The number of ways there are to form the teams so that Alice and Andrew are on opposite teams is 2 ways.
CombinationSince Alice, Andrew, and six other students are to be divided into two teams of four people, and we require the number of ways to form the teams so that Alice and Andrew are on opposite teams, this is a combination question since order doesn't matter.
Number of ways of combining the first teamFor the first team of 4, if Alice takes the first position, then there are 3 positions left to be occupied by the remaining 3 persons.
So, the number of ways of combining this team is n = 1 × ³C₃
= 1 × 1
= 1 way
Number of ways of combining the second team
Also, for the second team of 4, if Andrew takes the first position, then there are 3 positions left to be occupied by the remaining 3 persons.
So, the number of ways of combining this team is N = 1 × ³C₃
= 1 × 1
= 1 way
Number of ways of combining both teamsSo, the number of ways teams can be formed so that Alice and Andrew are on opposite teams is N' = n + N
= 1 + 1
= 2 ways
So, the number of ways there are to form the teams so that Alice and Andrew are on opposite teams is 2 ways.
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lcm of 42 and another number is 252 what is the largest possible value of this number
Answer:
252
Step-by-step explanation:
The largest possible value of the second number is the least multiple itself: 252.
For the function y=3x−1, when the input (x)= 7, the output (y) = ?
Answer:
y=3x-1 (replace x with 7 )
Step-by-step explanation:
y=3 (7)-1
y= 21-1
y= 20
note: multiply 3 with seven and minus 1 the answer is y so y=20
Brianna is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Brianna need to invest, to the nearest dollar, for the value of the account to reach $134,000 in 6 years?
Your answer would be 98086.
The value of money Brianna need to invest is,
⇒ P = $99,259
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Brianna is going to invest in an account paying an interest rate of 5.2% compounded continuously.
Here, We have;
Final amount (A) = $134,000
Time (n) = 6 years
Rate (r) = 5.2%
We know that;
⇒ Amount = P (1 + r)ⁿ
Substitute the values we get;
⇒ 134,000 = P (1 + 0.052)⁶
⇒ 134,000 = P (1.052)⁶
⇒ P = 134,000 / 1.35
⇒ P = $99,259
Thus, The value of money Brianna need to invest is,
⇒ P = $99,259
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-PLEASE ANSWER-
Find the other endpoint given one endpoint: (-14,9) and the midpoint: (-9,-4)
A. (-2.5, -6.5)
B. (-4, -17)
C. (-2.5, 6.5)
D. (-3.5, 7)
Students are making the scenery for a school play. They use a large piece of plywood to represent the front of a house, with a semicircular window cut out. Now they need to paint the plywood. Find the area that will be painted. 2. Describe your strategy for finding the area that needs to be painted. (2 points)
Considering the figures, the area that will be painted is of 38.9 square feet.
What is the area of a rectangle?
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
What is the area of a triangle?The area of a triangle of base b and height h is given by:
[tex]A = \frac{bh}{2}[/tex]
What is the area of a semi-circle?The area of a semi-circle of radius r is given by:
[tex]A = 0.5\pi r^2[/tex]
In this problem:
The rectangle with l = 6 ft and w = 8 ft will be painted, along with the triangle of dimensions b = 8 ft and h = 4 ft.The semi-circle with r = 4 ft will not be painted.Hence, the area that will be painted, in square feet, is given by:
[tex]A = 6 \times 8 + \frac{8(4)}{2} - 0.5\pi 4^2 = 64 - 8\pi = 38.9[/tex]
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Janile got 4 kilograms of candy when she went trick-or-treating at Halloween. Since she didn’t want to eat it all, she decided to share it with her 4 friends. If the 5 of them share the 4 kilograms, how much will each of them have?
200 grams
1,000 grams
500 grams
800 grams
HELP NEEDED!
Answer:
Each of them will have 0.8 kg of the Halloween candy. In a fraction form that would be 4/5.
Step-by-step explanation:
What is the answer?
-20 gallons per hour
-10 feet per minute
-0.1 kilograms per second
Answer:
im gonna assume they are negatives, if not you can just re-word it.
Step-by-step explanation:
a lake being drained by -20 gallons per hour
a paper airplane falling at -10 feet per minute
an intense workout burning -.1 kilograms per minute
F. Evelyn is running a snack sale during lunch to raise money for charity. She is selling hot Cheetos with
cheese for $1.50 each and chili-cheese fries for $2.50 each. At the end of the day she has raised $150 and
sold 80 items. How many of each item did she sell?
The number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.
What is a System of equations?A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.
Let the number of hot Cheetos with cheese sold be represented by x, while the number of chilli cheese is represented by y.
It is given that the total number of items sold by Evelyn during the event is 80. Therefore,
x + y = 80
x = 80 - y
Given that the cost of hot Cheetos with cheese is $1.50, while the cost of chilli cheese is $2.50, also the total amount that was collected in the event is $150. Therefore, we can write,
1.50x + 2.50y = 150
1.50(80 - y) + 2.50y = 150
120 - 1.50y + 2.50y = 150
1y = 150 - 120
y = 30
Substitute the value of y in the first equation,
x + y = 80
x + 30 = 80
x = 80 - 30
x = 50
Hence, the number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.
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The number of hot Cheetos with cheese sold is 50, while the number of chili cheese sold is 30.
What is a System of equations?
"A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The equations in the system can be linear or non-linear."
Let the number of hot Cheetos with cheese sold be represented by P, while the number of chili cheese is represented by Q.
It is given that the total number of items sold by Evelyn during the event is 80. Therefore,
P + Q = 80
P = 80 - Q --------- (1)
Given that the cost of hot Cheetos with cheese and chili cheese
So the equation
1.50P + 2.50Q = 150 --------- (2)
Put the equation (1) in equation (2)
1.50(80 - y) + 2.50y = 150
120 - 1.50Q + 2.50Q = 150
1Q = 150 - 120
Q = 30
Substitute the value of Q in the first equation,
P+Q = 80
P + 30 = 80
P = 80 - 30
P = 50
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What is the slope of the line in the following graph?
1. 1/3
2. 1/2
3. 2
4. 3
Answer:
1. 1/3
Step-by-step explanation:
Slope = Rise/run
=> It rises by 1, then runs by 3
=> Therefore, slope = 1/3
find the nth term of 67,56,45,34
Answer:
an = 67 -11(n -1)
Step-by-step explanation:
The terms of your arithmetic sequence have a common difference of -11. The first term is 67.
These values can be used in the generic formula for the n-th term:
an = a1 +d(n -1) . . . . . . first term a1, common difference d
an = 67 -11(n -1) . . . . . formula for the n-th term
What is the area of a regular triangle with perimeter = 36 in??
Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
Equilateral triangle
Solve for area
A≈62.35in²
P Perimeter
36
in
a
a
a
a
a
a
a
P
A
Using the formulas
A=3
4a2
P=3a
Solving forA
A=3P2
36=3·362
36≈62.35383in²
3x-5y=4
-2x+6y=18
solve for x and y
please help me!! I know the answer to the question but I don't know how to get it.
Answer:
S = 3770.25 in^2
Step-by-step explanation:
20/15 = 4/3
5027/ 4/3 = 3770.25
evaluate the answer
12 • (-5/4)
Answer:
-15
Step-by-step explanation:
12 * (-5/4)
= -60/4
= -15
Which equation will Alex want to use to determine the total amount of
food ( f ) a dolphin will eat over 5 years if a dolphin eats x pounds of food
per year?
A. f = 5 + x
B. f = 5x
C. f = [tex]\frac{5}{x}[/tex]
D. f = [tex]\frac{x}{5}[/tex]
Answer:
f= 5x
Step-by-step explanation:
x is the amount of food you want over 5 years so you would have to times it to get the whole amount eaten after 5 years.
Simplify: 1/2(8 - 6y) + 1/5(10y - 25)
Hey there!
1/2(8 - 6y) + 1/5(10y - 25)
DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES
= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)
= 4 - 3y + 2y - 5
COMBINE the LIKE TERMS
= (-3y + 2y) + (4 - 5)
= -3y + 2y + 4 - 5
= -1y - 1
≈ -y - 1
Therefore, your answer is: -y - 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Need help suck on this problem
Hi!
Given:
[tex]2xy*xy^2[/tex] if [tex]x=2[/tex] and [tex]y=4[/tex]
Plug in the numbers for [tex]x[/tex] and [tex]y[/tex]
[tex]2(2)(4)*(2)(4)^2[/tex]
Using PEMDAS (Order of Operations - see below), simplify exponents first:
[tex]2(2)(4)*(2)(16)[/tex]
Multiply from left to right:
[tex](4)(4)*(2)(16)[/tex]
[tex]16*32[/tex]
[tex]512[/tex]
Your answer is 512.
-------------------------------------------------------------------------------------------------------------
ORDER OF OPERATIONS:
P - Parentheses
E - Exponents
M/D - Multiplication/Division
A/S - Addition/Subtraction
-------------------------------------------------------------------------------------------------------------
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Which is the graph of the function y=3x^2?
Answer:
Top left
Step-by-step explanation:
Since the function has a degree of 2, the curve must have a parabolic (u) shape. The only option that satisfies this is the top left graph.
HELP PLEASE!!!!!!!!!!!! 100 bonus points!!!! NO LINKS OR GUESSES!
Answer:
The amount increased by 102 units. The amount has increased by 120%
Step-by-step explanation:
187-85=102
85x=187
(187/85)-1=1.2
1.2*100=120
Answer:
Step-by-step explanation:
187 - 85 = 102
( 102 ÷ 85 ) × 100 = 120
I hope everyone is having a lovely day!! Why is 3x+1 considered an impossible equation to solve? (basically TAKE THE POINTS!) :D love y'all!
Answer: there is no x on either sides of the equation
Step-by-step explanation:
Answer:
I answered in comments but I want the points :p
Step-by-step explanation:
Madison is entering a bicycle race for charity. Her mother pledges $0.80 for every .5 miles she bikes. If Madison bikes 12 miles, how much will her mother donate?
Answer:
19.2
Step-by-step explanation: take 0.80 and multiply by 24 instead of 12 so you can count the half mile
of the 35 students on student counsil 60% of the students are boys how many are girls
Known facts:
total number of students on the council: 3560% of the council students are boysResults:
therefore 40% of the total number of council students are girls.Calculation:
[tex]\frac{40}{100} *35=14[/tex]
Therefore there are 14 girls.
Hope that helps!
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
?
Answer:
9ft
Step-by-step explanation:
14 ft (top) - 5ft (bottom) = missing side (which is 9ft)
Answer:
9ft
Step-by-step explanation:
suppose that the side of 7ft was dragged to the right till it meets the side of 4ft
and the unknown side was dragged downwards till it meets the side of 5ft
Then, also considering that all angles are right angles, this structure becomes a square.
So the answer is 14ft - 5ft = 9ft
Jessica is building a cardboard box that has a length of 16 inches, width of 9 inches, and height of 4 inches. If she decided to triple the height of the box, how much more cardboard does she need?
Answer:
Step-by-step explanation:
I assume you have a prism with a length of 16 inches, a width of 9 inches and a height of 4 inches and you want to know the surface area
1st...convert these to feet
16 in = 1 + 1/3 ft = 4/3 ft
9 in = 3/4 ft
4 in = 1/3 ft
And the surface area =
2 [ 4/3 * 3/4 + 4/3 * 1/3 + 3/4* 1/3 ] =
2 [ 1 + 4/9 + 1/4 ] =
2 [ ( 36 + 16 + 9 ) / 36 ] =
(1/18) ( 61) =
(61 / 18) sq ft ≈ 3.38 sq ft.
(9.7 x 10^6) + (8.3 x 10^5)=
Hey there!
9.7(10^6)+8.3(10^5)
9.7(1,000,000) + 8.3(100,000)
9,700,000+830,000
=10,530,000
A tropical storm has been moving at 15 miles per hour for the past two days Bess recorded that the storm moved 135 miles yesterday and 75 miles today for how many hours has Bess been keeping track of the storm draw a bar diagram and a write equation to help you solve
About how many cells are in the human body?
You can assume that a cell is a sphere with radius 10-3 cm and that the density of a cell is approximately the density of water which is 1g/cm3.
please explain
I think its 30 trillion cells
hope it helps
f(x) = 2x + 7 Find a solution for the function if the dependent variable has a value of -1 Identify the independent and dependent variables. In the form of a paragraph, explain the steps necessary to find the solution. Complete your work in the space provided.
Answer:
x=-4
Step-by-step explanation:
-1=2x+7
-1-7=2x
2x=-8
x=-8/2=-4
Consider the following expression and determine which statements are true.
7
- 23
+ 11
Choose 2 answers:
The entire expression is a sum
В
The coefficient of sis 3.
The term is a quotient
T
The term 2 has a variable.
Answer:
The answer is -5 well that's what I think if you go in order so it would not be The entire explanation is a sum so that leaves three more The coefficient of sis 3, The term is a quotient T, and The term has a variable so And I think the answers are The term is the quotient T and the term 2 has a variable. Hopefully, this is helpful.
Step-by-step explanation:
Triangle ABC has vertices A(1,4), B(-2,4), and C(-1, -1). A dilation with a scale factor of 0.25 and center at the origin is applied to the triangle
What are the coordinates of B' in the dilated image?
Enter your answer by filling in the boxes.
B' has a coordinate pair of (__,__)
Please help! There is no picture btw
[Figured it out (see comments), putting this here so that it stops showing up as unanswered]