All categories

2 years ago

Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?

Mathematics

1 answer:

wolverine [178]2 years ago

6 0

ANSWER

$9\: < x \leqslant0$

EXPLANATION

The given compound inequality is

$- 33 \: > - 3x - 6 \geqslant - 6$

We need to simplify this inequality so that we can obtain x standing alone between the inequality signs.

We add 6 through out the inequality.

$- 33 + 6\: > - 3x - 6 + 6 \geqslant - 6 + 6$

This simplifies to:

$- 27\: > - 3x \geqslant 0$

We now divide through by -3 and reverse the inequality sign.

$\frac{- 27}{ - 3} \: < \frac{ - 3x}{ - 3} \leqslant \frac{0}{ - 3}$

We now simplify to get:

$9\: < x \leqslant 0$

You might be interested in

A really bad carton of eggs contains spoiled eggs. An unsuspecting chef picks eggs at random for his ""Mega-Omelet Surprise."" F

Dima020 [189]

Answer:

(a) The probability that of the 5 eggs selected exactly 5 are unspoiled is 0.0531.

(b) The probability that of the 5 eggs selected 2 or less are unspoiled is 0.3959.

Step-by-step explanation:

The complete question is:

A really bad carton of 18 eggs contains 8 spoiled eggs. An unsuspecting chef picks 5 eggs at random for his “Mega-Omelet Surprise.” Find the probability that the number of unspoiled eggs among the 5 selected is

(a) exactly 5

(b) 2 or fewer

Let X = number of unspoiled eggs in the bad carton of eggs.

Of the 18 eggs in the bad carton of eggs, 8 were spoiled eggs.

The probability of selecting an unspoiled egg is:

$P(X)=p=\frac{10}{18}=0.556$

A randomly selected egg is unspoiled or not is independent of the others.

It is provided that a chef picks 5 eggs at random.

The random variable X follows a Binomial distribution with parameters n = 5 and p = 0.556.

The success is defined as the selection of an unspoiled egg.

The probability mass function of X is given by:

$P(X=x)={5\choose x}(0.556)^{x}(1-0.556)^{5-x};\ x=0,1,2,3...$

(a)

Compute the probability that of the 5 eggs selected exactly 5 are unspoiled as follows:

$P(X=5)={5\choose 5}(0.556)^{5}(1-0.556)^{5-5}\\=1\times 0.05313\times 1\\=0.0531$

Thus, the probability that of the 5 eggs selected exactly 5 are unspoiled is 0.0531.

(b)

Compute the probability that of the 5 eggs selected 2 or less are unspoiled as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$=\sum\imits^{2}_{x=0}{{5\choose 5}(0.556)^{5}(1-0.556)^{5-5}}\\=0.0173+0.1080+0.2706\\=0.3959$

Thus, the probability that of the 5 eggs selected 2 or less are unspoiled is 0.3959.

(c)

Compute the probability that of the 5 eggs selected more than 1 are unspoiled as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-\sum\limits^{1}_{x=0}{{5\choose 5}(0.556)^{5}(1-0.556)^{5-5}}\\=1-0.0173-0.1080\\=0.8747$

Thus, the probability that of the 5 eggs selected more than 1 are unspoiled is 0.8747.

6 0

1 year ago

A brand new filled can of chicken broth is 12 cm tall and has a radius of 5 cm. Michele uses some of the broth to cook and now t

Natalka [10]

To find the awnser, the equation would be: the volume of the can - the volume left

to find the value,we can use 3.14 for 丌

The volume of the can would be the base area (丌r^2)times it's height,which in this case the volume is:

3.14(5)^2×12
=3.14×25×12
=942 cm³

The volume left:
3.14(5)^2×4
=314cm³

Thus,Mishka used:
942-314
=628 cm³

The answer is 628cm³

Hope it helps!

5 0

2 years ago

Read 2 more answers

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

andreyandreev [35.5K]

Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:

Rate of handheld hose = 1 job / 8 minutes ---> 1

Rate of lawn sprinkler = r ---> 2

Rate of the two combines = 1 job/ 5 minutes ---> 3

So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:

1 / 8 + r = 1 / 5

Multiplying both sides by 5:

(5 / 8) + 5 r = 1 ---> ANSWER

8 0

2 years ago

Read 2 more answers

Tony and Manuel were trimming the branches of a tree. Tony was using an 18 ft ladder and Manuel was using a 24 ft ladder. Both l

REY [17]

Answer:

9.33 feet = 111.96 inches

Step-by-step explanation:

If we have similar triangles, the rate between matching sides is the same.

So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):

18 / 7 = 24 / x

x = 7 * 24 / 18

x = 9.33 feet

To find this measure in inches, we just need to multiply by 12:

x = 9.33 * 12 = 111.96 inches

3 0

2 years ago

four times the first of three consecutive odd integers is five less than the product of three and the third integer find the int

Andre45 [30]

I don't understand what integer is being asked for. The question is poorly worded.

The three integers are 7, 9, 11.
4 times 7 = 28
and 3 times 11 = 33
and 28 is 5 less than 33.

8 0

1 year ago