GRADE 11 MATH

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

4 0

The amount that was invested 17 years ago is $2064.25.

The interest earned is $7935.75.

<h3>What is the amount invested 17 years ago?</h3>

The formula that would used to determine the amount that was invested 17 years ago is:

P = FV / (1 + r)^nm

Where:

FV = Future value = 10,000
P = Present value
R = interest rate = 9.5 / 2 = 4.75%
m = number of compounding = 2
N = number of years = 17

10,000 / (1.0475)^(17 x 2) = $2064.25

Interest earned = 10,000 - 2064.25 = $7935.75

To learn more about future value, please check: brainly.com/question/18760477

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$P(x)=\, ^nC_xp^x(1-p)^{n-x}$

Part A:

The probability of observing 8 heads and 12 tails is given by:

$P(8)=\, ^{20}C_8p^8(1-p)^{20-8}=\, ^{20}C_8p^8(1-p)^{12}$

Part B:

<span>You observe more than 8 heads and more than 8 tails, when you observe 9 heads and 11 tails, 10 heads and 10 tails, and 11 heads and 9 tails.

Therefore, the probability of </span><span>observing more than 8 heads and more than 8 tails</span> is given by:

$P(9)+P(10)+P(11) \\ \\ =\, ^{20}C_9p^9(1-p)^{20-9}+\, ^{20}C_{10}p^{10}(1-p)^{20-10}+\, ^{20}C_{11}p^{11}(1-p)^{20-11} \\ \\ =\, ^{20}C_9p^9(1-p)^{11}+\, ^{20}C_{10}p^{10}(1-p)^{10}+\, ^{20}C_{11}p^{11}(1-p)^{9}$