There are 10 cups placed on a table face down. Beneath each cup is one coin. Together, there are 5 quarters, 2 nickels, and 3 dimes. One cup is randomly selected, replaced, and then another cup is selected. What is the probability of getting a quarter then a nickel? The options are
- 3/20
- 1/10
- 1/9
- 7/10
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7/10

Step-by-step explanation:

Add the nickels and quarters together. 5+2=7

The sum of the two numbers is the answer out of ten because there are only 10 coins.

The domain is  -∞ < x < ∞

The range is y > -1

The x-intercept is 0

The y-intercept is 0

Step-by-step explanation:

∵ f(x) = 0.4^x - 1

∴ The domain is all real numbers -∞ < x < ∞

∴ The range of it is y > -1

Note: If the range of f(x) = b^x , where b > 0 and b ≠ 1 is y > 0 ,

If f(x) is shifted down 1 unit (f(x) - 1) , then the range will be y > -1

∵ f(x) = 0 ⇒ 0.4^x - 1 = 0

∴ 0.4^x = 1 ⇒ ∴ x = 0

∴ The x-intercept is 0

∵ f(0) = 0.4^0 - 1 = 1 - 1 = 0

∴ The y-intercept is 0

∴ The graph of f(x) = 0.4^x - 1 passing through the origin point

Table:

x ⇒ f(x)

-2 ⇒ 5.25

-1  ⇒ 1.5

0 ⇒ 0

1  ⇒ -0.6

2 ⇒ -0.84