X<br><img src="https://tex.z-dn.net/?f=x%200.8265%20%3D%2045%20" id="TexFormula1" title="x 0.8265 = 45 " alt="x 0.8265 = 45 " al

Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp. (a)How many

BigorU [14]

Answer:

a) 20 ways

b) 10 ways

Step-by-step explanation:

When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.

Part a)

We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2

General formula of permutations of n objects taken r at time is:

$nPr=\frac{n!}{(n-r)!}$

Using the value of n=5 and r=2, we get:

$5P2=\frac{5!}{(5-2)!} =20$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.

Part b)

Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.

The general formula of combinations of n objects taken r at a time is:

$nCr=\frac{n!}{r!(n-r)!}$

Using the value of n=5 and r=2, we get:

$5C2=\frac{5!}{2!(5-2)!} =10$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.

3 0

2 years ago

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Which model represents the factors of 4x2 – 9? An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 +x , 3 negativ

Arturiano [62]

Answer:

Step-by-step explanation:

4x² - 9

(2x)² - 3²

(2x + 3)(2x - 3)

Factor 1 spot:

2 tiles of x

3 tiles of positive 1

Factor 2 spot:

2 tiles of x

3 tiles of negative 1

5 0

2 years ago

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Quadrilateral ABDE is a rectangle. DE = 4 in. and BD = 6 in. If the rectangle is rotated about a line through CF, cylinder Y is

postnew [5]

Answer:

1 in. is the answer.

Step-by-step explanation:

Solution: A Rectangle ABDE in which DE=4 inches and BD= 6 inches

There are two kinds of rotations

1. one along the Breadth, side having length 6 inches,i.e rotated along line GH, Cylinder Z is created.

Radius of cylinder Z=6/2= 3 inches

2. Second along the Length, Side having length 4 inches,i.e rotated about a line CF, cylinder Y is created.

Radius of cylinder Y= 4/2= 2 inches

Difference in Radii= Radius of cylinder Z - Radius of cylinder Y

= 3 - 2= 1 inches

Diagram shown below of both the cases:

7 0

2 years ago

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A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.Let B = t

pentagon [3]

Answer:

$P(R\ and\ B) = 0.0256$

Step-by-step explanation:

Given

$Red = 22$

$Yellow = 38$

$Green = 20$

$Purple = 28$

$Blue = 26$

$Orange = 16$

Required

Determine the probability of red then blue jelly? i.e. P(R and B)

From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

$P(R\ and\ B) = P(R)\ and\ P(B)$