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3 years ago

The expression 27 + 45 as a product using the GCF and distributive property.

Mathematics

1 answer:

Bogdan [553]3 years ago

5 0

Answer:

(a) By Greatest Common Factor: (27 + 45 ) = 3( 9 + 15)

(b) By distributive property: (27 + 45 ) = 9(3) + 9(5)

Step-by-step explanation:

Here, the given expression is 27 + 45 .

Now, by Prime Factorization:

27 = 3 x 3 x 3

45 = 3 x 3 x 5

Here, the 3 is the ONLY prime common factor.

So, the Greatest Common Factor = 3

⇒ (27 + 45 ) = 3( 9 + 15)

Hence, by Greatest Common Factor: (27 + 45 ) = 3( 9 + 15)

Now, by distributive property:

A( B + C) = AB + AC

Here, in the given expression:

(27 + 45 ) = 9 ( 3 + 5) = 9(3) + 9(5)

or, (27 + 45 ) = 9(3) + 9(5)

Hence, by distributive property: (27 + 45 ) = 9(3) + 9(5)

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A fruit stand sells apples, peaches and tomatoes. Today, they sold 4 apples for every 5 peaches. They sold 2 peaches for every 3

Brrunno [24]

Answer:

He sold 32 apples, 40 peaches and 60 apples.

Step-by-step explanation:

We are given that

4 apples are sold every 5 peaches and

3 tomatoes are sold every 2 peaches.

i.e. the ratio is apples: peaches = 4 : 5 ...... (1)

and the ratio peaches: tomatoes = 2 : 3 ...... (2)

Peaches are the common link here in both the ratio terms.

Let us make the peaches value in both the <em>ratio as 10 </em>to make it equal in both the ratio terms.

Multiply (1) by 2 and (2) by 5:

The ratio becomes;

apples:peaches = 8:10

peaches: tomatoes = 10:15

In other words, the ratio becomes:

apples:peaches:tomatoes = 8:10:15

Let the number of apples = $8x$

Let the number of peaches = $10x\\$

Let the number of tomatoes = $15x$

We are given that total fruits are = 132

$\Rightarrow 8x+10x+15x = 132\\\Rightarrow 33x = 132\\\Rightarrow x =4\\$

So, number of apples sold = $8 \times 4 = 32$

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3 years ago

Suppose that lithium calculator battery with a charge of 3 volts, actually has a voltage with uniform distribution between 2.93

Dmitrij [34]

Answer:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

$M = \frac{a + b}{2}$

The standard deviation of the uniform distribution is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

Uniform distribution between 2.93 and 3.1 volts

This means that $a = 2.93, b = 3.1$ . So

Mean:

$M = \frac{2.93 + 3.1}{2} = 3.015$

Standard deviation:

$S = \sqrt{\frac{(3.1 - 2.93)^{2}}{12}} = 0.049$

What is the probability that a battery has a voltage less than 2.98?

$P(X \leq 2.98) = \frac{2.98 - 2.93}{3.1 - 2.93} = 0.2941$

So the correct answer is:

b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941

6 0

2 years ago