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2 years ago

How many positive integer factors of 100 factorial, are multiples of 2 or 3?

Mathematics

1 answer:

ikadub [295]2 years ago

5 0

100 factorial is 1*2*3*......*100

Number of multiples of 2 less than 100 = 49

Number of multiples of 3 less than 100 = 33

We are double counting those that are multiples of 2 and 3 (or 6)

Number of multiples of 6 less than 100 = 16

49+33-16 =66

There are 66 factors that are multiples or 2 or 3

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what is the y-intercept of the line perpendicular to the line y=-3/4x+5 that includes the point (-3,-3)?

Deffense [45]

Answer:

Step-by-step explanation:

For this question, your friend is the point-slope form.

Point-slope form = $y-y_1 = m(x-x_1)$

The only variables you replace are m = slope, y1 = y of a given point, and x1 = x of a given point.

First, we need to find the slope that is perpendicular to the equation $y=-\frac{3}{4}x+5$

An equation that is perpendicular to another equation have to be negative reciprocals (negative inverse) of each other.

If the slope is 3, then the negative reciprocal of 3 is $-\frac{1}{3}$ .

So, since the given slope is -3/4, the negative reciprocal is $\frac{4}{3}$ .

We will use the negative reciprocal as m since we are trying to find the equation of line that includes (-3, -3) and is perpendicular to the other equation.

We will use point slope form using the (-3, -3) points and negative reciprocal as m.

$y-y_1 = m(x-x_1)\\y-(-3) = \frac{4}{3} (x-(-3))\\y+3=\frac{4}{3}(x+3)$

Now, we need to convert this into slope-intercept form. The reason why we need to do this is because y = mx + b, where b is the y-intercept. To do this, solve for y - or in other words, isolate y..

$y+3=\frac{4}{3}(x+3)\\y+3=\frac{4x}{3}+4\\y+3-3=\frac{4x}{3}+4-3\\y=\frac{4}{3}x+1$

The y-intercept of the line is 1.

3 0

2 years ago

Each student in your class must do 14 homework problems. There are 23 students in the class. How many problems will your teacher

Ganezh [65]

Answer: 322

Step-by-step explanation:

23 students × 14 homework

=322 problems

The teacher will have to grade 322 problems

4 0

3 years ago

There is a number such that four times the number plus 3 is equal to 19. Find the number

frosja888 [35]

Answer:

Step-by-step explanation:

We have been given that it equals 19 when added to 3 and multiplied by 4 so follow these steps:

1. set the equation 4x+3=19

2. solve for x

4x+3-3=19-3

This is used to solve for x

3. 4x=16 is found

4. if 4x=16, we divide 16/4 and get 4!

That's your answer hope it helped!

3 0

3 years ago

Read 2 more answers

If two different people are randomly selected from the 864 subjects, find the probability that they are both heavy smokers. Roun

AlekseyPX

Answer:

P = 0.008908

Step-by-step explanation:

The complete question is:

The table below describes the smoking habits of a group of asthma sufferers

Nonsmokers Light Smoker Heavy smoker Total

Men 303 35 37 375

Women 413 31 45 489

Total 716 66 82 864

If two different people are randomly selected from the 864 subjects, find the probability that they are both heavy smokers.

The number of ways in which we can select x subjects from a group of n subject is given by the combination and it is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

Now, there are 82C2 ways to select subjects that are both heavy smokers. Because we are going to select 2 subjects from a group of 82 heavy smokers. So, it is calculated as:

$82C2=\frac{82!}{2!(82-2)!}=3321$

At the same way, there are 864C2 ways to select 2 different people from the 864 subjects. It is equal to:

$864C2=\frac{864!}{2!(864-2)!}=372816$

Then, the probability P that two different people from the 864 subjects are both heavy smokers is:

$P=\frac{82C2}{864C2}=\frac{3321}{372816}=0.008908$

4 0

2 years ago

What is 64x12 – 1,000 written as a difference of cubes? (4x)3 – 103 (8x)3 – 1003 (4x4)3 – 103 (8x4)3 – 1003

Ksju [112]

We have to choose the correct answer and to show what is 64 x^12 - 1,000 written as a difference of cubes.
64 = 4^3
x^12 = ( x^4 )^3
1,000 = 10^3
Finally:
64 x^12 - 1,000 = ( 4 x^4 )^3 - 10^3
Answer:
C ) ( 4 x^4 )^3 - 10^3

8 0

2 years ago

Read 2 more answers