The pattern in the series is straightforward. Each number is increasing by 2 from the previous number:
1. 2 + 2 = 4
2. 4 + 2 = 6
3. 6 + 2 = 8
4. 8 + 2 = 10
5. 10 + 2 = 12
To find the next number in the series, we add 2 to the last number in the given series (10):
10 + 2 = 12
So, the number that should come after 2, 4, 6, 8, 10 is 12.
The pattern in the given sequence is as follows:
1 (1^2) = 1
2^2 + 1 = 5
3^2 + 1 = 9
4^2 + 1 = 17
5^2 + 1 = 26
6^2 + 1 = 37
7^2 + 1 = 50
8^2 + 1 = 65
9^2 + 1 = 82
10^2 + 1 = 101
11^2 + 1 = 122
So, the missing number in the sequence is 81.
Union is denoted by the symbol ∪. Each value that is present in one (or both) of the sets is included in the union of the two sets.
The symbol ∩ stands for the junction. Only the elements of a set that are present in both sets are included in its intersection. In both sets X and Y, there are only two numbers:
{11,13}
The given coding involves reversing the word and then writing the letters in an alternating pattern. Let's apply the same coding rule to the word "PATTERN":
1. Reverse "PATTERN" to get "NRETTAP".
2. Write the letters in an alternating pattern to get "OTAETNR".
So, in this specific type of coding, "PATTERN" is represented as "OTAETNR".
When the distributive property is applied to the left side, we obtain:
3⁄7x +9⁄7 + 5 = 3x+2
Next, arrange all of the variables on the right and all of the constants on the left. then make each side simpler:
9⁄7 + 5 − 2 = 3x − 3⁄7x
9⁄7 + 3 = 3x − 3⁄7x
9⁄7 + 21⁄7 = 21x⁄7 − 3x⁄7
30⁄7 = 18x⁄7
To solve 18x⁄7 = 30⁄7
, Since the denominators are equal, we can equate the numerators, resulting in 18x=30. When we isolate and simplify, we obtain:
x= 30⁄18 = 5⁄3
To identify the pattern in the series, let's analyze the differences between consecutive numbers:
1. 2.3 - 1.5 = 0.8
2. 3.1 - 2.3 = 0.8
3. 3.9 - 3.1 = 0.8
4. ...
As we can see, the difference between each pair of consecutive numbers is always 0.8. Therefore, to find the next number in the series, we add 0.8 to the last number in the given series (3.9):
3.9 + 0.8 = 4.7
So, the number that should come after 1.5, 2.3, 3.1, 3.9, etc., is 4.7.
To identify the pattern in the series, let's analyze the differences between consecutive numbers:
1. 3 - 2 = 1
2. 7 - 6 = 1
3. 11 - 10 = 1
As we can see, the difference between each pair of consecutive numbers is always 1. Therefore, to find the next number in the series, we add 1 to the last number in the given series (11):
11 + 1 = 12
So, the number that should appear after 3, 2, 7, 6, 11, ? is 12. However, in the series provided, there seems to be an error in the pattern, as the next number is expected to be 12 based on the given pattern, not 10.
The pattern in the series is as follows:
1. 34 + 11 = 45
2. 45 + 11 = 56
3. 56 + 11 = 67
4. 67 + 11 = 78
To find the next number in the series, we add 11 to the last number in the given series (67):
67 + 11 = 78
So, the number that should appear after 34, 45, 56, 67 is 78.
Equations can be merged when terms corresponding to the same variable are present:
y+3y+5y=−18
9y=−18
y=−189
y=−2
The number of green marbles and the overall number of marbles both fall by one because Bruno maintains his marble. There will therefore be 25 marbles in total and 5 green marbles:
Probability = 5⁄25 = 1⁄5
We are informed that w is the combined weight of the truck and its load, and q is the number of castings it is transporting.
Q=0 if a truck is not transporting any castings.
W=500(0)+35,000=35,000 when q=0.
In other words, the truck weighs 35,000 lbs. on its own (i.e., without carrying any castings).
In the given series, the pattern involves alternating between the number 21 and a sequence of decreasing odd numbers (9, 11, 13, ...).
1. 21 (Start with 21)
2. 21, 9 (Subtract 12 from 21 to get 9)
3. 21, 9, 21 (Add 12 back to 9 to get 21)
4. 21, 9, 21, 11 (Subtract 10 from 21 to get 11)
5. 21, 9, 21, 11, 21 (Add 10 back to 11 to get 21)
6. 21, 9, 21, 11, 21, 13 (Subtract 8 from 21 to get 13)
To find the next number in the series, we continue with the pattern and add 8 back to 13:
13 + 8 = 21
So, the number that should come after 21 in the given series is 21.
We can set up a proportion to solve:
9 bottles/12 people = x bottles/8people
Cross-multiply to solve a proportion:
(9)(8)=(12)(x)
72=12x
6=x
The pattern is a simple sequence of even numbers in the given series, starting from 2 and increasing by 2 with each subsequent number. So, the number that should go in the empty space is 12.
The series is : 2, 4, 6, 8, 10, 12.
Each term's power is distributed in parenthesis:
(x cm7× y 3)5 = x 7x5 y 3 x 5 = x 35y 15
