Express as a trinomial: (2x+10)(x-9)
1 answer:
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Hey there!
In order to solve this problem, we can use the Pythagorean Theorem, which is . Since the Pythagorean Theorem would find only half of the length of x, we'll need to double it in the end.
First, let's plug in what we know to the Pythagorean Theorem:
Next, we'll simplify to that is by itself:
Then, we'll find the square root of 2.45, multiply that by 2 and round to the nearest tenth:
Therefore, x = 3.1 ft.
How to round to the nearest tenth:
In a decimal, the tenth is the first number after the decimal point. To round to the tenth, if the number in the hundredth place is less than 5, you keep the number as it is, but if the number in the hundredth place is more than 5, you increase the number in the tenth place by 1.
Hope this helps!! :)
Answer:
Step-by-step explanation:
We are given the length of the whole line and its two halves. Since JK and KL make up the line JL, adding them together would make the line JL.
Now we can plug the value of back into the expression we were given for the line KL.
Answer:
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
The home team therefore wins 50% of its games
This means that
Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Sample of 80 means that and, by the Central Limit Theorem:
This probability is 1 subtracted by the pvalue of Z when X = 0.65. So
By the Central Limit Theorem
has a pvalue of 0.9963
1 - 0.9963 = 0.0037
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games