Answer:
56
Step-by-step explanation:
Firstly, we know she sold 24 hot dogs at half price. We do not know the total number of hot dogs.
Secondly, we know that 30% of the hot dogs were sold at half of the price. This means 70% were sold at full price.
Now there are two approaches to this. I'm going to take the easier one.
What we are expressing mathematically is that 30% of a certain number equals 24. Let the total number of hot dogs she had that day at her stand be x.
This mean 30% of x = 24.
30/100 × x = 24
30x = 24× 100
30x = 2,400
x = 2,400/30 = 80.
This means she had a total of 80 hot dogs that day. Since we know the number she sold at half price, it's now easy to calculate the number she sold at full price.
This number now equals 80 - 24 = 56 hot dogs.
This mean Mandy sold 56 hot dogs at full price.
Answer: Do it yourself!
Step-by-step explanation:
Answer:
(4, 7)
Step-by-step explanation:
The point of interest is ...
P = (2Z +1Y)/(2+1) = ((2·3+6)/3, (2·9+3)/3)
P = (4, 7)
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The point that divides the segment into the ratio a:b is the weighted average of the endpoints, with the weights being "b" and "a". The weight of the first end point corresponds to the length of the far end of the segment.
ΔAOB is a right angled triangle. Therefore the Pythagorean Theorem applies in this situation.
θ is the angle from a standard position of the line OA
The length of the y component is √(1-0)2 +(-3-(-3))2] =√(12+ 02) = 1 A(-3,1) to B(-3,0) which is opposite
Then the length of the x-component is √[(-3-0)2 +(0-0)2] = √(9+0)= 3 B(-3,0) to O(0,0) which is adjacent
The length of vector OA is √[(-3-0)2 + (1-0)2] = √(9+1) = √(10) A(-3,1) to O(0,0) which is the hypotenuse of the triangle
θ = 180 - α
sinθ = sin(180-α) = opposite/hypotenuse = 1/√10
cosθ = adjacent/hypotenuse = -3/√10
tanθ = opposite/adjacent = 1/-3 = -1/3
α= arcsin(1/√10) ≈ 18
θ =180 -18 ≈162
