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Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)

vagabundo [1.1K]

Answer:

Considering the given equation $y = log_{3}x\\$

And the ordered pairs in the format $(x, y)$

I don't know if it is log of base 3 or 10, but I will assume it is 3.

For $(\frac{1}{3}, a_{0} )$

$x=\frac{1}{3}$

$y=a_{0}$

$y = log_{3}x\\y = log_{3}(\frac{1}{3} )\\y=-\log _3\left(3\right)\\y=-1$

So the ordered pair will be $(\frac{1}{3}, -1 )$

For $(1, a_{1} )$

$x=1$

$y=a_{1}$

$y = log_{3}x\\y = log_{3}1\\y = log_{3}(1)\\Note: \log _a(1)=0\\y = 0$

So the ordered pair will be $(1, 0 )$

For $(3, a_{2} )$

$x=3$

$y=a_{2}$

$y = log_{3}x\\y = log_{3}3\\y = 1$

So the ordered pair will be $(3, 1 )$

For $(9, a_{3} )$

$x=9$

$y=a_{3}$

$y = log_{3}x\\y = log_{3}9\\y=2\log _3\left(3\right)\\y=2$

So the ordered pair will be $(9, 2 )$

For $(27, a_{4} )$

$x=27$

$y=a_{4}$

$y = log_{3}x\\y = log_{3}27\\y=3\log _3\left(3\right)\\y=3$

So the ordered pair will be $(27, 3 )$

For $(81, a_{5} )$

$x=81$

$y=a_{5}$

$y = log_{3}x\\y = log_{3}81\\y=4\log _3\left(3\right)\\y=4$

So the ordered pair will be $(81, 4 )$

4 0

3 years ago

Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is t

RoseWind [281]

Answer:

0.193877

Step-by-step explanation:

The data given to us is

Pre-Employment Drug Screening Results

Positive test result Negative test result

Drug Use Is Indicated Drug Use Is Not Indicated

Subject Uses Drugs: 38 12

Subject Is Not a drug user: 19 29

Now the total of this is = 38+19+12+29= 98

Now the probability of false positive is = 19/98= 0.193877

The Subject Is Not a drug user  would suffer from a false positive. He is not a user and has a positive result.

7 0

2 years ago

Which scatterplot shows the weakest negative linear correlation? Ed2020

Komok [63]

Answer:

the last one

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

For the function P(x) = x3 − 9x, at the point (2, −10), find the following. (a) the slope of the tangent to the curve (b) the in

Shalnov [3]

Answer:

3, in both a), b)

Step-by-step explanation:

a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.

Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is $p'(x)=3x^2-9$ . In particular, the value we are looking for is $p'(2)=3(2^2)-9=12-9=3$ .

If you would like to compute the equation of the tangent line, we can use the point-slope equation to get $y=3(x-2)-10=3x-16$

b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to $p'(2)=3$ .

4 0

3 years ago

Emily's bill for dinner at a restaurant was $61. She left an 18% tip. What was the amount of the tip?

UkoKoshka [18]

You cross multiply. So 61 over 18 = x over 100. You multiply 61 and get the answer of 1600. Now with what you have left, you divide that with 18 and you should get your answer of 338.888889. Make sure to round it to whatever it tells you to round to!

7 0

3 years ago