1. As the geese are sitting in a row on their feeder, the first goose eats m kernels of cracked corn. Each goose in the row then eats 1 less than twice the number of kernels eaten by the previous goose. Which of the numbered choices expresses the total number of kernels of cracked corn eaten by the six geese?
1) 12m - 5 2) 21m - 20
3) 63m - 57 4) 72m - 68
2. On a given day, three of the geese (Amy, Amanda, and Arlene) produce a total of T eggs. If Amy produces 6 less than half this total, and Arlene produces two less than one-third this total, which expression represents the number of eggs produced by Amanda?
1) m11 2) m22 3) m33 4) m44
3. The six geese have called their friends to come to the pond for a party. The total number of their friends called can be expressed as f1.
a) Which of the numbered choices is equivalent to this expression?
1) x(3x + 1) 2) 3x(x + 4)
3) f2 4) f3
b) If the value of x in the expression f1 is equal to the solution to the equation 7x - 2 = 4x + 7, how many friends did the geese call?
4. Goose eggs take approximately one month to incubate. The babies are called goslings, and are able to swim immediately upon birth. The goslings can swim for approximately f4 feet underwater. How far, in feet, can the goslings swim underwater?
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1. #1. m.
#2. 2m-1.
#3. 4m-2-1 = 4m-3.
#4. 8m-6-1 = 8m-7.
#5. 16m-14-1 = 16m-15.
#6. 32m-30-1 = 32m-31.
m + 2m-1 + 4m-3 + 8m-7 16m-15 + 32m-31 = 63m - 57.
2. T-((T/2)-6 + (T/3)-2) =
T-((3T/6)-6 + (2T/6)-2) =
T - ((5T/6) - 8) = T - 5T/6 + 8 = 6T/6 - 5T/6 + 8 = T/6 + 8.
1. To find the total number of kernels of cracked corn eaten by the six geese, let's calculate the number of kernels eaten by each goose and then sum them up.
The first goose eats m kernels of cracked corn.
The second goose eats 1 less than twice the number of kernels eaten by the previous goose, which is (2m - 1) kernels.
The third goose eats 1 less than twice the number of kernels eaten by the second goose, which is (2(2m - 1) - 1) kernels.
The fourth goose eats 1 less than twice the number of kernels eaten by the third goose, which is (2(2(2m - 1) - 1) - 1) kernels.
The fifth goose eats 1 less than twice the number of kernels eaten by the fourth goose, which is (2(2(2(2m - 1) - 1) - 1) - 1) kernels.
The sixth goose eats 1 less than twice the number of kernels eaten by the fifth goose, which is (2(2(2(2(2m - 1) - 1) - 1) - 1) - 1) kernels.
Adding up all these expressions, we get:
m + (2m - 1) + (2(2m - 1) - 1) + (2(2(2m - 1) - 1) - 1) + (2(2(2(2m - 1) - 1) - 1) - 1) + (2(2(2(2(2m - 1) - 1) - 1) - 1) - 1)
Simplifying this expression gives us:
63m - 57
Therefore, the total number of kernels of cracked corn eaten by the six geese is 63m - 57. The correct choice is 3) 63m - 57.
2. Let's define the number of eggs produced by Amanda as A.
Amy produces 6 less than half of the total, which is (T/2) - 6.
Arlene produces two less than one-third of the total, which is (T/3) - 2.
The total number of eggs produced by all three geese is T. So we can write the equation:
(T/2) - 6 + (T/3) - 2 + A = T
Combining like terms, we get:
(T + (3T)/2 + 3A)/6 = T
Rearranging and simplifying:
(T + (3T)/2 + 3A) = 6T
(3T + 6A) = 12T
6A = 9T
A = (9/6)T
Simplifying this further:
A = (3/2)T
Therefore, the expression that represents the number of eggs produced by Amanda is (3/2)T. The correct choice is 3) m33.
3a. The total number of friends called by the geese can be expressed as f1.
The expression f1 can be written as x(3x + 1) by substituting 3x + 1 for x. So the correct choice is 1) x(3x + 1).
3b. To find how many friends the geese called, we need to solve the equation 7x - 2 = 4x + 7 for x.
Subtracting 4x from both sides and adding 2 to both sides to isolate x, we have:
3x = 9
Dividing both sides by 3, we get:
x = 3
Therefore, the value of x is 3. Substituting this value into f1 = x(3x + 1), we have:
f1 = 3(3(3) + 1)
f1 = 3(9 + 1)
f1 = 3(10)
f1 = 30
Therefore, the geese called 30 friends. The correct answer is f3.
4. The distance the goslings can swim underwater is given as f4 feet.
There is no information provided in the given question or link about how to calculate this value. Therefore, there is not enough information to determine the distance the goslings can swim underwater.
1. To find the total number of kernels of cracked corn eaten by the six geese, we need to find the sum of the kernels eaten by each goose.
The number of kernels eaten by each goose follows a pattern. The first goose eats "m" kernels, the second goose eats 1 less than twice that amount (2m-1), the third goose eats 1 less than twice the amount eaten by the second goose (2(2m-1)-1), and so on.
We can write the expression for the total number of kernels eaten as:
m + (2m - 1) + (2(2m - 1) - 1) + (2(2(2m - 1) - 1) - 1) + (2(2(2(2m - 1) - 1) - 1) - 1) + (2(2(2(2(2m - 1) - 1) - 1) - 1) - 1)
Simplifying this expression, we get:
m + 2m - 1 + 4m - 3 + 8m - 7 + 16m - 15 + 32m - 31
Combining like terms, we have:
63m - 57
Therefore, the correct choice is 3) 63m - 57.
2. To find the number of eggs produced by Amanda, we need to consider the given information about the total number of eggs produced by Amy, Amanda, and Arlene.
Let T represent the total number of eggs produced by the three geese. According to the information, Amy produces 6 less than half of T, which can be written as (T/2) - 6. Arlene produces two less than one-third of T, which can be written as (T/3) - 2.
To find the number of eggs produced by Amanda, we can subtract the eggs produced by Amy and Arlene from the total T:
T - [(T/2) - 6] - [(T/3) - 2]
Simplifying this expression, we get:
T - T/2 + 6 - T/3 + 2
Combining like terms, we have:
T/6 + 8
Therefore, the correct choice is 1) m11.
3a. The expression for the total number of friends called by the geese is given as f1. We need to determine the equivalent expression among the given choices.
The options provided do not directly represent f1. We need to evaluate the expression x(3x + 1) and simplify it to see if it is equal to f1.
4x + 7 is given as the solution to the equation 7x - 2 = 4x + 7. We need to solve the equation to find the value of x.
7x - 2 = 4x + 7
7x - 4x = 7 + 2
3x = 9
x = 3
Now, substituting the value of x (3) into the expression x(3x + 1):
3(3(3) + 1) = 3(9 + 1) = 3(10) = 30
Therefore, the correct choice is 3) f2.
3b. To determine how many friends the geese called, we need to substitute the value of x (3) into the expression f1.
f1 = x(3x + 1) = 3(3(3) + 1) = 3(9 + 1) = 3(10) = 30
Therefore, the geese called 30 friends.
4. The distance that the goslings can swim underwater is expressed as f4.
Unfortunately, the provided website link is not accessible, so we cannot find the exact expression or value for f4. Please check another resource for this information.