Terri buys five and seven eighths ounces of chocolate chips. She uses four and four sixths ounces in a recipe. How many ounces of chocolate chips does she have left? a one and ten forty eighths ounces
b one and three fourteenths ounces
c two and ten forty eighths ounces
d two and three fourteenths ounces

(A)

Step-by-step explanation:

To find how many chocolate chips are left, you have to subtract the amount used for the recipe from the original amount which is:

To subtract the two mixed numbers, first you have to convert them to improper fractions which would make the expression:

Then, in order to subtract the two improper fractions, since they have different denominators, you have to make them have the same denominator. The LCM (Least Common Multiple) of 8 and 6 is 24, so to subtract the two fractions, you need both of them to have a denominator of 24. That would make the expression:

To subtract these two fractions, since they have the same denominators, you can subtract the numerators and keep the denominators. That would make the

which is, as a mixed number, , which is .

Hope this helps :)

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.