A president, treasurer, and secretary, all di erent, are to be chosen from a club consisting of 12 people (whose names are I, J, K, L, M, N, O, P, Q, R, S, and T). How many di erent choices of ocers are possible if: (a) There are no restrictions
Answer:
There are 220 choices
Step-by-step explanation:
Given
[tex]People = 12[/tex]
[tex]Selection =3[/tex] (President, Treasurer and Secretary)
Required
Determine number of selection (if no restriction)
This is calculated using the following combination formula:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where
[tex]n = 12[/tex]
[tex]r= 3[/tex]
So, we have:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
[tex]^{12}C_3 = \frac{12!}{(12 - 3)!3!}[/tex]
[tex]^{12}C_3 = \frac{12!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10*9!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3*2*1}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{6}[/tex]
[tex]^{12}C_3 = 2*11*10[/tex]
[tex]^{12}C_3 = 220\ ways[/tex]
There are 220 choices
If we divide 2 and 6 by 2 what is our new simplified ratio?
Answer:
Step-by-step explanation:
A pair of jeans that originally costs $42 is 25% off. What is the sale price?
Answer:
$31.50
Step-by-step explanation:
42 x 0.25 = 10.5
42 - 10.50 = 31.50
$31.50
Explanation:
42 × 25% = 10.5
42 - 10.5 = 31.5
In the sixth grade, 54% of the students are boys. There are 189 boys in the sixth grade. What is the total number of students in sixth grade? A. 54 B. 161 C. 189 D. 350. (explain what did u do to get you're answer )
Answer:
D
Step-by-step explanation:
189 boys is 54%
x is 46%(100-54)
Cross multiply:
189*46%=54%*x
86.94=0.54x
x=161
189 boys 161 girls
350 altogether
So D
Hope this helps plz hit the crown :D
Write a unit rate for the situation. Round to the nearest hundredth if necessary.
traveling 216 miles in 5 hours
A. 54 miles/hour
B. 39.27 miles/hour
C. 43.2 miles/hour
D. 0.4 miles/hour
Answer: 43.2 miles/hour
Step-by-step explanation:
PLZ HELP ME! 1ST GETS BRAINIEST! THIS IS DUE TODAY!
Pretend a classmate missed the lesson today. What would you tell them about how to make a table to represent a rate? How would you tell them how to use the table to make a graph?
Answer:
You would tell them by labeling the x and y and the titles of the graph and what corresponds to it
Step-by-step explanation:
An ice cream cone with a diameter of 2 inches and a height of 3.5 inches is filled with ice cream and more ice cream on top in the form of a hemisphere with the radius equal to the radius of the cone. Compute the total volume of ice cream it contains.
Answer:
11pi/6 in^3 or
5.760 in^3 to the nearest thousandth.
Step-by-step explanation:
Volume of ice cream = volume of the cone + volume of the hemisphere
= 1/3 pi r^2 h + 1/2 * 4/3 pi r^3
= 1/3 pi 1^2 * 3.5 + 2/3 pi 1^3 (as the radius = 1/2 * diameter)
= (7/6 + 2/3) pi
= 11pi/6 in^3.
Which diagram represents the type of solution to this system of equations?
7x − 12y + z = -1
8x − 10y = 5
21x − 36y + 3z = -3
A.
B.
C.
D.
Answer: The answer should be A.
Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.
The correct diagram represents the type of solution to this system of equations is shown in Option A.
We have to given that,
System of equations are,
7x - 12y + z = -1 .. (i)
8x - 10y = 5 .. (ii)
21x - 36y + 3z = -3 .. (iii)
Now, From equation (i);
Multiply by 3;
3( 7x - 12y + z) = -1 × 3
21x - 36y + 3z = - 3
Which is same as equation (iii).
Hence, Equation (i) and (ii) are parallel to each other.
And, It's a triple relationship.
Thus, Only option A has parallel planes.
So, Option A is true.
Learn more about systems of equations at:
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You collect data on the color of cars driven by students in your statistics class, and want to display this information graphically. Which is the better choice for this data, a bar graph or a histogram?
Answer:
bar graph
Step-by-step explanation:
The best choice for this scenario would be a bar graph. This is because a histogram is used to represent data ranges or data in a specifically given time interval. For example, age ranges, time ranges, and income ranges are all common examples of data that is represented using histograms. Bar graphs on the other hand tend to represent the quantity of specific pieces of data in a large set of data, such as the number of specific color cars that appear out of a wide set of colors.
Helllllllpppppppppppppppp
Answer:
50x50=1000000
Step-by-step explanation:
What is the answer to -7(-6)
Answer:
42
Step-by-step explanation:
Hope this helps and have a great day! :)
Answer: -7(-6) is 42
hope this helps :)
Step-by-step explanation:
when You multiply two negative numbers, the answer is positive.
:D
I’m kinda confused with this need help
Answer: 2n + 1 = n + 11
Write an equation in slope-intercept form for the line shown in the graph.
Answer:
y=2x-2
Step-by-step explanation:
(2,2), (3,4)
4-2=2
3-2=1
2/1
Answer:
y = 2x - 2
Step-by-step explanation:
In the formula for a line, y = mx + b,
The slope, or m, is 2 because this line goes up 2 units and right 1 unit. The y-intercept, or b, is -2 because the line touches the y-axis at -2.find the value of w(u(-4)) i need some help lol
Answer:
The functions u and w are defined as follows. u(x) =-2x+2 w(x) = 2x2 +1 Find the value of w (u (4)). w (u (4)) = 05Step-by-step explanation:
The data was modeled with a linear best-fit function. What was the initial
purchase price?
X Y
4. 5,000
7. 6,875
9. 8,125
12. 10,000
A. $625
B. $2,500
C. $5,000
D. $5,625
Answer:
c
Step-by-step explanation:
A virus takes 13 days to double its original population (A = 2A0). How long will it take to triple its population? Round to
the nearest tenth.
Answer:
20.6
Step-by-step explanation:
The exponential function to solve the problem.
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
A = population in time t.
[tex]A_0[/tex] = Initial population.
r = growth rate.
t = time
The number of days taken to triple the population is 20.7 days.
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The exponential function to solve the problem.
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
A = population in time t.
[tex]A_0[/tex] = Initial population.
r = growth rate.
t = time
Now,
A = 2[tex]A_0[/tex]
t = 13
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
[tex]2A_0[/tex] = [tex]A_0e^{13r}[/tex]
2 = [tex]e^{13r}[/tex]
Taking logs on both sides.
log 2 = 13r log e
0.30 = 13r
r = 0.30/13
r = 0.023
Now,
A = 3[tex]A_0[/tex]
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
3 = [tex]e^{rt}[/tex]
log 3 = rt
0.48 = 0.023t
t = 0.48/0.023
t = 20.7 days.
Thus,
The number of days taken to triple the population is 20.7 days.
Learn more about functions here:
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Two pounds of grapes cost $6.
Complete the table showing the price of different amounts of grapes at this rate
Answer:
2, 6
4, 12
8, 18
and so on
Step-by-step explanation:
multiply the number on the right by itself and do the same with the number on the left, this pattern could go on forever,
Factor 16x – 12 by the GCF.
Answer:
148 i thk i did 16x-12
Step-by-step explanation:
what is 42/18 written as a mixed number?
Step-by-step explanation: 2 1/3
What is the area in square feet?
Answer:
426 square feet
Step-by-step explanation:
First, find the angle of each shape separately.
Area of a triangle = 1/2 base times height
1/2(9x8)
1/2(72) = 36
Area of a rectangle = base times height.
26 x 15 = 390
Now, add the numbers together to get the total area. 390+36=426
Answer:
426 square feet
Step-by-step explanation:
-First find the area of the rectangle:
26 x 15 = 390
-Next, find the area of the triangle on top:
9 x 8/2 = 36
-Finally, add the two to get the full area of the figure:
390 + 36 = 426
Answer: 426 square feet
Hope this helps! :)
Could some help with this problem it is due in about 20 mins and I am really stuck I will give a brainlist to the best answer :)
Answer:
Step-by-step explanation:
29.
2x+4+x+2x-9=180
5x-5=180
5x=180
x=36
Q=76°
P=63°
R=36°
30.
C=90° (Given)
4x+7+8x-1+90=180
12x+96=180
12x=84
x=7
B=55°
A=35°
What is the length of segment DA?
Answer:
Step-by-step explanation:
The length of this line segment is the distance between its endpoints A and B. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
Answer: DA = 6
====================================================
Explanation:
The triangles are similar, allowing us to make the proportion below
DB/DA = DA/DC
Plug in the given values. Cross multiply and solve for x
DB/DA = DA/DC
9/DA = DA/4
9*4 = (DA)*(DA)
36 = (DA)^2
(DA)^2 = 36
DA = sqrt(36)
DA = 6
The length of DA is exactly the geometric mean of the lengths BD and DC
geometric mean of x and y = sqrt(x*y)
(b) 45% of 80 is what?
Answer: the answer is 36
Hope this helps :)
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
what is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2cm and a height of 9 1/2cm?
Answer:
8075.
Step-by-step explanation:
Volume of the prism
= 12 1/2 * 8 1/2 * 9 1/2
= 25/2 * 17 / 2 * 19/2
= 8075/8 cm^3
The volume of the small cubes = (1/2)^3 = 1/8 cm^3
So the number required = 8075 / 8 / 1/8
= 8075*8 / 8
= 8075.
For a school project, Max made a pyramid using 587 sugar cubes. On his way to school 34 of the sugar cubes fell off. When he got to school his friends took 18 more cubes off the pyramid to eat.
Estimate how many sugar cubes remain on Max's pyramid.
Answer:
535
Step-by-step explanation:
587-34-18=
535
Answer:
550
Step-by-step explanation:
just is the answer
Solve this system of equations using elimination. Write your answer as an ordered pair,
5x-2y = 10
4x + 2y = 8
Answer:
Solving the system of equations using elimination method, we get x=2, y=0
The ordered pair is: (2,0)
Step-by-step explanation:
We need to solve the system of equations using elimination method.
[tex]5x-2y = 10\\4x + 2y = 8[/tex]
Let:
[tex]5x-2y = 10--eq(1)\\4x + 2y = 8--eq(2)[/tex]
Add both equations to eliminate y and find value of x
[tex]5x-2y = 10\\4x + 2y = 8\\------\\9x=18\\x=\frac{18}{9}\\x=2[/tex]
We get value of x=2
Now, finding value of y by putting value of x in eq(1)
[tex]5x-2y=10\\Put\:x=2\\5(2)-2y=10\\10-2y=10\\-2y=10-10\\-2y=0\\y=0[/tex]
We get value of y= 0
Solving the system of equations using elimination method, we get x=2, y=0
The ordered pair is: (2,0)
Answer:
the answer is C
Step-by-step explanation:
Carlos drove 200 miles in 5 hours. If he drove at a constant rate, how many miles did Carlos drive per hour?
Answer:
40
Step-by-step explanation:
200/5=x/1
Answer:
40
Step-by-step explanation:
200/5 = 40
nice dumb questions
In which quadrant does the point S(-3, -4) lie?
quadrant I
quadrant II
quadrant III
quadrant IV
It would be quadrant III
Answer:
Quadrant 3
Step-by-step explanation:
Quadrant 3: (-, -)
The sum of three consecutive numbers is 84. What is the largest of these numbers? (1 point)
26
27
28
29
WILL GIVE BRAINLEST!!!!!!
Answer:
29
Step-by-step explanation:
First, we have to find three numbers out of the four that add up to 84. But, it has to be in order because the question says consecutive numbers. In case you don’t know, consecutive numbers are numbers that increase at the same rate. In this problem, the numbers increase by one. I first did 26+27+28, which equaled 81. I have to get to 84 though. So, I did 27+28+29, which equaled 84. I did it correctly because 27, 28, and 29 are consecutive number, since they go inorder, and I added them up to 84. But the question is asking which of the three is the largest number. So, out of 27, 28, and 29, 29 is the largest number.
Hope this helps and answers your question! :)
Answer:
Step-by-step explanation:
i just took the test its 29
Alex is ordering his girlfriend a bouquet of flowers for their anniversary. Roses cost $5 each and carnations cost $2 each. He would like to include at least 3 flowers in the bouquet. To stay in his budget, he must not spend more than $36. Write a system of inequalities to represent the situation. Let x represent the number of roses and y represent the number of carnations.
Question 5 options:
x+y≥35x+2y≤36
5x+2y≥3x+y≤36
x+y≤35x+2y≥36
5x+2y≤3x+y≥36
0 of 5 questi
Answer:
32
Step-by-step explanation:
32=y
5=x
5x2
Is the equivalent to 32
Answer:
5x+2y≥3x+y≤36
Step-by-step explanation: