Please: Use "^" to denote exponentiation: <span>2x^2 + 8x - 12 = 0
Reduce this by div. every term by 2: </span><span>x^2 + 4x - 6 = 0
Here a=1, b=4 and c = -6. Square half of b, obtaining (4/2)^2 = 4, and add, and then subtract, this 4 to x^2 + 4x - 6:
</span> x^2 + 4x +4 - 4 - 6 = 0. Rewrite the square as (x+2)^2, obtaining new equation
(x+2)^2 = 10. Take the sqrt of both sides: x+2 = plus or minus sqrt(10).
Finally, solve for x: x = -2 plus or minus sqrt(10).
Answer:
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
Step-by-step explanation:
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:

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.
Mean of 90 grams and a standard deviation of 2 grams.
This means that 
What percentage of the grasshoppers weigh between 86 grams and 94 grams?
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So
X = 94



has a p-value of 0.9772.
X = 86



has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544*100% = 95.44%
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
Let's review the terminology. A product is what you get when you multiply two numbers. So, the product of 5 and 2 is basically "5*2," and the product of 5 and 1 is "5*1."
The difference means when you subtract one from the other. So, the difference of 5*2 and 5*1 means "(5*2)-(5*1)". (Note: I put in parentheses to make sure the reader understands that 5*2 is separate from 5*1. 5*2-5*1 is confusing: you might not know what to do first!)
So, "(5*2)-(5*1)" can be your answer, OR you can simplify it further by actually doing the multiplication: "10-5". If you want the answer, just subtract--the expression is equal to 5.
Answer: "<span>(5*2)-(5*1)" OR "10-5" OR "5"</span>
Answer:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always