Apound of popcorn is popped for a class party. the popped corn is put into small popcorn boxes that each hold 130 popped kernels. there are 1450 kernels in a pound of unpopped popcorn. if all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last box?

12 boxes are needed

Last box contain only 20 kernels

Step-by-step explanation:

It is given that,

a pound of popcorn is popped for a class party.

The popped corn is put into small popcorn boxes that each hold 130 popped kernels.

There are 1450 kernels in a pound of unpopped popcorn.

If all the boxes are filled except for the last box,

To find the number of boxes

number of boxes  = Total number of kernels/Number of kernel in each box

= 1450/130 = 11 2/13

Therefore total number of boxes = 11 + 1 =12 boxes

number of kernels in 11 boxes = 11x 130 =1430 kernels

So last box contain = 1450 - 1430 = 20

Last box have only 20 kernels

12 boxes.

20 kernels in the last box.

Step-by-step explanation:

Hi, to answer hits question, first we have to divide the total number of kernels in one pound (1450) by the number of kernels that each box holds (130).

Mathematically speaking

1450 /130 = 11.15 boxes

This means that 11 boxes can be fully filled, and one box will be not be fully filled.

11+1 = 12 boxes needed

So, the 12th box is no fully filled

11.15boxes -11 full boxes =0.15 =15% filled

Since each box holds 130 kernels, we have to multiply that value by how much the last box can hold  (15% in decimal form).

130 x 15/100 = 19.5 ≅ 20 kernels  

In the last box there are 20 kernels

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!