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Pavlova-9 [17]
3 years ago
8

HELP! i’m confused! question is in the picture

Mathematics
1 answer:
TEA [102]3 years ago
4 0

Answer:

[-6,-3]

Step-by-step explanation:

So we have the compound inequality:

2x+7\leq x+4\leq 3x+16

Let's solve for each of the inequalities:

1)

We have:

2x+7\leq x+4

Subtract x from both sides:

x+7\leq 4

Subtract 7 from both sides:

x\leq -3

So that's one of our answers.

2)

We have:

x+4\leq 3x+16

Subtract 3x from both sides:

-2x+4\leq 16

Subtract 4 from both sides:

-2x\leq 12

Divide both sides by -2. Since we're dividing by a negative, flip the sign:

x\geq -6

Therefore, our entire answer is:

-6\leq x\leq -3

This means all values in between -3 and -6 including -3 and -6.

In interval notation, this is:

[-6,-3]

So, A is -6.

And B is -3.

And we're done :)

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Answer: (1) d, f     (2) c, d, f     (3) e, f      (4) a, b, c, d, f     (5) e, f

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

a) Natural Numbers:            1, 2, 3, ...

b) Whole Numbers:          0, 1, 2, 3, ...     <em>(add zero to the Natural numbers)</em>

c) Integers:   ..., -3, -2, -1, 0, 1, 2, 3, ...   <em>(add negatives to the Whole numbers)</em>

d) Rationals: Add terminating and repeating decimals to Integers.

************

e) Irrationals: Non-repeating decimals that are non-terminating.  <em>This is its own category so cannot be a Rational number or above.</em>

f) Real Numbers: ALL of the above (a - e) are Real numbers.

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3 years ago
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blsea [12.9K]

Answer:

\textbf{$P(S \cap T) = \frac{89}{90}$ }\\

Step-by-step explanation:

\textup{Mutually events are events that cannot occur at the same time.}\\\textup{When you toss a coin you get only $head$ or only $tail$ but never both.}\\ \textup{In mathematical terms $P(A) \cup  P(B) = 0$, where $A$ and $B$ are mutually exclusive events. }\\\textup{We know the formula:}\\$$ P(A \cup B) = P(A) + P(B) - P(A \cup B) $$\\\textup{When $A$ and $B$ are mutually exclusive, it will simply be:}\\$$ P(A \cup B) = P(A) + P(B) $$\\\textup{Now given:}\\ $P(S) = 8/9$ , $P(T) = 1/10$\\

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3 years ago
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