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solong [7]
3 years ago
9

8. The Wilson family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child bein

g a girl is 0.5, find the probability that the Wilson family had: at least 4 girls? at most 5 girls?
Mathematics
1 answer:
melamori03 [73]3 years ago
7 0
Total children = 6
1) Probability of 4 girls =4/6=0.66
Probability of at least 4 girls >_ 0.66

That is greater or equal to 0.66


2) probability of 5 girls = 5/ total children
=5/6=0.83
Probability of at most 5 girls <_ 0.83
That is less than equal to 0.83

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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
Which description matches the graph of the inequality y ≥ |x + 2| – 3? a shaded region above a solid boundary line a shaded regi
Alex777 [14]
The given inequality is y ≥ |x + 2| -3.

This inequality may be written two ways:
(a) y ≥ x + 2 - 3
    or
    y ≥ x - 1

(b) y ≥ -x -2 - 3
    or
     y ≥ -x - 5

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Answer: A shaded region above a solid boundary line.

6 0
3 years ago
Crawling Crayfish!
boyakko [2]

Answer: Crayfish, 25 s

Step-by-step explanation:

Given

The length of race is 60 cm

Flicker gets a 10 cm head-start

Cray fish covers 6 cm in 5 s i.e. its speed is

\Rightarrow \dfrac{6}{5}=1.2\ cm/s

Flicker covers 4 cm in 5 s, its speed is

\Rightarrow \dfrac{4}{5}=0.8\ cm/s

Time taken by Cray fish to cover the race is

\Rightarrow t_1=\dfrac{60}{1.2}\\\\\Rightarrow t_1=50\ s

Time taken by flicker to cover race with 10 cm head start

\Rightarrow t_2=\dfrac{60-10}{0.8}\\\\\Rightarrow t_2=62.5\ s

Time taken by crayfish is less. Hence, crayfish wins the race

When they both covers the same distance, they tied momentarily i.e.

\Rightarrow 1.2t=10+0.8t\\\Rightarrow 0.4t=10\\\\\Rightarrow t=\dfrac{10}{0.4}\\\\\Rightarrow t=25\ s

After 25 s, they tied the race.

5 0
3 years ago
You have 20 coins in your pocket that are either quarter or dimes. They total $3.95. How many quarters do you have? A.16 B.13 C.
bekas [8.4K]

Answer:

B. 13

Step-by-step explanation:

Solve this by setting up system of equations:

0.25x + 0.10y = 3.95

x + y = 20

x equals the number of quarters and y equals the number of dimes. 0.25 is the value of a quarter and 0.10 is the value of a dime.

1. Multiply one equation to have the same coefficient as the other

0.10 · (x + y = 20) = 0.10x + 0.10y = 2

2. Subtract to find the value of one variable

 0.25x + 0.10y = 3.95

<u>- 0.10x + 0.10y = 2</u>

0.15x = 1.95

3. Solve for x by dividing both sides by 0.15

x = 13

3 0
3 years ago
The corners of a square lie on a circle of diameter d = 0.35 m. each side of the square has a length l. find l.
sergeinik [125]

Refer to the attached image.

As we can observe ABCD is a square, whose corners that is A,B,C and D lie on the circle.

The diameter AC = 0.35 meter.

We have to find the side of square.

Let the measure of side of a square be 'l' meter

In triangle ABC,

By Pythagoras theorem, we get

(AC)^2 = (AB)^2 + (BC)^2

(0.35)^2 = (l)^2 + (l)^2

(0.35)^2 = 2(l)^2

\frac{(0.35)^2}{2} = (l)^2

l^2 = 0.06125

So, l = 0.25 meter

Therefore, the measure of side of the square is 0.25 meter.


6 0
3 years ago
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