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Dennis_Churaev [7]
3 years ago
9

Reese will choose one headband, one

Mathematics
1 answer:
IRINA_888 [86]3 years ago
5 0

Answer:

\dfrac{1}{18}

Step-by-step explanation:

Number of Headband Types=3

P(Reese will  choose a blue headband)=1/3

Number of Types of Necklace=2

P(Reese will  choose a  silver  necklace)=1/2

Number of Types of Earrings=3

P(Reese will  choose a  silver earrings)=1/3

In Probability Theory,

P(A AND B)=P(A) X P(B)

Therefore, the probability that Reese will  choose a blue headband, a silver  necklace, and a silver pair of earrings

=\dfrac{1}{3}X \dfrac{1}{2}X\dfrac{1}{3}\\\\=\dfrac{1}{18}

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Answer:

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Step-by-step explanation:

The area of the triangle ABC is 24 square units.

1. Triangles ABC and FBG are similar with scale factor \frac{1}{3}, then

\dfrac{A_{\triangle FBG}}{A_{\triangle ABC}}=\dfrac{1}{9}\Rightarrow A_{\triangle FBG}=\dfrac{1}{9}\cdot 24=\dfrac{8}{3}\ un^2.

2. Triangles ABC and DBE are similar with scale factor \frac{2}{3}, then

\dfrac{A_{\triangle DBE}}{A_{\triangle ABC}}=\dfrac{4}{9}\Rightarrow A_{\triangle DBE}=\dfrac{4}{9}\cdot 24=\dfrac{32}{3}\ un^2.

3. Thus, the area of the quadrilateral DFGE is

A_{DFGE}=A_{\triangle DBE}-A_{\triangle FBG}=\dfrac{32}{3}-\dfrac{8}{3}=8\ un^2.

and the area of the quadrilateral ADEC is

A_{ADEC}=A_{\triangle ABC}-A_{\triangle DBE}=24-\dfrac{32}{3}=\dfrac{40}{3}\ un^2.

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Answer:

Area of the rectangle = 95 cm²

Step-by-step explanation:

Perimeter of the rectangle = Sum of the measures of the sides of the rectangle

From the figure attached,

Perimeter of the rectangle = 2[(3x -1) + (2x + 3)]

                                       39 = 2(5x + 2)

                                       39 = 10x + 4

                                      10x = 39 - 4

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Therefore, measure of the given sides will be,

Length = (3x - 1) cm

3x - 1 = (3×3.5) - 1

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Width = (2x + 3) cm

2x + 3 = (2×3.5) + 3

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Area of the rectangle = Length × width

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Therefore, area of the rectangle is 95 cm².

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2 years ago
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