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Tju [1.3M]
3 years ago
5

Triangle ABC was dilated using the rule Y, 5/4. FCA is equal to eight what is C’A’ 10 units 12 and 16 units 20 units

Mathematics
1 answer:
seropon [69]3 years ago
8 0

Answer:

C'A' = 10units (A)

Question

A complete question related to this found at brainly(question ID 2475535) is stated below.

Triangle ABC was dilated using the rule Dy, 5/4

If CA = 8, what is C'A'?

10 units

12 units

16 units

20 units

Step-by-step explanation:

Given:

Scale factor = 5/4

CA = 8units

Find attached the diagram for the question.

This is a question on dilation. In dilation, figures have the same shapes but different sizes.

Y is the center of dilation

Lengths of ∆ABC: CB, AB, CA

Lengths of ∆A'B'C': C'B', A'B', C'A'

C'B' = scale factor × CB

A'B' = scale factor × AB

C'A' = scale factor × CA

C'A' = 5/4 × 8

C'A' = 40/4

C'A' = 10units (A)

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The time needed to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes
Komok [63]

Answer:

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b. The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. The number of students will be unable to complete the exam in the allotted time is 8

Step-by-step explanation:

a. According to the given we have the following:

The time for completing the final exam in a particular college is distributed normally with mean (μ) is 77 minutes and standard deviation (σ) is 12 minutes

Hence, For X = 60, the Z- scores is obtained as follows:

Z=  X−μ /σ

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Using the standard normal table, the probability P(Z≤−1.4167) is approximately 0.0783.

P(Z≤−1.4167)=0.0783

Therefore, The probability of completing the exam in one hour or less is 0.0783.

b. In this case For X = 75, the Z- scores is obtained as follows:

Z=  X−μ /σ

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Z=−0.1667

Using the standard normal table, the probability P(Z≤−0.1667) is approximately 0.4338.

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is obtained as follows:

P(60<X<75)=P(Z≤−0.1667)−P(Z≤−1.4167)

=0.4338−0.0783

=0.3555

​

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

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Z=  X−μ /σ

Z=90−77 /12

Z​=1.0833

UsING the standard normal table, the probability P(Z≤1.0833) is approximately 0.8599.

Therefore P(Z>1.0833)=1−P(Z≤1.0833)

=1−0.8599

=0.1401

​

Therefore, The number of students will be unable to complete the exam in the allotted time is= 60×0.1401=8.406

The number of students will be unable to complete the exam in the allotted time is 8

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hope ur day will full of happiness

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