4 For the pair of triangles shown, select the shortcut that proves they are congruent.

Anettt [7]

$\dfrac{3}{4}\cdot92=3\cdot23=69$

7 0

3 years ago

A cable car starts off with n riders. The times between successive stops of the car are independent exponential random variables

nikitadnepr [17]

Answer:

The distribution is $\frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

Solution:

As per the question:

Total no. of riders = n

Now, suppose the $T_{i}$ is the time between the departure of the rider i - 1 and i from the cable car.

where

$T_{i}$ = independent exponential random variable whose rate is $\lambda$

The general form is given by:

$T_{i} = \lambda e^{- lambda}$

(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:

$S_{n} = T_{1} + T_{2} + ........ + T_{n}$

$S_{n} = \sum_{i}^{n} T_{n}$

Now, the sum of the exponential random variable with $\lambda$ with rate $\lambda$ is given by:

$S_{n} = f(t:n, \lamda) = \frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

5 0

3 years ago

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or

Irina18 [472]

Answer:

4) i) The numbers can represent the side lengths of a triangle

ii) Right triangle

5) i) The numbers can represent the side lengths of a triangle

ii) Isosceles triangle

6) i) The numbers can represent the lengths of the sides of a triangle

ii) Pythagoras theorem

7) The numbers do not represent the lengths of sides of a triangle

8) i) The numbers can represent the side lengths of a triangle

ii) Scalene triangle

Step-by-step explanation:

In a triangle, the sum of the lengths of the two shorter sides is longer than the length of the longest side

The given numbers are;

4) i) 15, 20, 25

Given that 15 + 20 < 25, the numbers can represent the side lengths of a triangle

ii) 15² + 20² = 25²

Therefore, the sides lengths are in line with the side length of a right triangle as their relation is given by Pythagoras theorem

The triangle is a right triangle

5) i) The given numbers are;

2, 6, 6

Given that 2 + 6 > 6, the numbers can represent the side lengths of a triangle

ii) Given that the lengths of two sides are equal (6 each), the triangle formed by the numbers is an isosceles triangle

6) i) 0.27, 0.36, 0.45

0.27 + 0.36 = 0.63 > 0.45, therefore, the numbers can represent the lengths of the sides of a triangle

ii) Given that 0.27² + 0.36² = 0.45², according to Pythagoras theorem, the type of triangle formed is a right triangle

7) 2.5, 1.5, 4

Given that 2.5 + 1.5 = 4, the numbers do not meet the criteria for forming triangles and therefore they cannot represent the side lengths of a triangle

8) i) 12, 16, 25

12 + 16 = 28 > 25, the numbers can represent the side lengths of a triangle

ii) 12² + 16² = 400 < 25² = 625, therefore, the triangle formed by the numbers is not a right triangle but a scalene triangle.

7 0

2 years ago

What is the sum of the interior angles of the polygon shown below

DanielleElmas [232]

Answer:

720 degrees.

Step-by-step explanation:

The sum of the interior angles of a convex polygon with n sides is

180(n - 2) degrees.

In this case, n = 6 sides, so the angle sum is

180(6 - 2) = 180(4) = 720 degrees.

The reason this works is that if you draw a diagonal from one vertex to the others (see attached image), you get 2 fewer triangles than the number of sides. Each triangle contains a total of 180 degrees, so the total of all the interior angles is 180(n - 2).

7 0

2 years ago

A submarine sandwich 1.5feet long is cut into 0.25 foot pieces. how many pieces will there be?

MA_775_DIABLO [31]

There would be 6 pieces.

6 0

2 years ago

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