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zimovet [89]
3 years ago
14

Assume that the probability of any newborn baby being a boyboy is one half 1 2 and that all births are independent. if a family

has threethree children​ (no twins), what is the probability of the event that none of themnone of them areare boysboys​?
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0
I think the correct answer should be 1/8 or 1:8
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An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn
Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0
2 years ago
What is the standard deviation of the following data? If necessary, round your answer to two decimal places.
blsea [12.9K]
Total numbers=10
mean(average)=14.8
standard deviation=3.4254
variance_standard deviation)=11.73333
population standard deviation=3.24962
variance(population standard deviation)=10.56
3 0
2 years ago
A container is the shape of an inverted right circular cone has a radius of 4.00 inches at the top and a height of 5.00 inches.
Len [333]

The rate at which the water from the container is being drained is 24 inches per second.

Given radius of right circular cone 4 inches .height being 5 inches, height of water is 2 inches and rate at which surface area is falling is 2 inches per second.

Looking at the image we can use similar triangle propert to derive the relationship:

r/R=h/H

where dh/dt=2.

Thus r/5=2/5

r=2  inches

Now from r/R=h/H

we have to  write with initial values of cone and differentiate:

r/5=h/5

5r=5h

differentiating with respect to t

5 dr/dt=5 dh/dt

dh/dt is given as 2

5 dr/dt=5*-2

dr/dt=-2

Volume of cone is 1/3 πr^{2} h

We can find the rate at which the water is to be drained by using partial differentiation on the volume equation.

Thus

dv/dt=1/3 π(2rh*dr/dt)+(r^{2}*dh/dt)

Putting the values which are given and calculated we get

dv/dt=1/3π(2*2*2*2)+(4*2)

=1/3*3.14*(16+8)

=3.14*24/3.14

=24 inches per second

Hence the rate at which the water is drained from the container is 24 inches per second.

Learn more about differentaiation at brainly.com/question/954654

#SPJ4

5 0
2 years ago
NEED ASAP:
k0ka [10]

Step-by-step explanation:

the area of this rectangle is

(10 + 2x)(8 + 2x) = 168

80 + 20x + 16x + 4x² = 168

4x² + 36x = 88

because for the whole length you need to add x twice (left and right). the same for the width (top and bottom).

7 0
1 year ago
-2(x+1)-x+5 what do you think it is
Archy [21]

Answer:

The answer is -3x + 3

4 0
2 years ago
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