Answer:
first blank = 10 (for table 1)
second blank = 30 (for table 2)
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Explanation:
You could use a calculator to determine the value of b, then compute b^x for that first box. But as the instructions state, we don't need to use one. Why is that? Because the tables provide enough information to fill in the blanks.
Table 1 shows x = 2.096 lead to some unknown y value. Meanwhile, table 2 has x = 10 lead to y = 2.096; note the 2.096 shows up again. The exponential and log functions are inverses of each other. They undo each other's operation. This is similar to how division undoes multiplication, and vice versa.
Going in reverse of table 2, we will conclude that 10 must go in the blank for table 1. Therefore, b^x = 10 when x = 2.096
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Similarly, we will have 30 in the blank for table 2. Table 1 shows x = 3.096 lead to y = 30. Table 2 is the reverse of that as it is the inverse.
Throughout either section, we didn't need to find the value of b.
For each ounce of the product, let
x = ounces of moisturizing lotion used,
y = ounces of self-tanning lotion used.
The sum of the two lotions per ounce is equal to one ounce. Therefore
x + y = 1 (1)
Moisturizing lotion costs $0.70 per ounce.
Self-tanning lotion costs $22 per ounce.
Because the product costs $1.30 per ounce. Therefore
0.70x + 22y = 1.30 (2)
From (1), obtain
y = 1 - x (3)
Substitute (3) into (2).
0.70x + 22(1 - x) = 1.30
0.70x - 22x + 22 = 1.30
-21.3x = -20.7
x = 0.9718 ounces
From (3), obtain
y = 1 - 0.9718 = 0.0282 ounces.
A batch of the product is 700 ounces. Therefore the amount of self-tanning lotion used is
700*y = 700*0.0282 = 19.74 ounces
Answer: 19.74 ounces
Answer:
0- 11 times
1,2,3,4,5,6,7,8,9- 12 times
The question is basically asking<em> "What is 1¼ × 6?"</em>
There are multiple ways to arrive at a solution for this.
The first is to break the 1¼ into parts.
1¼ = 1 + ¼. When we multiply 1¼ by 6, that's equal to 1×6 + ¼×6.
1×6 = 6.
¼×6 = 6/4 = 1½.
6 + 1½ = 7½ hours
You could also put 1¼ as an improper fraction and then multiply.
1¼ = 1 + ¼.
1 = 4/4.
4/4 + 1/4 = 5/4.
5/4 × 6 = (5×6)/4 = 30/4.
30/4 = 15/2 = 7½ hours
On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 57 miles with the wind, he could go only 33 miles against the wind.What is his normal bicycling speed with no wind?
