Kacie bought x, number of pencils. She paid $0.91, including tax, per pencil. She gave the cashier $10 and received $6.36 back in change. How many pencils did she purchase?

She purchased 4 pencils

Step-by-step explanation:

Here, we are to calculate the number of pencils bought given the information in the question.

The amount per pencil is $0.91. The total amount of this since she bought x number of pencils is $0.91 * x = $0.91x

Now, after paying $10, she was given $6.36 as change

what this means is that what the pencils cost is 10-6.36 = $3.64

Now we equate the cost in terms of x to this;

0.91x = 3.64

x = 3.64/0.91

x = 4 pencils

4 pencils

Step-by-step explanation:

From the question, Kacie bought x, number of pencils. She paid $0.91, including tax, for a pencil and gave the cashier $10 and received $6.36 back in change.

Let the number of pencils bought be x.

Since she paid $0.91 per pencil, and gave the cashier $10 and collected $6.36 as change, this will be:

10 - 0.91x = 6.36

Collect like terms

0.91x = 10 - 6.36

0.91x = 3.64

x = 3.64/0.91

x = 4

She bought 4 pencils

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.