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Maurinko [17]
3 years ago
12

In how many ways can you answer a set of 6 true-or-false questions?

Mathematics
1 answer:
fiasKO [112]3 years ago
8 0
6 - true 
6 - false 
5 true 1 false 
5 false 1 true 
4 true 2 false 
4 false 2 true 
3 true 3 flase  
The answer : 7 ways



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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108
Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

4x+L=108

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

V=x^2L

If we express L in function of x using the restriction equation, we get:

4x+L=108\\\\L=108-4x

We replace L in the volume formula and we get

V=x^2L=x^2*(108-4x)=-4x^3+108x^2

To maximize the volume we derive and equal to 0

\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18

We can replace x to calculate L:

L=108-4x=108-4*18=108-72=36

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0
3 years ago
Read 2 more answers
Maggie is participating in her school reading challenge. She reads 40 books in 6 months. If 26 of the books are fiction, what pe
pentagon [3]
Answer: 35%

1. 26 fiction books divided by all 40 books equals 65% fiction books.

2. Then do 100% - 65% to get 35%

OR

1. All 40 books minus 26 fiction books
= 14 nonfiction books.

2. Do 14 divided by 40 to get 0.35, = 35%
4 0
3 years ago
In the given figure, C is the midpoint of AB and M is the midpoint of AC . Find the length of NB if MC = 4 and AN = 14.
Elina [12.6K]

Answer:

Given MC = 4

AN = 14

To Find, the length of NB

Step-by-step explanation:

AB is a line which has midpoint “C”. Now the line is divided into two equal portion AC and CB.

The AC has midpoint “M” and MC is 4, so AM will also be 4.

N is the midpoint of CB. So, CB = CN + NB

Now we know AC = AM + MC = 4  + 4 =8

Given, AN = 14

AN = AC + CN

14 = 8 + CN

CN = 6

Since N is the midpoint of CB then, CN = NB

Therefore, the NB is 6

8 0
3 years ago
Plz help me with a and b <br>who can answer in a minute
Irina18 [472]
(a) \frac{1}{4}
(b) The Road Tennis Court occupies \frac{1}{3} of the shaded portion.

I hope it helps! ;)
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3 years ago
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If Gabby wants to make an octagon with a side length of 20 inches, how much wire she need ?
RideAnS [48]

Answer:

160 inches

Step-by-step explanation:

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