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klio [65]
3 years ago
11

Determine the solution to each linear system by using the substitution method.

Mathematics
1 answer:
lana66690 [7]3 years ago
3 0
A. 2x+3×5=34
    2x+15=34
   2×9.5=19 
     2×9.5+15=34

x=9.5
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KengaRu [80]

At Venn diagram there are 4 parts (20 pieces):

1. Colored only in blue - quadrilaterals with four equal side lengths (3 pieces);

2. Colored only in orange - quadrilaterals with four right angles (6 pieces);

3. Colored in both blue and orange - quadrilaterals with four right angles and with four equal side lengths (2 pieces);

4. Colored in white - quadrilaterals withoutprevious two properties (9 pieces).

Consider events:

A - a randomly chosen quadrilateral has four right angles;

B - a randomly chosen quadrilateral has four equal side lengths;

Use formula Pr(B|A)=\dfrac{Pr(A\cap B)}{Pr A} to find the probability that a randomly selected quadrilateral with 4 right angles also has four equal side lengths:

Pr(A\cap B)=\dfrac{2}{20},\\Pr(A)=\dfrac{8}{20},\\Pr(B|A)=\dfrac{\frac{2}{20}}{\frac{8}{20}} =\dfrac{2}{8}=\dfrac{1}{4} =0.25

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