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Mathematics

1 answer:

soldi70 [24.7K]3 years ago

5 0

Answer:

For a triangle to be equiangular all its three interior angles must be equal, that is, each angle should measure 60˚.

Step-by-step explanation:

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Suppose we want to choose 5 objects, without replacement, from 13 distinct objects. (a) How many ways can this be done, if the o

Arisa [49]

Answer:

A. 1, 287 ways

B. 154,440 ways

Step-by-step explanation:

A. We want to choose 5 objects from a total 13, without considering the order in which they are chosen.

The correct way to do this is by using the combination formula since order is not considered;

Thus we have ; 13 C 5 read as 13 combination 5;

Mathematically, n C r is ; n!/(n-r)!r!

Thus, we have ;

13!/(13-8)!8! = 13!/5!8! = 1,287 ways

B. By considering order, we shall be using the permutation formula;

Mathematically n P r = n!/(n-r)!

Read as n permutation r;

Using the numbers involved, we have ; 13 P 5

= 13!/(13-5)! = 13!/8! = 154,440 ways

8 0

3 years ago

Which of the following shows an inconsistent system of equations?

77julia77 [94]

The third set is equivalent to

2x + y = 2
2x + y = -2

clearly inconsistent.

3 0

3 years ago

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determi

grandymaker [24]

The mass of the first shipment at time t is
$m_{1}=100( \frac{1}{2} )^{ \frac{t}{10}}$

The mass of the second shipment at time t is
$m_{2}=100( \frac{1}{2} )^{ \frac{t-3}{10} }$

At time t, the ratio of m₁ to m₂ is
$\frac{m_{1}}{m_{2}} = \frac{100}{100}. \frac{(1/2)^{t/10}}{(1/2)^{(t-3)/10}} \\ = \frac{(1/2)^{t/10}}{(1/2)^{t/10}}. \frac{1}{(1/2)^{-3/10}} \\ = (1/2)^{3/10} \\ = 0.8123$

Therefore as a percentage,
$\frac{m_{1}}{m_{2}} =100*0.8123 = 81.23 \%$

Answer: B. 81.2%

4 0

4 years ago

Proving Pythagorean Theorem

MrRissso [65]

Answer:

Step-by-step explanation:

${a}^{2} + {b}^{2} = {c}^{2}$