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lilavasa [31]
3 years ago
7

Use complete sentences to explain the process of converting a logarithmic equation to its equivalent exponential form to obtain

solutions to the graph of the logarithmic equation.
Mathematics
2 answers:
aalyn [17]3 years ago
7 0

Answer:

To convert a logarithmic equation to its equivalent exponential form : We must first state the definition of log :

For x > 0 and b > 0 , b ≠ 1 ,

y=\log _b x\text{ is equivalent to }b^y=x

Now, follow these steps to convert logarithmic to exponential function :

  1. To change from logarithmic form to exponential form, first identify the base of the logarithmic equation.
  2. Now, After moving the base the current variable or number changes to the exponent.
  3. Do not move anything but only the bases so that the other number or variables will not change sides .
  4. Hence, The log function will be removed.
DanielleElmas [232]3 years ago
5 0
Knowing that logarithm functions and exponential functions are inverse to each other, the procees to convert a logarithmic equation to its equivalent is to perform all the operations to set an equation of the typ:

 log _{b}x = y,

 then invert to show it equivalent form:

 x= b^{y}.

With that you have solved the equation for x.
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5
masya89 [10]

Answer:

z= \frac{3.44-2.54}{0.45}=2

P(X>3.44) = P(Z>2) = 0.025

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties

Where \mu=2.54 and \sigma=0.45

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

z= \frac{3.44-2.54}{0.45}=2

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

P(X>3.44) = P(Z>2) = 0.025

5 0
3 years ago
Whats (4.2×10^6)+(2.25 × 10^5) in scientific form
lys-0071 [83]
We are going to rewrite both numbers:
 (4.2 × 10 ^ 6) = 4200000
 (2.25 × 10 ^ 5) = 225000
 Adding we have:
 4200000 + 225000 = 4425000
 Rewriting in exponential notation we have:
 4425000 = 4,425 * 10 ^ 6
 Answer:
 
(4.2 × 10 ^ 6) + (2.25 × 10 ^ 5) is equal to:
 
4,425 * 10 ^ 6
8 0
3 years ago
Solve y=(x-1)^ +4
Dimas [21]

Answer:

,nm

Step-by-step explanation:

3 0
2 years ago
The map shows the length of two trails used for a race around a lake. What is the total distance of the race? A trail race map.
ra1l [238]

Answer:

2

Step-by-step explanation:

4 0
3 years ago
Please help! Explain as well since I need to know material for the test
Illusion [34]

3a)

<h3>Answer: The sum of a+b+c+d is equal to 220</h3>

-------------

How I got this answer:

a+b+e = 180

c+d+f = 180

angles 'e' and 'f' are marked in the attached drawing below (see figure 1)

Add the two equations to get

(a+b+e)+(c+d+f) = 180+180

a+b+e+c+d+f = 180+180

a+b+e+c+d+f = 360

(a+b+c+d)+(e+f) = 360

(a+b+c+d)+(140) = 360 substutition (see below)

a+b+c+d = 360-140

a+b+c+d = 220

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

3b)

The angles of the triangles add to 180 degrees each. The three angles e, f, and 40 add to 180 as well as they form a straight angle, so e+f+40 = 180 leading to e+f = 180-40 = 140. This will help us with the substitution rule I marked above

So the idea is you add up all the angles, and then take away the angles we don't want (e and f) so we end up with the sum of a+b+c+d

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

4

<h3>Answer: 290</h3>

---------------------

Explanation:

Check out the attached image figure 2.

Angle DAE is given to be 30 degrees. Angle ADC is also equal to 30 because they are alternate interior angles.

Angle DCB is 40 degrees. The missing angle x of the triangle DCB is unknown for now, but we can solve for x

x+40+30 = 180

x+70 = 180

x = 180-70

x = 110

Therefore the purple angle marked in that diagram is 180-x = 180-110 = 70

The reflex angle to the 70 degree angle is 360-70 = 290

which is the shaded angle we want to determine

5 0
3 years ago
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