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2 years ago

Part of a shape is drawn.

Mathematics

1 answer:

frosja888 [35]2 years ago

6 0

Answer:

The points of the rotated shape are: (4, 1), (5, 3), (4, 4), (2, 1), (1, 3), (2, 4)

Step-by-step explanation:

From the part of the shape we can see and the symmetry, the missing points are:

(-2, -1)

(-1, -3)

(-2, -4)

Rotation 180° about the origin transforms the point (x, y) into (-x, -y). Applying this rule to our figure, we get:

(-4, -1) -> (4, 1)

(-5, -3) -> (5, 3)

(-4, -4) -> (4, 4)

(-2, -1) -> (2, 1)

(-1, -3) -> (1, 3)

(-2, -4) -> (2, 4)

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A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

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This is a binomial probability. For i, we will apply the Binomial probability formula

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Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes