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3 years ago

(x-4)(ax^2+3x+b)=3x^2+cx^2+dx-12

Mathematics

1 answer:

Mkey [24]3 years ago

7 0

Answer:

a=3, b=3, c=-9, d=-9

Step-by-step explanation:

Expand the left side, Then combine like terms, then set the term on the left side equal to the term on the right with the same power of x (ex. set ax^3=3x^2) Then a=3. Do this for a,b,c, and d

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Write the sum of the numbers as the product of their GCF and another sum <br> 56+64

olga2289 [7]

This is a question about finding the GCF or the greatest common factor for these two numbers. The real question there is what is the largest number that both 56 and 64 can be divided by and still give out integers (meaning, whole regular counting numbers). This number turns out to be 8. 56/8 = 7. 64/8 = 8. The GCF gets pulled to the outside of the parenthesis and the divided numbers remain on the inside being added together. It looks like this, 8(7+8).

7 0

3 years ago

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes. Assu

denis-greek [22]

Answer:

43.46% probability that the person will need to wait at least 9 minutes total

Step-by-step explanation:

To solve this question, we need to understand conditional probability and the exponential distribution.

Conditional probability:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Expontial distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

In this question:

Event A: Waited at least 4 minutes.

Event B: Waiting at least 9 minutes.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.

This means that $m = 6, \mu = \frac{1}{6}$

Probability of waiting at least 4 minutes.

$P(A) = P(X \geq 4) = P(X > 4)$

$P(A) = P(X > 4) = e^{-\frac{4}{6}} = 0.5134$

Intersection:

The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So

$P(A \cap B) = P(X > 9) = e^{-\frac{9}{6}} = 0.2231$

What is the probability that the person will need to wait at least 9 minutes total

$P(B|A) = \frac{0.2231}{0.5134} = 0.4346$

43.46% probability that the person will need to wait at least 9 minutes total

8 0

4 years ago

A rectangular garden measuring 13 meters by 15 meters is to have a gravel pathway of constant width built all around it. There i

Shtirlitz [24]

Let w represent width of the pathway.

We have been given that a rectangular garden measuring 13 meters by 15 meters is to have a gravel pathway of constant width built all around it.

Since pathway will be on all sides, so new length and width of garden with pathway would be $13+2w$ by $15+2w$ .

We are also told that there is enough gravel to cover 80 square meters. This means that area f pathway should be equal to 80 square meters.

The area of the pathway will be equal to area of garden with new dimensions minus area of garden with original dimensions.

We know that area of rectangle is width times length.

$\text{Area of pathway}=(15+2w)(13+2w)-15(13)$

Since we are asked to write an inequality that represents all possible widths(w), in meters, of the pathway, so area of pathway should be less than or equal to 80 square meters.

$(15+2w)(13+2w)-15(13)\leq 80$