Mathematics, 15.07.2019 20:30, ayoismeisalex

At a concession stand, five hot dogs and two hamburgers cost $8.50; two hot dogs and five hamburgers cost $10.75. find the cost of one hot dog and the cost of one hamburger

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answered: Jasten

Call hot dogs x and hamburgers y. 5 hot dogs is represented as 5x, and 2 hamburgers is represented as 2y. The cost of these together is 8.50, so that equation is 5x + 2y = 8.50. The second equation where there are 2 hot dogs is represented as 2x, and 5 hamburgers is represented by 5y, and those together cost 10.75. That equation is 2x + 5y = 10.75. We now have a system of equations...2 equations for 2 unknowns. We will use the elimination method to eliminate one variable to solve for the other. Multiply the first equation by -2 and the second equation by 5, and in this process we will eliminate the x terms. Doing that multiplication, we get the 2 equations -10x-4y= -17 and 10x + 25y = 53.75. The x-terms cancel out, leaving us with (-4y = -17)+(25y = 53.75). Doing that addition, we have 21y = 36.75 and y = 1.75. That tells us that the cost of the hamburger is $1.75 each. Fill that value into the y in another equation to solve for x. 2x + 5(1.75) = 10.75. That simplifies to 2x + 8.75 = 10.75 and 2x=2. x = 1, so a hot dog costs $1.

answered: Guest

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;

answered: Guest