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3 years ago

If Logan(3)=5, what is the value of a^5?

Mathematics

2 answers:

Archy [21]3 years ago

8 0

Answer:

$a^5=3$

Step-by-step explanation:

When it comes to exponential expressions and logarithms, the following relationship applies:

$\log_b{(x)}=a\ \leftrightarrow\ b^a=x$

Here, it means ...

$\boxed{a^5=3}$

sammy [17]3 years ago

3 0

Answer:

$\huge \purple { \boxed{{a}^{5} = 3}}$

Step-by-step explanation:

$log_{a}(3) = 5 \\ 3 = {a}^{5} \\ \huge \red { \boxed{{a}^{5} = 3}}$

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3 years ago

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Solve the linear equation 2x+2/4=189.5

seraphim [82]

Change 2/4 to 1/2
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Subtract 1/2 from both sides(1/2 = .5)
2x=189
Divide both sides by 2
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3 years ago

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3 years ago

Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. 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.

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

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.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

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

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

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

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

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

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

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

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

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

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

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

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

8 0

3 years ago

John is buying food for his cat, Fluffy. Fluffy LOVES a fancy wet food which costs $1.50 per day. Fluffy will also tolerate dry

Vedmedyk [2.9K]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of days that fluffy eats wet food in a week and y represents the number of days that fluffy eats dry food in a week.

Hence:

x + y = 7 (1)

Also, John wants to spend at most $9.00 on cat food each week. Hence:

1.5x + 0.75y ≤ 9 (2)

The list of possible points after solving graphically are:

(0,7), (6,0), (0,12) and (5, 2). If x,y > 0, then the point that satisfies the inequality is:

(5, 2) i.e. 5 wet food and 2 dry food

5 0

2 years ago

If Logan(3)=5, what is the value of a^5?​

If Logan(3)=5, what is the value of a^5?