![x^{\frac{1}{2}} = \sqrt[2]{x}](https://tex.z-dn.net/?f=%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%3D%20%5Csqrt%5B2%5D%7Bx%7D%20)
and ![3^{-\frac{1}{2}} = \frac{1}{3^{\frac{1}{2}} } = \frac{1}{\sqrt[2]{3}}](https://tex.z-dn.net/?f=%203%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%5B2%5D%7B3%7D%7D%20)
so
and you rationalize denominator by multiplying numerator and denominatr by 
so that gives--
Your answer is 
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 12
For the alternative hypothesis,
µ < 12
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 12 minutes
x = 8 minutes
σ = 12 minutes
n = 36
z = (8 - 12)/(12/√36) = - 4/2 = - 2
Test statistic = - 2
First lets see how much room there is for holding video games.
There are 3 shelves that can hold 40 video games each, that is:
3*40 = 120
so we can hold 120 video games total.
If now there are 85 video games, how many we can hold still? That is:
120 - 85 = 35
So we still can hold 35 more video games.
In a Chemical formula, Subscript figures tell us how numerous of the element to their upper-left there are in the patch.
What is a chemical formula?
- In chemistry, a chemical formula is a way of presenting information about the chemical proportions of titles that constitute a particular chemical emulsion or patch, using chemical element symbols, figures, and occasionally also other symbols, similar as hiatuses, dashes, classes, commas, and plus() and disadvantage( −) signs.
- These are limited to a single typographic line of symbols, which may include subscripts and subtitles.
- A chemical formula may indicate certain simple chemical structures, it isn't the same as a full chemical structural formula.
The subscript number indicates the total number of titles of an element present in a patch.
While witting a chemical formula, first we've to write the symbol of an element and also write the number at the bottom of the symbol.
For illustration,
is the chemical formula of the glucose patch. The glucose patch is made up of six carbon titles, twelve hydrogen titles, and 6 oxygen titles.
The number 6 of the carbon snippet is written after and at the bottom ( lower- right) of the symbol of carbon element (C). also, the number 12 is written lower-right of the symbol of hydrogen element (H), and the number 6 is written lower-right of the symbol of oxygen element( O).
thus, the subscript figures tell us how numerous of the element to their upper-left there are in the patch.
Learn more about subscript here:
brainly.com/question/18452587
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Answer:
x = 5 and x = -19
Step-by-step explanation:
You're on the right track. It's the "discriminant" that tells you what you want to know here. Before starting, arrange the terms of your quadratic in descending orders of x: 5x^2 + 14x - 19 = 0 (Note that I assumed you meant 14x instead of just 14).
Then the coefficients of this quadratic are a = 5, b = 14 and c = -19.
You are referring to the "quadratic formula." It states this:
-b ± √(b²-4ac)
x = -----------------------
2a
So, we insert the a, b and c values as indicated above:
-14 ± √( 14² - 4[5][-19] ) -14 ± √(196 - 4[5][-19] ) -14 ± √576
x = ----------------------------------- = ---------------------------------- = ----------------------
2(10) 20 20
This comes out to:
x = (-14 + 24) / 2 and x = (-14 - 24) / 2
or:
x = 5 and x = -19
