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Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

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Answer: Choice C

The probability of getting all heads is the same as the probability of getting all tails

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Explanation:

H = heads

T = tails

In the first row, we have HHH to signify three heads. This shows up 1 time out of 8 outcomes total (each row is a different outcome). The probability of getting HHH is 1/8.

In the last row, TTT means we got three tails. Like with HHH, it only shows up once out of eight times, so the probability of getting TTT is 1/8 as well.

Therefore, both HHH and TTT have the same probability. This is because both sides of the coin have equal chances to land on. If the coin was more biased toward heads for example, then HHH and TTT would have different probabilities.

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Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magne

NikAS [45]

The total number of gifts = x+y.
The inequality is:
$x+y \geq 24$

Key chains cost $1, Magnets $0.50
Total Cost = x + 0.5y
Inequality is:
$x+0.5y \leq 20$

Without graphing you can solve system by using substitution:
$y = 24 - x \\ \\ x + 0.5(24-x) = 20 \\ \\ 0.5x +12 = 20 \\ \\ x = 16 \\ \\ y = 24-16 = 8$

This is one solution where the maximum x value is given.
So the most keychains that can be purchased is 16. However, because magnets are cheaper, more can be purchased as long as cost remains under 20.

If you solve both inequalities for "y", you get the upper and lower bounds for how many magnets can be purchased given a quantity of keychains.

$24-x \leq y \leq 40 -2x \\ \\ x \leq 16$

This is complete solution which gives all possible combinations.
(Graph is Attached)