You have a set of numeric tiles, from 1 and 6. You randomly chose one tile. How many possible outcomes are there?

The graphs of f(x) = 10x and its translation, g(x), are shown. On a coordinate plane, 2 exponential functions are shown. f (x) a

cricket20 [7]

Answer:

$g(x)=(10)^{x-3}$

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial amount (x = 0) , b is the growth factor

- If b > 1 , then the function is exponential growth function

- If 0 < b < 1 , then the function is exponential decay function

- If the function translated horizontally by h units to the right , then

the new function is $g(x)=a(b)^{x-h}$

- If the function translated horizontally by h units to the left , then

the new function is $g(x)=a(b)^{x+h}$

- If the function translated vertically by k units up , then the new

function is $g(x)=a(b)^{x}+k$

- If the function translated vertically by k units down , then the new

function is $g(x)=a(b)^{x}-k$

* Lets solve the problem

∵ f(x) is an exponential function

∵ Points (0 , 1) , (1 , 10) , (2 , 100) belong to f(x)

- g(x) is the image of f(x) after translation

∵ Points (3 , 1) , (4 , 10) , (5 , 100) belong to g(x)

∵ point (0 , 1) on f(x) becomes (3 , 1) on g(x)

∵ point (1 , 10) on f(x) becomes (4 , 10) on g(x)

∵ point (2 , 100) on f(x) becomes (5 , 100) in g(x)

∵ All the y-coordinates of the points on the function f(x) are the same

with the y-coordinates of the points on the function g(x)

∴ There is no vertical translation

∵ The x-coordinates of the points on the function f(x) are added by

3 units to give the x-coordinates of the points on the function g(x)

∴ f(x) is translated 3 units to the right

∵ $f(x)=(10)^{x}$

∴ $g(x)=(10)^{x-3}$

- Look to the attached graph for more understand

# Red graph represents f(x)

# Blue graph represents g(x)

4 0

2 years ago

Read 2 more answers

Find the correlation coefficient of the line of best fit for the points (-3,-40), (1,12), (5,72), (7,137). Explain how you guy y

vodka [1.7K]

Answer:

r = 0.9825; good correlation.

Step-by-step explanation:

One formula for the correlation coefficient is

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}$

The calculation is not difficult, but it is tedious.

1. Calculate the intermediate numbers

We can display them in a table.

x y xy x² y²

-3 -40 120 9 1600

1 12 12 1 144

5 72 360 25 5184

7 137 959 49 18769

Σ = 10 181 1451 84 25697

2. Calculate the correlation coefficient

$r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}$

The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.

3 0

1 year ago

Jenny is taking a vacation to Florida. She travels 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. O

Helga [31]

Jenny traveled 70 km/h over 2 hours and 63 km/h over 5 hours. Her travel time was a total of 7 hours.

We need to find out how far she traveled during this 7-hour period.

70 km/h * 2 h = 140 km
63 km/h * 5 h = 315 km

Then, we can add 140 km and 315 km to get a total distance traveled of 455 km/h.

We were asked to find the average speed. We can find it now, since we have total distance traveled (455 km) and total time taken (7 hours).

Then,
455km / 7h = 65 km/h.

6 0

2 years ago

In which set do all of the values make the inequality 2x - 1 < 10 true?

igomit [66]

$2x - 1 < 10\Leftrightarrow 2x < 11\Leftrightarrow x < \frac{11}{2}$