Complete Question
1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match.
(a) How many schedules are there?
(b) How many schedules include neither sister?
Answer:
a
[tex]N = 1,411,200[/tex]
b
[tex]M = 302, 400[/tex]
Step-by-step explanation:
From the question we are told that
The number of players in Taft High School is t = 8
The number of players in McKinley High School is k = 7
The number of rounds is n = 4
The highest number of match each player can play is w = 1
Generally the total number of schedules is
[tex]N = ^tP_4 * ^k P_4[/tex]
[tex]N = ^8P_4 * ^7 P_4[/tex]
=> [tex]N = \frac{8!}{(8-4)!} * \frac{7!}{(7-4)!}[/tex]
=> [tex]N = \frac{8!}{4!} * \frac{7!}{3!}[/tex]
=> [tex]N = \frac{8*7 *6*5*4*3*2*1}{4*3*2*1} * \frac{7*6*5*4*3*2*1}{3*2*1}[/tex]
=> [tex]N = 1,411,200[/tex]
Generally the number of schedules that include neither of the sisters is mathematically represented as
[tex]M= \ ^{t-1}P_4 *\ ^ {k-1} P_4[/tex]
[tex]M= \ ^{8-1}P_4 *\ ^ {7-1} P_4[/tex]
=> [tex]M= \ ^{7}P_4 *\ ^ {6} P_4[/tex]
=> [tex]M = \frac{7!}{(7-4)!} * \frac{6!}{(6-4)!}[/tex]
=> [tex]M = \frac{7!}{3!} * \frac{6!}{2!}[/tex]
=> [tex]M = \frac{7 *6*5*4*3*2*1}{3*2*1} * \frac{6*5*4*3*2*1}{2*1}[/tex]
=> [tex]M = 302, 400[/tex]
Applying the Pythagorean Theorem
What is the value of x?
x = ?
Answer :
hyp² = base² + perp²
by putting the values we get
10² = 8² + perp²
100 = 64 + perp²
taking 64 to left side.
100 - 64 = perp²
36 = perp²
Now taking underroot on both sides we get
[tex] \sqrt{36 \: } = \sqrt{perp { }^{2} } [/tex]
therefore
6 = perp
perp is x in the above solution.
The solution is x = 6
The value of x in the triangle is x = 6
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Triangle ABC is a right triangle
Now , the measure of sides of the triangle are
The measure of side AB = x
The measure of side BC = 8
The measure of side AC = 10
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
10² = x² + 8²
Subtracting 8² on both sides of the equation , we get
x² = 10² - 8²
x² = 100 - 64
x² = 36
Taking square roots on both sides of the equation , we get
x = 6
Therefore , the value of x is 6
Hence , the measure of side AB of the triangle is x = 6
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The assets (in billions of dollars) of the four wealthiest people in a particular country are 47, 30, 28, 18. Assume that samples of size n=2 are randomly selected with replacement from this population of four values. a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.
Step-by-step explanation:
The 16 possible permutations and their means are:
47, 47: μ = 47
47, 30: μ = 38.5
47, 28: μ = 37.5
47, 18: μ = 32.5
30, 47: μ = 38.5
30, 30: μ = 30
30, 28: μ = 29
30, 18: μ = 24
28, 47: μ = 37.5
28, 30: μ = 29
28, 28: μ = 28
28, 18: μ = 23
18, 47: μ = 32.5
18, 30: μ = 24
18, 28: μ = 23
18, 18: μ = 18
So the frequency distribution of the sample means is:
[tex]\left[\begin{array}{cc}Mean&Frequency\\18&1\\23&2\\24&2\\28&1\\29&2\\30&1\\32.5&2\\37.5&2\\38.5&2\\47&1\end{array}\right][/tex]
The mean of a dataset is the average value of the dataset.
The dataset is given as:
47, 30, 28 and 18
From the above dataset, we can see that the data elements are 4
The sample size is given as:
n = 2
So, the number of different samples is:
[tex]Samples = 4^2[/tex]
[tex]Samples = 16[/tex]
The 16 samples are: {(47,47), (47,30), (47,28), (47,18),(30,47), (30,30), (30,28), (30,18),(28,47), (28,30), (28,28), (28,18),(18,47), (18,30), (18,28), (18,18)}
The mean values of the above samples are: {47, 38.5, 37.5 , 32.5 , 38.5 , 30 , 29 , 24 , 37.5 , 29 , 28 , 23 , 32.5 , 24 , 23 , 18}
Rearrange in ascending order
18, 23, 23, 24, 24, 28, 29,29, 30, 32.5, 32.5, 37.5, 37.5, 38.5, 38.5, 47
So, the table of the sample means is:
Mean Frequency
18 1
23 2
24 2
28 1
29 2
30 1
32.5 2
37.5 2
38.5 2
47 1
Total 16
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Hi i need help with this "The cost of a theme park ticket is $25. The cost for 2 ticket is $50 what is the cost of 4 theme park tickets
Answer:
$100
Step-by-step explanation:
If 1=$25, 2=$50, then 4*25=100 and 50*2=100
The exam in a course consists of 25 true/false questions, each worth two points, 35 multiple-choice questions, each worth one point, and 5 fill-in-the-blank questions, each worth three points. The probability that a student answers a true/false question correctly is 0.8, the probability that they answer a multiple-choice question correctly is 0.75, and the probability that they answer a fill-in-the-blank question correctly is 0.65. What is the expected score on the exam? Now consider the case where an incorrect answer on a true/false question results in a penalty of −1 point. 2 What is the resulting expected score?
Answer:
Expected Score (No Negative Marking) = 135 points
Expected Score (with penalty) = 130 points
Step-by-step explanation:
First we find no. of true false answered correctly:
True/False Correct = (Total No. of True/False)(Probability to correctly answer true/false)
True/False Correct = (25)(0.8)
True/False Correct = 20
Now, for points scored from true/false:
True/False Score = (True/False Correct)(Points for 1 True/False)
True/False Score = (20)(2)
True/False Score = 40 points
Now, we find no. of mcqs answered correctly:
MCQs Correct = (Total No. of MCQs)(Probability to correctly answer MCQs)
MCQs Correct = (35)(0.75)
MCQs Correct = 26.25 = 26
Now, for points scored from MCQs:
MCQ Score = (MCQs Correct)(Points for 1 MCQ)
MCQ Score = (26)(1)
MCQ Score = 26 points
Now, we find no. of fill in the blanks answered correctly:
Fill in the blanks Correct = (Total No. of Fill in the blanks)(Probability to correctly answer Fill in the blanks)
Fill in the blanks Correct = (35)(0.65)
True/False Correct = 22.75 = 23
Now, for points scored from true/false:
Fill in the blanks Score = (Fill in the blanks Correct)(Points for 1 Fill in the blanks)
Fill in the blanks Score = (23)(3)
Fill in the blanks Score = 69 points
So, the expected total score will be:
Expected Score = 40 points + 26 points + 69 points
Expected Score = 135 points
IN CASE OF PENALTY:
We know that:
Incorrect True/Flase = Total True/False - Correct True/False = 25 - 20 = 5
Therefore,
Total Penalty = (Incorrect True/False)(Penalty on one)
Total Penalty = (5)(- 1 points)
Total Penalty = - 5 points
Now, expected score will be;
Expected Score (with penalty) = 135 points - 5 points
Expected Score (with penalty) = 130 points
convert decimal number 0.25 in rational numbers
Answer:
0.25 = 25/100
=> 1/4
Therefore 1/4 is the rational form of 0.25 ,
If my answer helped, kindly mark me as the brainliest!!
Thank You!
Answer:
not sure but 1/4
Step-by-step explanation:
0.25 = 25/100
1/4
Write an equation that represents this comparison sentence.
24 is 4 times as many as 6
Answer:
4x6=24
Since 24 is 4 times as many as six, it means 4x6 is 24.
The scale on a map is 2 cm = 15 miles. Dave measures the distance to the next town at 7 cm. how may miles away is the next town?
Answer:
15x3.5 = 52.5
Step-by-step explanation:
Answer:
52.5
Step-by-step explanation:
Multiplication method
Help with this plz plz ASAP
845001 rounded to nearest ten thousands
Justify each step.
3•(10•12)=3•(12•10)
=(3•12)•10
=36•10
=360
Answer:
3•(10•12)=3•(12•10) = 360 = True
Step-by-step explanation:
left-hand side Simplify the following:
3×10×12
10×12 = 120:
3×120
3×120 = 360:
Answer: 360
______________________
Right-hand side:
Simplify the following:
3×12×10
Hint: | Multiply 12 and 10 together.
12×10 = 120:
3×120
Hint: | Multiply 3 and 120 together.
3×120 = 360:
Answer: 360
I need help "The cost of 1 movie ticket is $7.50. The cost of 2 movie tickets is $15. Based on the constant rate of change what is the cost of 4 movie tickets?
Answer:
4 tickets cost $30
step by step:
15+7.50=22.5 (3 tickets)
22.5+7.50=30 (4 tickets)
Select the correct answer.
Which Triangles in the diagram are congruent?
Answer:
D. its all hope this helps :)
Step-by-step explanation:
Answer:
triangles 1 and 3 I'd say
Jennifer and Jacob took 3h5min to decorate the Christmas tree.they took 1h55min longer to decorate the Christmas tree than to wrap the present.what is the total time they took to decorate the Christmas tree and wrap the present?
Answer:
5 hours
Step-by-step explanation:
3h5min+1h55min=5hours
Answer:
3+1=4
55+5=60
60 minutes make an hour
=5
Step-by-step explanation:
what is the answer? 5
points who says the right answer.
thank you.
Answer:
1/4 of the jar is left to fill.
1.Find the missing angle
2.what is the measure of angle 1
3.what is the measure of angle 2?
What categories does the number -3/17 belong in ?
Answer:
Irrational
Step-by-step explanation:
-3/17= -0.1764705882 and irrational numbers does not repeat
What is the value of x in the equation 8x-5(x-1)=20
1. 25/3
2. 21/4
3. 5
4. 7
In lisa class ,24of students are tall and 12 are short. In pauls class 15 studens are tall and 20 students are short. Which class has a higher ratio of tall to short students.
Answer:
Lisa's class because she has 24:12 and paul has 15:20
Solve for x
5x – 2(x+1)= 1/4
Enter your answer as a fraction in simplest form in the box.
X =
Basic
Answer:
x = 3/4
Step-by-step explanation:
Step 1: Write equation
5x - 2(x + 1) = 1/4
Step 2: Solve for x
Distribute -2: 5x - 2x - 2 = 1/4Combine like terms: 3x - 2 = 1/4Add 2 to both sides: 3x = 9/4Divide both sides by 3: x = 3/4Step 3: Check
Plug in x to verify it's a solution.
5(3/4) - 2(3/4 + 1) = 1/4
15/4 - 2(7/4) = 1/4
15/4 - 14/4 = 1/4
1/4 = 1/4
Find the exact length of the third side.
Answer:
5
Step-by-step explanation:
The answer is 5 I just used google.
Solve for b.
ab +c=d
Answer:
[tex]ab + c = d \\ ab = d - c \\ b = \frac{d - c}{a} [/tex]
PLZZ HELP Will give brainlist plz help its for my 9 week exam
Which statement BEST describes a situation in which opposite quantities combine to make zero?
A. Shawna made 8 cups of soup and divided the soup into 8 containers.
B. Marcos missed 4 questions on a test in which each question was worth 4 points.
C. Peter scored 2 goals in the first period of a soccer game and 2 goals in the second period.
D. Melanie deposited $10 in her savings account and later withdrew $10 from the account.
Step-by-step explanation:
i think the correct answer is d because one you combine what she had with what she withdrawed she will have $0 left
5,5,3 Is this a triangle? Explain.
8,8,8,Is this a triangle? Explain.
7,8,15 Is this a triangle? Explain.
5,6,10 Is this a triangle? Explain.
No clown answers or you'll get reported please help me I have until 3:00 am desperate please solve
Answer:
None of these points form a right triangle.
Step-by-step explanation:
IF YOU'RE TRYING TO FIND IF THE POINTS FORM A RIGHT TRIANGLE, THIS SHOULD WORK.
5,5,3 Explantation: To first start things off, we know our hypotenuse is the longest side of the right triangle. Using this information, we know that 5*2( 5 squared) is 25 and that 3 squared is 9. Now we add these two points and we get 34. (Don't forget to square the other side.) Now we have 34=25 which is not true sooo we know the points given do not form a RIGHT triangle.
The same goes with the other points. Once you solve them, neither of them form a right triangle. (Don't forget that we use a*2 + b*2=c*2) (The c should be the biggest point given!)
Hope this helps, if you have any questions please feel free to ask! :)
Does the equation y = x/2 represent a proportional relationship
Answer:yes
Step-by-step explanation:Y=x/2 because it goes through the origin
In five towns in the state of Idaho, a new recycling policy started. A sample of 5,000 homes found that 0.56 put out a
recycling bin each week. Using a 95% confidence level, what is the estimate of the population proportion that recycles?
between 55.65% and 56,69%
between 54.97% and 57.03%
between 54.65% and 56.35%
between 55.31% and 56.35%
Find the area of the geometric figure.
Square
9.5
Answer:
90.25
Step-by-step explanation:
multiply 9.5×9.5
or
9.5²
PLZ ANSWER FAST (40 POINTS + BRAINLIEST)
Rewrite the expression y 2/3 as a radical expression.
Answer:
[tex]\sqrt[3]{y^2}[/tex]Step-by-step explanation:
Rewrite the expression y^2/3 as a radical expression.
if n is a positive integer that is greater than x and a is a real number or a factor, then aˣ/ⁿ = [tex]\sqrt[n]{a^x}[/tex]
use the rule to convert y²/₃ to a radical
where a =, x =, and n =.
therefore, the radical expression is [tex]\sqrt[3]{y^2}[/tex]
what is 2.1 divided by 12.6
Answer:
0.16666666666
Answer:
0.16666667
Step-by-step explanation:
can you help me find the answer please
Answer:
Its B (4.69 * 10^8)
Step-by-step explanation:
if u add them all together thats what you get I typed it into a calculator
-8x-10 y= 24
6.0 + 5y = 2
(-16)-10y=24
-10y=24+16
this steps has been cropped in the pic
so try to understand
hope you like the answer
please mark as brainlist