Answer:
Step-by-step explanation:
The amount that Alexa owes after t weeks is given by a linear equation in the following format:
In which L(0) is the initial amount borrowed and b is how much is paid per week.
Alexa agreed to pay back her friend $10 per week and originally borrowed $170.
This means that, respectivelly, . So
Answer:
150 oz.
Step-by-step explanation:
There are already 150 ounces of alloy of nickel.
Of this 150 oz, 70% is pure i.e. nickel content = 150(0.7) = 105 oz
Now available is
Nickel Other metals
105 45
Let x oz of pure nickel is added.
Then new alloy will have 105+x oz nickel in total of 150+x oz.
Percentage pure =
Simplify to get
Hence answer is 150 oz should be added.
Answer: THE GRAPH IS ATTACHED.
Step-by-step explanation:
We know that the lines are:
Solving for "y" from the first line, we get:
In order to graph them, we can find the x-intercepts and the y-intercepts.
For the line the x-intercepts is:
And the y-intercept is:
For the line the x-intercepts is:
And the y-intercept is:
Now we can graph both lines, as you can observe in the image attached (The symbols and
indicates that the lines must be dashed).
By definition, the solution is the intersection region of all the solutions in the system of inequalities.
we have
Step
<u>Clear the variable y</u>
Adds both sides
Step
<u>Convert in function notation</u>
Let
therefore
<u>the answer is</u>
Answer:
a) 57.35%
b) 99.99%
c) 68.27%
Step-by-step explanation:
When we have a random variable X that is normally distributed with mean and standard deviation
, then
The probability that the random variable has a value less than a, P(X < a) = P(X ≤ a) is the area under the normal curve with mean and standard deviation
to the left of a.
The probability that the random variable has a value greater than b, P(X > b) = P(X ≥ b) is the area under the normal curve with mean and standard deviation
to the right of b.
The probability that the random variable has a value between a and b, P(a < X < b) = P(a ≤ X ≤ b) = P(a < X ≤ b)= P(a ≤ X < b) is the area under the normal curve with mean and standard deviation
between a and b.
In this case, the random variable is the collagen amount found in the extract of the plant. The mean is 63 g/ml and the standard deviation is 5.4 g/ml
(a) What is the probability that the amount of collagen is greater than 62 grams per mililiter?
As we have seen, we need to find the area under the normal curve with mean 63 and standard deviation 5.4 to the right of 62 (see picture).
You can find this value easily with a calculator or a spreadsheet. If you prefer the old-style, then you have to standardize the values and look up in a table.
<em>If you have access to Excel or OpenOffice Calc, you can find this value by introducing the formula: </em>
<em>1- NORMDIST(62,63,5.4,1) in Excel </em>
<em>1 - NORMDIST(62;63;5.4;1) in OpenOffice Calc </em>
<em>and we will get a value of 0.5735 or 57.35% </em>
(b) What is the probability that the amount of collagen is less than 90 grams per mililiter?
Now we want the area to the left of 90
<em>NORMDIST(90,63,5.4,1) in Excel </em>
<em>NORMDIST(90;63;5.4;1) in OpenOffice Calc </em>
You will get a value of 0.9999 or 99.99%
(c) What percentage of compounds formed from the extract of this plant fall within 1 standard deviations of the mean?
You can use either the rule that 68.27% of the data falls between and
or compute area between 63 - 5.4 and 63 + 5.4, that is to say, the area between 57.6 and 68.4
<em>In Excel </em>
<em>NORMDIST(68.4,63,5.4,1) - NORMDIST(57.6,63,5.4,1) </em>
<em>In OpenOffice Calc </em>
<em>NORMDIST(68.4;63;5.4;1) - NORMDIST(57.6;63;5.4;1) </em>
In any case we get a value of 0.6827 or 68.27%
Answer:
14 gallons
Step-by-step explanation:
If 11 2/3 gallons represents 5/6 full bucket then we can equate that
x=1 full
Therefore, the bucket requires 14 gallons