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3 years ago

Find the derivative. 4) y=(4x+3)^5

Mathematics

1 answer:

Feliz [49]3 years ago

7 0

Answer:

$y'=20(4x+3)^{4}$

Step-by-step explanation:

We can find the derivative using the <u>chain rule.</u>

To get the derivative of an expression with an exponent you multiply the expression by the exponent and raise it to the power of the exponent minus one.

Then multiply it by the derivative of the expression inside the parentheses.

The derivative of 4x+3 is 4, so multiply the rest by 4.

Therefore the derivative is:

$y'=5(4x+3)^{4} *4\\y'=20(4x+3)^{4}$

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Answer:

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d) 0.2375

Step-by-step explanation:

We are given the following:

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Then the securities lose value follows a binomial distribution, where

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c) P(at least 15 of them lose value.)

$P(x \geq 15)\\= P(x=15) + P(x = 16) + P(x=17) + P(x=18) +P(x = 19) +P(x = 20)\\ \binom{20}{15}(0.7)^{15}(1-0.7)^{5} +...+ \binom{20}{20}(0.7)^{20}(1-0.7)^{0} \\=0.4163$

d) P(less than 5 of them gain value.)

P(gain value) = 1 - 0.7 = 0.3

$P(x < 5)\\= P(x=0) + P(x = 1) + P(x=2) + P(x=3) +P(x = 4)\\ \binom{20}{0}(0.3)^{0}(1-0.3)^{20} +...+ \binom{20}{4}(0.3)^{4}(1-0.3)^{16} \\=0.2375$

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