What's the taxes on $1,500

nventing is a difficult way to make money. Only 5% of new patents earn a substantial profit. A certain city has just had30 indep

Arlecino [84]

Answer:

$P(X \geq 2) = 1-P(X$

And we can find the individual probabilities using the probability mass function and we got:

$P(X=0) = (30C0) (0.05)^0 (1-0.05)^{30-0} =0.2146$

$P(X=1) = (30C1) (0.05)^1 (1-0.05)^{30-1} = 0.3389$

And replacing we got:

$P(X \geq 2) = 1-P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=30, p=0.05)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Solution to the problem

For this case we want this probability:

$P(X \geq 2)$

And we can use the complement rule and we got:

$P(X \geq 2) = 1-P(X$

And we can find the individual probabilities using the probability mass function and we got:

$P(X=0) = (30C0) (0.05)^0 (1-0.05)^{30-0} =0.2146$

$P(X=1) = (30C1) (0.05)^1 (1-0.05)^{30-1} = 0.3389$

And replacing we got:

$P(X \geq 2) = 1-P(X$

3 0

3 years ago

Sam decides to build a square garden. If the area of the garden is 25x2 + 30x + 9 square feet, what is the length of one side of

seropon [69]

The correct answer is C. (5x+3) feet, and here is how I got it.
This is the equation you need to use:
(a+b)^2 = (a+b) (a+b)
So, let us plug in 5x and 3 here:
(5x+3)^2 = (5x+3)(5x+3) = 25x^2 + 15x + 15x + 9 = 25x^2 + 30x + 9 which is the area of the garden.

5 0

3 years ago

Adam has been asked to post a parcel for a family member. He has been told that the parcel weighs 12 lbs 8 oz. 1lb = 16 oz 1lb =

yarga [219]

Answer:

Weight of parcel to the nearest whole kilogram = 6 kg

Explanation:

Weight of parcel = 12 lbs 8 oz

1lb = 16 oz also we have 1lb = 454 g

Weight of parcel = 12 lbs 8 oz = 12 + (8/16) lbs = 12.5 lbs

Weight of parcel in g = 12.5*454 = 5675 g

Weight of parcel = 5675 g = 5.675 kg

Weight of parcel to the nearest whole kilogram = 6 kg

8 0

3 years ago

Write and equation of the line that passes through the pair of points (4,6) and (-1,1)

bazaltina [42]

Answer:

y = x + 2

Step-by-step explanation:

Step 1: Find the slope

$m=\frac{y2-y1}{x2-x1} = \frac{6-1}{4-(-1)}=\frac{6}{6} =1$

Step 2: Substitute the slope and a point in to find y intercept

(6)=(1)(4)+b

6 = 4 + b

b = 2

Step 3: Substitute all the information in

y = x + 2

Therefore the equation for a line that passes through (4,6) and (-1,1) is y = x + 2

7 0

3 years ago

Read 2 more answers

A band consists of 3 woodwinds for every 7 members of the band. The independent quantity represents the total members of the ban

IgorC [24]

Answer: $k=\frac{3}{7}$

Step-by-step explanation:

For this exercise it is important to remember the following:

The constant of proportionality, which is represented as "k", describe the constant ratio of two quantities that are proportional (the independent and dependent variables).

In this case we know that the independent quantity represents the total members of the band and the dependent quantity represents the woodwind members of the band.

Since the band consists of 3 woodwinds for every 7 members of the band, we can conclude that the constant of proportionality for this relationship is:

$k=\frac{3}{7}$

8 0

3 years ago