Order from Least to Greatest: 1/4 -0.8 0.5 -1.2

Suppose that the weights of 5400 registered female Labrador retrievers in the United States are distributed normally with a mean

Maurinko [17]

Answer:

$N= 4543$ Labrador retrievers

Step-by-step explanation:

We know that the mean $\mu$ is:

$\mu = 62.5$

and the standard deviation $\sigma$ is:

$\sigma=2.5$

The probability that a randomly selected Labrador retriever weighs less than 65 pounds is:

$P(X$

We calculate the Z-score for X =65

$Z = \frac{X-\mu}{\sigma}\\\\Z =\frac{65-62.5}{65}=1$

So

$P(X$

Looking in the table for the standard normal distribution we have to:

$P(Z$ .

Finally the amount N of Labrador retrievers that weigh less than 65 pounds is:

$N = P(X$

$N = 0.8413*5400$

$N= 4543$ Labrador retrievers

6 0

3 years ago

Given y = log3(x + 4), what is the range?

lora16 [44]

Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

$y=\log_3(x+4)$ only exists when $x+4$ is positive.

You can take the log of a negative or 0 number.

So $x+4>0$ implies $x>-4$ . (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range. The range is where the curve exist for the y-values.

The equivalent exponent form of $y=\log_3(x+4)$ is $3^{y}=x+4$

We can solve this for x be subtract 4 on both sides:

$x=3^y-4$

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of $y=\log_3(x+4)$ you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

$y=3^x-4$ .

If we look at the domain and range of this we can just swap it to get the domain and range of $y=\log_3(x+4)$ .

$y=3^x-4$ is an exponential function of 3^x that has been moved down 4 units.

The range since it has been moved down 4 units is $(-4,\infty)$ .

The domain of an exponential function is all real numbers. There are no restrictions on what you can plug in for x.

So swapping these to find the domain and range of $y=\log_3(x+4)$ :

Domain: $(-4,\infty)$

Range : $(-\infty,\infty)$

4 0

3 years ago

Consider the line y = 7x-9.

KatRina [158]

$y = \frac{-1}{7}x -\frac{8}{7}$ is the equation of the line that is perpendicular to this line and passes through the point (6, -2)

y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)

Solution:

Given that line is:

y = 7x - 9

The equation of line in slope intercept form is given as:

y = mx + b ------ eqn 1

Where, "m" is the slope of line and "b" is the y intercept

On comparing eqn 1 with y = 7x - 9 we get,

m = 7

<h3>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</h3>

We know that,

Product of slope of a line and slope of line perpendicular to given is always -1

Therefore,

$7 \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{-1}{7}$

Now find the equation of line:

$\text{ Substitute } m = \frac{-1}{7} \text{ and } (x, y) = (6, -2) \text{ in eqn 1}$

$-2 = \frac{-1}{7} \times 6 + b\\\\-2 = \frac{-6}{7} + b\\\\b = -2+\frac{6}{7}\\\\b = \frac{-14+6}{7}\\\\b = \frac{-8}{7}$

$\text{Substitute } m = \frac{-1}{7} \text{ and } b = \frac{-8}{7} \text{ in eqn 1}\\\\y = \frac{-1}{7}x -\frac{8}{7}$

Thus the equation of line perpendicular to given line is found

<h3>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</h3>

Slopes of parallel lines are equal

Therefore, m = 7

Substitute m = 7 and (x, y) = (6, -2) in eqn 1

-2 = 7(6) + b

-2 = 42 + b

b = -44

Substitute m = 7 and b = -44 in eqn 1

y = 7x - 44

Thus equation of line parallel to given line is found

8 0

3 years ago

Find the largest prime divisor of 11! + 12!

kari74 [83]

Answer: 23

Step-by-step explanation:

Oh hi 11+12= 23!!!

7 0

3 years ago

Read 2 more answers

HALP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Katyanochek1 [597]

Answer:

its 24 you welcome

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers