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3 years ago

14

Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

1 answer:

Sonbull [250]3 years ago

6 0

The correct answer is x = 2 and x = -4.

In order to solve for this, you first need to plug in the f(x) value and solve for the absolute value statement.

f(x) = -5|x + 1| + 3

-12 = -5|x + 1| + 3 ---> subtract 3 from both sides.

-15 = -5|x + 1|----> divide both sides by -5.

3 = |x + 1|

Now that we have solved for the absolute value portion, we need to solve this equation twice. Once removing the absolute value and solving and the other by removing it and making the 3 negative. This is because even if the inside of the markers was -3, it would give us a 3 answer.

3 = x + 1

2 = x

Then the negative version.

-3 = x + 1

-4 = x

And there are your two answers.

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Find the 95% confidence interval for estimating the population mean μ

AVprozaik [17]

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

$\displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}$

We are given these variables:

$\overline{x}=50$
$n=60$
$\sigma=10$

Plug these values into the formula for the confidence interval:

$\displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}$

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

$\displaystyle \frac{1-C}{2}=A$

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

$\displaystyle \frac{1-.95}{2}=.025$

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

$t^*=1.96$

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

$\displaystyle 50\pm 1.96 \big{(}\frac{10}{\sqrt{60} } \big{)}$

We can calculate the confidence interval, using this formula, to be:

$\boxed{(47.4697, \ 52.5303)}$

<h3>Interpreting the Confidence Interval</h3>

We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

8 0

2 years ago

Pls help on #9 ASAP. thank you. I’ll give u as much points as i can ♡

Alinara [238K]

A. X> lobsters
7 + x <= 18
X <= 11 lovsters.

B. (7+3+10)
x= additional lobsters
10 + x <= 24
x<= 14 lobsters

C. 24/4 = 6 lobsters

Hope this helps.

6 0

3 years ago

Read 2 more answers

Bonnie is making a dipping sauce. She mixes 150 milliliters of soy sauce with 100 milliliters of vinegar. How much soy sauce doe

oksian1 [2.3K]

Answer:

Bonnie is mixing 1.50 milliliter of soy sauce with 1 milliliter of vinegar

Step-by-step explanation:

Given

Bonnie mixes 150 milliliters of soy sauce with 100 milliliters of vinegar

So, in order to find the amount of soy sauce mixed with one ml of vinegar, we have to divide the amount of soy sauce by vinegar.

So,

$Soy\ sauce\ mixed\ with\ 1\ ml\ of\ vinegar\ =\frac{150}{100}\\ = \frac{3}{2}\\=1.50$

Hence,

Bonnie is mixing 1.50 milliliter of soy sauce with 1 milliliter of vinegar

3 0

3 years ago

The radius of a cone is 5cm the heigth of the cone is 18 cm what is the volume of the cone

nikitadnepr [17]

6-8 cm is the answer!! Hope this helps!

3 0

3 years ago

What is the range of this relation (3,2) (-3,0) (-4,0) (-2,4)

Sveta_85 [38]

Answer:

-4 to 3

Step-by-step explanation:

look at the first number in each set then find the smallest and the biggest that is how you find range

4 0

3 years ago