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erik [133]
3 years ago
13

Keiko has seven colors of lanyard. She uses three different colors to make a keychain. How many different combinations can she c

hoose?
Mathematics
1 answer:
AleksAgata [21]3 years ago
7 0
Combination = doesn't matter what order
Permutation = order matters

There are <u>two</u> methods to work out combinations.

Method 1 List out possibilities
123 124 125 126 127 134 135 136 137 145 146 147 156 157 167
234 235 236 237 245 246 247 256 257 267
345 346 347 356 357 367
456 457 467
567

For a total of 35 combinations.

Method 2 Use a formula.
It's a rather complicated one, so only use it if you have a lot of possibilities.

\frac{n!}{r!(n-r)!} = \frac{7!}{3!(7-3)!} = \frac{7!}{3!*4!} = \frac{7*6*5*4*3*2*1}{3*2*1*4*3*2*1} = \frac{7*6*5}{3*2*1}=\frac{210}6=35

(n is the number of choices, r is the amount you choose, and ! is a function that multiplies together all numbers down to 1)


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Remy drinks 214 cups of water every 145 hours.
Tcecarenko [31]

Answer:

1  69/145 cups

Step-by-step explanation:

We can use ratio's to solve this problem.  We will put water over time

214 cups           x cups

--------------- = --------------

145 hours        1 hours


Using cross products

214 *1 =145 x

Divide both sides by 125

214/145 = 145x/145

214/145 = x

145 goes into 215 1 time with 69 left over

1 69/145


4 0
3 years ago
Read 2 more answers
Given QT = SR, QV = SU, and the diagram, prove that triangles QUT and SVR are congruent. Write a paragraph proof.
QveST [7]

Answer:

Triangles QUT and SVR are congruent because the defining two sides and an included angle of triangles QUT and SVR are equal

Step-by-step explanation:

Here we have QT = SR and

QV = SU

Therefore,

QT = √(UT² + QU²)........(1)

RS = √(VS² + RV²)..........(2)

Since QS = QU + SU = QV + VS ∴ QU = VS

Therefore, since SR = QT and QU = VS, then from (1) and (2), we have UT = RV

Hence since we know all sides of the triangles QUT and SVR are equal and we know that the angle in between two congruent sides of the the triangles QUT and SVR that is the angle in between sides QU and UT for triangle QUT and the angle in between the sides RV and VS in triangle SVR are both equal to 90°, therefore triangles QUT and SVR are congruent.

5 0
3 years ago
Leslie decides to join a gym. She must pay a monthly fee plus a one time fee to open a membership. This situation can be modeled
omeli [17]

Step-by-step explanation:

Given function is,

y=55x+80

Where,

y = amount paid to the gym in dollars

x = number of months

So when x = 0, y =55(0)+80 = 80

i.e when number of months is 0, you have to pay a fee of $80.

This is the one time fee to open a membership.

After that for each month you have to pay $55 for each months.

So 55 is multiplied with x.

3 0
2 years ago
Please help is for now
cupoosta [38]
3 because I did the quiz and got it right txt me if you need help
8 0
3 years ago
Read 2 more answers
Find the 67th term of the arithmetic sequence –17, -23, -29,...
Maksim231197 [3]

Answer:

T₆₇ = -413

Step-by-step explanation:

7 0
3 years ago
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