The airport security randomly selected 36 suitcases from the security line. Of these bags, they screened 8 suitcases. Based on this information, what is the most reasonable prediction for the number of suitcases they will screen in a group of 180?

The ratio of suitcases to screened suitcases is 36:8. The second ratio is 180:?.

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180 is 5 times 36 which can be proven by dividing 180 by 36.

180 ÷ 36 = 5

Multiply 5 by 8 to find the amount of suitcases that would be screened if there were 180 total suitcases.

5 × 8 = 40

The first ratio is 36:8, and with a scale factor of 5 we get the second equivalent ratio 180:40.

Forty suitcases will be screened.

I hope this helps :)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4