A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism and has a side length of 9.5 inches. How much volume is available to be filled with packing material the shipping company wants the box completely full? Round your answer to the nearest tenth. 1,190.2 in^3
774.2 in^3
1,805.6 in^3
5,115.8 in^3
524.5 in^3

524.5 in³

Step-by-step explanation:

First, we can find the volume of the box:

V = s³

V = 9.5³

V = 857.38 in³

Then, we can find the volume of the soccer ball:

V = (4/3)r³

V = (4/3)(4.3)³

V = 333.04 in³

Then, subtract the volume of the ball from the volume of the box:

857.4 - 333.0 = 524.4

So, this is closest to the answer 524.5 in³

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)