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3 years ago

In how many arrangements can 3 boys and 4 girls stand in a row such that no two boys are together?

Mathematics

1 answer:

Sophie [7]3 years ago

5 0

Answer: 1440

Step-by-step explanation:

To arrange 3 boys and 4 girls such that no two boys are together.

Since boys should be arranged between the girls.

So first arrange the girls.

Assume that the girls are placed, then there will be 5 spaces left for 3 boys.

The number of combinations to fill these places = $^5C_3=\dfrac{5!}{3!2!}=\dfrac{5\times4}{2}=10$

Also, 3 boys can arrange themselves in 3! =3 x 2 x 1 = 6 ways

4 girls can arrange themselves in 4! = 4x 3 x 2 x 1 = 24 ways

Then, the total number of arrangements = 10 x 6 x 24 = 1440

Hence, the required number of arrangements = 1440

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The average speed to go by car from home to college is 30 miles per hour. The average speed to go back home from college is 20 m

Levart [38]

Answer:

24 mph for both 60 miles and 40 miles.

Step-by-step explanation:

We need to find how long it takes to get to college and from it.

Speed x time (x) = Distance (60)

30x = 60

x=2

It takes two hours to get to college

20x = 60

x = 3

It takes 3 hours to get back. It's a total of 5 hours, 2 hours at 30mph and 3 at 20. Now we need to find the average

30+30+20+20+20=120

120/5= 24

The average speed for the round trip is 24.

To do the second part, we follow the same process, but replace 60 with 40 for distance.

30x=40

x= 1.33

20x=40

x=2

We can add the total distance and divide by total time to find the average.

The total distance is 80. Time is 3.33

80/3.33=24

The average speed is still 24.

3 0

3 years ago

A researcher determines that students are active about 60 + 12 (M + SD) minutes per day. Assuming these data are normally distri

rjkz [21]

Answer:

The correct option is (b).

Step-by-step explanation:

If X $\sim$ N (µ, σ²), then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z $\sim$ N (0, 1).

The distribution of these z-variate is known as the standard normal distribution.

The mean and standard deviation of the active minutes of students is:

μ = 60 minutes

σ = 12 minutes

Compute the z-score for the student being active 48 minutes as follows:

$Z=\frac{X-\mu}{\sigma}=\frac{48-60}{12}=\frac{-12}{12}=-1.0$

Thus, the z-score for the student being active 48 minutes is -1.0.

The correct option is (b).

4 0

3 years ago

What is root 3 × 2 root 3

Nezavi [6.7K]

Answer:

Step-by-step explanation:

The principal, real, root of:

$\sqrt[2]{3}$

=1.73205081

All roots:

1.73205081

−1.73205081

3 is not a perfect square

5 0

3 years ago

Or the past 100 years, the average high temperature on october 1 is 78° with a standard deviation of 5°. what is the probability

valina [46]

Answer:

The probability is 0.683

Step-by-step explanation:

To calculate this, we shall be needing to calculate the z-scores of both temperatures

mathematically;

z-score = (x-mean)/SD

From the question mean = 78 and SD = 5

For 73

z-score = (73-78)/5 = -5/5 = -1

For 83

z-score = (83-78)/5 = 5/5 = 1

So the probability we want to calculate is within the following range of z-scores;

P(-1 <z <1 )

Mathematically, this is same as ;

P(z<1) - P(z<-1)

Using the normal distribution table;

P(-1<z<1) = 0.68269 which is approximately 0.683

3 0

4 years ago

Find the volume of the prism. 3 ft 7 ft 5 ft

Taya2010 [7]

Answer:

105

Step-by-step explanation:

I am guess this prism is a rectangle

So 3 times 7 times 5 is 105

Thus the answer is 105

Hope this helps!

6 0

3 years ago

Read 2 more answers