What are the first two steps of drawing a triangle that has all side lengths equal to 12 centimeters?

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 100 hou

hodyreva [135]

Answer:

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

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:

$\alpha = \frac{1-0.9}{2} = 0.05$

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 $1-0.05 = 0.95$ , so $z = 1.645$

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.

$M = 1.645*\frac{600}{\sqrt{100}} = 98.7$

The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons

The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

4 0

3 years ago

Calculus graph please help

tresset_1 [31]

Answer:

See Below.

Step-by-step explanation:

We are given the graph of y = f'(x) and we want to determine the characteristics of f(x).

Part A)

f is increasing whenever f' is positive and decreasing whenever f' is negative.

Hence, f is increasing for the interval:

$(-\infty, -2) \cup (-1, 1)\cup (3, \infty)$

And f is decreasing for the interval:

$\displaystyle (-2, -1) \cup (1, 3)$

Part B)

f has a relative maximum at x = c if f' turns from positive to negative at c and a relative minimum if f' turns from negative to positive to negative at c.

f' turns from positive to negative at x = -2 and x = 1.

And f' turns from negative to positive at x = -1 and x = 3.

Hence, f has relative maximums at x = -2 and x = 1, and relative minimums at x = -1 and x = 3.

Part C)

f is concave up whenever f'' is positive and concave down whenever f'' is negative.

In other words, f is concave up whenever f' is increasing and concave down whenever f' is decreasing.

Hence, f is concave up for the interval (rounded to the nearest tenths):

$\displaystyle (-1.5 , 0) \cup (2.2, \infty)$

And concave down for the interval:

$\displaystyle (-\infty, -1.5) \cup (0, 2.2)$

Part D)

Points of inflections are where the concavity changes: that is, f'' changes from either positive to negative or negative to positive.

In other words, f has an inflection point wherever f' has an extremum point.

f' has extrema at (approximately) x = -1.5, 0, and 2.2.

Hence, f has inflection points at x = -1.5, 0, and 2.2.

7 0

2 years ago

you are riding a train. your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds. How much more can you add

Strike441 [17]

Let the additional weight that can be added be = x

Current weight of the bag = 38 pounds

Total weight can be = 50 pounds

The equation becomes:

$38+x\leq50$

$x\leq50-38=12$

Hence, a weight of 12 pounds cab be added to the current wight.

8 0

3 years ago

TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested

kow [346]

4000.00 x 2.0 = $80.00 per year x 2 years = $160.00 so 6 months would earn $40.00 taking it to the $200, so 2 yrs 6 mos.

3 0

3 years ago

(3x-7)+(-4x-8)........ what is the sum of this pls

yarga [219]

Answer:

(3x-7)+(-4x-8)

3x-7-4x-8

3x-4x-7-8

-x-15

6 0

3 years ago