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3 years ago

If f(x)= -6x+6 then f^-1(x)=

1 answer:

3 0

Recall that, to get the inverse relation of any expression, we start off by doing a quick switcharoo on the variables, then we solve for "y".

$\bf \stackrel{f(x)}{y}=-6x+6\qquad inverse\implies \boxed{x}=-6\boxed{y}+6
\\\\\\
x-6=-6y\implies \cfrac{x-6}{-6}=y\implies -\cfrac{x}{6}+1=\stackrel{f^{-1}(x)}{y}$

You might be interested in

Can someone help me out with the Ángel measures

dexar [7]

To solve all of these, you put the expressions you've been given into an equation that equals whatever number the sheet tells you is the sum of the angle measures. Then you just substitute it in to find the angle measures. I'll do the first one for you but tell me if you want me to do the rest:
2k + k + 45 = 180
3k + 45 = 180
- 45
3k = 135
÷ 3
k = 45°
45 × 2 (2k) = 90
Again let me know if you want the answers and working to the other two :)

3 0

3 years ago

. If a landfill has a density of 1,200 pounds per cubic yard, what would be the volume required for 15- years worth of MSW to th

bazaltina [42]

Here is the full data for the question.

Each person in the state of Texas generate roughly 7.5 pounds of municipal solid waste each day. Of this amount, roughly 35 percent of the waste is currently recycle in Texas. Studies have shown that the maximum amount of waste that could be realistically recycled or otherwise diverted from the landfill is 50 percent.

(NOTE: for tons, use I ton -2,000 pounds unless otherwise specified)

11. For a community/service area of 200,000 people, calculate the amount:

Total MSW each year, in pounds? ? Tons?

II. Total MSW currently recycled each year, in pounds? Tons?

III Amount of the MSW that could realistically be diverted from the landfill if recycling was maximized to the nearest pound.

12. Using the current recycling rate, calculate the amount of MSW sent to a landfill over 15 years period to the nearest pound.

13. If a landfill has a density of 1,200 pounds per cubic yard, what would be the volume required for 15- years worth of MSW to the nearest cubic yard?

Answer:

Step-by-step explanation:

11)

I) The amount of total MSW generated per day in pounds is = 1,500,000 Pounds

The total MSW generated per day in tons is = 750 Tons

The amount of the total MSW generated per year in pounds will be:

= 1,500,000 × 365

= 547,500,000 Pounds

The amount of the total MSW generated per year in tons is

= 750 × 365

= 273,750 Tons

II)

The amount of the total MSW currently recycled per day is pounds

= 1,500,000 × (35/100)

= 525,000 Pounds

Total MSW currently recycled per day in tons is

= 750 × 35/100

= 262.5 Tons

The amount of the total MSW currently recycled per year in pounds is

= 525,000 × 365

= 191,625,000 Pounds

The amount of the total MSW currently recycled each year in tons is

= 262.5 × 365

= 95812.5 Tons

III) The required amount of MSW which could realistically be diverted from the landfill suppose that the recycling was maximized (for each person) is

= 7.5 × (50/100)

= 3.75 Pounds

≅ 4 Pounds

The required amount of MSW which could realistically be diverted from the landfill suppose recycling were maximized (for the total population) is:

= 1,500,000 × (50/100)

= 750,000 Pounds

12)

Applying the current rate of recycling, the amount of MSW sent to landfill over a 15 year period (for each person) is:

= 7.5 × (100-35)/100

= 4.875 Pounds each day

= 4.875 × 365 × 15

= 26690.625 Pounds/ 15 years/person

≅ 26,691 Pounds/ 15 years/person

For 1 year period:

By applying the current rate of recycling, the required amount of MSW sent to landfill over (for total population) is:

= 547,500,000 × (100-35)/100)

= 355,875,000 Pounds

For 15 years period:

By applying the current rate of recycling, the amount of MSW sent to landfill (for total population) is:

= 355875000 × 15

= 5,338,125,000 Pounds

13)

The volume required for the landfill for 15 years worth of MSW is:

= 5,338,125,000/1,200

= 4,448,437.5 Cubic yard

≅ 4,448,438 Cubic yard

3 0

3 years ago

The First National Bank of Wilson has 700 checking account customers. A recent sample of 50 of these customers showed 29 have a

attashe74 [19]

The margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

<h3>What is the margin of error(MOE)?</h3>

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

$\rm MOE = Z\times \dfrac{s}{\sqrt{n}}$

Where Z is the z-score at the confidence interval

s is the standard deviation

n is the number of samples.

We have:

n = 50, X = 29,

Estimate point p = 29/50 = 0.58

q = 1-p = 1-0.58 = 0.42

Z at 0.05/2 (95% confidence interval) = 1.96

$\rm MOE = 1.96\sqrt{\dfrac{0.58\times0.42}{50}}$

After calculating:

MOE = 0.137

Confidence interval will be: (p - MOE, p+MOE)

= (0.58-0.137, 0.58+0.137)

= (0.443, 0.717)

Thus, the margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

Learn more about the Margin of error here:

brainly.com/question/13990500

#SPJ1

3 0

2 years ago

Can someone please explain this to me

Gre4nikov [31]

What's happening is that every subtraction can be written as "addition of the opposite."

18-5 = 18 + (-5)

One reason this is done in the work you showed is that they're trying to show why you distribute the negative and the 1 into the parentheses, why you multiply everything in the parentheses by "-1" and not just 1.

The other reason is to later to be able to move the individual terms around, so you'll be able to combine like terms.

When you move terms around, the sign has to stay attached to the term, so writing all the subtractions as addition helps keep the sign attached.

8 0

3 years ago

D=a+b+c solve for b I need some help

Hoochie [10]

Hi Walker

d=a+b+c

Flip

a+b+c=d

Add -a to both sides

a+b+c-a=d-a

b+c=-a+d

Now add -c to both sides

b+c-c=-a+d-c

b= -a-c+d

I hope that's help:0

4 0

3 years ago