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3 years ago

The sum of three consecutive even numbers is 48. what is the smallest of these numbers?

Mathematics

1 answer:

wlad13 [49]3 years ago

5 0

Answer:

The smallest number is 14

Step-by-step explanation:

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The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit

wolverine [178]

Answer:

(a) $\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

(b)P'(5)=-($4.54) Thousand

(c)P'(11)=-($2.10) Thousand

(d)The fifth Month

Step-by-step explanation:

Given the monthly profit model:

$P(t)=\frac{240t-40t^2}{t^2+20}$

(a)We want to derive a model that gives the Marginal Profit, P' of the book.

We differentiate

$P(t)=\frac{240t-40t^2}{t^2+20}$ using quotient rule.

$\frac{dP}{dt}=\frac{(t^2+20)(240-80t)-(240t-40t^2)(2t)}{(t^2+20)^2}$

Simplifying

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

$\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}$

$P^{'}(5)=\frac{4800-1600(5)-240(5)^2}{(5^2+20)^2}$

=-($4.54) Thousand of dollars

(c)Marginal Profit 11 Months after book release

$P^{'}(11)=\frac{4800-1600(11)-240(11)^2}{(11^2+20)^2}$

=-($2.10) Thousand of dollars

(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.

6 0

3 years ago

perform the steps for dividing the two polynomials using synthetic division. state the quotient, q(x), and the remainder, r(x).

Ad libitum [116K]

Answer:

This particular equation cannot be solved using synthetic division as you can only use synthetic division when divided by a linear factor.

Step-by-step explanation:

5 0

3 years ago

If bc is the diameter of the circle below, what is the area of the circle

dangina [55]

Answer:

option a.

radius of the circle=3 units.

area of the circle= pi×r²

area of circle=pi×3²

area of circle=pi×9units²

5 0

3 years ago

Read 2 more answers

What is blank/11 = 12/44 equivalent fractions

nordsb [41]

Answer:

3/11

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these ho

riadik2000 [5.3K]

Answer:

Step-by-step explanation:

Suppose F represents the value that a room is unlocked.

Then, we can assume that the probability of unlocked homes is:

P(unlocked homes) = P(U)

P(unlocked homes) = 40%

P(unlocked homes) = 0.40

Also, let us represent the value of the locked room with G.

P(locked homes) = P(G)

P(locked homes) = (1 - 0.40)

P(locked homes) = 0.60

Let the probability of selecting a correct key be P(S)

It implies that for the agent to use 3 keys, we have a combination of $^8C_3$ possible ways for the set of keys.

Now; since only one will open the house, then:

P(select correct key) = P(S)

$P(S) = \dfrac{ (^1_1) (^7_2) }{ ^8_3 }$

$P(S) = \dfrac{21}{56}$

P(S) = 0.375

Finally, for the real estate agent to have access to specific homes supposing the agent select three master keys at random prior to the time he left his office, Then:

P(F ∪ (G∩S) = P(F) + P(G∩S)

P(F ∪ (G∩S) = P(F) + P(G) × P(S)

P(F ∪ (G∩S) = 0.40 + (0.60×0.375)

P(F ∪ (G∩S) = 0.40 + 0.225

P(F ∪ (G∩S) =0.625

5 0

3 years ago