As a result, the singers can finish first, second, third, fourth, or fifth in 524,160 different ways.
Permutation, where order is important:
_nP_{r}=\dfrac{n!}{(n-r)!}
P r = (n−r)!n!
Combination of definitions (order is irrelevant):
_nC_{r}=\dfrac{n!}{r!(n-r)!}n C r equals r!(nr)!n!
with n!=n, cdot (n-1) ..., cdot 2..., cdot 1n!=n(n1)...2,1.
We want to know how many different ways we can choose five people from a group of 16 (ranked first, second, third, fourth, and fifth).
n=16 n=16 r=5 r=5 Because we are interested in the first, second, third, fourth, and fifth places, order is important (changing the first and second places results in different rankings and prizes for the people), so we need to use a "textbf permutation" permutation.
Analyze the permutation definition:
"Begin align*" means "16P_5" and "dfrac" 16! color#8895cetextDefinition combination &=dfrac16!11!&color#8895cetext Evaluate difference &=dfrac16cdot 15cdot 14cdot 13cdot 12cdot 11cdot 10cdot...cdot 111cdot 10...cdot 1
16!= 11!
16! = 11⋅10⋅...⋅1
16⋅15⋅14⋅13⋅12⋅11⋅10⋅...⋅1
=16⋅15⋅14⋅13⋅12
=524,160
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Full Question = There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth?
$1,000 at 9% compounded semiannually for 2 years
Answer:
Total = principal * (1 + rate / compounding periods ) ^ years * compounding periods
Total = (1,000 * (1 + .09 / 2)^2*2)
Total = (1,000 * (1.045)^4
Total = (1,000 * 1.1925186006)
Total = 1,192.52
Source: http://www.1728.org/compint3.htm
Step-by-step explanation:
Emanuel read 150 pages in 5 hours.
Find his average reading rate.
Answer:
30 pages per hour
Step-by-step explanation:
If the measure of ∠C and ∠T are supplementary and the measure of ∠T is 120º, what is the measure of ∠C?
Answer:
60
Step-by-step explanation:
180-120
fill in the blanks with the correct missing term of each given sequence
8,11,_,17,20
Answer:
14 i think
Step-by-step explanation:
im not that sure but yeah
2020-2021-T-Math-Gr05-T11 Question: 1-16
Jason helped his dad put plastic and aluminum items into the recycling container. The container is a large cube with a length, width, and height of 6 feet. What is the volume of the recycling container?
0 36 cubic feet
72 cubic feet
O 216 cubic feet
O 396 cubic foet
Given:
The side length of a cube is 6 feet.
To find:
The volume of the cube.
Solution:
We know that the volume of a cube is:
[tex]V=a^3[/tex]
Where, a is the side length of the cube.
Putting [tex]a=6[/tex] in the above formula, we get
[tex]V=(6)^3[/tex]
[tex]V=216[/tex]
The volume of the cube is 216 cubic feet. Therefore, the correct option is C.
help please i need it asap
What are the solutions of the quadratic equation 5x2 – 10x – 15 = 0?
The period is . On a coordinate plane, the points on a function curve are shown. The curve crosses the y-axis at (0, 5) and then decreases to the minimum. The minimum is at (0.748, 2) and the maximum is at (1.870, 6). After the green point, the curve increases and then decreases again. A green point is at y = 4.
The Period of the Function Curve with the green point at y = 4 on the given coordinate plane is; 2.244
How to find the period of a wave?We are given;
Minimum Point; (0.748, 2)
Maximum Point; (1.870, 6)
The green point is the lowest point and from drawing the curve, we see that the next highest point coordinate is (4.114, 6).
The period is the x-coordinate distance between the two highest points. Thus;
Period of wave = 4.114 - 1.87
Period of wave = 2.244
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Answer:
Here are the correct answers:
Step-by-step explanation:
~Hope this helps! :)
Hi, do you know how to get the ratio?
hope it help you
please follow me
someone please help me answer this!!
Answer:
10 units is the answer.
Step-by-step explanation:
points are (-3,2) and (-9,-6)
Pythagorean theorem can be written as,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(-9-(-3))^2 + (-6-2)^2}\\\\d=\sqrt{(-6)^2+(-8)^2} \\\\d=\sqrt{36+64} \\\\d=\sqrt{100} \\\\d=10[/tex]
∴ distance between the points = 10 units
Help me plzzzzzzzzzz I give u BRAINLY
The answer is
X= 3 and Y= -4
Answer:
If you are solving for substitution then the anwser is x+3, and y = -4 (3, -4)
Step-by-step explanation:
First you solve for x
x-2y=11 to x = 11 + 2y
Then you plug it in to the first equation.
-7 (11 + 2y)- 2 = -13 Then Simplify. -77 - 16y= -13
Solve for Y.
Add 77 to both sides. -16y= 64
Divide both sides by -16
y= -4
The Solve for X
x=11 + 2 x -4
X=3
Therefore the anwser is (3, -4)
Determine whether the data in the table display exponential behavior. Explain why or why not.
Answer:
The Answer is B
Step-by-step explanation:
If you borrowed $646 at an interest rate of 5% for 6 years, how much interest will you pay? Round to the nearest tenth if necessary.
PLEASE HELP!!!!!!!!!!
Answer:
Total interest you will pay is $103.07.
The total you will pay for interest and loan amount is $749.07
iStep-by-step explanation:
A line with a slope of 4 passes through
the point (2, 1). What is the equation of
this line?
Answer:
y = 4x - 7
Step-by-step explanation:
Slope = 4 ; x1 = 2 , y1 = 1
Slope point form: y -y1 = m(x -x1)
y - 1 = 4(x - 2)
y - 1 = 4x - 2*4
y -1 = 4x - 8
y = 4x - 8 +1
y = 4x - 7
Which situation can be represented by the equation y = 5x?
Answer: answer is 5
Step-by-step explanation:
ASAP GIVING BRAINLIEST ASAP
Answer:
202
Step-by-step explanation:
70+32 would equal 102, then you would times 102 by 2 and the answer would be 202
Brainliest?
Any help would be appreciated
Answer:
$8.25
Step-by-step explanation:
I don't know how to explain it to you but if I'm wrong tell me I'll try it aagain.
6) Four bacteria are placed in a petri dish. The population will double every day. The formula for the
number of bacteria in the dish on day tis
N(t) = 4(2)
where t is the number of days after the four bacteria are placed in the dish. How many bacteria are
in the dish five days after the four bacteria are placed in the dish?
Answer:
128
Step-by-step explanation:
N(t)=4(2)^t
N(t)=4(2)⁵
N(t)=4(32)
N(t)=128
\sqrt{-x+26}=x-6 −x+26=x−6
Answer:
x = 1 and 10
Step-by-step explanation:
Given the equation \sqrt{-x+26}=x-6, we are to find the value of x
Take the square of both sides
(\sqrt{-x+26})²= (x-6)²
-x+26 = (x-6)²
Expand the parenthesis
-x+26 = x²-12x+36
x²-12x+36+x-26 = 0
x²-11x+10 = 0
x²-10x-x +10 = 0
x(x-10) -1()-10) = 0
(x-1)(x-10) = 0
x - 1 =0 and x - 10 = 0
x = 1 and 10
Hence the value of x is 1 and 10
I need help I’ll mark brainy
Answer:
14.75
Step-by-step explanation:
12.50*0.18 = 2.25
12.50 + 2.25 = 14.75
-4x-6 whats the answer ? :)
Answer:
24 I think???
Answer:
-1.5
Step-by-step explanation:
-4x-6=0
+6 +6
-4x=6
---------
-4
x=-1.5
-4(-1.5)-6=0
6-6=0
0=0
Show me how to solve
Answer:
0
Step-by-step explanation:
all the details see in the attached picture, note (sinx)/x (when x->0) is 1.
A rectangle has a length of 12 meters and a width of 500 centimeters. What is the
area of the rectangle in meters?
1 meter = 100 centimeters
Answer:
600m / 600 metres
Step-by-step explanation:
12 m = 1200cm
1200cm × 500cm = 600,000cm
600,000cm = 600 m
Its 600m,
good luck,
:3 :3
PLEASE HELP ASAP ITS DUE SOON!!!!
Answer:
A
Step-by-step explanation:
Look at the y axis and find the highest point.
Answer:
I believe it would be a: y=30; The maximum height...
Step-by-step explanation:
It's where the line would be, and describes exactly where the line of symmetry would be. Hope this helps :)
Two polls were conducted about the upcoming election for new governor. The first poll said that 45% of the people asked would vote for Mr. Johnson with a margin of error of plus or minus 4.6%. The second poll said that 42% of the people asked would vote for Mr. Johnson with a margin of error of plus or minus 3.6%.
Can the conclusions of both polls be correct?
a. yes, the two corresponding confidence intervals overlap.
b. no, the difference between 45% and 42% is too large.
c. no, the two corresponding confidence intervals do not overlap.
Answer:
A. Yes, the two corresponding confidence intervals overlap.
Step-by-step explanation:
The correct option is - A. Yes, the two corresponding confidence intervals overlap.
Reason -
P(1) = 45% = 0.45
E(1) = 4.6% = 0.046
Confidence Interval = P(1) ± E(1)
= 0.45 ± 0.046
So, the interval is -
0.45 + 0.046 ≤ P ≤ 0.45 - 0.046
⇒0.496 ≤ P ≤ 0.404 .............(1)
Now,
P(2) = 42% = 0.42
E(2) = 3.6 % = 0.036
Confidence Interval = P(2) ± E(2)
= 0.42 ± 0.036
So, the interval is -
0.42 + 0.036 ≤ P ≤ 0.42 - 0.036
⇒0.456 ≤ P ≤ 0.384 ...............(2)
From equation (1) and (2), we get
The two corresponding confidence intervals overlap.
I can't figure this out
9514 1404 393
Answer:
143 in²
Step-by-step explanation:
The figure is dimensioned in such a way that it can be divided easily into three rectangular areas. The top rectangle is 10 in wide and 7 in high. The vertical rectangle below that is 4 in wide and 12 in high, and the square appendage on the right is 5 in square.
Then the total area is the sum of products of length and width:
A = (10 in)(7 in) + (4 in)(12 in) + (5 in)(5 in) = (70 +48 +25) in²
A = 143 in²
The area of the irregular figure is 143 in².
If you can solve it please tell me (20 points)
Answer:
D E false, F true
Step-by-step explanation:
Can someone help me pls I’m stuck
Answer:
∠A = 53.58°
Step-by-step explanation:
cos A = 19/32 = 0.5938
∠A = 53.58°
Find the domain and range of the function of the graph multiple choice.
Domain
A. X>-1
B. All real numbers except 5
C. X less than or equal to-3
D. All real numbers
Range
A. all real numbers
B. Y less than or equal to -3
C. All real numbers except-3
D. Y> -3
PLS HELP ME, pls no link answers
Answer:
Step-by-step explanation:
y+123
x=178
D=99
Which is bigger 1/4 or 3/5
Answer:
3/5
Step-by-step explanation: