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Reason:
There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.
If order mattered, then we'd have 20*19*18 = 6840 permutations.
However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.
Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = 1140 combinations.
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Here's a more formulaic approach using the nCr combination formula.
Plug in n = 20 and r = 3
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]
fill in the missing values of the following number patterns
a) 24;12;0;__ ; __
b) -36; -25; -16; __; __
Answer:
A) 24;12;0;-12;-24 because the numbers are gradually going down and they go into the negatives which means they repeat the numbers in the beginning.
B)-36;-25;-16;-9;-4 i am uncertian on this one but i think im doing it right.
What is the value of the expression "two less than six times the difference of a number and five" when n = 9?
O22
O 16
O 32
O 31
Work out
(4 x 10-6) - (2 x 10-8)
Give your answer in standard form.
Answer:
20x + 2
Step-by-step explanation:
To save money for his daughter's college tuition, Pablo invests $279 every quarter in an annuity that pays 6% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 22 years. Do not round any intermediate computations, and round your final answer to the nearest cent
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\dotfill &279\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &22 \end{cases}[/tex]
[tex]A=279 \left[ \cfrac{\left( 1+\frac{0.06}{4} \right)^{4 \cdot 22}-1}{\frac{0.06}{4}} \right]\implies A=279\left[\cfrac{1.015^{88}~~ - ~~1}{0.015} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 50348.47~\hfill[/tex]
complete the squares
i wanted to ask what exactly the question is
??
If it is known that a and b are positive integers and that a-b=2 evaluate the following.
9 1/2^b/3^a
The value of the expression such that a and b are integers is 1/9
Indices and exponentsAn exponential function is a mathematical function in the form y = ab^x
Given the indices expression
[tex]\frac{(9\frac{1}{2} )^b}{3^a}[/tex]
This can be simplified as:
[tex]=\frac{(3^{2*\frac{1}{2}} )^b}{3^a}\\=\frac{3^b}{3^a}[/tex]
According to the law of indices, the expression will becomes;
[tex]\frac{3^b}{3^a} =3^{b-a}[/tex]
Recall that a - b = 2, such that b - a = -2. Substitute into the result to have:
[tex]\frac{3^b}{3^a} =3^{b-a}\\3^{b-a}=3^{-2}\\3^{b-a}=1/9[/tex]
Hence the value of the expression such that a and b are integers is 1/9
Learn more on indices here: https://brainly.com/question/10339517
How would you use the formula "V = BH" to find the volume of a tent? Explain.
Explanation:
The volume formula ...
V = BH
is a formula for the volume of a general prism whose cross sections parallel to the base all have area B. The distance between the parallel bases is represented by H.
__
To use this formula to find the volume of a tent, the area of the end of the tent would be substituted for B, and the length of the tent (distance between the ends) would be substituted for H.
An appropriate formula would need to be used for the end area.
What's the value of x in the equation -6 + x = -4?
Brainliest to best and quickest answer!
Answer:
[tex]\boxed{\sf{x=2}}[/tex]Step-by-step explanation:
To find the value of x, isolate it on one side of the equation.
→ -6+x=-4First, add by -6 from both sides.
→ -6+x+-6=-4+6
Solve.
→ -4+6=2
x=2
Therefore, the correct answer is x=2.I hope this helps you! Let me know if my answer is wrong or not.
find the volume of a cylinder with radius 5.7cm and height 10 cm, correct to 1 decimal place
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5.7\\ h=10 \end{cases}\implies \begin{array}{llll} V=\pi (5.7)^2(10)\implies V=324.9\pi \\\\\\ V\approx 1020.7 \end{array}[/tex]
(5x+30)=7x ??
Can anyone help me
Answer:
the answer is x=15.....
Answer:
Step-by-step explanation:
(5x+30)=7x Subtract 7x from both sides. 5x+30−7x=0 Combine 5x and −7x to get −2x. −2x+30=0 Subtract 30 from both sides. Anything subtracted from zero gives its negation. −2x=−30 Divide both sides by −2. x= −2 −30 Divide −30 by −2 to get 15. answer should be x=15
please help me i dont know the answer to this one
Answer:
centroid (2, 2.666666666...)
circumcenter (2, 1.75)
orthocenter (2, 2.5)
Step-by-step explanation:
the coordinates of the centroid of a triangle are
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
so, we have
(-4 + 2 + 8)/3 = 6/3 = 2 = x
(0 + 8 + 0)/3 = 8/3 = y = 2.666666666...
the circumcenter is the crossing point of the lines going perpendicular through the midpoint of each side.
the orthocenter is the crossing point of the lines going perpendicular on each side through the opposing vertices (the heights of the triangle).
so, we need to calculate additionally the slopes of 2 sides and their midpoints before we can get these 2 centers. the third side would only confirm the result but not provide additional information.
A = (-4, 0), B = (2, 8), C = (8, 0)
midpoint D of AC = ((-4 + 8)/2, (0+0)/2) = (2, 0)
the slope of AC is
(y2 - y1)/(x2 - x1) = (0 - 0)/(8 - -4) = 0/12 = 0 (a flat line)
the slope of the perpendicular line is -1/slope of original line. which is -1/0 = -infinity.
but don't worry, that means it is a constant line x = ...
and since it has to go through the midpoint D, the perpendicular line is x = 2
midpoint E of BC = ((2+8)/2, (8+0)/2) = (5, 4)
the slope of BC is
(0-8)/(8-2) = -8/6 = -4/3
so, the slope of the perpendicular line is 3/4.
that line is then y = 3/4 x + b
it has to go through the midpoint E
4 = 3/4 × 5 + b = 15/4 + b
16 = 15 + 4b
4b = 1
b = 1/4
so, the full perpendicular line is
y = 3/4 x + 1/4
crossing both perpendicular lines is simply using the first in the second equation :
y = 3/4 × 2 + 1/4 = 6/4 + 1/4 = 7/4 = 1.75
for the orthocenter we can use the same slopes, but the lines go now through the opposing vertices instead through the side midpoints.
so, line 1 is going through B, which makes it also x = 2.
line 2 is going through A, so
0 = 3/4 × -4 + b
0 = -1 + b
b = 1
line 2 is then
y = 3/4 x + 1
crossing these 2 lines gives us
y = 3/4 × 2 + 1 = 6/4 + 4/4 = 10/4 = 5/2 = 2.5
WORTH 1 POINT
GIVING 15 POINTS AWAY
HELP PLS!!!!
Answer:
y = 29
Step-by-step explanation:
Since it is a vertical angle, both angles represented by the equations are equal. Meaning we can set them equal to each other and find y by simplifying.
4y-8 = 79+y
-79 -79
4y-87 = y
-4y -4y
-87 = -3y
Divided by -3
29 = y
Help picture below problem 4
Answer:
The answer is A
Step-by-step explanation:
A pentagon is a polygon that has 5 sides and 5 vertices.
solve by using properties of whole number
a,16×25×10×4 b,49×99
Answer:
Step-by-step explanation:
a.16×25×10×4
= 100 * 160
= 16,000
b,49×99
= 49 * 100 - 49
= 4900 - 49
= 4,851.
A.
B.
5x
x
=20
=4
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Multiply/divide both sides by the same non-zero constant
(Choice B)
B
Multiply/divide both sides by the same variable expression
(Choice C)
C
Add/subtract the same quantity to/from both sides
(Choice D)
D
Add/subtract a quantity to/from only one side
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
Answer:
Divide both sides by 5.
Step-by-step explanation:
Divide both sides by same non-zero constant.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
160
Step-by-step explanation:
FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.
For which values of k would the product of k/3 X 12 be greater than 12
Answer:
[tex]\text{k = 4, 5, 6, 7, 8... and onwards}[/tex]
Step-by-step explanation:
The product of k/3 and 12 be greater than 12.
⇒ k/3 × 12 > 12
The first step in determining the possible values of "k" is to simplify the left-hand-side (L.H.S) of the inequality.
⇒ (12 × k)/3 > 12
⇒ (12 ÷ 3) × k > 12
⇒ (4) × k > 12
The next step in determining the possible values of "k" is to isolate the variable. To do this, we can divide 4 both sides.
⇒ [4 × k]/4 > 12/4
⇒ k > 12/4
⇒ k > 3
To satisfy the inequality, the value of k must be greater than 3. Thus, the values of k could be [tex]\text{4, 5, 6... }[/tex] and so on.
MATH which graph has an axis of symmetry at x=-1
What's the median for 0 2 4 6 8 10
Answer:
5 would be the midian
Step-by-step explanation:
You would need to add 0+2+4+6+8+10
Then count how many numbers there are (6)
Then put it in a fraction
30/6
Then divide and then you get 5
Answer:
21,67
Step-by-step explanation:
0+2+4+6+8+10 all divided by numbers in the set data[6]=21,67
How many times larger is 450.000,000 than 4,500?
100
1,000
10,000
100,000
Answer:
100,00
Step-by-step explanation:
In order to find this, you would divide 450,000,000 by 4500. You would then get the final answer of 100,000. Hope this helps!
HELP MEEEEE
Write the equation for each translation of the graph y=|1/2x-2|+3
one unit to the right
Acontainer ship left Hawaii and traveled
toward Tahiti at an average speed of 25
km/h. An aircraft Cimier left sometime
later traveling in the opposite direction
with an average speed of 25 km/h. After
the container ship had traveled for six
hours the ships 200 km apart Find
the number of hown heraft carrien
hohe
Answer:
Step-by-step explanation:
-lukelaws
did i help?
The function f is defined as follows.
f(x) =5x² +8
If the graph off is translated vertically downward by 5 units, it becomes the graph of a function g.
Find the expression for g(x).
Answer:
g(x) = 5x² + 3
Step-by-step explanation:
8 units are added directly to each input so just subtract 5 from that to get + 3.
A credit card company receives numerous phone calls throughout the day from customers reporting fraud and billing disputes. Most of these callers are put “on hold” until a company operator is free to help them. The company has determined that the length of time a caller is on hold is normally distributed with a mean of 2.5 minutes and a standard deviation 0.5 minutes. If 1.5% of the callers are put on hold for longer than x minutes, what is the value of x?
Using the normal distribution, it is found that the value of x is of 3.585.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of XIn this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 2.5, \sigma = 0.5[/tex].
The value of x is the 100 - 1.5 = 98.5th percentile, which is X when Z = 2.17, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.17 = \frac{X - 2.5}{0.5}[/tex]
[tex]X - 2.5 = 0.5(2.17)[/tex]
[tex]X = 3.585[/tex]
Hence the value of x is of 3.585.
More can be learned about the normal distribution at https://brainly.com/question/24663213
The graph of a system of two linear equations is a pair of
lines that intersect at the origin. Which statement is true of
the system?
Answer:
They both have a y intercept of 0
Step-by-step explanation:
Linear equations are written in the form y = mx + b. m is the slope and b is the y-intercept. It also states that they intersect at the origin, so they must have a y-intercept of 0.
what is the slope of the line pls help
Answer:
1/2
Step-by-step explanation:
The slope is the rise over the run, also known as the change in y value over the change in x value
m = 2/4 =1/2
We know it is positive since it goes up from the left to the right
Which relation represents the pattern in the table of values?
y = 3x - 2
y = 3x + 2
y = 2x + 3
y = 2x - 3
Answer:
y = 3x + 2
Step-by-step explanation:
The easiest way to do this, would be to substitute a point (e.g., (2,8)) into your equations to find the one that is true.
(2, 8)
y = 3x - 2
8 = 3(2) - 2
8 = 6 - 2
8 = 4
This statement is false
(2, 8)
y = 3x + 2
8 = 3(2) + 2
8 = 6 + 2
8 = 8
This statement is true
(2, 8)
y = 2x - 3
8 = 2(2) - 3
8 = 4 - 3
8 = 1
This statement is false
(2, 8)
y = 2x + 3
8 = 2(2) + 3
8 = 4 + 3
8 = 7
Therefore, b is the correct answer.
Hope this helps!
The relation that represents the pattern in the table of values is given as; y = 3x + 2
How to find derive linear equation from a table?Let us first find the slope of the values from;
m = (y₂ - y₁)/(x₂ - x₁)
m = (8 - 5)/(2 - 1)
m = 3
Thus, the y-intercept is;
5 = 3(1) + c
c = 2
Thus, equation is;
y = 3x + 2
Read more about Linear Equation at; https://brainly.com/question/16834757
#SPJ5
If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of getting exactly 3 ones?
Answer:
0.1317
Step-by-step explanation:
How to graph (x-2)(y-3)=0
Answer:
This is what it should look like. The slope is 0 and there are two points. (0,3) (1,3)
Alge
If the number of bacteria in a colony doubles every 203 minutes and there is currently a
population of 40 bacteria, what will the population be 812 minutes from now?
bacteria
Submit
Answer:
640 Bacteria
Step-by-step explanation:
First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.
812÷203=4
The population will double 4 times.
Now figure out what the population will be after it doubles 4 times. Multiply the population by 2 a total of 4 times.
402222=640
That calculation could also be written with exponents:
4024=640
After 812 minutes, the population will be 640 bacteria.