Can you answer and explain please

Suppose five pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that y

Fudgin [204]

Answer:

Step-by-step explanation:

Every pair of boots has one boot for the right leg and one for left leg ,It is given that there are 5 pairs of boots

Number of single boots = 5 x 2 = 10

Pair Number Left Leg Right Leg 

1 (L) R

2 L (R)

3 L (R)

4 (L) R

5 (L) R

Now, Let us start picking the boots at random ,with at most one boot from each pair.

For example, let the first boot be the left of pair 1, the second boot be the right of pairs 2 , and so on .

Let us circle the boots that are picked in the table.

If the above rule of at most one boot from a pair is followed , we can see that we can pick 5 boots and still not get a pair.

But as soon as we choose the 6th boot from the remaining boots, it is clear that it will complete a pair

for example ,if we pick the left boot of pair 2, it will complete pair 2.

therefore,

Since there are 5 pairs of boots in the pile, if at most one boot is chosen from each pair ,the maximum number of boots chose would be 5. It follows that if a minimum of 6 boots are chosen ,at least two must be from the same pair.

4 0

3 years ago

Jonathan's antiques purchased an old wooden sled at an auction for $210. Jonathan wants to markup the sled 60 percent of the sel

e-lub [12.9K]

210 * 60% = 126
126 + 210 = 336
So, $336 would be your answer.

3 0

3 years ago

Which pair of points has a negative slope?

uysha [10]

The answer is a)(-3,17),(2,-8)

8 0

3 years ago

A. f(x) = 2|2| is differentiable overf X B. g(x) = 2 + || is differentiable over -f

kramer

Recall the definition of absolute value:

• If x ≥ 0, then |x| = x

• If x < 0, then |x| = -x

(a) Splitting up f(x) = x |x| into similar cases, you have

• f(x) = x ² if x ≥ 0

• f(x) = -x ² if x < 0

Differentiating f, you get

• f '(x) = 2x if x > 0 (note the strict inequality now)

• f '(x) = -2x if x < 0

To get the derivative at x = 0, notice that f '(x) approaches 0 from either side, so f '(x) = 0 if x = 0.

The derivative exists on its entire domain, so f(x) is differentiable everywhere, i.e. over the interval (-∞, ∞).

(b) Similarly splitting up g(x) = x + |x| gives

• g(x) = 2x if x ≥ 0

• g(x) = 0 if x < 0

Differentiating gives

• g'(x) = 2 if x > 0

• g'(x) = 0 if x < 0

but this time the limits of g'(x) as x approaches 0 from either side do not match (the limit from the left is 0 while the limit from the right is 2), so g(x) is differentiable everywhere except x = 0, i.e. over the interval (-∞, 0) ∪ (0, ∞).

5 0

3 years ago

A trapezoid is 64cm^2. The height is 12 cm and one base is 4cm. What is the length of the missing base?

Debora [2.8K]

Answer:

20/3

Step-by-step

(base1+base2)/2 * height = area of a trapezoid

64/12=16/3

16/3*2 = 32/3

32/3-4 = 20/3

4 0

4 years ago