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3 years ago

The number of ways 8 cars can be lined up at a toll booth would be computed from

Mathematics

1 answer:

stepladder [879]3 years ago

5 0

Answer: c. 8!

Step-by-step explanation:

We know , that if we line up n things , then the total number of ways to arrange n things in a line is given by :-

$n!$ ( in words :- n factorial)

Therefore , the number of ways 8 cars can be lined up at a toll booth would be 8! .

Hence, the correct answer is c. 8! .

Alternatively , we also use multiplicative principle,

If we line up 8 cars , first we fix one car , then the number of choices for the next place will be 7 , after that we fix second car ,then the number of choices for the next place will be 6 , and so on..

So , the total number of ways to line up 8 cars = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1 = 8!

Hence, the correct answer is c. 8! .

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each morning a gardener uses 24 3/4 gallons of water from a barrel. each afternoon, she adds 15 1/4 gallons of water to the barr

Nimfa-mama [501]

Answer:

$47\frac {1}{2}\ gallons$

Step-by-step explanation:

Assuming that the tank is only for agricultural use, also no significant leakages then at the end of the day, the amount consumed will be equivalent to $24\frac {3}{4}-\ 15\frac {1}{4}=9\frac {1}{2}$

For 5 days, the quantity reduces by 9.5*5=47.5 gallons

Therefore, the barrel would have changed by $47\frac {1}{2}\ gallons$

6 0

3 years ago

Find a polar equation for the conic with its focus at the pole and the given vertex or vertices:

Schach [20]

Answer:

A) r = 2/(1 - sinθ)

B) r = 16/(5 + 3 cosθ)

C) r = 2/(1 + 2 cosθ)

Step-by-step explanation:

A) We are given the parabola vertex as:

(r, θ) = (1, -π/2)

The vertex coordinates indicates that it's below the pole and thus the equation of the conic section is represented by;

r = ed/(1 - e sinθ)

Since the equation is a parabola, then the eccentricity is 1.

Thus,plugging in the relevant values;

1 = (1 × d)/(1 - (1 × sin-π/2))

1 = d/(1 - (-1))

1 = d/(1 + 1)

1 + 1 = d

d = 2

Therefore the general equation would be gotten by putting 2 for d and 1 for E.

Thus;

r = (1 × 2)/(1 - (1 × sinθ))

r = 2/(1 - sinθ)

B) vertices of Ellipse are given as;

(2,0) and (8, π)

The equation will be represented by;

r = ep/(1 + e cosθ)

Where e which is the eccentricity is given by: e = c/a

c = (8 - 2)/2

c = 6/2

c = 3

And, a = (8 + 2)/2

a = 10/2

a = 5

Thus,e = 3/5

Thus;

r = (3/5)p/(1 + (3/5) cosθ))

Multiply both numerator and denominator by 5;

r = 3p/(5 + 3 cosθ))

Now, using the vertex (2,0) and plugging it, we have;

2 = 3p/(5 + 3 cos0))

2 = 3p/(5 + 3(1))

2 = 3p/8

p = 16/3

Thus,the equation is;

r = 3(16/3)/(5 + 3 cosθ))

r = 16/(5 + 3 cosθ)

C) Since the directrix is x = p, then the function in the denominator would be cosine. This is because x = 4 which is greater than 0.

It means that there will be an addition sign in the denominator. We use the standard form of;

r = ep/(1 + e cosθ)

So, e = 2 and p = 1

Then;

r = (2 × 1)/(1 + 2 cosθ)

r = 2/(1 + 2 cosθ)

3 0

3 years ago

A frozen pizza cost $3.00 in 2000. In 2015 it cost $2.50

user100 [1]

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3 years ago

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Find the inverse of the given function.<br><br> f(x) = -1/2√x + 3, x ≥ -3

inna [77]

<span>Find the inverse of the given function.

f(x) = -1/2√x + 3, x ≥ -3

I will have to assume that you meant f(x) = -(1/2)sqrt(x) + 3. If you actually meant f(x) = -(1/2)sqrt(x+3), then obviously the correct result would be different.

1. Replace "f(x)" by "y:" y </span>= -(1/2)sqrt(x) + 3
2. Interchange x and y: x = -(1/2)sqrt(y) + 3
3. Solve for y: x-3=-(1/2)sqrt(y), so that 2(3-x)= sqrt(y) and y=+sqrt(2[3-x])
4. Replace "y" with

-1
f (x) = sqrt(2[3-x])

Here, there are restrictions on x, since the domain of the sqrt function does not include - numbers. The domain here is (-infinity,3]

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3 years ago

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Ted likes to run long distances. He can run 20 km 95 minutes. He wants to know how many kilometers (k) he will go if he runs at

maxonik [38]

He will run 60km in 285 minutes.

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3 years ago

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