Suppose that 18 red beads, 12 yellow beads, eight blue beads, and 12 black beads are to be strung in a row. how many different arrangements of the colors can be formed
The number of different arrangements of the colors that can be formed will be 5.13498 x 10²⁶.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
Assume that 18 red globules, 12 yellow dabs, eight blue dots, and 12 dark dots are to be hung in succession.
The total number of bread will be calculated as,
Total bread = 18 + 12 + 8 + 12
Total bread = 50
Then the number of different arrangements of the colors that can be formed will be given as,
⇒ 50! / (18! x 12! x 8! x 12!)
Simplify the expression, then we have
⇒ 50! / (18! x 12! x 8! x 12!)
⇒ 5.13498 x 10²⁶
The number of different arrangements of the colors that can be formed will be 5.13498 x 10²⁶.
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The number of arrangements is: [tex]\(\frac{{50!}}{{18!12!8!12!}}\)[/tex]
To calculate the number of different arrangements of the beads, we can use the formula for permutations of multiset:
[tex]\(\frac{{n!}}{{n_1!n_2!n_3!n_4!}}\)[/tex]
where:
n is the total number of items to arrange,
n_1, n_2, n_3, n_4 are the numbers of indistinguishable items of each type.
For our beads, we have:
Total beads n = 18 (red) + 12 (yellow) + 8 (blue) + 12 (black) = 50 beads,
n_1 = 18 (red),
n_2 = 12 (yellow),
n_3 = 8 (blue),
n_4 = 12 (black).
So, the number of arrangements is: [tex]\(\frac{{50!}}{{18!12!8!12!}}\)[/tex]
This value gives us the total number of different color arrangements possible when stringing these beads in a row.
Hector is competing in a 42 mile bicycle race. He has already completed 18 miles of the race and is traveling at a constant speed of 12 miles per hour when Wanda starts the race. Wanda is traveling at a constant speed of 16 miles per hour.
Write and solve an equation to find when Wanda will catch up to hector
Answer:
Step-by-step explanation:
Alarm for 20 yards of fencing he used fit 5.9 yards to surround one flower garden and 10.3 yards to surround another garden write the amount remaining as a fraction in. Simplest form
use pictures and numbers to show all the ways to take apart 8
When she subtracts 4 from both sides, 1/2x = –1/2x results. What is the value of x?
Answer: The value of x is 0.
Explanation:
Since we have given that
[tex]\frac{1x}{2}=\frac{-1x}{2}[/tex]
According to question,
If she subtracts 4 from both sides, our equation becomes,
[tex]\frac{1x}{2}-4=\frac{-1x}{2}-4\\\\\text{ by transposing the like terms on the both sides, we get}\\\\\frac{1}{2}+\frac{1x}{2}=-4+4\\\\x=0[/tex]
Hence, the value of x is 0.
How many up/down runs are there in this data? observations 1 2 3 4 5 6 7 8 9 10 # of defects 5 2 3 5 4 3 2 1 2 4?
what is the value of n (9x23) +(3 ×39) - 28 = n
There are 130 calories in a cup of whole milk and only 74 in a cup of skim milk. In switching to skim milk, find the percent decrease in number of calories.
Given three collinear points, which of the following is true?a.. There is exactly one plane that contains all three points. b..They form a triangle. c.They are not coplanar. d.They are contained in multiple planes.
Option: d is the correct answer
d. They are contained in multiple planes.
Step-by-step explanation:Since, the three points are collinear.
This means that there is a line which pass through these three given points and as we know that a line always lie in a plane so all the three points will be coplanar and there may be multiple planes which contain a line.
Also, a triangle is formed with the help of three non-collinear points.
Hence, the correct option is:
Option: d
If josh spends 4,000 a year on tuition and fees, 1,200 a year on books, and forgoes earning 10,000 a year, how much will his four year degree cost
The total cost of the four-year degree for Josh, when considering tuition and fees, book costs, and his foregone earnings, would be 60,800 dollars.
Explanation:The cost of a four-year degree would be the sum of tuition and fees, book costs, and forgoing potential earnings per year, multiplied by the four years of the degree. Let's break it down:
Tuition and fees cost: 4000 dollars/yearBook costs: 1200 dollars/yearForgone earnings: 10000 dollars/yearTherefore, the annual cost would be the sum of these, which is 4000 + 1200 + 10000 = 15200 dollars/year. Then we multiply this by the 4 years, 15200 * 4 = 60800 dollars. So, the four-year degree would cost Josh 60800 dollars, considering the provided expenses and forgone earnings.
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A gallon of gasoline costs $2.96 your car has a 25- gallon gas tank and can travel 28.8 miles one each gallon of gasoline find the cost of filling your gas tank if it’s already 3/8 full
what is 22119 rounded to the nearest hundredth
Answer:
22119 to the nearest hundred is 22100
Step-by-step explanation:
When rounding the number to the nearest hundred. Follow the given rules:
When rounding to the nearest hundred, look at the TENS DIGIT of the number.
If that digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.In other words if the number at the tenth position is less than 5 then we will convert all the digits after the hundred to zeros
If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.In other words if the number at the tenth position is greater than or equals to 5 then we will add one to the hundred and convert all digits after the hundred to zeros.Now look at the given number which is: 22119
The number at the hundredth position is 1.
And the number at the tenth position is also 1.
Then according to the defined rule if the number at the tenth position is less than 5 then we will convert all the digits after the hundred to zeros.
So, for the given number (22119) we just convert all digits after the hundred to zeros
Therefore, 22119 to the nearest hundred is 22100...
jeremy can type 220 words in 4 minutes what is the unit rate and what does mean and to your answers in the box
the difference of a given month's rainfall from the average monthly rainfall is called the deviation. What is the deviation for each month shown?
average monthly rainfall 3.6
given month may 2 3/5; june 7/8; July 4 1/4
Answer:
Deviation:
may : 1
june: 0.875
july: 0.65
Step-by-step explanation:
It's given that the difference of a given month's rainfall from the average monthly rainfall is called the deviation .
To find : deviation for each month: may 2 3/5; june 7/8; July 4 1/4:
Solution :
Average monthly rainfall = 3.6
Rainfall in may = [tex]2\frac{3}{5}[/tex] = 2.6
Deviation = Average monthly rainfall - month's rainfall ( may ) = 3.6 - 2.6 = 1
Rainfall in june = 3.6 - 0.875 = [tex]\frac{7}{8}=2.725[/tex]
Deviation = Average monthly rainfall - month's rainfall ( june ) = 0.875
Rainfall in july = [tex]4\tfrac{1}{4}=\frac{17}{4}=4.25[/tex]
Deviation = Average monthly rainfall - month's rainfall ( july ) = 4.25 - 3.6 = 0.65
Compute a · (b ✕ c), where a = i − 3j + k, b = 4i + j + k and c = 9i − j + 3k.
We need to find the answer of the expression [tex]a\cdot (b\times c)[/tex]
The required expression is [tex]a\cdot (b\times c)=0[/tex]
The vectors are
[tex]a=\hat{i}-3\hat{j}+1\hat{k}[/tex]
[tex]b=4\hat{i}+\hat{j}+\hat{k}[/tex]
[tex]c=9\hat{i}-\hat{j}+3\hat{k}[/tex]
Solving the term in the bracket
[tex]b\times c=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\ 4 & 1 & 1 \\ 9 & -1 & 3 \end{vmatrix}\\ =\hat{i}(3+1)-\hat{j}(4\times3-9\times1)+\hat{k}(4\times-1-9\times 1)\\ =4\hat{i}-3\hat{j}-13\hat{k}[/tex]
[tex]a\cdot (b\times c)=(\hat{i}-3\hat{j}+1\hat{k})(4\hat{i}-3\hat{j}-13\hat{k})\\ =1\cdot 4+(-3)\cdot (-3)+1\cdot (-13)\\ =4+9-13\\ =13-13=0[/tex]
So, [tex]a\cdot (b\times c)=0[/tex]
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Which of the following best explains how a single nucleotide substitution can cause hemoglobin molecules to chain together instead of forming the appropriate protein product?
The mutation causes the removal of an amino acid, which results in a different protein product
. The mutation causes the same amino acid to be repeated multiple times in the protein product, which results in a linear protein structure.
The mutation causes the wrong amino acid to be incorporated into the protein product, which results in improper protein folding.
The mutation causes the protein product to be lengthened due to an increased number of amino acids being incorporated.
estimate the product. choose a method. 81×38
in your own words explain the steps you would need to take to find slope from data in a table
Answer:
see the explanation
Step-by-step explanation:
we know that
To calculate the slope we need to take two points from data in a table
point 1 (x1,y1) and point 2(x2,y2)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values and solve for m
The slope formula can be applied to find the slope from data in a table using any two set of points given on the table.
First, select any two pair of points given in the table. For example, let's assume the two set of points selected are:
[tex](a, b) $ and $ (c, d)[/tex]
Use the slope formula which is:
[tex]Slope(m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
The slope is the change of y over the change of x.
To use the slope formula:
Let,
[tex](a, b) = (x_1, y_1)\\(c, d) = (x_2, y_2)[/tex]
Then, plug in the values into the formula and solve.
The value you get is the slope of the data represented by the table.
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what is the interval notation for -3<x<4
The inequality is , -3<x<4. Thus, the correct interval notation for the given inequality is (-3, 4),
The question concerns how to express the inequality -3<x<4 in interval notation. Interval notation is a way to denote a range of numbers on the real line where certain numbers are included or excluded in the set.
The notation uses brackets and parentheses to indicate closed or open intervals, respectively. A closed interval means the endpoint is included, while an open interval means the endpoint is not part of the set.
In this instance, the inequality suggests that x can take any value between -3 and 4, but cannot equal -3 or 4.
Thus, we use parentheses to denote that both -3 and 4 are not contained within the interval.
Therefore, the correct interval notation for the given inequality is (-3, 4), where the round parentheses indicate that -3 and 4 are not included in the solution set.
Solve the equation.
5p/7 - 18 = -43
A. -35
B. -31
C. -85 2/5
D. -50
Please explain your answer.
Answer:
-35
Step-by-step explanation:
The Leukemia and Lymphoma Society sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.
If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw, how much would you expect to win on average?
Using the numbers 8, 6, 4, and 2 write an expression that equals 7.
( You can not change the order of the numbers and you can only use: parentheses, divided by, multiplication, addition, and subtraction).
A batch of chicken required 4 6⁄7 cups of flour. If a fast food restaurant was making 3 3⁄4 batches, how much flour would they need?
The fast food restaurant would need 255/14 cups of flour for 3 3/4 batches of chicken.
To find out how much flour a fast food restaurant needs for 3 3/4 batches of chicken, let's start by calculating the flour required for one batch.
One batch requires 4 6/7 cups of flour.
To convert the mixed number to an improper fraction:
4 6/7 = (4 * 7 + 6)/7 = 34/7 cups
So, one batch requires 34/7 cups of flour.
Now, let's find out how much flour is needed for 3 3/4 batches:
3 3/4 batches = (3 + 3/4) batches
To convert the mixed number to an improper fraction:
3 3/4 = (3 * 4 + 3)/4 = 15/4 batches
Now, we multiply the amount of flour needed for one batch by the number of batches:
15/4 * 34/7 = (15 * 34)/(4 * 7) = 510/28
Now, we simplify the fraction:
510/28 = (510 ÷ 2)/(28 ÷ 2) = 255/14
So, the fast food restaurant would need 255/14 cups of flour for 3 3/4 batches of chicken.
Evaluate the function t(x)=19-x, when x=-3
find the equation of the passing through p(4,6) which is parallel to the line with equation 4x-2y+6=0
The equation for the line passing through point P(4,6) that is parallel to the given line 4x - 2y + 6 = 0 is y = 2x - 2.
Explanation:The subject of the question is climbing up a function of mathematics known as linear algebra. The equation of the original line given is 4x - 2y + 6 = 0. First, you need to rearrange the equation to the slope-intercept form to identify the slope of the line, which gives you y = 2x + 3. Because parallel lines have identical slopes, the line passing through point P(4,6) will have the same slope, so the equation would be y = 2x + b. To find the exact equation of the line, substitute the coordinates of point P into this equation and solve for 'b', which gives you 6 = 2*4 + b. Thus, solving for 'b' we get b = -2. Therefore, the equation of the line that passes through point P(4,6) and is parallel to the given line is y = 2x - 2.
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What is the domain and the range of the relation represented by the ordered pairs? {(6,6),(−1,3),(3,6),(0,4)}{(6,6),(−1,3),(3,6),(0,4)} Select each correct answer.
if (7,2) is an ordered pair of the function f(x) which of the following must be an ordered pair of the inverse of f(x)?
(2,7)
(2,2)
(7,2)
(7,7)
Answer:
(2,7)
Step-by-step explanation:
Here is an example just to show that it works.
3x+2y=25
3(7) + 2(2) = 21 + 4 = 25
3y+2x=25
25-2x=3y
25/3 - 2/3x = y
25/3 -2*2/3=25-4/3=21/3=7
Which line on the graph below has a slope
In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. find how many had taken one course only.
Final answer:
To find the number of students who took only one course among mathematics, chemistry, or physics at a university, we use the principle of inclusion and exclusion. After calculating, we find that 154 students had taken exactly one course.
Explanation:
To determine how many university students had taken only one course among mathematics, chemistry, and physics, we can use the principle of inclusion and exclusion. From the information given, we know the following:
Students who took mathematics (M): 64
Students who took chemistry (C): 94
Students who took physics (P): 58
Students who took both mathematics and physics (M∩P): 28
Students who took both mathematics and chemistry (M∩C): 26
Students who took both chemistry and physics (C∩P): 22
Students who took all three courses (M∩C∩P): 14
Let's define S as the number of students who took only a single course. We can calculate S using the formula:
S = (M + C + P) - (M∩P + M∩C + C∩P) + M∩C∩P
Substituting the values we get:
S = (64 + 94 + 58) - (28 + 26 + 22) + 14
S = 216 - 76 + 14
S = 140 + 14
S = 154
Therefore, 154 students had taken only one course.