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3 years ago

9

A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to

9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

1 answer:

miskamm [114]3 years ago

7 0

Answer:

The answer is 4536.

Step-by-step explanation:

Each number is to consist of four different digits(no repetition) from 0 to 9, except that the first digit cannot be 0.

Total numerals from 0 to 9 = 10

For 1st place you have 9 options for 1st digit (0 is not selected here).

For the 2nd place you again have 9 numbers (0 is available but 1 digit less from 10 as it is already selected in first place) so, you get 9c1 ways = 9

For the 3rd place you have 8c1 ways = 8

For the 4th place you have 7c1 ways = 7

Total number of identification numbers are : $9\times9\times8\times7=4536$

Therefore, there are 4536 different identification numbers.

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An aquarium has a base in the shape of a trapezoid. The base is 100

Nat2105 [25]

Answer:

$Volume = 210L$

Step-by-step explanation:

Given

Base:

$Front = 100cm$

$Back = 50cm$

$Width = 40cm$

$Height = 70cm$

Required

Determine the volume (in litres)

First, we need to calculate the area;

Base on the parameters given, we have:

$Area = \frac{1}{2}(Front + Back) * Width$

$Area = \frac{1}{2}(100cm + 50cm) * 40cm$

$Area = \frac{1}{2}(150cm) * 40cm$

$Area = 75cm * 40cm$

$Area = 3000cm^2$

$Volume = Area * Height$

$Volume = 3000cm^2 * 70cm$

$Volume = 210000cm^3$

$1cm^3 = 0.001L$

So:

$Volume = 210000 * 0.001L$

$Volume = 210L$

4 0

4 years ago

Joseph’s garden is 9 feet wide and 12 feet long. Alana’s garden is 7 feet wide and 25 feet long.

sertanlavr [38]

area of Josephs garden = 9*12 = 108 square feet

area for Alana's garden = 7 *25 = 175 square feet

175/108 = 1.62

Alan's garden is 1.62 times larger

3 0

3 years ago

3×the fraction blank 3 =1

Sedaia [141]

Answer:

1/3

Step-by-step explanation:

3 in fraction form =3/1

and 3/1 x 1/3= 3/3 or 1

3 0

3 years ago

What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides $12-2x$ and $16-2x$ , and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

$(12-2x)(16-2x)x = 4x^3-56x^2+192x$

The derivative of this function is

$12x^2-112x+192$

and it equals zero if and only if

$12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}$

If we evaluate the volume function at these points, we have

$f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)$

So, the maximum volume is given if you cut a square with side length

$x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7$

5 0

3 years ago

Dallia earns $108.75 for working 15 hours as a holiday helper for wrapping gifts. At this rate how much money will she earn if s

krek1111 [17]

She will earn $130.5 dollars.

First we find how much she makes per hour.
108.5/15=$7.25 per hour.

Then we take $7.25 per hour and she will work 18 hours next week so,
7.25•18=130.5 considering the same rate.

Now we can also make an equation which is,
7.25x=y in which x is the number of hours worked and y is the amount earned.
7.25(18)=130.5 :)

4 0

2 years ago