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3 years ago

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

const2013 [10]3 years ago

4 0

Function:

f(x) = 30x (75%) + 1

Bacteria after 2 hours:

10,890 bacteria

Zina [86]3 years ago

3 0

Answer:

I'm not sure about the function but here is the answer: 3

Step-by-step explanation:

Well, 75% of 1 is 0.75 + 75% of that + 75% of that and so on until you do it four times. Why four? Well it increases every 30 MINUTES so 30 min + 30 min + 30 min + 30min = 2 hours!

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If f(x)=2x+5x and g(x)=3x-5,find (f+g)(x)

kati45 [8]

The answer is $(f+g)(x)=10x-5$

Step-by-step explanation:

Given that $f(x)=2x+5x$ and $g(x)=3x-5$

To find : $(f+g)(x)$

Now, assign the value $g(x)=3x-5$ in $(f+g)(x)$

$(f+g)(x)=(f+3x-5)$

Also, assign the value $f(x)=2x+5x$ in $(f+g)(x)$

$(f+g)(x)=(2x+5x+3x-5)$

Now, adding the like terms , we get,

$(f+g)(x)=10x-5$

Thus, the value of $(f+g)(x)$ is $(f+g)(x)=10x-5$

3 0

4 years ago

Read 2 more answers

Express 3^4 = x as a logarithmic equation.

meriva

Note that the base in both the exponential form of the equation and the logarithmic form of the equation (above) is "b", but that the x and y switch sides when you switch between the two equations. If you can remember this — that whatever had been the argument of the log becomes the "equals" and whateverhad been the "equals" becomes the exponent in the exponential, and vice versa — then you should not have too much trouble with solving log equations.

Solve log2(x) = 4.

Since this is "log equals a number", rather than "log equals log", I can solve by using The Relationship:
 log2(x) = 4 
24 = x
16 = x

Solve log2(8) = x.

I can solve this by converting the logarithmic statement into its equivalent exponential form, using The Relationship:log2(8) = x
2 x = 8But 8 = 23, so:2 x = 23
x = 3

Note that this could also have been solved by working directly from the definition of a logarithm: What power, when put on "2", would give you an 8? The power 3, of course!

If you wanted to give yourself a lot of work, you could also do this one in your calculator, using the change-of-base formula:

log2(8) = ln(8) / ln(2)

Plug this into your calculator, and you'll get "3" as your answer. While this change-of-base technique is not particularly useful in this case, you can see that it does work. (Try it on your calculator, if you haven't already, so you're sure you know which keys to punch, and in which order.) You will need this technique in later problems.

Solve log2(x) + log2(x – 2) = 3I can't do anything yet, because I don't yet have "log equals a number". So I'll need to use log rules to combine the two terms on the left-hand side of the equation:log2(x) + log2(x – 2) = 3 
log2((x)(x – 2)) = 3 
log2(x2 – 2x) = 3Then I'll use The Relationship to convert the log form to the corresponding exponential form, and then I'll solve the result:log2(x2 – 2x) = 3 
23 = x2 – 2x 
8 = x2 – 2x 
0 = x2 – 2x – 8 
0 = (x – 4)(x + 2) 
x = 4, –2But if x = –2, then "log2(x)", from the original logarithmic equation, will have a negative number for its argument (as will the term "log2(x – 2)"). Since logs cannot have zero or negative arguments, then the solution to the original equation cannot be x = –2.The solution is x = 4.

Keep in mind that you can check your answers to any "solving" exercise by plugging those answers back into the original equation and checking that the solution "works":

log2(x) + log2(x – 2) = 3 
log2(4) + log2(4 – 2) ?=? 3 
log2(4) + log2(2) ?=? 3

Since the power that turns "2" into "4" is 2 and the power that turns "2" into "2" is "1", then we have:

log2(4) + log2(2) ?=? 3 
log2(22) + log2(21) ?=? 3 
2 + 1 ?=? 3 
3 = 3

Solve log2(log2(x)) = 1.This may look overly-complicated, but it's just another log equation. To solve this, I'll need to apply The Relationship twice:log2(log2(x)) = 1
21 = log2(x) 
2 = log2(x) 
x = 22 
x = 4Then the solution is x = 4.Solve log2(x2) = (log2(x))2.First, I'll write out the square on the right-hand side:log2(x2) = (log2(x))2 
log2(x2) = (log2(x)) (log2(x))Then I'll apply the log rule to move the "squared", from inside the log on the left-hand side of the equation, out in front of that log as a multiplier. Then I'll move that term to the right-hand side:2log2(x) = [log2(x)] [log2(x)] 
0 = [log2(x)] [log2(x)] – 2log2(x)This may look bad, but it's nothing more than a factoring exercise at this point. So I'll factor, and then I'll solve the factors by using The Relationship:0 = [log2(x)] [log2(x) – 2] 
log2(x) = 0 or log2(x) – 2 = 0 
20 = x or log2(x) = 2 
1 = x or 22 = x 
1 = x or 4 = xThe solution is x = 1, 4.

3 0

3 years ago

Read 2 more answers

Please answer this <3

luda_lava [24]

Answer:

600 sq in

Step-by-step explanation:

5 0

3 years ago

19. A scale drawing of a doctor's office is shown. What are the

Digiron [165]

Answer: 40 by 60

Step-by-step explanation:

You are given a scale of 1 inches=20 ft

For the 2 inch dimension, you get:

2*20=40

For the 3 inch dimension, you get:

3*20=60

Therefore, the real dimensions of the doctors office from 2 in. by 3 in. are respectively 40 ft, by 60 ft.

Hope this helped!

6 0

4 years ago

Read 2 more answers

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable

Deffense [45]

Answer:

C. The random variable is discrete. The possible values are x= 0, 1, 2... 100

C. The random variable is continuous. The possible values are a > 0.

Step-by-step explanation:

Here is the complete question :

Determine whether the random, variable is discrete or continuous.

In each case, state the possible values of the random variable.

(a) The number of people in a restaurant that has a capacity of 100

(b) The square footage of a house.

(a) Is the number of people in a restaurant that has a capacity of 100 discrete or continuous?

A. The random variable is discrete. The possible values are 0≤x≤ 100.

B. The random variable is continuous. The possible values are 0≤x≤ 100.

C. The random variable is discrete. The possible values are x= 0, 1, 2... 100

D. The random variable is continuous. The possible values are x= 0, 1, 2... 100

b) Is the square footage of a house discrete or continuous?

A. The random variable is discrete. the possible values are a > 0

B. The random variable is discrete. The possible values are a = 1, 2, 3...

C. The random variable is continuous. The possible values are a > 0.

D. The random variable is continuous. The possible values are a = 1,2, 3,

A discrete variable is a variable that can be counted. It has a finite amount of values. The number of people in the restaurant is finite. It cannot exceed 100. At any point in time when you count the number of people in the restaurant and it would be between 0 - 100

A continuous variable has an infinite amount of values it can take on. The square footage of a house can be of any size. there is no limit to the size of a house. it can be as small or big as the architect's imagination allows.

8 0

3 years ago