Answer:
0.13
Detailed explanation:
In a bag containing 5 nickels, 8 dimes, and 7 quarters, we randomly select 5 coins at once.
This means we need to pick 2 nickels from the 5 available, 2 dimes from the 8, and 1 quarter from the 7 quarters.
In total, there are 5 + 8 + 7 = 20 coins.
Selecting 5 coins from the entire set of 20 coins.
2 nickels can be chosen from 5 in 5C2 ways.
2 dimes can be taken from 8.
1 quarter from 7 quarters.
5 coins chosen from 20.
The probability of obtaining 2 nickels, 2 dimes, and 1 quarter is given by:
The sale price S (in dollars) of an item is calculated using the formula
S = L - rL, where L represents the list price (dollars) and r denotes the discount rate.
Rearranged, this becomes:
rL = L - S
and thus
r = 
which simplifies to
r = 
Given the shirt's list price is $30, we will compute the discount rate accordingly.
Hence, the discount rate r equals 
.
Response:
45.54m
Step-by-step breakdown:
See the provided figure
Scarlett's height is represented as AB = 1.65 meters
She stands 90 meters away from the dam, so BE = AC = 90 m
Scarlett measures the angle of elevation to the dam's summit at 26º, which is ∠DBE = 26°
Height of the Dam = DC = EC+DE
AB = EC = 1.65
In triangle BDE
Height of the Dam = DC = 1.65 + 43.89 = 45.54 m
Therefore, the dam's height is 45.54 m.
Answer: The unknown values x and y correspond to 8 and 20, specifically;
(x, y) = (8, 20)
Step-by-step explanation: The equation y = 16 + 0.5x represents a linear relationship that can be illustrated with a graph. This indicates that values for x and y can be located at various points on the line.
The ordered pairs signify that for each x value, there exists a matching y value.
The values listed in a two-column format for x and y all fulfill the equation y = 16 + 0.5x. Observing the first example, the pair (-4, 14) is presented.
This reveals that when x is -4, y will be 14.
Where y = 16 + 0.5x
y = 16 + 0.5(-4)
y = 16 - 2
y = 14
Thus, the first pair, similar to the other pairs, satisfies the equation.
Consequently, by reviewing the options provided, we can deduce which one fulfills the equation.
(option 1) If x = 0
y = 16 + 0.5(0)
y = 16 + 0
y = 16
(0, 16)
(option 2) If x = 5
y = 16 + 0.5(5)
y = 16 + 2.5
y = 18.5
(5, 18.5)
(option 3) If x = 8
y = 16 + 0.5(8)
y = 16 + 4
y = 20
(8, 20)
Our calculations confirm that the third option (8, 20) is the correct ordered pair for x and y.
Step-by-step explanation:
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