Apromotional sale at department store offers 25% off the sale price. the sale price is 25% off the regular price. is this same as a sale that offers 50% of regular price? ( try both with a coat whose original cost was $100

This is not the same. The 50% discount would be better.

Step-by-step explanation:

The reason for this is that when you take 25% off the already marked down price, you are not getting 25% off the whole $100. As a result, you wind up getting less off. See the example below.

$100 (cost) - $100*25% (discount) = Sale Price

$100 - $25 = Sale Price

$75 = Sale Price

$75(Sale Price) - $75*25%(Promo) = Overall price

$75 - $18.75 = Overall price

$56.25 = Overall price

This is the cost of the two discounts, whereas if you take all 50% at once, you'll only pay $50.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west