Given the equation y-5=5x determine whether the points (2,12) and (-2,-5) are solutions on the graph

The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.

ozzi

Answer:

The 80% confidence interval for the mean usage of water is between 18.4 and 18.6 gallons per day.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.1 = 0.90$ , so $z = 1.28$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28*\frac{2.3}{\sqrt{717}} = 0.1$

The lower end of the interval is the sample mean subtracted by M. So it is 18.5 - 0.1 = 18.4 gallons per day.

The upper end of the interval is the sample mean added to M. So it is 18.5 + 0.1 = 18.6 gallons per day.

The 80% confidence interval for the mean usage of water is between 18.4 and 18.6 gallons per day.

6 0

3 years ago

To dilute a solution that is 40% saline, a chemist combines it with a solution that is 15% saline. How much of each solution sho

KonstantinChe [14]

Answer:

60 ml of 40% saline and 90 ml of 15% saline

Step-by-step explanation:

We can call the amount of 40% solution x and the amount of 15% solution y.

x + y = 150 -- (1)

0.40x + 0.15y = 150 * 0.25 -- (2) --- 150 * 0.25 = 37.5

40x + 15y = 3750 (Multiply (2) by 100 to get rid of decimals)

15x + 15y = 2250 -- (3) (Multiply (1) by 15)

25x = 1500 (Subtract (3) from (1)

x = 60

y = 150 - 60 = 90

3 0

3 years ago

Read 2 more answers

For your college interview, you must wear a tie. You own 3 regular (boring) ties and 5 (cool) bow ties. 36 1. Counting (a) How m

fgiga [73]

Answer:

a) 8

b) 15

c) 34

Step-by-step explanation:

Part a) Choices for the neck-wear

Number of regular ties = 3

Number of bow ties = 5

Total number of ties = 3 + 5 = 8

For the neck-wear any tie can be chosen among these 8 available ties. Therefore, the number of choices for the neck-wear would be 8.

Part b)

For this part we need to calculate the number of choices if both neck and bow ties are to be used.

Choosing a regular tie is independent of choosing the bow tie. According to the fundamental rule of counting, if two events are independent of each other, the number of ways of occurrence of both will be equal to the product of their individual occurrences. i.e.

Number of ways to choose both ties = Product of number of ways of choosing each tie

So,

Number of choices for wearing both ties= 3 x 5 = 15 ways

Part c)

Number of shirts = 5

Number of skirts = 4

Number of pants = 3

Number of dresses = 7

Following options are available for the outfits:

Shirt with Skirt or Pants
Just a dress

Number of ways to choose a pant is 3. Number of ways to chose a skirt or pant is 9.

Using the fundamental rule of counting again:

Number of ways to wear a shirt with skirt or pant = 3 x 9 = 27

Number of ways to chose a dress = 7

Therefore, we have in total 27 +7 = 34 ways of choosing the outfit.

5 0

3 years ago

Anybody know the integration for this... The answer is k=3

yanalaym [24]

You know that $y^2=4x$ so $x=\dfrac{y^2}{4}$ .
Area of a shaded region is:

$$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}$

so k:

$\dfrac{k^3}{12}=\dfrac{9}{4}\\\\\\k^3=\dfrac{9\cdot12}{4}\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}$

3 0

4 years ago

Which represents the number 7,776 in exponential form? 68 36 28 65

arlik [135]

6^5 = 6 x 6 x 6 x 6 x 6 = 7776

5 0

3 years ago