The following two triangles have the same angles, and are similar. What is the ratio of height to base for the triangles?
2 answers:
Answer: The correct option is (A) 0.75.
Step-by-step explanation: Given that the two right-angled triangles in the figure are similar. We are to find the ratio of the height to the base for the triangles.
In the first triangle,
height, h = 6 units and base, b = 8 units,
In the second triangles,
height, h' = 3 units and base, b' = 4 units.
Since the two triangles are similar, so the corresponding sides will be proportional.
We can see that
Hence, we can write
Therefore, the ratio of the height to the base of the triangles is 0.75.
Thus, (A) is the correct option.
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Answer:
Probability that the student scored between 455 and 573 on the exam is 0.38292.
Step-by-step explanation:
We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.
<u><em>Let X = Math scores on the SAT exam</em></u>
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean score = 514
= standard deviation = 118
Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)
P(455 < X < 573) = P(X < 573) - P(X 455)
P(X < 573) = P( <
) = P(Z < 0.50) = 0.69146
P(X 2.9) = P(
) = P(Z
-0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146 = 0.30854
<em>The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.</em>
Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = <u>0.38292</u>
Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.