Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units. What is AF? 11 units 15 units 43 units 51
units
2 answers:
see the attached figure to better understand the problem
we know that
The point G is where all medians intersect and is often described as the triangle's center of gravity or centroid. It is formed by the intersection of the medians. The centroid divides each median in a ratio of
so
<u>Find the value of FA</u>
therefore
<u>the answer is </u>
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Answer:
The price of the television before taxes is $420
Step-by-step explanation:
* Lets explain how to solve the problem
- The purchased price = cost price + taxes
- A new television set was recently purchased for the common room
in a residence hall for $436.80
- This price including tax
- The tax rate is 4%
- We need to find the price of the television before taxes
* <em>Lets solve the problem</em>
- Assume that the price of the television before tax is 100%
∵ The tax rate is 4%
∵ The price after tax = price before tax + tax
∵ The price before tax = 100%
∴ The price after tax = 100% + 4% = 104%
∵ 104% equivalent to $436.80
∴ 100 ⇒ ?
104 ⇒ 436.80
- <em>By using cross multiplication</em>
∴ ? =
∴ The price of the television before taxes is $420
Answer:
85.31% probability that their mean rebuild time exceeds 8.1 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.
This is 1 subtracted by the pvalue of Z when X = 8.1. So
By the Central Limit Theorem
has a pvalue of 0.1469
1 - 0.1469 = 0.8531
85.31% probability that their mean rebuild time exceeds 8.1 hours.