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1 year ago

Write the verbal sentence as an algebraic equation.

Mathematics

1 answer:

Dmitry_Shevchenko [17]1 year ago

6 0

Step-by-step explanation:

product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20

3×x +5=20

3x+5=20

Subtract 5 from both sides

3x+5-5=20-5

3x=15

3x/3=15/3

x=5

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If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

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Determine Upper P (Upper F or Upper G )using the general addition rule. Select the correct choice below and fill in any answer b

Lilit [14]

Answer:

S= {8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 }

event F= {10 , 11 , 12 , 13 , 14}

event G= {14 , 15 , 16 , 17}

a) List of outcomes in F or G

answer;

(F or G) = { 10 , 11, 12 , 13 , 14 , 15 , 16 , 17}

b) P ( F or G) = by counting the number of outcomes in F or G

Ans ( F or G) = No. of outcomes in ( F or G) / Total no. of outcomes

= 8/12 = 2/3

c) P ( F or G) using general addition rule

Ans P (F or G) = P(F) = P(G) - P( F and G)

= 5/12 + 4/12 - 1/12

= (5+4-1)/12 = 8/12 =2/3

Step-by-step explanation:

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