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tankabanditka [31]

3 years ago

15

Triangle A B C is cut by line segment S T. Line segment S T goes from side A B to side C B. Lines S T and A C are parallel. The

length of S B is 10 feet, the length of B T is 9 feet, and the length of C T is 2.7 feet. What is the length of Line segment S A? a) 1.89 ft b) 2.43 ft c) 3 ft d) 7 ft.

2 answers:

maksim [4K]3 years ago

8 0

Answer:

Option C.

Step-by-step explanation:

Given information: In triangle ABC, ST║AC, SB=10 ft, BT=9 ft and CT=2.7 ft.

Triangle proportionality theorem: If a line segment parallel to a side of a triangle then the line segments divides the remaining sides proportionally.

Using triangle proportionality theorem we get

$\dfrac{SA}{SB}=\dfrac{CT}{BT}$

$\dfrac{SA}{10}=\dfrac{2.7}{9}$

On cross multiplication we get

$9\times SA=2.7\times 10$

$9SA=27$

Divide both sides by 9.

$SA=3$

The length of SA is 3ft.

Therefore, the correct option is C.

valentina_108 [34]3 years ago

7 0

Answer: C on edg.

Step-by-step explanation:

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Find the sum of last ten terms of the AP : 8, 10, 12,...., 126.

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For finding, the sum of last ten terms, we write the given AP in reverse order i.e, 126, 124, 122,..., 12, 10, 8

Hence,first term (a) = 126, common difference, (d) = 124 - 126

So, $S _{10} = \frac{10}{2} [ 2a + (10 - 1)d ] \:$
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A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his cla

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For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Additionally, to find the proportion of students who scored an A, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion of students that scored an A:

Scores have a mean of 79 and a standard deviation of 11.3, which means that $\mu = 79, \sigma = 11.3$

Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{90 - 79}{11.3}$

$Z = 0.97$

$Z = 0.97$ has a p-value of 0.8340.

1 - 0.8340 = 0.166

The proportion of students that scored an A is 0.166.

Probability that 6 students or more will score an "A" on the final exam:

Binomial distribution.

22 students, which means that $n = 22$

The proportion of students that scored an A is 0.166, which means that $p = 0.166$

The probability is:

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184$

$P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807$

$P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687$

$P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239$

$P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117$

$P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517$

Then

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551$

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449$

Thus

0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

For a problem that used the normal distribution, you can check brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check brainly.com/question/15557838

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