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Goryan [66]
3 years ago
10

A group of 10 people need to form a line. The line will consist of exactly 8 of the people. Person X and Person Y have to be eit

her fifth or sixth in line. How many different orders are possible?
Mathematics
1 answer:
skad [1K]3 years ago
6 0

Answer: N = 40,320

Step-by-step explanation:

To arrange 10 people to a line of 8 people.

The number of ways is n = 10P8.

But since the condition given states that 2 people must stay in two particular slots.

The number of possible arrangements becomes;

N = number of ways of arranging the remaining people × number of ways of arranging the other 2.

N = 8P6 × 2P2

N = 8!/2! × 2!

N = 20,160 × 2

N = 40,320 ways

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Point C is in the interior of angle DEF. If angle DEC and angle CEF are congruent, then segment EC is the _____ of angle DEF.
emmasim [6.3K]

Answer:

Option A

Step-by-step explanation:

Line EC splits the angle into two equal angles so it is an angular bisector of DEF.

7 0
3 years ago
Q.23 Prove that: (sin4A - cos4A + 1) = 2sin2A
FrozenT [24]

Answer:

Step-by-step explanation:

I think you have the question incomplete, and that this is the complete question

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

To do this, we can start my mirroring the equation.

x² + y² = (x + y)² - 2xy,

This helps us break down the power from 4 to 2, so that we have

(sin²a)² + (cos²a)² = (sin²a + cos²a) ² - 2(sin²a) (cos²a)

Recall from identity that

Sin²Φ + cos²Φ = 1, so therefore

(sin²a)² + (cos²a)² = 1² - 2(sin²a) (cos²a)

On expanding the power and the brackets, we find that we have the equation proved.

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

4 0
3 years ago
There are 680 raisins in 8 bags. If each bag has the same number of raisins, how many raisins are in 12 bags?
dmitriy555 [2]

Answer:

  1020 raisins

Step-by-step explanation:

The problem tells you the number of raisins is proportional to the number of bags, so there will be "r" raisins in 12 bags:

  r/12 = 680/8 = raisins/bag

  r = (12/8)(680) = 1020

There will be 1020 raisins in 12 bags.

6 0
3 years ago
The pie chart shows the information about the favourite ice creme flavour of each student in a schcool.There are 720 students at
Novay_Z [31]

Answer:

there would be many diffrent answers

Step-by-step explanation:

provide the full question, i can deduct that there are many ice cream flavors.

6 0
3 years ago
What is the value of x in the equation below?
zubka84 [21]
First you multiply 6(x) then you multiple 6(8)

Your equation should now look like this: 6x-48=72

Subtract 48 from both sides

Your equation should now look like 6x=120

Divide by 6

Answer is 20
7 0
2 years ago
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