Complete a well-organized write-up with clear answers or proofs to the following. Demonstrate appropriate work and justification of solutions. Note: Your write-up wil be evaluated on its math ematical correctness and completeness AND the quality and clarity of its presentation Note: For assignment problems, collaboration with other people and use of online resources is NOT permitted. Let f : R → R be defined by f(x)= 5x^3--7. Prove that f is biective.
List the ordered pairs in the relation R from
A={1,2,3,4} to B = {0, 1,2,3,4}, where (a, b) E R if and only if
a) a < b
b) a+b=2 a+b=4
c) the standard English name (e. g. 0's names zero", 's names o, etc.) of a and b have the same length in terms of number of letters.

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

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;