1. In the 30 day month of April, for every three days it rained, there were two days it did not rain. The number of days in April on which it rained was how much greater than the number of days on which it did not rain?
2. Each terms of a certain sequence is greater than the term befor it. The difference between any two consecutive terms in the same sequence is always the same number. If the third and sixth terms of the sequence are 17 and 77, respectively, what is the 8th term?
3. |x-3|= 1/2
What is the least value of x that satisfies the equation above?
4. A four digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.
A. X= W+Y+Z
B. W= Y+1
C. Z= W-5
What is the four digit integer?
1) 2 out of 5 days it rained. 5 goes into 30 6 times, sooo, multiple 6 by 2, and you get 12 days it did not rain in April.
Apply that same concept to the 3 out of 5 days it does rain...you get 18 days it DID rain, so the answer would be 18 (days it rained) subtract 12 (days it didn't rain). Answer is it rained 6 more days than the amount of days it didn't rain
1. To solve this problem, we need to find the difference between the number of days it rained and the number of days it did not rain in the month of April.
First, let's determine the number of three-day cycles in April. Since each cycle consists of three rainy days followed by two non-rainy days, we can divide the total number of days in April by 5 (3 + 2) to find the number of cycles.
Assuming April has 30 days, we have:
Number of cycles = 30 / 5 = 6
Next, we can find the number of days it rained by multiplying the number of cycles by the number of rainy days in each cycle (3):
Number of rainy days = 6 cycles * 3 rainy days = 18
Similarly, we can find the number of days it did not rain by multiplying the number of cycles by the number of non-rainy days in each cycle (2):
Number of non-rainy days = 6 cycles * 2 non-rainy days = 12
Finally, to find the difference between the number of rainy days and non-rainy days, we subtract the latter from the former:
Difference = Number of rainy days - Number of non-rainy days = 18 - 12 = 6
Therefore, the number of days on which it rained in April is 6 days greater than the number of days on which it did not rain.
2. In this problem, we need to find the common difference of an arithmetic sequence and then use it to determine the 8th term.
Given that the third term is 17 and the sixth term is 77, we can calculate the common difference by subtracting the third term from the sixth term and dividing by the number of positions between them (2 positions in this case):
Common difference = (77 - 17) / 2 = 30
Now, to find the 8th term, we can use the formula for the nth term of an arithmetic sequence:
n-th term = first term + (n - 1) * common difference
Since the common difference is 30 and the third term is 17, we can substitute these values into the formula to find the first term:
17 = first term + (3 - 1) * 30
17 = first term + 2 * 30
17 = first term + 60
first term = 17 - 60
first term = -43
Finally, we can find the 8th term by substituting the values into the formula:
8th term = -43 + (8 - 1) * 30
8th term = -43 + 7 * 30
8th term = -43 + 210
8th term = 167
Therefore, the 8th term of the sequence is 167.
3. To solve the equation |x - 3| = 1/2, we need to consider two cases:
Case 1: x - 3 = 1/2
In this case, we can simply add 3 to both sides of the equation:
x = 1/2 + 3
x = 3.5
Case 2: x - 3 = -1/2
Similarly, we add 3 to both sides of the equation:
x = -1/2 + 3
x = 2.5
Thus, the two values of x that satisfy the equation are 3.5 and 2.5. However, the question asks for the least value of x, which is 2.5.
4. Let's solve this problem step by step according to the given rules to find the four-digit integer.
From rule B: W = Y + 1
Since W, X, Y, and Z represent different digits, let's consider the possible values for Y: 1, 2, 3, 4, 5, 6, 7, 8, or 9.
If Y = 1, then W = 1 + 1 = 2. However, Z = W - 5 = 2 - 5 = -3, which is not a valid digit.
If Y = 2, then W = 2 + 1 = 3. Z = W - 5 = 3 - 5 = -2, which is also not valid.
If we continue this process, we find that Y = 6 satisfies the conditions. Then, W = 6 + 1 = 7, and Z = W - 5 = 7 - 5 = 2.
Now, from rule A: X = W + Y + Z = 6 + 7 + 2 = 15.
Therefore, the four-digit integer is 7625.
How much greater is 3 than 2? 50Percent greater.
17,17+n, 17+2n, 17+3n
17+3n=77 n=20
seventh: 97
eighth: 117
3. c can be 3.5, 2.5.
4. well, X>2 assuming w,y,or z is zero.
but W =1 of y=0
if z is zero, W=5, but in any case, W=>5
Try W=5, that makes y=4, and z=0, and X=9
5940
check this.