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3 years ago

Write the following inequality in slope-intercept form. 12x-3y≤-21

Mathematics

2 answers:

VladimirAG [237]3 years ago

4 0

Answer:

$y\geq4x+7$

Step-by-step explanation:

$12x-3y\leq -21$

To get slope intercept for of inequality we need to get y alone

To isolate y , first we subtract 12x on both sides

$12x-3y\leq -21$

$-3y\leq -12x-21$

Now we divide each term by -3

When we divide an inequality by a negative number then we reverse the inequality sign ≤ becomes ≥

$y\geq4x+7$ (inequality in slope intercept form)

Brut [27]3 years ago

3 0

12x - 3y ≤ -21
Subtract 12x from both sides
-3y ≤ -12x - 21
Divide both sides by -3.
y $\geq$ 4x + 7

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3 years ago

You are running a race. The probability that you win is 3/5. What is the probability that you lose at most 2 out of your 6 races

Veronika [31]

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 races

r = number of success = at most 2 lost

p = probability of success which in our question is probability that

you lose a race = 1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$

= $1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}$

= 0.54432

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3 years ago