There is 1820 ways of teams of 4 can she make without repetition using combination formula.
What is combination?
Selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organise anything here. We are going to choose them. We use the notation nCr to indicate how many distinct r-selections or combinations there are among a set of n objects. A combination is distinct from an arrangement or a permutation. No matter how the objects are arranged, combinations are produced by choosing some or all of them.
Here There are 16 total swim team members and 4 swimmers that will be chosen for each relay team.
So, n=16 and r=4. Then
=> nCr = [tex]\frac{n!}{r!(n-r)!}[/tex]
=> 16C4 = [tex]\frac{16!}{4!(16-4)!}[/tex]
=> 16C4 = [tex]\frac{16!}{4!*12!}[/tex]
=> 16C4 = [tex]\frac{16*15*14*13}{4*3*2*1}[/tex]
=>16C4 = 4*5*7*13 = 1820
Hence there is 1820 ways of teams of 4 can she make without repetition.
To learn more about combination refer the below link
https://brainly.com/question/28065038
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An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Answer:
The margin of error is of 623.2016.
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.
This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]
A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.
This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]
Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
The mean is:
[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]
The standard deviation is:
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.96*317.96 = 623.2016[/tex]
The margin of error is of 623.2016.
The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016
The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Stock in Macy's costs $25.75 per share. Hector buys 200 shares of Macy's
through his broker who charges a commission of $25.75. How much did George
pay in total to purchase the stock?
Answer: $5175.75
Step-by-step explanation:
The amount that is paid in total to buy the stock will be gotten through the addition of the cost of the shares and the commission paid. This will be:
= (200 × $25.75) + $25.75
= $5150 + $25.75
= $5175.75
Therefore, the total amount that is paid to buy the stock will be $5175.75.
expanded form :32,456
Answer:
30,000 + 2,000 + 400 + 50 + 6
Step-by-step explanation:
[tex]\text{The expanded form of 32,456 would be 30,000 + 2,000 + 4,000 + 50 + 6.}[/tex]
[tex]\text{We would have to identify what each number stands for.}[/tex]
[tex]\text{For example, 3 in 32,456 stands for 30,000.}[/tex]
[tex]\text{Hence, following this rule, we can conclude that the answer above is correct.}[/tex]
[tex]\text{I hope I helped you suceed!}[/tex]
Write an equation that you can use to find the value of x.
The perimeter of the triangle: 16 in.
Answer:
This question seems incomplete
What are the answers
Answer:
3. 5cm
[tex]4. \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Step-by-step explanation:
3. the hypotenuse C squared = side A squared + side B squared. So 3 × 3=9 and 4 × 4 =16 therefore 9 + 16 =25 and the square root of 25 = 5.
4. In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
Hope it is helpful....Can somebody tell me which one of these options do I put? (I need to put two)
Answer:
B D and E
Step-by-step explanation:
Expressions do not contain equal signs
14. The Manilow family paid their electric bill using balanced billing all last year. The monthly
payment was m dollars. At the end of the year, the electric company told them they used more
electricity than they were billed for, and they owed d dollars. Express the value of the electricity
used by the Manilows last year algebraically.
Z
Answer:
12mx
Step-by-step explanation:
Given that
The monthly payment was m dollars
And, they used more electricity
We need to determine the value that should be expressed in algebraically
The Monthly payment is m dollars
Using balance billing, it would be mx dollars
So, the equation is
= mx × 12
= 12mx
hence, the same would be relevant and considered too
You determine that you can make 72 donuts in 2 hours. At that rate, how
many donuts can you make in 8 hours?
Answer:
576
Step-by-step explanation:
Determine the median of the following numbers: 8, 11, 11, 12, 13, 15, 16, 16, 18, 21
Answer:
The median of the following numbers is 14
Step-by-step explanation:
Use the picture below and determine which of the lines or line segments 20 points
is/are a diameter
mA
VE
Line m
Line Segment BC
Ο Ο Ο Ο Ο
Line Sesnent AB or AC
Line Segment DE
Line 1
What is 1/3 of $4.89 dollars
Answer:
im pretty sure its 1.63
Step-by-step explanation:
lmk if im wrong
Can I please get help with this math problem? Thanks in advance.
Answer:
answer: scale factor is 3
Hope this helps
Answer:
ans :; scale factor is 3
this is the correct ans.
(50 points) please help! no links, brainliest, extra points.
I understand if you need points, you can go to my old questions and answer them for points, please only answer if your 100% sure you're correct. I've redone this over 20 times, asked over 50, and failed all those times. thank uu.
Students were asked to find the median of this data set.
Darcy said, "The median is the number in the middle of the list. So, the median is 21."
Darcy made a mistake.
Her mistake is that she did not _____
A) choose the data point that is in the data set most often
B) order the data points from least to greatest before finding the middle data point
C) ignore the data points that repeat in the data set
D) divide the middle data point by the total number of data points
,
The correct median of the data set is ___
A) 14
B) 16
C) 15
D) 14.5
E) 15.5
Answer:
The answer is B. The correct median of the data set is C, 15.
Step-by-step explanation:
To do a quick recap:
Mode is the average value that is found by adding up all the values and dividing them by the number of values you used.
Median is the number found in the very middle, so Darcy is correct about what a median is.
Mode is the number that appears most.
Notice that the numbers are not arranged in numerical order from least to greatest. She just took the number that she saw in the middle, without considering where it would stand if the numbers were ranked from least to most.
Here's a ranking of all the numbers from least to greatest:
8, 9, 9, 12, 13, 14, 15, 15, 16, 16, 16, 17, 21
From this ranking, we can see that there are a total of 13 numbers. Therefore, the 7th number is the median, which means that the median is 15.
Answer:
as the person before me said, it is b and 15.
Step-by-step explanation:
i know study island can be hard but keep going, you can do it!
Write equivalent fractions for 1 2/3 and 1 7/8 using 24 as the common denominator 2 24 7 1 0
Answer:
2×8=16
7×3=21
2/3 + 7/8 = 16/24 + 21/24
A student formed a pattern in which each term is represented by a sum. The first four terms of the pattern are shown below Which expression can be used to determine the value of the sum in any term, n
Answer:
n2
Step-by-step explanation:i did this last year
What is -13 decreased by 9
Answer:
-4
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
-13 - 9
When both the numbers have the same sign, we add them. After adding we put the same sign of the numbers to the answer
-13-9 = -22Find the geometric mean between each pair of numbers 8 and 12
Step-by-step explanation:
......................................................
What type of correlation is shown in the graph?
Answer:
no correlation
Step-by-step explanation:
it shows no trend or a line thing
also i think your pic is upside down haha
Simplify 25a/8 x 2a/5
Answer:
If the slashes mean divisions and the x means multiplication, the answer would be 25a²/4/5
can someone help, please :)
Sandy is getting ready for the day. She can wear either a balck or white shirt and then either pants, shorts, or a skirt. Create a tree diagram or label all the combinations she can make. How many are there total?
the sum of the first four terms of an A.p is 62.if the difference between 4 terms and 2nd terms is 14. find the first term and common difference
Answer:
-2 -4 -6 -8
Step-by-step explanation:
I got the answer off of khan academy
PLEASE HELP ME TO ANSWER THIS QUESTION.
A right pyramid PQRST has a rectangular base QRST. Given
that W is the midpoint of QS and RT, the lengths of QT = 8 cm,
TS = 6 cm and point P is vertically above point W, calculate
(a) PT, in cm, if PW = 12 cm
(b) the value of < PTR [angle PTR]
THANK YOU!!!
Answer:
(a) PT = 13 cm
(b) <PTR = [tex]39.7^{o}[/tex]
Step-by-step explanation:
(a) Applying the Pythagoras theorem to QST, we have;
[tex]QS^{2}[/tex] = [tex]ST^{2}[/tex] + [tex]QT^{2}[/tex]
= [tex]6^{2}[/tex] + [tex]8^{2}[/tex]
[tex]QS^{2}[/tex] = 36 + 64
100
QS = [tex]\sqrt{100}[/tex]
= 10
QS = 10 cm
Since QS = TR, then;
WT = [tex]\frac{1}{2}[/tex] TR
= [tex]\frac{1}{2}[/tex] x 10
WT = 5 cm
Thus, applying Pathagoras theorem to PWT;
[tex]PT^{2}[/tex] = [tex]PW^{2}[/tex] + [tex]WT^{2}[/tex]
= [tex]12^{2}[/tex] + [tex]5^{2}[/tex]
= 144 + 25
[tex]PT^{2}[/tex] = 169
PT = [tex]\sqrt{169}[/tex]
= 13
PT = 13 cm
(b) To determine <PTR, TR = 10 cm. Apply the required trigonometric function;
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos θ = [tex]\frac{10}{13}[/tex]
= 0.7692
θ = [tex]Cos^{-1}[/tex] 0.7692
= 39.7179
θ = [tex]39.7^{o}[/tex]
Therefore, <PTR = [tex]39.7^{o}[/tex]
Help ASAP 6x - 3(2 – 3x)
Answer:
First: we expand
6x-(6-9x)
Then we simplify
6x-6+9x
Collect like terms
(6x+9x)-6
Simplify:
15x-6
The answer is 15x-6
Should we take care of useless equipment and avoid the "trash pile" that is growing in space?
I personally think yes.
please help me here im begging you it won't let me just skip it
Answer:
ABCD in statement and the other in reasoning
Step-by-step explanation:
What is the volume of a rectangular prism with a length of 2 1/2 inch width of 4 inches, and a height of 3 inches? * 21: 36 cu, in O 30 cu in 9.5 cu in 0 26 cu.in
Answer:
30 cubic inch
Step-by-step explanation:
A triangle has side lengths 8, 7, 4. In a similar triangle the smallest side is represented by x + 5 and the longest side is represented by x - 3. What is the value of x?
Answer:
x = 11
Step-by-step explanation:
8/4 = (x+5)/(x-3)
cross-multiply:
8(x-3) = 4(x+5)
8x - 24 = 4x + 20
4x = 44
x = 11
Answer:
Step-by-step explanation:
X=11
The longest known is double than samallest known
2(x-3) = x+5
2x-6 = x+5
x= 11
11-3 = 8
11+5 = 16
Sides of the known triangle 8,7,4 (side 8 double than side 4)
Sides of the similar triangle 16,14,8 (side 16 double than side 8 )
(05.03 LC) What is the equation of a horizontal line passing through the point (2, 10)? (5 points)
Answer:
y=10
Step-by-step explanation: a horizontal line has no slope
Can someone here please help me out?
Answer:
hope you can now substitute and find y