Convert the measurement. Use unit fractions or the metric conv

1. You and your friend are going to Boston but

Nataly [62]

Answer:

speed acquired by me = 40 miles / hour

speed acquired by my friend = 50 miles / hour

Step-by-step explanation:

Here's the solution :-

time taken by both = 6 hours

( 10 AM - 4 PM )

1. Now, the required speed for me to reach boston at 4 PM is :

=》

$\frac{distance}{time}$

=》

$\frac{240}{6}$

=》

$40 \: mph$

2. Now, the required speed for my friend to reach boston at 4 PM is :

=》

$\frac{distance}{time}$

=》

$\frac{300}{6}$

=》

$50 \: mph$

3 0

3 years ago

Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 33% of all homeowners are ins

Lina20 [59]

Answer:

(a) The probability mass function of X is:

$P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...$

(b) The most likely value for X is 1.32.

(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.

Step-by-step explanation:

The random variable X is defined as the number among the four homeowners who have earthquake insurance.

The probability that a homeowner has earthquake insurance is, p = 0.33.

The random sample of homeowners selected is, n = 4.

The event of a homeowner having an earthquake insurance is independent of the other three homeowners.

(a)

All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.

The probability mass function of X is:

$P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...$

(b)

The most likely value of a random variable is the expected value.

The expected value of a Binomial random variable is:

$E(X)=np$

Compute the expected value of X as follows:

$E(X)=np$

$=4\times 0.33\\=1.32$

Thus, the most likely value for X is 1.32.

(c)

Compute the probability that at least two of the four selected have earthquake insurance as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015$

Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.

3 0

3 years ago

What is 5/12 + 5/12?

agasfer [191]

Answer:

$\frac{5}{6}$

Step-by-step explanation:

1) Join the denominators.

$\frac{5 + 5}{12}$

2) Simplify.

$\frac{10}{12}$

3) Simplify.

$\frac{5}{6}$

Therefor, the answer is 5/6.

and in decimal from it will be, 0.8333333.

5 0

2 years ago

The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle. Juan’s triangle is shown. Write a numerical expr

denpristay [2]

The perimeter of a triangle is the sum of all side lengths of the triangle. The numerical expression for the perimeter of Stephanie's triangle is: $\frac 12 \times 25$

Let the sides of Juan's triangle be x, y and z. So:

$x = 5 \\ y = 8\\ z = 12$

The perimeter (J) of Juan's triangle is calculated by adding all sides.

So:

$J =x +y +z$

This gives:

$J =5 + 8 + 12$

$J =25$

From the question, we understand that:

The perimeter (S) of Stephanie's triangle is half that of Juan.

This means that:

$S = \frac 12J$

Substitute 25 for J

$S = \frac 12 \times 25$

Hence, the numerical expression for the perimeter of Stephanie's triangle is: $\frac 12 \times 25$