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3 years ago

Assume that the probability of any newborn baby being a girl is one half

Mathematics

1 answer:

asambeis [7]3 years ago

7 0

Answer:

1/32

Step-by-step explanation:

P(0 girls)

= P(5 boys)

= (1 − ½)⁵

= 1/32

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Find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts. Use C for the constant o

umka2103 [35]

Answer:

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2 ln⁡(1+x^2 )+C

Step-by-step explanation:

∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗

Let 1st=arctan⁡(x)

And 2nd=1

∫▒〖arctan⁡(x).1 dx=arctan⁡(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗

As we know that

derivative of arctan(x)=1/(1+x^2 )

∫▒〖1 dx〗=x

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1

Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now

Let 1+x^2=u

du=2xdx

Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get

1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)

1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)

1/2 ∫▒(2xdx/u) =1/2 ln⁡(u)+C

1/2 ∫▒(2xdx/u) =1/2 ln⁡(1+x^2 )+C

Putting values in Eq1 we get

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2 ln⁡(1+x^2 )+C (required soultion)

3 0

3 years ago

Read 2 more answers

Solve the equation 15p2 + 7p − 4 = 0 by completing the square.

natulia [17]

Answer:

p=0 or p=-7/15

Step-by-step explanation:

15p2+7p=0

p(15p+7)=0

p=0 or 15p+7=0

4 0

2 years ago

One card is selected at random from a deck of card. Determine the probability that the card selected is not a 4

Ganezh [65]

Answer:

12/13

Step-by-step explanation:

A probability is the number of desired outcomes over the total number of outcomes.

Assuming that this is a standard deck of playing cards, there will be 52 cards, and there will be 4 "4" cards.

First, find the number of desired outcomes, and put it over the total number of outcomes.

Out of the total number of outcomes (52), there are 4 outcomes that are not wanted, hence the equation is:

52 - 4 = 48

So out of the 52 possible outcomes, 48 are desired. Set up the fraction and

simplify:

48/52

/4 /4

= 12/13

7 0

3 years ago

What’s 18.938+23.57 to the nearest whole number

horsena [70]

Answer: 43

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

A square with side x is changing with time where x(t)=3t+1. What is rate of change of the area of the square when t=2 seconds.

GuDViN [60]

Answer:

Rate of change of the area of the square is 42 units at t = 2.

Step-by-step explanation:

We note that the area of the square is given by: $A(x) = x^2$ but we aim to find $\frac{dA}{dt}$ . But we can use the chain rule to pull out that dA/dt. Doing so gives us:

$\frac{dA}{dt} = \frac{dA}{dx} \times \frac{dx}{dt}.$

Now, $\frac{dA}{dx} = 2x$ (by the power rule and $\frac{dx}{dt} = 3.$

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

$\frac{dA}{dt} = 2(7) \times 3 = 14 \times 3 = 42.$

7 0

3 years ago