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3 years ago

How do you solve 3x+1 = 15 for x using the change of base formula log base b of y equals log y over log b?

Mathematics

2 answers:

DerKrebs [107]3 years ago

8 0

Anwser is 14/3

Subtract the 1 and divide by 3

Ket [755]3 years ago

7 0

Answer with explanation:

The given equation in single variable x, is

⇒3 x+1=15

Subtracting 1 from both sides

⇒ 3 x +1 -1 = 15- 1

⇒3 x =14

Dividing both sides by, 3 we get

$x=\frac{14}{3}\\\\x=log_{10}\frac{14}{3}\\\\ \log_{a}b=\frac{\log b}{\log a}$

Because ,log 10=1

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Sean’s mom asks him how long his homework will take

horrorfan [7]

I mean at least 45 min to finish it

8 0

3 years ago

On a biased dice the probability of getting 1 is 0.3. The ice is rolled 150 times. How many ones would you expect to roll?

Montano1993 [528]

Answer: 45

=====================================================

Work Shown:

n = number of rolls = 150

p = probability of rolling a "1" = 0.3

n*p = expected number of "1"s that show up out of the 150 rolls

n*p = 150*0.3

n*p = 45

We expect about 45 ones will show up.

8 0

2 years ago

PLEASE HELP!!!!!

Zielflug [23.3K]

Question #1

Part A:
The y-intercept can be found when x = 0. If you look at your table, when x = 0, y = 5. So the y-intercept is 5.

Part B:
$\sf Slope = \frac{27-5}{1-0} = \frac{22}{1} = \boxed{22}$
The slope is 22.

Part C:
y = mx + b
y = 22x + 5

We are given 225 as the range, or in place of y.
225 = 22x + 5
220 = 22x
x = 10

The domain is 10.

Question #2

Part A:

(2,255)
(5,480)

Standard form is Ax + By = C

$\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{480-225}{5-2} = \frac{255}{3} = \boxed{85}$

Let's plug this into this form first:
$y - y_1 = m(x-x_1)\\\\y -225 = 85(x-2)\\\\y - 225 = 85x - 170\\\\y = 85x + 55$

Now, let's make it into Standard Form.
$y = 85x + 55\\\\y - 85x + 55\\\\ -85x + y = 55\\\\ -1(-85x +y) = -1(55)\\\\\boxed{85x - y = -55}$
What, which is in the box, is your final answer. :)

Part B:
Function notation simply means replacing y with f(x).
We had y = 85x + 55
So your answer is:
$\boxed{f(x) = 85x + 55}$

Part C:
Using the final answer which we got in Part A, we would know that the y-intercept is (0,55) and the x-intercept is (-55/85, 0). We would plot these 2 points, and then draw a line between them. :)

5 0

3 years ago

Emerson earns money from walking dogs and answering surveys. He earns $5 a week for each dog he walks and $0.10 for each survey

maria [59]

Part A: X=(35-(100*0.10))/5 35= 5X+(100*0.10)
Where X is the number of dogs he walked.

Part B: To solve the equation just simplify it by using inverse operations. It should give you 5 dogs walked. The algebraic property justifying this is inverse operations.

Part C: Emerson walked 5 dogs last week.

8 0

2 years ago

Read 2 more answers

Which measure of center will provide the most accurate estimation of the deposits for the savings account? Why?

faust18 [17]

Hello,

First you have order all the number least to the greater. That gives 30, 75, 80, 85, 85, 95, 95, 100, 100, 110.

Afterwards you have to find the median. Why ?

I will explain you. It's because the median is robust. In fact, it can't be influenced by extreme values (example : 110) but the mean yes. So the mean won't be accurate.

"Then why don't you choose the mode ? " you will ask me. That's because the mode takes the number which appears most often in a set of numbers. It couldn't be accurate at all. It will be useless for this set of numbers.
Furthermore, here there are 3 numbers which appears the most ( 2 times for each) : $85, $95 and $100. Which one will you take ?

Therefore the median is the most suitable and the most accurate to know the center because it is robust.

Now, let's find the median :

There are 10 values, so the median will be the average of the 5th and 6th values.

5th value = 85
6th value = 95

$\frac{(85+95)}{2}$
$= 90$

Therefore the median is 90.

Hope this helps !

Photon

4 0

3 years ago