1 / (2/3)
= 1 × (3/2)
= 3/2
Substitute x = 1 and y = -1 into the expression:
13(x + y) = 13(1 + (-1)) = 13(0).
Therefore, 13(0) = 0.
To evaluate the expression 7/12 - 3/8 - 4/9:
Step 1: Find the least common multiple (LCM) of 12, 8, and 9.
The LCM of 12, 8, and 9 is 72.
Step 2: Convert each fraction to have a denominator of 72.
7/12 = (7 × 6) / (12 × 6) = 42/72
3/8 = (3 × 9) / (8 × 9) = 27/72
4/9 = (4 × 8) / (9 × 8) = 32/72
Step 3: Subtract the fractions.
42/72 - 27/72 - 32/72 = (42 - 27 - 32) / 72
= (42 - 59) / 72
= -17/72
A probability greater than 0.5 but less than 1 indicates that the event is more likely than not to occur.
A probability of 1 means certainty, so anything between 0.5 and 1 leans toward happening.
Joining the midpoints of an equilateral triangle forms 1 smaller triangle inside.
That smaller triangle and 3 corner triangles (each between a vertex and midpoints) make a total of 4 triangles.
Given tan θ < 0 and cos θ > 0:
Since cos θ > 0, θ lies in either the 1st or 4th quadrant.
Given tan θ < 0, θ lies in either the 2nd or 4th quadrant.
Combining both conditions, θ must lie in the 4th quadrant.
To evaluate the expression, we need to find a common denominator. The least common multiple (LCM) of 9, 8, and 3 is 72.
Let's convert each fraction:
7/9 = (7 × 8) / (9 × 8) = 56/72
6/8 = (6 × 9) / (8 × 9) = 54/72
6/3 = (6 × 24) / (3 × 24) = 144/72
Now, add the fractions:
56/72 + 54/72 + 144/72
= (56 + 54 + 144) / 72
= 254/72
Simplify the fraction:
254/72 = 127/36
2² × 3² means (2 × 2) × (3 × 3) = 4 × 9 = 36.
The prime factorization of 36 is 2² × 3².
Let's find the HCF (Highest Common Factor) of 14, 56, and 98:
Step-by-step:
Factors of 14: 1, 2, 7, 14
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 98: 1, 2, 7, 14, 49, 98
Common factors: 1, 2, 7, 14
→ HIGHEST common factor = 14