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meriva
3 years ago
13

Alice and Bill are planning to have three children.(Assume that it is equally likely for a boy or girl to be born.) The probabil

ity that all three children will be girls?
Mathematics
1 answer:
ankoles [38]3 years ago
4 0
<span>The probability that all three children will be girls is 1/3 because 3 are about to be born</span>
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by
11111nata11111 [884]

Answer:

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is V=l\times b\times h

V=(11-2x)\times (7-2x)\times x

V=4x^3-36x^2+77x

Derivate w.r.t x,

V'(x)=4(3x^2)-2(36x)+77

V'(x)=12x^2-72x+77

The critical point when V'(x)=0

12x^2-72x+77=0

Solve by quadratic formula,

x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}

x=4.607,1.392

Derivate again w.r.t x,

V''(x)=24x-72

Now, V''(4.607)=24(4.607)-72=38.568>0 (+ve)

V''(1.392)=24(1.392)-72=-38.592 (-ve)

So, there is maximum at x=1.392.

The length of the box is l=11-2x

l=11-2(1.392)=8.216

The breadth of the box is b=7-2x

b=7-2(1.392)=4.216

The height of the box is h=1.392.

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is V=l\times b\times h

V=8.216\times 4.216\times 1.392

V=48.217\ in.^3

The volume of the box is 8.217 cubic inches.

5 0
3 years ago
stions 5-7 the Grade 6 pupils graduated? In a school of 680 Grade 6 pupils, 646 graduated. What percent of the Grade 6 pupils gr
Natalka [10]

Answer:

95% of Grade 6 pupils graduated

8 0
2 years ago
Read 2 more answers
Will mark brainliest and thank you!!! Please help!
borishaifa [10]

The solution to the equation is x = 0, 2

The graph is posted

hope that helps :)

5 0
3 years ago
How do you tell if it's possible to make a triangle out of these side lengths?<br> PLZ HELP!!!!!
Nastasia [14]

Answer:

A

Step-by-step explanation:

square root of 73 is about 8.5

square root of 10 is about 3. multiply by 3, you get 9.

square root of 7 is about 2.6. multiply by 5, you get 13.

when determining if you can make a triangle, if all variants of two sides can add up to be greater than the third side, you can make the triangle. so 8.5+9 > 13; 13+9 > 8.5; 13+8.5 > 9. this means it can make a triangle and all you have to do is order the sides.

8.5 is smallest which corresponds to angle c because it's opposite. 9 goes to angle a, then finally 13 goes to angle b. thus, angles c, a, b is the order.

side note: the smallest side length will always correspond with the smallest angle.

hope this helps :)

3 0
3 years ago
What is the measure of the third angle?
SCORPION-xisa [38]
The total amount of degrees in a triangle is 180. All three angles should add up to 180˚

We know that 40+60 = 100

The next step is to do 180-100 to get the other angle.
180-100 = 80

So the measure of the third angle is 80˚

Hope this helps!

(Also if you want to do this in one equation, you would do 40+60+x = 180
40+60+x = 180
100+x = 180 (combine like terms)
x = 80 (Subtract 100 from both sides)
7 0
3 years ago
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