In exercises 1 and 2, Find the value of x.
1 answer:
From the given picture, we can see that 2 sides are congruen, then the given triangle is an isosceles triangle. In this triangle the base angles are congruent, so we can draw the following picture:
Now, since interior angles of any triangle add up to 180 degrees, we have
By combining similar terms, we get
Then, x is given as
Therefore, the answer is x=90 degrees
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Answer:
Option A, C and D are correct choices.
Step-by-step explanation:
Let x be the number of rides that Tomas has been on so far. Each ride costs 5 tickets. This means that cost of x rides will be 5x.
We are told that Tomas bought 80 tickets for rides at an amusement park.
To find the number of of tickets that Tomas has left we will subtract cost of x rides from total number of tickets that Thomas bought.
We can represent this information in an expression as:
Now let us see which of our given choices in equivalent to our expression.
A.
Upon looking at option A we can see that it is same as our expression, therefore, option A is the correct choice.
B.
We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option B is not a correct choice.
C.
Upon distributing 5 we will get,
Now this expression is same same as our expression, therefore, option C is the correct choice.
D.
This expression is also same as our expression as we can rearrange the terms in this expression as: , therefore, option D is a correct choice as well.
E.
Upon distributing 5 we will get,
We can see that in this expression cost of x rides in being added instead of subtraction, therefore, option E is not a correct choice.
Answer:
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload
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 normal distributions can be 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n values of a distribution, the mean is and the standard deviation is
An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.
This means that
If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload
Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So
has a pvalue of 0.5
1 - 0.5 = 0.5
0.5 = 50% probability that a random sample of 100 independent persons will cause an overload