Fill in the table 1. 1 2. 3 4 15

What is the maximum product of two numbers that add to 24?

Flura [38]

Let x and y represent the two numbers that add up to 24.

x + y = 24

=> y = 24 - x

The product of the two numbers is P = x*y = x*(24 - x) = 24x - x^2.

To maximize the product P, solve P' = 0 for x.

P' = 24 - 2x

24 - 2x = 0

=> x = 12

Also P'' = -2 which is negative

for x = 12

The product when x = 12 is 12*12 = 144

hope it helps!

6 0

3 years ago

How much times is 1,700,000,000 greater than 400,000,000

Yuri [45]

Answer:

4.25(Divided) or 1,300,000,000(subtracted)

5 0

2 years ago

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

Alex_Xolod [135]

Answer:

a) 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) 80.5% probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

c) 4.074

d) Variance 3.24, standard deviation 1.8

Step-by-step explanation:

For each internet browser user, there are only two possible outcomes. Either they use chrome, or they do not. They are chosen at random, which means that the probability of an user using chrome is independent from other users. So we use the binomial probability distribution 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.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

20.37% share of the browser market

This means that $p = 0.2037$

Group of 20 Internet browser users

This means that $n = 20$

(a) Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is $P(X = 8)$

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

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

(b) Compute the probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

Either less than 3 users use Chrome, or at least 3 do. The sum of the probabilities of these events is decimal 1. So

$P(X < 3) + P(X \geq 3) = 1$

So

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.195$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.195 = 0.805$

80.5% probability that at least 3 of the 20 Internet browser users use Chrome as their Internet browser.

(c) For the sample of 20 Internet browser users, compute the expected number of Chrome users.

$E(X) = np = 20*0.2037 = 4.074$

(d) For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

$V(X) = np(1-p)$

$V(X) = 20*0.2037*0.7963 = 3.24$

The standard deviation is the square root of the variance. SO

$\sqrt{V(X)} = \sqrt{3.24} = 1.8$

8 0

3 years ago

Which term best describes a major arc of a circle that has the same starting

sashaice [31]

Answer:

Circumference! it's the major arc whose starting and ending point coincide.

8 0

3 years ago

The five marathon runners weigh an average weight of 92 pounds, Nicole weighs 89 pounds, Jon weighs 95 pounds, Jenny and Kim wei

Juli2301 [7.4K]

Answer:

Jordin weighs 96 pounds

Step-by-step explanation:

The Mean Value of a Data Set

The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:

$\displaystyle \bar x=\frac{\sum x_i}{n}$

Where xi is the value of each data and n is the total number of values.

We are given the average weight of n=5 marathon runners:

$\bar x=92$

Multiplying the formula by n and expanding the sum:

$n\bar x=\sum x_i=x_1+x_2+x_3+x_4+x_5$

We are given the weighs of four of the runners:

$5*92=89+95+90+90+x_5$

$460=364+x_5$

Solving for x5:

$x_5 = 460-364=96$

Jordin weighs 96 pounds

7 0

3 years ago