-1.12345...
rational, irrational and or real number?
Answer: Irrational Number
Step-by-step explanation: It's Irrational because it cant be represented as a simple fraction.
3=
X/
3
One step equations with positive whole number
If every 4 cm on a scale drawing is equal to 3 yards in rea
scaled-drawing lengths below would be less than 9 yards in real life? Select all that apply. A) 16 cm B) 6 cm C) 8 cm D) 24 cm
The scale drawing which is equal to 9 yards in real time is 12 cm.
Given that 4cm on the scale, drawing is equal to 3 yards in real-time
we have to find the scale drawing which is equal to 9 yards in real-time.
Let the scale drawing be 'x'
Now it can be written as
4 cm ------ 3 yards
x cm ------- 9 yards
Now we can divide this as
4/x = 3/9
By cross multiplication, we get
4 * 9 = 3 * x
x = 4 * 9 / 3
x = 12
Therefore, the scale drawing which is equal to 9 yards in real time is 12 cm.
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Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = – 2x + 10.
The equation of the line that passes through the point (0,0) and is perpendicular to the line y=-2x+10 is .
We will be using the concept of slope and equation of straight line for this question. Here it has been said that the line passes through (0,0) which is the origin, so we know the point ([tex]x_{1},y_{1}[/tex]) is (0,0).This point will be required while solving the equation for the straight line. The line is said to be perpendicular to another line given by y=-2x+10. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes is equal to -1. The slope of a line can be found from the equation of the line by dividing the coeeficient of x by the coefficient of y.
Slope of y=-2x+10 is -2
mx-2=-1⇒m=1/2
equation of a straight line,
[tex](y-y_{1} )=m(x-x_{1} )\\[/tex]
⇒y-0=[tex]\frac{1}{2}[/tex](x-0)
⇒y=[tex]\frac{x}{2}[/tex]
⇒2y=x
⇒2y-x=0
Thus the equation of the line that passes through (0,0) and is perpendicular to y=-2x+10 is 2y-x=0.
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Michael grabs a marble from a bag. There are 5 green marbles and 1 red marble. If he grabs the red marble he loses everything he bet on. The marbles are not put back into the bag. The max amount of times Michael can bet on the same game is 4. If he bets 300 and wins 578 (having 278 as winnings), he has the choice to bet again with everything he earned for 682. Then he has the choice to do so again for 945, then 1312 at max. At what point in the game should Michael stop playing to gain the most given the percent of risk of losing the game? What point in the game is the least beneficial for Michael's gains?
First bet (300 -> 578)
Second bet (578 -> 682)
Third bet (682 -> 945)
Fourth bet (945 -> 1312)
If Michael wins every round he would go from 300 to 1312. If he loses, he doesn't gain any of the rewards and is 300 in debt.
Using the expected value of a discrete distribution, it is found that:
Michael should stop playing the game after the first round.The fourth round is the least beneficial round for Michael.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For the probabilities, we consider that it is given by the number of desired outcomes divided by the number of total outcomes.
For one bet, the distribution is given as follows:
P(X = 578) = 5/6 (5 green marbles out of 6).P(X = -300) = 1/6.Hence the expected value is given by:
E(X) = 578 x 5/6 - 300 x 1/6 = $431.67.
For two bets, the distribution is given as follows:
P(X = 682) = 5/6 x 4/5 = 2/3.P(X = -300) = 1/3.Hence the expected value is given by:
E(X) = 682 x 2/3 - 300 x 1/3 = $354.67.
For three bets, the distribution is given as follows:
P(X = 945) = 5/6 x 4/5 x 3/4 = 1/2.P(X = -300) = 1/2.Hence the expected value is given by:
E(X) = 945 x 1/2 - 300 x 1/2 = $322.5.
For four bets, the distribution is given as follows:
P(X = 1312) = 5/6 x 4/5 x 3/4 x 2/3 = 1/3.P(X = -300) = 2/3.Hence the expected value is given by:
E(X) = 1312 x 1/3 - 300 x 2/3 = $237.33.
Hence, considering the greatest and the smallest expected values, we have that:
Michael should stop playing the game after the first round.The fourth round is the least beneficial round for Michael.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
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The formula below relates distance, rate, and time. Solve this formula for t.
The equation when solved for t gives d/r
What is subject of formula?Subject of formula can be defined as a variable or element expressed in terms of other variables in an equation.
Iris also known as the variable that is being worked out in equation.
From the information given, we have the equation as;
d = rt
Where;
d is the distancer is the ratet is the timeNow, let's make 't' the subject
Divide both sides by the coefficient of t
d/r = rt/r
t = d/r
Thus, the equation when solved for t gives d/r
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The complete question:
The formula below relates distance, rate, and time. Solve this formula for t.
d = rt
find the value of x in 5/9 = x/54
Answer:
[tex] \large \sf \: x=30[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
5/9 = x/54
Step 1: Cross-multiply.
5/9 = x/54
(5)*(54)=x*(9)
270=9x
Step 2: Flip the equation.
9x=270
Step 3: Divide both sides by 9.
9x/9 = 270/9
x=30
Jill swam 200 meters in 2 minutes and 42 seconds. If each lap is 50 meters long which time is her estimated time in seconds per lap
Answer:
36.3 seconds per lap
Step-by-step explanation:
200m in 2.42 if each lap = 50m
50m = 36.3 seconds
Which is the graph of the cube root function f(x) = ^3√x
Solve the inequality and express your answer in interval notation. x² + 8x + 3 < 0
Solution:
A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]
Hope this helps!
X - y = 5 and x + y = -10
The value of x and y by using the given expressions is x = -5/2 and y = -15/2.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.
Simplifying the expressions for x and y
The given expressions are:
x - y = 5 —--- 1
x + y = -10 —---- 2
Adding the expression 1 and 2, we get,
2x = -5
x = -5/2
Subtracting the expression 1 and 2, we get,
-2y = 15
y = -15/2
Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.
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A spring with a spring constant of 1N/cm is stretched and has elastic potential energy of 30 j. Calculate the extension experienced by
the spring.
Give your answer to 2 decimal places.
Th elastic potential energy of two decimal places is k=60×1^2 N/M
Given that,
Spring has a potential energy of =30 J
we know that,
Energy of a spring=1/2 kx^2
here, x=1cm
x^2=0.01m
30=1/2 kx^2
30=1/2 k(0.01)^2
60=k(0.01)^2
k=60/(0.01)^2
k=60×1^2N/M
Hence the potential energy of two decimal places is k= 60×1^2 N/M
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Zaria wants you to solve this puzzle: “I am thinking of a number. If you divide my number by 2 and subtract 4, you will get 2. What is my number?” Show how you know your answer is correct.
Answer:
Let
x--------> the number
we know that
solve for x
Adds both sides
Multiply by both sides
therefore
the answer is
the number is 12
Step-by-step explanation:
Given h(x) = -3x +5. Find the indicated values. h (10)
Answer:
h(10) = -25
Step-by-step explanation:
h(x) = -3x + 5
h(10) = -3(10) + 5
= -30 + 5
= -25
I hope this helps!
FACT or FIB?
-3-4-(-12)
-19
11 ft
7 ft 8 ft
20 ft What is the area of the shape?
Answer:
Area = 192.5 ft.²
Step-by-step explanation:
By splitting the shape in 2, we can find the area much simpler.
Starting with the parallelogram (on the left), the area formula is A = b × h.
b (base) = 11 ft.
h (height) = 7 ft.
A (area) = (11 ft.)(7 ft.)
A = 77 ft.² (save this for later)
Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.
a (first base) = 8 ft.
b (second base) = (20 - 7) = 13 ft.
h (height) = 11 ft.
A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.
A = [(21 ft.) ÷ 2] × 11 ft.
A = (10.5 ft.) × 11 ft.
A = 115.5 ft.²
Now, bringing back the first area, we can add them together to find the total:
A = 77 ft.² + 115.5 ft.²
A = 192.5 ft.²
Hope this helps! I'd appreciate Brainliest but if not it's totally fine!
What is the domain of f(x) = 7/(x-10) - 7
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
For the given function :
[tex]\qquad \sf \dashrightarrow \: f(x) = \dfrac{7}{x - 10} - 7[/tex]
f(x) is defined for all real values of x, except the value of x for which the denominator becomes 0, because if denominator is 0, the function at that instant will be undefined.
that is : f(x) is not defined when :
[tex]\qquad \sf \dashrightarrow \: x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 10[/tex]
Hence, f (x) is defined for all real values of x except 10
It can be represented as :
[tex]\qquad \sf \dashrightarrow \: f(x) : x \in R \sim \{10 \}[/tex]
Question
Consider the following two loans for Po = $15,000.
• Loan A: 5 year loan, annual interest rate of 8%, monthly repayments of $304.15.
Loan B: 3 year loan, annual interest rate of 11%, monthly repayments of $491.08.
Calculate the absolute difference between the total interest paid on both loans. Give your answer to the nearest ten dollars.
Do not include the dollar sign in your answer
Answer:
570
Step-by-step explanation:
570
The absolute difference that is between the loans paid as 570
How to solve for the absolute differenceWe have the following details:
Po = $15000
loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars
Loan b
3 year loan, interest = 11 percent repayments = $491.08
Total number of repayments = 5 x 12 = 60
Total repayments = 304.15 dollars x 60
= $18249
The total interest that is paid for A would be
$18249 - $15000
= $3249
For the second loan
Total number of repayments = 3 x 12 months = 36
Total repayment = 36 x 491.08 = $17678.88
The total interest for the loan B would be: $17678.88 - $15,000
= $2678.88
Then the absolute difference between the paid loan would be
$3249 - $2678.88 = 570.12
Hence we would have the absolute difference that is between the loans paid as 570.
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(3x 3 +4x 2 )+(3x 3 −4x 2 −9x)
Answer:
9x
Step-by-step explanation:
=9x+8x+9x-8x-9x
=9x
A 13 foot ladder is leaning on a wall. the bottom of the ladder has a diatance of 5 feet from the base of the wall.
What is the distance, in feet, between the ground and the top of the lafder?
Answer:
Subscribe to itsIceboiiYT
4+ -1 -5= -2
Please help me know how did I Got this answer the working thank you
Answer:
4 + -1 = 3, 3 - 5 = -2.
Step-by-step explanation:
Hope this helps!!
lisa's plant was 7 3/4 inches tall when she bought it. Three weeks later, it was 4 2/5 times as tall. How tall is lisa's plant after three weeks?
Answer:
[tex]\frac{341}{10} =34\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{4} *4\frac{2}{5}[/tex]
→ Convert both fractions into improper
[tex]\frac{31}{4} *\frac{22}{5}[/tex]
→ Simplify
[tex]\frac{31}{2} *\frac{11}{5}[/tex]
→ Calculate
[tex]\frac{341}{10} =34\frac{1}{10}[/tex]
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (3,-2) and perpendicular to the line whose equation is x-8y-3=0
The equation of the line in point-slope form is.
(Type an equation. Use integers or fractions for any numbers in the equation.)
Answer:
Step-by-step explanation:
Question 1 (5 points)
Saved
Which description is best for this set of ordered pairs: (1,4) (2,5) (3,6) ?
A) only a relation
B) only a function
C) relation and function
D) a relation but not a function
Since the pairs of y values have singular and unique x values, the following set of points are a function.
Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.
[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]
Option: C
This week Andrei got a promotion at work that came with a 2 % pay increase. If now his monthly salary is $ 1683 , how much was he making before the raise?
Enter your answer as a decimal. If needed, round to the nearest penny. Do not use commas.
1683 доллара - 102% . Найдем 1 процент и умножим его на 100%, тем самым получив ответ:
1) 1683 / 102 = 16.5 доллара - 1 % от всей зарплаты
2) 16.5 * 100 = 1650 - изначальная сумма, которую получал Андрей до повышения.
Ответ : 1650 $
How to solve this problem? -2x + 4 < 16
Answer:
the answer is 7+1-7+0/xx{12
Step-by-step explanation:
the answer above stated is correctly corrected correct
Susie divided a 3 pound bag of apples into 2 equal piles. How many pounds of apples are in each pile?
Answer:
1.5 pounds
Step-by-step explanation:
3/2 = 1.5
What is: -28/-4 + -48/6
Answer: The answer is -1
Step-by-step explanation:
-28/-4+-48/6
7-8
-1
Answer: -1
Step-by-step explanation:
-28 divided by -4 is 7
-48 divided by 6 is -8
7 - 8 would be a total of -1
Jack has 80 marbles.
He gives 1/5
of the marbles to his friends.
(c) Work out how many marbles Jack now has.
inq
Answer:
He now has 64 marbles.
Step-by-step explanation:
This is because 1/5 of 80 is 16.