A problem states: "There are 9 more children than parents in a room. There are 25 people in the

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

3 years ago

A. Statistics is the science ofâ€‹ manipulating, reorganizing, and editing information to produce the desired results. Inâ€‹ add

Jlenok [28]

Answer:

The correct definition of statistics is

B. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw a conclusion and answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.

Explanation:

Statistics is the science of collecting, organizing, summarizing, and analyzing the information and based on this information a conclusion is drawn about the collected information. There are two main divisions of statistics:

1. Descriptive statistics: It deals with providing the summary about the information collected.

2. Inferential statistics: This division deals with using a sample from the population and drawing the conclusion about the population using the sample. It also includes providing a measure of confidence in any conclusions.

8 0

3 years ago

. Mrs. Khan makes cookies for the school bake sale. She uses the equation c = 0.75x to determine the cost, c, for x cookies. Whi

IRINA_888 [86]

Answer:

The answer is D.

Step-by-step explanation:

3 0

2 years ago

Find the equation of the line that passes through the points : (4 , -1 ) and (0 , -3)

Sergio [31]

Answer:

B. y= 1/2 x - 3

Step-by-step explanation:

base equation: y= mx+ b

slope(m) equation: $\frac{y_{2}-y_{2} }{x_{2} -x_{1} }$

y2= -1 y1= -3

x2= 4 x1= 0

$\frac{-1 - (-3)}{4-0} =\frac{2}{4} = \frac{1}{2}$

y- intercept: -3

found by taking the y from (0,-3)

3 0

2 years ago

PLEASE MATH HELP WILL GIVE BRAINLIEST

hram777 [196]

The answer is 32.72 degree.
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7 0

2 years ago