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3 years ago

8. Which graph correctly shows the solution of the compound inequality 3x > 3 and 9x < 54?

Mathematics

1 answer:

borishaifa [10]3 years ago

6 0

The answer is shown in the image attached

Compound inequality is an inequality made up of two inequalities joined together using 'or' or 'and'.

Given the inequalities 3x > 3 and 9x < 54. Solving both inequalities gives:

3x > 3 and 9x < 54

x > 1 and x < 6

x > 1 is equivalent to x ∈ (1, ∞)

x < 6 is equivalent to x ∈ (-∞, 6)

Therefore, combining the two inequalities together gives:

(1, ∞) ∩ (-∞, 6) = (1, 6)

Find out more at: brainly.com/question/24540195

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5/6(2x+12)-8=4-(x+1)

alekssr [168]

For this case we have the following equation:

$\frac {5} {6} (2x + 12) -8 = 4- (x + 1)$

We apply distributive property on the left side of the equation:

$\frac {5 * 2} {6} x + \frac {5 * 12} {6} -8 = 4- (x + 1)\\\frac {10} {6} x + \frac {60} {6} -8 = 4- (x + 1)$

We simplify the left side of the equation:

$\frac {5} {3} x + 10-8 = 4- (x + 1)$

Different signs are subtracted and the major sign is placed.

$\frac {5} {3} x + 2 = 4- (x + 1)$

On the right side we must take into account that:

$- * + = -$

So:

$\frac {5} {3} x + 2 = 4-x-1\\\frac {5} {3} x + 2 = 3-x$

We add x to both sides of the equation:

$\frac {5} {3} x + x + 2 = 3\\\frac {5 * 1 + 3 * 1} {3} x + 2 = 3\\\frac {5 + 3} {3} x + 2 = 3\\\frac {8} {3} x + 2 = 3$

We subtract 2 from both sides of the equation:

$\frac {8} {3} x = 3-2\\\frac {8} {3} x = 1$

We multiply by 3 on both sides of the equation:

$8x = 3$

We divide by 8 on both sides of the equation:

$x = \frac {3} {8}$

Thus, the solution of the equation is:

$x = \frac {3} {8}$

Answer:

$x = \frac {3} {8}$

4 0

3 years ago

Which of the following is an advantage of using systematic random sampling?

bekas [8.4K]

This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Systematic:

One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.

Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.

It also does not reduce sampling variability, thus the first option is wrong.

From this, it can be concluded that the correct option is:

Systematic random sampling does not require a finite population size.

For another example of systematic random sampling, you can check brainly.com/question/21100042

8 0

3 years ago

What is the common denominator 2 1/3+1/2?

nirvana33 [79]

Six. 2 1/3=7/3-> to get to have a denominator of 6 multiply by 2 to get 14/6
Then 1/2=3/6
14/6 + 3/6 = 17/6
17/6= 2 5/6

5 0

3 years ago

1) Billy walks 15 miles every day to soccer practice, and catches a ride home from his grandma. Billy had 5 practices last week.

nignag [31]

1 ) Billy walks 15 miles every day to soccer practice and he had 5 practices last week.

We know that, 1 mile = 1760 yards

So, 15 miles = (15× 1760) yards = 26400 yards

Thus the total distance walked in 5 practices will be: $(26400*5)yards = 132000 yards$

2) Mark's current age is $t$ years

So, his age was in 10 years ago $=(t-10)years$

Given that, his current age is 3 times his age 10 years ago.

So, the equation to represent this situation will be : $t= 3(t-10)$

3 0

3 years ago

-2 (x + 4) – (3x – 8)<br> What it equals

Alja [10]

Answer:

-2x+-8-3x-8

Step-by-step explanation:

-2 times x =-2x

-2 times 4=-8

8 0

3 years ago

Read 2 more answers