Answers:
(a) 73440(b) 3060=====================================================
Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
18 choices for slot A17 choices for slot B16 choices for slot C15 choices for slot DWe started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
-----------------------------------
Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
[tex]_nC_r = \frac{_nP_r}{r!}[/tex]
which can be rearranged into
[tex]_nP_r = r!*\left( _nC_r \right)[/tex]
these formulas are handy to help us go back and forth between nCr or nPr.
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
What are combination and permutation?Combination is a way of selecting items from a collection where the order of arrangement is not relevant.
It is given by:
[tex]^nC_r[/tex] = n! / r! (n-r)!
Permutation is a way of selecting items from a collection where the order of the arrangement is relevant.
It is given as:
[tex]^nP_r[/tex] = n! / (n-r)1
We have,
Number of distinct colors = 18
Number of colors to be chosen = 4
The number of ways the four colors be chosen when the order is not relevant:
= [tex]^{18}C_4[/tex]
= 18! / 4! 14!
= 18 x 17 x 16 x 15 / 4 x 3 x 2
= 3060
The number of ways the four colors be chosen when the order is relevant:
= [tex]^{18}P_4[/tex]
= 18! / 14!
= 18 x 17 x 16 x 15
= 73440
Thus,
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
Learn more about combination here:
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y =-x^2+6x-5
Explain how you can find the x-intercept
and show the work to find them
Step-by-step explanation:
y = -x²+6x-5
x-intercept => y= 0
-x²+6x-5=0
x²-6x+5=0
(x-5) (x-1) =0
x= 5 or x=1
(1, 0) and (5, 0)
LM is the midsegment of trapezoid RSXY. What is the length of RS?
Can somebody help me with this
Solve for x: 4/x - x/8 = 0
Answer:
[tex]x = \sqrt{32}[/tex]
Step-by-step explanation:
[tex]\frac{4}{x} - \frac{x}{8} = 0\\\\\frac{4}{x} = \frac{x}{8}\\\\x^2 = 32\\\\x = \sqrt{32}[/tex]
Mai is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Mai rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. She loses $0.50 if a 4, 5, or 6 is rolled.
a) Find the expected value of playing the game.
b) What can Elsa expect in the long run, after playing the game many times?
1) Elsa can expect to gain money. She can expect to win___dollars per roll.
2) Elsa can expect to lose money She can expect to lose___dollars per roll.
3) Elsa can expect to break even (neither gain nor lose money).
Answer:
A. 0.75
B. Elsa can expect to gain 0.75 dollars
Step-by-step explanation:
We have six outcomes
Using the table in the attachment, the expected value was calculated.
Expected value = 0.166667+0.3333+0.5-0.083333-0.083333-0.083333
= 0.75
B. From the answer in part A , we can conclude that Elsa can expect to gain money. She can expect to win 0.75 dollars per roll.
Please help due tomorrow
Answer:
Here's What you do:
Draw a line that comes straight through the middleIt has to create 4 - 90° angles (use a protractor to measure)There's a picture attached on how a perpendicular lines should look like.
Step-by-step explanation:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Step-by-step explanation:
You determined that you can make 72 donuts in 2hours. At rate,how many donuts can you make in 8 hours?
Answer:
288 donuts
Step-by-step explanation:
Answer:
288 donuts
Step-by-step explanation:
72 divided by 2 is 36 so that means you will make 36 donuts in 1 hour so now we have our unit rate which is 36. so then you multiply 36 by 8 and you get 288. that is your answer
Help please!!!!!!!!!
Answer:
1,5
Step-by-step explanation:
there is an obvious pattern in the coordinate plane and the coordinates (5, 1) completes that pattern
hope that helped :)
Answer: (4,2), (1,2), (4,5]
Step-by-step explanation: hope this helps
The distribution of student scores on the quantitative section of the SATs have an approximately normal distribution with a mean score of 501 points, and a standard deviation of 85 points. If you randomly select one student who has taken the SAT, what is the probability that the student will have scored greater than 600 points on the quantitative section of the SATs
Answer:
0.122 = 12.2% probability that the student will have scored greater than 600 points on the quantitative section of the SATs.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean score of 501 points, and a standard deviation of 85 points.
This means that [tex]\mu = 501, \sigma = 85[/tex]
What is the probability that the student will have scored greater than 600 points on the quantitative section of the SATs?
This is 1 subtracted by the p-value of Z when X = 600. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{600 - 501}{85}[/tex]
[tex]Z = 1.165[/tex]
[tex]Z = 1.165[/tex] has a p-value of 0.878.
1 - 0.878 = 0.122
0.122 = 12.2% probability that the student will have scored greater than 600 points on the quantitative section of the SATs.
Can i get some help hear
Answer:
Step-by-step explanation:
Since this is a assignment, I'll give a hint.
To find the area of a trapezoid, it'ls h(b1*b2)/2.
The height is how long the trapezoid is from each base.
The bases are the lines parralel to each other.
Mars is on average 2.25 x 108 miles away from Earth. The moon is on average 2.388 x 105 miles away from Earth. Approximately how many times
farther is Mars from Earth than the moon is ?
A.0.94 times
B.9.4 times
C.94 times
D.940 times
Answer:
I believe the answer is D
Step-by-step explanation:
Mars is approximately 940 times farther away from Earth than the Moon.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
Mars is on average 2.25 x 10⁸ miles away from Earth.
The moon is on average 2.388 x 10⁵ miles away from Earth.
To calculate the answer, we need to divide the distance from Mars to Earth by the distance from the Moon to Earth. This gives us:
2.25 x 10⁸ miles / 2.388 x 10⁵ miles = 942.42
Rounded to the nearest whole number, this means that Mars is approximately 940 times farther away from Earth than the Moon is.
Therefore, the answer is D) 940 times.
To learn more about the division operation click here :
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Help plz I don't wanna fail my diagnostic I already have full on C's I only have 1 week left I really need to go to the next grade :)
Answer:
hundreds
Step-by-step explanation:
NEED HELP ASAP!!!!
3/4 + (1/3 ÷ 1/6) - (-1/2)=?
A:1/4
B:1 1/4
C:3/4
D:2 1/4
⚠️NO LINKS OR I WILL REPORT⚠️
Answer:
anser is 3.24 or 3 and 1/4
Step-by-step explanation:
Answer:
3 1/4
Step-by-step explanation:
3/4+(1/3 ÷1/6)-(-1/2)=
3/4+(2)+1/2
3/4+5/2
3/4+10/4
13/4
3 1/4
How many two-digit counting numbers are greater than 80 or a multiple of 5?
There are numbers that meet the given conditions.
(Type a whole number.)
Answer:
10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90y95
Verne has 5 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny
Answer: 96
Step-by-step explanation:
Given
Verne has 5 math books to line up on a shelf
Jenny has 4 english books to line up on a shelf
No of ways Verne can arrange the books are [tex]5![/tex]
No of ways Jenny can arrange the books are [tex]4![/tex]
Difference between them
[tex]=5!-4!\\=120-24\\=96[/tex]
Thus, Verne can line up 96 more orders than Jenny
brainliestt for answerrrrrrrrrrrr fast
Answer:
1/9 ÷ 2
= 1/9 × 1/2
= 1/18
Step-by-step explanation:
THAT IS MY ANSWER HOPE IT HELPS
Help with volume all help is appreciated :)
Answer:
It would be 0.41 ft^3
Step-by-step explanation:
Alright, to start, lets get the volume of the entire cinder block and the holes within it.
1.31 * 0.66 * 0.66 ---> 0.5706...
Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.
0.33 * 0.39 * 0.66 ---> 0.0849...
Since there's two of them: 0.1698...
To finish it, subtract the hole volume from the total volume;
0.5806 - 0.1698 = 0.4108
Rounds to 0.41 ft^3
Look at this net for a rectangular prism.
What is the surface area of the solid created by the net? Show your work.
the second part of the question EXPLAIN YOUR THINKING PLZ HELP
The length of the rectangular face is 15 cm, and there are 4 rectangular faces in the rectangular prism. If the length of the rectangular faces in the prism was tripled to 45 cm, what would happen to the size of the 2 rectangular bases of the prism? Explain your thinking.
Answer:
Step-by-step explanation:
the surface area = area of the 4 faces+ area of the 2 bases
4 *(15*8) + 2*( 8*6) = 480+96 = 576 cm²
if the length of the faces tripled, the two bases remain unchanged because the prism just gets taller on the same bases.
What is the GCF of xy3 and x3y?
Answer:
xy
Step-by-step explanation:
xy³ and x³y
GCF is xy
Answer:
I think it's xy
Step-by-step explanation:
just find the prime factors of each term
Round your answer to the nearest hundredth.
pls help :((
Answer:
Angle B = 29.74
Step-by-step explanation:
Tan(x)=opp/adj
Tan(x)=4/7
x=[tex]Tan^{-1} (\frac{4}{7} )[/tex]
x=29.74
Find an
angle in each quadrant with a common reference angle with 146°, from
o°=0<360°
Answer:
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
The equivalent angle on the third quadrant is 214º.
The equivalent angle on the fourth quadrant is 316º.
Step-by-step explanation:
On the first quadrant:
The equivalent in the second quadrant of a angle on the first quadrant a is 180 subtracted by the angle, that is, 180 - a.
In this question, the reference angle is 146º, which is on the second quadrant.
So, on the first quadrant:
146 = 180 - a -> a = 180 - 146 = 44.
The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.
Third quadrant:
The equivalent angle on the third quadrant is 2 multiplied by 180 and subtracted by the second quadrant angle. So
2*180 - 146 = 360 - 146 = 214º.
The equivalent angle on the third quadrant is 214º.
Fourth quadrant:
The equivalent angle on the fourth quadrant is 360 subtracted by the angle on the first quadrant. So
360 - 44 = 316º
The equivalent angle on the fourth quadrant is 316º.
a man 1.30 m tall is on a top of a building. he observed a car on the road at an angle of 60 degrees if the building is 30 m high,how far is the car from the building?
Given :
A man 1.30 m tall is on a top of a building. He observed a car on the road at an angle of 60 degrees if the building is 30 m high.
To Find :
How far is the car from the building.
Solution :
Let, distance between car and the building is x m.
So,
[tex]tan \ \theta = \dfrac{height\ of\ building + height\ of\ man}{distance \ between \ car \ and \ building}\\\\tan \ 60^o = \dfrac{30+1.3}{x}\\\\x = \dfrac{31.3}{1.73}\ m\\\\x = 18.09\ m[/tex]
Hence, this is the required solution.
Amanda financed a new living room set at the furniture store for $2,700. The store offered no interest for 6 months or 20 percent annually if the balance was not paid in full prior to the end of the interest free period. How much interest will she need to pay if she lets the account go for 6 months and 1 day before paying the bill?
Answer:
She will need to pay $269.36 in interest if she lets the account go for 6 months and 1 day before paying the bill.
Step-by-step explanation:
Given that Amanda financed a new living room set at the furniture store for $ 2,700, and the store offered no interest for 6 months or 20 percent annually if the balance was not paid in full prior to the end of the interest free period, to determine how much interest will she need to pay if she lets the account go for 6 months and 1 day before paying the bill, the following calculation must be performed:
((2,700 x 0.2) / 365) x 182 = X
(540/365) x 182 = X
1.48 x 182 = X
269.36 = X
Therefore, she will need to pay $ 269.36 in interest if she lets the account go for 6 months and 1 day before paying the bill.
Find the missing angle measurement.
Answer:
54°
Step-by-step explanation:
54°
Answer:
the missing angle is 54
Step-by-step explanation:
so first we need two triangle angles to get our measurement and we know straight lines add up to 180 so
180-123=57
57+69(other angle)=126
all triangle angles add up to 180 so subtract the two other angles to get your result
180-126=54
54 is your anwser
P(C)= 0.02. What is the complement of P(C)?
Answer:
P'(C) = 0.98
Step-by-step explanation:
Given that,
P(C) = 0.02 (The probability of getting C)
We need to find the complement of P(C) i.e. P'(C).
We know that,
P(C)+P'(C)=1
P'(C) = 1-P(C)
= 1-0.02
= 0.98
So, the complement of P(C) is equal to 0.98.
I will make you brainlist
Answer:
for what? do you need a question answered?
Lucas wants to make a bigger pencil holder. 5 cubes wide, 12 cubes long, 3 cubes high and 1 cube thick. How many cubes were used for the base of the pencil holder?
Answer:
60
Step-by-step explanation:
5 * 12 = 60
Write the fraction 2/3 as the sum of unit fraction
9514 1404 393
Answer:
1/2 + 1/6
Step-by-step explanation:
2/3 = 1/2 + 1/6
__
The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...
2/p
where p is a small prime. Then the sum can be written as ...
1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6
A different algorithm is used when p is a composite number.
__
Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...
1/ceil(3/2) = 1/2
Then the largest unit fraction in the remainder is similarly found. The remainder is ...
2/3 -1/2 = 1/6 . . . . already a unit fraction
So, the sum is ...
2/3 = 1/2 + 1/6
Which statement is given in the diagram?
Answer:
D
Step-by-step explanation:
The expression 4x* represents 144
Answer:
x=36
Step-by-step explanation:
because 4x36=144
Answer:
4x = 144
4 • 36 = 144
The answer to the equation is 36
Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 81st percentile.
Answer:
[tex]P(81)=56.16[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\mu=50[/tex]
Standard Deviation [tex]\sigma=7[/tex]
Percentile 81st
Generally Probability of 81st Percentile
[tex]P(Z<x)=81\%[/tex]
Using Standard normal Table
[tex]P(Z<0.88)=81\%[/tex]
Therefore the 81st percentile is given as
[tex]P(81)=z*\sigma *\mu[/tex]
[tex]P(81)=0.88*7*50[/tex]
[tex]P(81)=56.16[/tex]