Step-by-step explanation:
From Trig
1 + tan²x = Sec²x
Also
Sec²x = 1/cos²x
Now
Cot²x = 1/tan²x = cos²x/sin²x
Putting all together
Cot²x(1+tan²x)
= Cot²x(sec²x)
= cos²x/sin²x(1/cos²x)
cos²x on the numerator and that one the denominator cancels out
we have
= 1/sin²x
From Trig
1/sin²x = cosec²x
So Our Answer = cosec²x.
Answer:
The number of candles each girl needs to sell so that the total amount raised is the same for both is
<em>Hailey </em>70 candles
<em>Kacie </em>40 candles
Step-by-step explanation:
Let
x------> the number of candles sold
y----> total amount raised
we know that
<em>Hailey's equation</em>
-----> equation A
Please note that Hailey has already raised $160, so he has sold 40 candles.
<em>Kacie's equation</em>
-----> equation B
Please note that Kacie has already raised $70, so he has sold 10 candles.
equate equation A and equation B solve for x
The number of candles each girl needs to sell so that the total amount raised is the same for both is
<em>Hailey</em>
40+30=70 candles
<em>Kacie</em>
10+30=40 candles
Answer:
The estimate of the percentage of millionaires in each of these cities:
Bridgeport San Jose Washington Lexington Park
CT CA D.C. MD
Percentage of
Millionaires 9% 12% 9% 8.3%
Step-by-step explanation:
Data and Calculations: City
Bridgeport, San Jose, Washington, Lexington Park,
Millionaire CT CA D.C. MD
Yes 45 36 36 33
No 455 264 364 367
Sample 500 300 400 400
Percentage of
Millionaires 45/500 36/300 36/400 33/400
= 0.09 0.12 0.09 0.0825
= 9% 12% 9% 8.3%
Answer:
See explanation
Step-by-step explanation:
Assuming the given equation is

To solve for r, we first divide both sides by a.

We now subtract 5 from both sides:

We now divide through by - 1 to get:

Or

Explanation:
If your actual answer is very far from your estimate, you probably made a mistake somewhere.
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<em>Additional comment</em>
50 years ago, when a slide rule was the only available calculation tool, making an estimate of the result was a required part of doing the calculation. Not only were the first one or two significant digits needed, but also the power of 10 that multiplied them. Use of a slide rule required the order of magnitude be computed separately (by hand) from the significant digits of the result.
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You may also find it useful to estimate the error in your estimate. That is, you may want to know the approximate answer to 2 (or more) significant digits in order to gain confidence that your calculation is correct.