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3 years ago

Use the change of base formula to evaluate log3(73).

1 answer:

3 0

The change of base formula allows you to write a logarithm in terms of logarithms with another base. It follows this pattern,

$log_{a}x = \frac{ log_{b}x }{log_{b}a }$

where a≠1 and b≠1

Assigning the base to be 7,

$log_{3}73 = \frac{ log_{7}73 }{log_{7}3 }=3.9$

I hope I was able to answer your question. Have a good day.

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Suppose a basketball player has made 231 out of 361 free throws. If the player makes the next 2 free throws, I will pay you $31.

statuscvo [17]

Answer:

The expected value of the proposition is of -0.29.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Suppose a basketball player has made 231 out of 361 free throws.

This means that $p = \frac{231}{361} = 0.6399$

Probability of the player making the next 2 free throws:

This is P(X = 2) when n = 2. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.6399)^{2}.(0.3601)^{0} = 0.4095$

Find the expected value of the proposition:

0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.

1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So

$E = -31*0.4095 + 21*0.5905 = -0.29$

The expected value of the proposition is of -0.29.

3 0

2 years ago

In bungee jumping, a bungee jump is the amount the cord will stretch at the bottom of the fall. The stiffness of the cord is rel

aleksandr82 [10.1K]

Answer:

6.7ft

Step-by-step explanation:

190÷28=6.7 is correct

6 0

3 years ago

Please help!!

postnew [5]

$2 \frac{5}{8} \div 2 \frac{1}{2}$
Change the mixed fractions to improper fractions.
To do this, multiply the whole number part by the denominator. Add that to the numerator. Then write the result on top of the denominator.

You would now have:
$\frac{21}{8} \div \frac{5}{2}$
Change the division sign to a multiplication sign by turning the second fraction upside down.
That is,
$\frac{21}{8} \times \frac{2}{5}$

The answer is:
$\frac{42}{40}$

This can be simplified to:
$\frac{21}{20}$

8 0

3 years ago

I dont understand linear equations.

Sonbull [250]

Ck12 has great sources

3 0

2 years ago

Read 2 more answers

A study done recently 3out of 5 results used brand x how many used brand x out of 2000

Afina-wow [57]

(3/5 )*2000 would give you 1200, which is your answer

6 0

3 years ago