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3 years ago

Four couples have reserved seats in a row for a concert. In how many different ways can they be seated if

Mathematics

1 answer:

Murljashka [212]3 years ago

3 0

Answer:

a) 40320 ways

b) 384 ways

Step-by-step explanation:

a) if there are no seating restrictions, the number of ways the 4 couples can be seated is the permutation of 8 persons in 8 seats then

number of ways= permutation of 8 persons in 8 seats = 8! = 40320

b) if each couple will sit together then the number of ways is:

number of ways= number of permutation of 4 integrants of each couple in 4 pairs of seats * number of permutation for a couple in a pair of seats^ number of pair of seats = 4! * 2^4 = 384

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Please someone answer this.

klio [65]

The triangle ABC may be rotated along a fixed point, translated to a different position and reflected across a mirror line.

<h3>Types of transformation</h3>

The three types of transformation are;

Rotation
Reflection
Translation

Rotation of shapes entails moving them around a fixed point. The shape remains the same, but its position in the space changes.

Translating a shape means moving it entirely to a different position, without changing it in any way.

Reflecting a shape is to flip it across a mirror line. Each point in the shape is moved to the other side of the mirror line but has same distance away from the line. The reflected image faces the opposite direction to the original object.

Thus, the triangle ABC may be rotated along a fixed point, translated to a different position and reflected across a mirror line.

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2 years ago

Sadie invested $13,000 in an account paying an interest rate of 2.3% compounded daily. Assuming no deposits or withdrawals are m

Yuki888 [10]

Answer: 11.4 (on delta math)

Step-by-step explanation:

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3 years ago

A car is traveling at a constant speed of 45 miles per hour. How many feet does it travel in 3 seconds? Remember that 1 mile is

Dafna1 [17]

First you can convert 45 miles per hour to feet per hour:

45 × 5,280 = 237,600 feet per hour

Now you must remember that there are 60 minutes in an hour, and 60 seconds in a minute. So you can divide 237,600 feet per hour by 60 to get feet per minute:

237,600 ÷ 60 = 3,960 feet per minute

Now you just have to divide 3,960 by 60 again to get feet per second:

3,960 ÷ 60 = 66 feet per second

Now you know how fast the car can travel (in feet) in a second. So to work out how many feet it travels in 3 seconds, you just have to multiply 66 by 3:

66 × 3 = 198 feet

Therefore your final answer is <em>198 feet</em> :)

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3 years ago

If a $500 investment receives 4% interest per year, how long will it take for the investment to double? Pls help

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3 years ago

Read 2 more answers

Write an equation perpendicular to x - 4y = 20 that passes through the point (4, -3)

Nina [5.8K]

Answer:

y = - 4x + 13

Step-by-step explanation:

In order to do this problem you would need a whole new equation, but you will use what is given to you:

instead of going with:

x - 4y = 20

Turn it into y = mx + b form, also known as slope-intercept form:

x - 4y = 20

-x = -x

_________

- 4y = 20 - x

Then divide both sides by - 4:

$\frac{-4y}{-4} = \frac{-x + 20}{-4}$

You will then get:

y = $\frac{1}{4}x - 5$

From this equation we will only need the slope!

m || = $\frac{1}{4}$

(This slope is for parallel)

but if you want perpendicular to the slope, then we need the negative reciprocal!

Negative reciprocal is a flipped version of the value that is negative, for example:

2 = $-\frac{1}{2}$

Because $\frac{2}{1}$ = 2

Now we will find the perpendicular slope which is:

m ⊥ = - 4

Now substitute this slope into slope intercept form:

y = mx + b

(-3) = -4(4) + b

(Take away parentheses)

-3 = -16 + b

(Move - 3 to the other side, by making it positive, but what you do to one side, you do to the other)

= -13 + 6

(Move - 13 to the other side, by make - 13 into +13)

+13 = +13

________

13 = b

(This is you b, also known as you intercept)

Your answer is:

y = -4x + 13

8 0

3 years ago