1. an equation of a line perpendicular to the line represented by the equation y=-1/2x-5 and passing through (6,-4) is
a. -1/2x+4
b. -1/2+1
c. y=2x+14
d. y=2x-16

2. consider the line given by the equation 5x+2y=8. which of the following gives the equation a line parallel to the given line but with a different y-intercept
a. y=-5/2x+4
b. y=-5/2x+8
c. y=-2/5x+4
d. y=-2/5x+8

3. which two lines are perpendicular?
a.) 2x-y=5 b.) 2x+y=3 c.) y=2x+3
a. a and b
b. a and c
c. b and c
d. none of the equations are parallel

4. which kine is perpendicular to the given line? y=2/5x-3
a. 5x+2y=4
b. y=2/5x+3
c. -2/5x+y=5
d. 2x+5y=3

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;

step-by-step explanation:

find the vertical and horizontal asymptotes of the function f x = 5 x − 1 . to find the vertical asymptote, equate the denominator to zero and solve for . since the degree of the polynomial in the numerator is less than that of the denominator, the horizontal asymptote is .

step-by-step explanation:

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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