Answer:
1) 144
2) 1
Step-by-step explanation:
1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7
2. (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR 3 1/5
3. (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11
4. (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
-30 = x
Answer: i think (4n+1)^2(4n-1)^2 isnt a multiple of 8 for all integers of n because:
(4n + 1)²(4n - 1)²
= [(4n + 1)(4n - 1)]²
= (16n² - 1)²
= 16².n².n² - 2.16.n² + 1
= 8n²(32n² - 4) + 1
can see 8n²(32n² - 4) is a multiple of 8 but 1 isnt a multiple of 8
=> (4n + 1)²(4n - 1)² isnt a multiple of 8 for all integers of n.
Step-by-step explanation:
The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118 .
In the question ,
it is given that ,
the probability of committing at least , type I error is = 0.7
we have to find the number of tests ,
let the number of test be n ,
the above mentioned situation can be written as
1 - P(no type I error is committed) ≥ P(at least type I error is committed)
which is written as ,
1 - (1 - 0.01)ⁿ ≥ 0.7
-(0.99)ⁿ ≥ 0.7 - 1
(0.99)ⁿ ≤ 0.3
On further simplification ,
we get ,
n ≈ 118 .
Therefore , the number of tests are 118 .
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6.4 rounded to the nearest whole number will be 6.
if the decimal was 5 or larger, it would’ve been 7.
