81x^2 - 4y^2 Note this is the difference of 2 perfect squares
a^2 - b^2 = (a + b)(a - b)
so here we have a = 9x and b = 2y
and our factors are
(9x + 2y)(9x - 2y)
the dimensions are 9x + 2y and 9x - 2y
Answer:
x ≤ 9 or x ≥ 10
Step-by-step explanation:
2x + 7 ≥ 27
2x ≥ 20
x ≥ 10
or
3+ 3x ≤ 30
3x ≤ 27
x ≤ 9
Answer:
2520 patterns
Step-by-step explanation:
In 'n' 10! ways, books can be arranged. But, there are also 5! permutation of blue books 'n1', 2! permutation of identical green books 'n2', and 3! permutation identical black books 'n3'.
Therefore, for non identical arrangements:
= 2520
Therefore, the books can be arranged on a shelf in 2520 patterns
Yes.
8 + 1 + 1 = 10, so there are 10 parts to the ratio.
3.5 litres divided by 10 would mean that each part of the ratio is worth 0.35 litres.
The colour is worth 8 parts of the ratio. 0.35 litres multiplied by 8 would give 2.8 litres, meaning 2.8 litres of colour are required.
Fiona has 2.9 litres of colour, which is more than enough to make 3.5 litres of paint mix.
Answer:
95% confidence interval for the population variance is (2.89, 5.11)
Step-by-step explanation:
Confidence Interval (CI) = variance + or - (t×s)/√n
Standard deviation (s) = 2, variance (s^2) = 2^2 = 4, n = 15, degree of freedom = n - 1 = 15 - 1 = 14
t-value corresponding to 14 degrees of freedom and 95% confidence interval is 2.145
Lower bound = variance - (t×s)/√n = 4 - (2.145×2)/√15 = 4 - 1.11 = 2.89
Upper bound = variance + (t×s)/√n = 4 + (2.145×2)/√15 = 4 + 1.11 = 5.11
95% confidence interval is (2.89, 5.11)