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3 years ago

C is directly proportional to d such that

Mathematics

1 answer:

defon3 years ago

5 0

Answer:

we have

C = 1.5d

d=C/1.5

Step-by-step explanation:

when d is 12

C=1.5×12=18

when c=15

d=15/1.5=10

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Factor the expression completely over the complex numbers.

nekit [7.7K]

Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

$x^3-4x^2+4x-16$

It can be written as

$f(x)=x^3-4x^2+4x-16$

According to the rational root theorem, all possible rational roots are in the form of

$\frac{a_0}{a_n}$

Where, a₀ is constant term and $a_n$ is leading coefficient.

$f(4)=4^3-4(4)^2+4(4)-16=0$

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

$(x^3-4x^2+4x-16)=(x-4)(x^2+4)$

$(x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)$

$(x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)$

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

8 0

4 years ago

Read 2 more answers

3. Uniform A package delivery service breaks up its shipping charges into weight classes, where the package weights are uniforml

Tamiku [17]

Answer:

a) 50% of packages in this class would weigh less than 11 lbs.

b) 25% would weigh more than 11.5 lbs.

c) The average weight for a package in this class is 11 lbs.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

For this problem, we have that:

a. Suppose one of the shipping classes is 10 to 12 lbs. What proportion of packages in this class would weigh less than 11 lbs?

Uniform distribution from 10 lbs to 12 lbs, this means that $a = 10, b = 12$ .

The answer is $P(X \leq 11)$ .

$P(X \leq 11) = \frac{11 - 10}{12-10} = 0.5$

50% of packages in this class would weigh less than 11 lbs.

b. What proportion would weigh more than 11.5 lbs?

Either a package weighs 11.5 lbs or less, or it weighs more than 11.5 lbs. The sum of the probabilities of these events is decimal 1. So:

$P(X \leq 11.5) + P(X > 11.5) = 1$

$P(X > 11.5) = 1 - P(X \leq 11.5)$

$P(X > 11.5) = 1 - \frac{11.5-10}{12-10}$

$P(X > 11.5) = 0.25$

25% would weigh more than 11.5 lbs.

c. What would the average weight for a package in this class be?

The mean M of the uniform distribution is:

$M = \frac{a+b}{2}$

$M = \frac{10+12}{2} = 11$

The average weight for a package in this class is 11 lbs.

5 0

3 years ago

12. The following list shows the number of new memberships that a gym

MrRissso [65]

The answer is B.

Arrange the data in ascending order:
0,2,2,3,4,8,9

The median is the 4th data
= 3

5 0

3 years ago

A company is considering making a new product. They estimate the probability that the new product will be successful is 0.75. If

tensa zangetsu [6.8K]

<span>You take the probability of success (and the revenue generated by it) and the probability of failure (and the cost associated with trying it) and get an expected value:

aP(a) + bP(b)

I hope my answer has come to your help. God bless and have a nice day ahead!

</span>

8 0

4 years ago

Read 2 more answers

It took the Farhats 85 minutes to drive 102 miles. If they this same driving rate, how long will it take them (in minu get to th

STALIN [3.7K]

Answer:

255 minutes

Step-by-step explanation:

306 can be subtracted by 102 a total of 3 times. We know that for every 102 miles = 85 minutes. So 85 * 3 = 255.

8 0

3 years ago