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3 years ago

Select all possible values for x if −3x < 15.

Mathematics

2 answers:

makkiz [27]3 years ago

4 0

Step-by-step explanation:

When dividing or multiplying by a negative number, remember to flip the inequality sign.

-3x < 15

x > -5 (divide -3 on both sides, flip the inequality sign)

The correct options are 2 and 9. (D and E)

Maru [420]3 years ago

4 0

Answer:

D. 2

E. 9

Step-by-step explanation:

$- 3x < 15 \\ \\ x > \frac{15}{ - 3} \\ \\ x > - 5 \\ \\$

Since x > - 5,

Therefore possible values of x would be 2 and 9 out of the given ones.

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3 years ago

Need help on probability. Please explain how you did it so I can know how to do it.

Galina-37 [17]

Answer:

$\text{P}(B \text{ or }C)=\dfrac{5}{6}$

Step-by-step explanation:

Mutually Exclusive Events

For two events, A and B, where A and B are mutually exclusive:

$\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}$

Probability distribution table:

$\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}$

where X is the score on a fair, six-sided dice.

P(B or C) means "the probability of rolling an even number or a multiple of 3".

As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.

Calculate the probabilities for events B and C.

Event B

Rolling an even number.

$\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}$

Event C

Rolling a multiple of 3.

$\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}$