Let's find the unknown value x using the proportion x : 5 :: 6 : 15.
We can set up the proportion as x/5 = 6/15.
Step 1: Cross-multiply
15x = 6 * 5
Step 2: Simplify
15x = 30
Step 3: Solve for x
x = 30 / 15
x = 2
The complement of set A (written as A′ or U – A) includes all elements in the universal set U that are not in A.
Hence, it's the difference between U and A.
Given the markup (interest) is Rs. 5550 for 5 years at 5% interest rate:
Let's denote the principal as P. Using the simple interest formula I = P * r * t:
5550 = P * 0.05 * 5
5550 = P * 0.25
P = 5550 / 0.25
P = 22200
Let's denote the number as x. According to the problem:
133 added to a number (x) is equal to 75 more than 4 times the number (4x + 75)
The correct equation is:
133 + x = 4x + 75
Now, let's solve for x:
133 - 75 = 4x - x
58 = 3x
x = 58 / 3
x = 19.33
The correct equation is indeed:
B - A represents the set of elements that are in B but not in A.
The correct notation is: {x | x ∈ B and x ∉ A}
To simplify the expression:
ac + ad + bc + bd
Factor out the common terms:
a(c + d) + b(c + d)
Then, factor out the common binomial factor:
(a + b)(c + d)
Given: √x = 10
Squaring both sides: (√x)² = 10² → x = 100
Solution set: {100}
Given equations:
a + b = 10 ... (1)
3a + 2b = 40 ... (2)
We need to find 3a + b.
Multiply equation (1) by 2:
2a + 2b = 20 ... (3)
Subtract equation (3) from equation (2):
(3a + 2b) - (2a + 2b) = 40 - 20
a = 20
Now, find b:
a + b = 10
20 + b = 10
b = -10
Calculate 3a + b:
3a + b = 3(20) + (-10)
= 60 - 10
= 50
To simplify the given expression:
6/8 + 2 1/2 + 4/12
Simplify each fraction:
6/8 = 3/4
2 1/2 = 5/2
4/12 = 1/3
Now, add the simplified fractions:
3/4 + 5/2 + 1/3
The given sequence appears to be obtained by dividing the previous term by 3:
2187 ÷ 3 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3