Answer:
Step-by-step explanation:
we know that
The equation of a exponential growth function is given by
where
y is the population of rabbits
x is the number of years since 1991
a is the initial value
r is the rate of change
we have
substitute
For the year 1998
the number of years is equal to
x=1998-1991=7 years
so
we have the ordered pair (7,18,000)
substitute in the exponential equation and solve for r
elevated both sides to 1/7
therefore
Predict the population of rabbits in the year 2006
Find the value of x
x=2006-1991=15 years
substitute the value of x in the equation
I think 0? Correct me if I’m wrong
Answer:
A. 3.2307692308 batches of Muffins
B. 16 1/4 cups of flour
Step-by-step explanation:
Lauren is making muffins. Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.
A. Explain a method for determining the number of batches of the muffin recipe Lauren can make. Then use your method to find the number of batches she can make.
Her muffin recipe calls for 3 1 −4 cups of flour. She has 10 1 −2 cups of flour.
3 1/4 cups of flour = 1 batch of Muffin recipe
10 1/2 cups of flour = x
3 1/4 × x = 10 1/2 × 1
x = 10 1/2 ÷ 3 1/4
x = 21/2 ÷ 13/4
x = 21/2 × 4/13
x = 42/13
x = 3.2307692308 batches of Muffins
B. If Lauren plans to make 5 batches of the muffin recipe, use what you know about operating with rational numbers to predict the amount of flour she needs. Justify your prediction.
3 1/4 cups of flour = 1 batch of Muffin recipe
Hence,
1 batch = 3 1/4 cups of flour
5 batches = x
Cross Multiply
x = 5 × 3 1/4 cups of flour
x = 5 × 13/4
x = 65/4
x = 16 1/4 cups of flour
6x^2 + 37x - 60 = 6x^2 - 8x + 45x - 60 = 2x(3x - 4) + 15(3x - 4) = (3x - 4)(2x + 15)
Answer: Option #4: the 0.2 could be changed to 2.
Explanation:
The table is designed to make the concept of percentages more understandable. The table first allocates the total amount of 70 in terms of its "fifths," or 20% parts. Then it expresses these parts in the last row of the table, showing that 20% of 70 is 14 and all the five parts sum up to 70 again.
Now, Mikel is supposed to express 40% of the amount. So she writes (incorrectly): 0.2 * 14. This statement needs to be changed to 2 * 14 (two times 14 = 28), to correspond to 2 times 20%, or 40% of 70.
This is reflected in the last (fourth) option "The 0.2 in the expression could be changed to 2."
Option #3 is incorrect because changing 14 to 70, will result in an incorrect number (2.8).
Options 1 and 2 are similarly incorrect (as can be easily verified)
