Answer:
Step-by-step explanation:
Expand the brackets.
Multiply.
Which correctly describes how the graph of the inequality -4y - x > 7 is shaded?
1 answer:
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Answer:
The bottom for an A is 75. Round to the nearest whole number as needed.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the scores on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
2) The bottom for an A is _____. Round to the nearest whole number as needed.
And we want the top 5.5% of the scores, so we need a value a such that:
or
We need on the right tail of the distribution a value a that gives to us 94.5% of the area below and 5.5% of the area above. Both conditions are equivalent.
Let's use the condition , the best way to solve this problem is using the z score with the following formula:
So we need a value from the normal standard distribution that accumulates 0.945 of the area on the left and 0.055 on the right. This value on this case is 1.598 and we can founded with the following code in excel:
"=NORM.INV(0.945,0,1)"
If we apply the z score formula to our case we have this:
So then based on the equalities we have this:
And if we solve for a we got:
So then we need a score of 84.186 rounded to the nearest whole number 75 or higher in order to get an A
Mini inequality crash course:
<em />
<em>Is it greater than or less then?</em>
This can be a bit tricky to remember. How I do this is looking at the shape of the sign?
So the number that is BIGGER is on the side where the mouth opens or the WIDDER side. Biggest number goes on widest side
Bigger number goes here---> __ >
< __ <--- Bigger number goes here
The number that is the SMALLEST goes on the side where the "pointy" part is
Smallest number goes here---> ___<
> ___ <---Smallest number goes here
***There's an image bellow that also explains it. Hopefully it makes sense
(This all applies the same way to ≥ and ≤ )
You read and say inequalities from left to right. For example I will use example 6:
s < -6 ...............….......S is less then -6
-6 > s..........................-6 is greater then s
^^^Notice that these show the exact same thing yet they are said differently
Here is another example, but with some easy numbers I made up:
3 < 6.........Three is less then six
6 > 3.........Six is greater then three
There are two kind of inequalities:
≥ / ≤
Or
> / <
≥ / ≤
^^^ These two are the greater then or equal to / less then or equal to signs
This means that it includes the number.
***How I remember is the little bar underneath the symbol is like half an equal sign, so the numbers can be equal or not***
For example in number 5:
x ≤ 3 ---> x is less than or equal to 3
^^^This means that x can be three OR any number SMALLER then three
Another example:
x ≥ -34 ---> x is any number greater then OR equal to -34
Graphing inequalities on a number line:
The circles will always be placed on the number that the variable is greater then, less the, greater then or equal to, or less then or equal to
<em>How to tell if the circle is colored or not:</em>
If the inequality has either > or < then the circle is hollow/empty/not colored in
If the inequality has either ≥ or ≤ then the circle is shaded/colored in
***How I remember this is that the symbol has the extra bar at the bottom so the circle will have a little extra something in it
Which direction will the arrow go?
If it is x < # or x ≤ # or # > x or # ≥ x then the arrow will go to the left of the circle. It signifies that x is any number less then/ less then or equal to the #
****How I remember it is if the variable is<em> L</em>ess then it goes <em>L</em>eft
If it is x ># or x ≥ # or # < x or # ≤ xthen the arrow will go to the right of the circle. It signifies that x is any number more then/ more then or equal to the #
16. She has 3,187 signatures but she still needs more, so the expression would be 3,187 + x (x being how many more signitures she needs to reach her goal)
She needs at least 5,000. It has to be more or equal to 5,000
So we have the equation:
5,000 ≤ 3,187 + x or 3,187 + x ≥ 5,000
Now solve for x by subtracting 3,187 to both sides
x ≥ 1, 813
To reach her goal she has to still get 1,813 or more signitures
I really hope this helped and that you understand now!
