Which sequence of transformations would change two congruent figures into two similar figures that are no longer congruent ?

Mathematics

1 answer:

Natali [406]4 years ago

8 0

Hello there! The answer would be B) translation and dilation.

When shapes are congruent, they are the same shape and size. To be changed where the shapes are no longer congruent , the size or shape has to change. In the options you've provided, B would be the correct option since it is the only one that includes changing size, when mentioning dilation (or making something bigger, hence changing it's size). In the other options, which include reflection and translations and rotations, they just change the placement of the shape, but other than that the shape is the same as the others.

I hope this helps, have a great day!

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

i. Exactly 2 are defective

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

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

Hence the answer is 0.1157

(ii) None is defective becomes