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3 years ago

What is the absolute value of | r - 8| = 5?

Mathematics

1 answer:

fomenos3 years ago

3 0

Answer:

r = 13, 3

Step-by-step explanation:

| r - 8| = 5

All solutions for r by breaking the absolute value into the positive and negative components

r = 13, 3

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Mr. Sánchez owns a square field. The side lengths are 0.9 kilometers. There are 1,980 prairie dog burrows in the fields. What is

Simora [160]

The first thing we are going to do is find the area of the field. To do this we are going to use the area of a square formula: $A=s^2$
Were
$A$ is the area in square kilometers
$s$ is one of the sides of the square
We know for our problem that the side lengths of the field are 0.9 kilometers, so $s=0.9$ . Lets replace that value in our formula to find $A$ :
$A=(0.9)^2$
$A=0.81$

Now, to find the population density of the filed, we are going to use the population density formula: $P_{d}= \frac{I}{A}$
where
$P_{d}$ is the population density in <span>in burrows per square kilometer
</span> $I$ is the number of burrows
$A$ is the are of the field
We know that $I=1980$ and $A=0.81$ , so lets replace those values in our formula:
$P_{d}= \frac{1980}{0.81}$
$P_{d}=2444.4$

We can conclude that the <span>density of prairie dog burrows is approximately 2444 burrws per square kilometer.</span>

5 0

3 years ago

A machine fills containers with a particular product. Assume the filling weights are normally distributed with a variance of 0.1

Ghella [55]

Answer:

$z=-0.674$

And if we solve for $\mu$ we got

$\mu=12 +0.674*0.4=12.270$

So then the mean is $'mu = 12.270$ for this case.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sqrt{0.16}= 0.4)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>12)=0.85$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.85 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.85

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for $\mu$ we got

$\mu=12 +0.674*0.4=12.270$

So then the mean is $'mu = 12.270$ for this case.

8 0

3 years ago

Can someone help me on questions 10-15

Mazyrski [523]

Answer:

10. Supplementary

11. Congruent

12. Congruent.

13 . congruent

14 supplement

15 supplementary

<h3>Hope this helps you </h3><h3>Do mark as brainliest! </h3>

3 0

3 years ago

Four added to 3 times a number is 25

lukranit [14]

The answer is 13. To solve this you have to do 4*3 which is 12. Then you subtract 25 and 12 to get an answer of 13.

4 0

3 years ago

Order 34 × 102, 1.2 × 107, 8.11 × 10–3 and 435 from least to greatest.

andrey2020 [161]

I will assume that this question is about scientific notation (also assuming that the first number is 3.4*10^2), where you can arrange the numbers by the exponent of the 10, so from least to greatest:
$8.11*10^{-3}$ , $3.4*10^{2}$ , 435, and $1.2*10^{7}$

6 0

3 years ago