How many students in ms. Leal class are more than 42 inches tall?

Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

8 0

3 years ago

your $440 gets 5.8% interest compounded annually for for 8 years what will your $440 be worth in 8 years l?

Dmitriy789 [7]

Answer:

The answer is $690.78

Step-by-step explanation:

7 0

2 years ago

Braydon is at the 10-mile Marker at the park to run. He can run at a pace of 3 miles per hour. Lauren is at the 12-mile marker a

madreJ [45]

it will take 1.33 hours for Braydon and Lauren to get to the same mile marker on the path in the park .

<u>Step-by-step explanation:</u>

Here we have , Braydon can run at 3 miles per hour , he's initially at 10 mile marker . Lauren is at the 12-mile marker at the park, She is walking at a pace of 1.5 miles per hour. We need to find How long will it take for Braydon and Lauren to get to the same mile marker on the path in the park .Let's find out:

Let after time t they meet each other so , Braydon can run at 3 miles per hour , he's initially at 10 mile marker . Distance traveled is given by :

⇒ $3t+10$

Now , Lauren is at the 12-mile marker at the park, She is walking at a pace of 1.5 miles per hour , Distance traveled is given by :

⇒ $1.5t + 12$

Equating both we get :

⇒ $3t+10=1.5t+12$

⇒ $1.5t=2$

⇒ $t=\frac{2}{1.5}$

⇒ $t=1.33$

Therefore , it will take 1.33 hours for Braydon and Lauren to get to the same mile marker on the path in the park .

7 0

2 years ago

Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? E

slamgirl [31]

Answer:

Diego is correct.

He has correctly divided 1 in groups of $\frac{5}{6}$ .

Step-by-step explanation:

The question 'How many groups of 5/6 are in 1?' means that we need to divided 1 into groups of $\\frac{5}{6}$ .

When we form groups from a given total, we divided the total by the size of the group.

If we are dividing $N$ number of people in groups of $x$ number of people, then the expression to find the number of groups formed can be given as:

⇒ $\frac{N}{x}$

For this question the data given is:

$N=1$

$x=\frac{5}{6}$

So, the number of groups formed can be given as:

⇒ $\frac{1}{\frac{5}{6}}$

When divisor is a fraction, then we multiply the reciprocal of the divisor with the dividend.

⇒ $1\times\frac{6}{5}$

⇒ $\frac{6}{5}$

In order to convert fraction to mixed number we will divide numerator with denominator and then write the quotient as whole number, remainder as numerator and the denominator remains as it is.

On dividing 6 by 5, the quotient =1 and remainder =1. Thus the mized number is:

⇒ $1\frac{1}{5}$

Thus, there are $\frac{6}{5}$ or $1\frac{1}{5}$ groups in 1. This matches with Diego's answer and hence he is correct.

3 0

2 years ago

Is 19 a prime number or composite?

Alexandra [31]

Prime, because the only number that can go into it are 19 and 1

5 0

2 years ago

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