The height of the candles when they first burn down to the same height is 10 cm
<h3>What is an equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
Let y represent the height of the candle after x hours.
For the first candle:
y = -(5/6)x + 15
For the second candle:
y = -(5/2)x + 25
To have the same height:
-(5/6)x + 15 = -(5/2)x + 25
x = 6 hours
y = -(5/2)(6) + 25 = 10 cm
The height of the candles when they first burn down to the same height is 10 cm
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The first book you select can be any one of 700.
. . . For each of those ...
The second book can be any one of the other 699.
. . . For each of those ...
The third book can be any one of the remining 698.
The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = <em>341,531,400 ways</em> .
<em>BUT ...</em>
When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.
So, even though there are 341,531,400 ways to<em> </em>gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.
In 9 days, the number of bacteria in the culture will reach 800,000.
- A process called exponential growth sees a rise in quantity over time. It happens when a quantity's instantaneous rate of change with respect to time is equal to the quantity itself.
- B = 50[10^(d/2)]
- Small, single-celled creatures called bacteria exist. Nearly all areas of the world are home to bacteria, which are essential to its ecosystems.
- A microbiological culture, also known as a microbial culture, is a technique for growing microbial organisms in a controlled laboratory environment while allowing them to reproduce in a predefined culture medium. In molecular biology, microbial cultures are fundamental diagnostic techniques that are employed as research tools.
- We want to find the number of days to reach 800,000 bacteria in the culture.
- 800000 = 50[10^(d/2)]
- 16000 = 10^(d/2)
- d/2 =
- d/2 = 4.204
- d = 8.408
- d = 9 days
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Answer
B
If it increases 6% after 3 years it would be something like B
The amount in gallons of each milk containing 9% butterfat and milk containing 4% butterfat which must be used to obtain the desired 365 gallons are;
- 219 gallons of 9% fat.
- 146 gallons of 7% fat.
<h3>What quantity of each type of milk is required for the desired 365 gallon?</h3>
It follows from the task content that the quantity of each type of milk required to arrive at the targeted fat content and quantity of milk are to be determined.
Let x = quantity of 9% fat milk and
Let y = quantity of 4% fat milk
Therefore, by mass balance; we have;
x + y = 365.
Where; y = 365 - x.
Also, by fat balance; we have;
(9% × x) + (4% × y) = (7% × 365)
9x + 4y = 2555
Therefore, the two equations to be solved simultaneously by substituting y from the first equation into the second equation as follows;
9x + 4 (365 - x) = 2555
5x = 1095
x = 1095/5
x = 219 gallons.
Also, y = 365 - 219 = 146 gallons.
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