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3 years ago

What is the value of 4a3 – 2b2 + 5 when a = 3 and b = −2?

Mathematics

2 answers:

kenny6666 [7]3 years ago

8 0

4a(3)-2b(2)+5
4(3)(3)-2(-2)(2)+5
12(3)-(-4)(2)+5
36-(-8)+5
44+5
49
The answer is 49.

Fittoniya [83]3 years ago

6 0

4a3 – 2b2 + 5

= 4 * 3^3 - 2 * (-2)^2 + 5

= 4 * 27 - 2 * 4 + 5

= 96 - 8 + 5

= 93

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<u>Use the Binomial Theorem</u>

$\displaystyle P(X=x)=\binom{n}{x}p^xq^{n-x}\\\\P(X=4)=\binom{30}{4}(0.30)^4(1-0.30)^{30-4}\\\\P(X=4)=\frac{30!}{4!(30-4)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30!}{4!(26)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30*29*28*27}{4*3*2*1}(0.30)^4(0.70)^{26}\\ \\P(X=4)=27405(0.30)^4(0.70)^{26}\\\\P(X=4)\approx0.0208$

We have the probability of success, $p=0.30$ , and the probability of failure, $q=1-0.30=0.70$ . The binomial coefficient, $\binom{n}{k}$ , represents the amount of possible combinations that $k$ items can be chosen out of $n$ items, with its respective formula $\frac{n!}{k!(n-k)!}$ .

Hence, the best choice for the probability that 4 students chosen at random from the class of 30 that want the next test to be on Monday will be option B, 0.02

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2 years ago