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3 years ago

Suppose we want to choose 5 objects,without replacement from 16 distinct objects

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

4368 ways

Step-by-step explanation:

We want to choose 5 objects,without replacement from 16 distinct objects.

We can use combination in this case. The formula for the combination is given by :

$_{n}C_r=\dfrac{n!}{r!(n-r)!}$

We have, n = 16 and r = 5

So,

$_{16}C_5=\dfrac{16!}{5!(16-5)!}\\\\_{16}C_5=\dfrac{16!}{5!11!}\\\\=4368$

So, there are 4368 ways in which we want to choose 5 objects,without replacement from 16 distinct objects.

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Help me out please.<br><br> i need to find the function rule,

Ksivusya [100]

Replace x in the equations and see which one gets the matching y :

-5(0) = 0 +1 = 1

-5(1) = -5 + 1 = -4

-5(-1) = 5 +6 = 6

The first equation works.

7 0

3 years ago

Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these

ANEK [815]

Answer:

The correct option is;

∠A ≅ ∠X

Step-by-step explanation:

The given coordinates of the points of triangle ACB are;

A(-4, 4), C(-1, 3), B(-4, 0)

The given coordinates of the points of triangle XYZ are;

X(0, 8), Y(8, 8), Z(6, 2), therefore, we have

The length. l. of segment is given by the following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

For the length of the segment AC; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-1, 3), l = √(10)

For the length of the segment AB; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-4, 0), l = 4

For the length of the segment BC; (x₁, y₁) = (-4, 0), (x₂, y₂) = (-1, 3), l = 3·√2

For the length of the segment XY; (x₁, y₁) = (0, 8), (x₂, y₂) = (8, 8), l = 8

For the length of the segment XZ; (x₁, y₁) = (0, 8), (x₂, y₂) = (6, 2), l = 6·√2

For the length of the segment ZY; (x₁, y₁) = (6, 2), (x₂, y₂) = (8, 8), l = 2·√(10

Therefore;

XY ~ AB, XZ ~ BC, ZY ~ AC

Which gives;

∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z

8 0

3 years ago

Read 2 more answers

In the figure LMV is similar to UTK. what's the value of x the length of side LM?

Kipish [7]

To solve this problem, all we need to do is just set up a proportion. The two shapes are similar, which means that they are the same shape, but different sizes. Using the wording/letter arrangement in the problem, we can figure out which side of one triangle corresponds to which side of the other triangle.

Triangle LMV (with segments LM, MV, and VL) is similar to triangle UTK (with segments UT, TK, and KU).

Corresponding pairs:

LM(x) : UT(39)

MV(30) : TK(65)

VL : KU

However, we need only be interested in the first two pairs. Here is the proportion with letters:

LM / UT = MV / TK

and as numbers:

x / 39 = 30 / 65

Solve for x:

x / 39 = 30 / 65

Cross multiply:

(x)(65) = (39)(30)

Simplify:

65x = 1170

Divide:

65x/65 = 1170 / 65

Simplify:

x = 18

<h2>Answer:</h2>

The length of side LM (x) in triangle LMV is 18 units.

7 0

3 years ago

Two ducklings wander away from the nest while their mother is away. The first duckling's displacement (distance and direction) f

aksik [14]

the second duckling is wandering by 2.6 units distance than the first duckling .

<u>Step-by-step explanation:</u>

Here we have , Two ducklings wander away from the nest while their mother is away. The first duckling's displacement (distance and direction) from the nest is (12,5) The second duckling's displacement is (13,-8) . We need to find How much farther did the second duckling wander than the first duckling. Let's find out:

Let a = (12,5) and b =(13,-8)

The distance each duckling wandered is the magnitude of its displacement vector. Therefore, the expression Distance second duck wandered is given by :

⇒ $D = |b|-|a|$