Evaluate the expression,<br> if x = 9, y = 3, and z = 5.<br> z²(x

Unit activity: exponential and logarithmic functions

nirvana33 [79]

We will conclude that:

The domain of the exponential function is equal to the range of the logarithmic function.
The domain of the logarithmic function is equal to the range of the exponential function.

<h3>Comparing the domains and ranges.</h3>

Let's study the two functions.

The exponential function is given by:

f(x) = A*e^x

You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:

y > 0.

For the logarithmic function we have:

g(x) = A*ln(x).

As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:

$\lim_{x \to \infty} ln(x) = \infty \\\\ \lim_{x \to0} ln(x) = -\infty$

So the range of the logarithmic function is the set of all real numbers.

<h3>So what we can conclude?</h3>

The domain of the exponential function is equal to the range of the logarithmic function.
The domain of the logarithmic function is equal to the range of the exponential function.

If you want to learn more about domains and ranges, you can read:

brainly.com/question/10197594

3 0

1 year ago

In each bouquet of flowers, there are 5 roses and 8 white carnations. Complete the table to find

VLD [36.1K]

Answer:

25 roses and 40 white carnations

Step-by-step explanation:

7 0

2 years ago

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What property of equality would you use to solve the equation n/4 = 16.

Triss [41]

Answer:

Multiplication Property of Equality.

Step-by-step explanation:

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other.

Multiply 4 to both sides of the equation:

(n/4) * 4 = (16) * 4

n = 16 * 4

n = 64

n = 64 will be your answer.

~

3 0

2 years ago

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Complete this table to show the sample space for each roll in the game

leva [86]

I'm assuming you only need help with part B. If that's the case, then all we do is add up the values outside of the table to get the inner cell results. For example, in row 1, column 1, we have 1's outside. They add to 1+1 = 2. So we'll have 2 in the first row and first column of the table. The other cells are computed in this way. In figure 1 (see attached image), I show the intermediate step of adding. Then in figure 2, I actually add up the values and show the final result of what the table will look like when all said and done. Take note of the color coding to help see how the values match up for each inner cell of the table. The color coding is optional.

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Edit:

Part C -- Part 1) Probability of rolling double sixes

There are five copies of "6" in the table (see figure 2 of the attached image) out of 36 total possibilities. How did I get 36? It's the result of multiplying 6*6. This is because there are 6 faces per die. As the table shows, there are 6 rows and 6 columns giving 36 cells total.

So we divide the number of times "6" shows up (5 times) out of the number of total possibilities (36 total) to get: 5/36 = 0.1389 = 13.89%

Answer as a fraction: 5/36

Answer as a decimal: 0.1389

Answer as a percent: 13.89%

The decimal and percent forms are approximate

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Part C -- Part 2) Probability of rolling doubles

To roll doubles, all we need to do is roll the same number twice on each die. In other words, we have "twin values" so to speak. Back in part 1 above, we dealt with just '6's showing up twice. There are other doubles as well

The doubles possibilities are:

1 and 1

2 and 2

3 and 3

4 and 4

5 and 5

6 and 6

Each combo listed above only shows up once. So we have 6 instances where we have doubles (one instance per side of the die). This is out of 36 total

Divide the values mentioned: 6/36 = 1/6 = 0.1667 = 16.67%

Answer as a fraction: 1/6

Answer as a decimal: 0.1667

<span>Answer as a percent: 16.67%</span>

The decimal and percent forms are approximate

7 0

2 years ago

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Jen is making a receipt for pancakes.A receipe calls for 4/10 kilogram flour and 12/100 sugar.<br /> if Jen measures corre

lorasvet [3.4K]

If you take the numerator and the denominator from flour and multiply both by 10, you'll get 40/100. then, add 40/100 to 12/100. your answer should be 52/100. if not, look back through your math. hope that helped.

6 0

2 years ago

Evaluate the expression, if x = 9, y = 3, and z = 5. z²(x - y)