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2 years ago

Please can you give me the answers to the questions above in standard form.

Mathematics

1 answer:

ivanzaharov [21]2 years ago

3 0

Answer:

a) $4.5 \times 10^{11}$

b) $3.5 \times 10^{3}$

Step-by-step explanation:

a) We have to simplify the below expression in standard form.

The expression is $(5\times 10^{3}) \times (9 \times 10^{7})$

Now, $(5\times 10^{3}) \times (9 \times 10^{7})$

= $(9 \times 5) \times (10^{3} \times 10^{7})$

= $45 \times 10^{(3 + 7)}$ {Since $a^{b} \times a^{c} = a^{(b + c)}$ }

= $45 \times 10^{10}$

= $4.5 \times 10^{11}$ (Answer)

b) We have to simplify the below expression in standard form.

The expression is $(7\times 10^{5}) \div (2 \times 10^{2})$

Now, $(7\times 10^{5}) \div (2 \times 10^{2})$

= $(7 \div 2) \times (10^{5} \div 10^{2})$

= $3.5 \times 10^{(5 - 2)}$ {Since $a^{b}\div a^{c} = a^{(b - c)}$ }

= $3.5 \times 10^{3}$ (Answer)

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There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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$P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219$

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3 years ago

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3 years ago

Please can you give me the answers to the questions above in standard form.​

Please can you give me the answers to the questions above in standard form.