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3 years ago

Consider the equation |1/4+12|=x/2.Without calculating, how do you know x=-16 is an extraneous solution?

1 answer:

5 0

Without calculating, you can immediately see the absolute value sign, which implies that the final result (x) should be positive, not negative.

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A community action committee is planning a block party. The party will be successful only if at least 70 adults and children att

Sergeeva-Olga [200]

Answer:

A. a + c ≥ 70; 15a + 4c ≤ 1000

Step-by-step explanation:

Given data:

A community action committee is planning a block party

The party will be successful if at least 70 adults (a) and children (c) attend

Their budget for the party is $1,000

The cost for each adult will be $15

And the cost for each child will be $4

Solution:

At least 70 adults and children attend.

So the inequality here is a + c ≥ 70

The budget for the party is $1,000.

So the cost for all adults plus the cost for all children cannot exceed $1,000

And hence the inequality here is; 15a + 4c ≤ 1,000

3 0

3 years ago

Read 2 more answers

The green arcs show a pair of SAME SIDE INTERIOR ANGLES.

kramer

It would be purple and green

4 0

3 years ago

Help please problem is worded weird

Vadim26 [7]

Answer:100

Step-by-step explanation:

Expand

x = 150 - 0.5x

Add 0.5x to both sides

x + 0.5x = 150

Simplify x + 0.5x to 1.5x

1.5x = 150

Divide both sides by 1.5

x = 150/1.5

Simplify 150/1.5 to 100

x = 100

5 0

4 years ago

Read 2 more answers

What is true about the absolute values of the slopes of parallel and perpendicular lines?

GenaCL600 [577]

They are the reciprocals of each other, meaning the denominator and the numerator are in switched positions

5 0

3 years ago

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The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

VMariaS [17]

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

Assume that a recent survey suggests that about 87% of adults have heard of the brand.

This means that $\pi = 0.87$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?

This is n for which M = 0.05. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}$

$0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}$

$\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}$

$(\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2$

$n = 122.4$

Rounding up:

He must survey 123 adults.

6 0

3 years ago