Please help this question..

Step-by-step explanation:

2).

Given that 1/(7+5√2)

We know that

The Rationalising factor of a+√b is a-√b

The denominator = 7+5√2

The Rationalising factor of 7+5√2 is 7-5√2

On Rationalising the denominator then

=> [1/(7+5√2)]×[ (7-5√2)/(7-5√2)]

=> [1×(7-5√2)]/(7+5√2)(7-5√2)]

=> (7-5√2)/[(7+5√2)(7-5√2)]

=> (7-5√2)/[7²-(5√2)²]

Since , (a+b)(a-b) = a²-b²

Where , a = 7 and b = 5√2

=> (7-5√2)/(49-50)

=> (7-5√2)/(-1)

=> -7+5√2

=> 5√2-7

3).

Given that (x-2)³

This is in the form of (a-b)³

Where, a = x and b = 2

We know that

(a-b)³ = a³-3a²b+3ab²-b³

=> (x-2)³ = x³-3(x²)(2)+3(x)(2)²-2³

=> (x-2)³ = x³-6x²+12x-8

The coefficient of x² is -6

.19875994384

step-by-step explanation:

1699/ 8548

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;