How many 7-digit numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 7 and less than or equal to 8? repeated digits are allowed?

1,600,000

(this is one single number and not 3 different numbers)

Explanation:

Imagine having seven slots labeled A, B, C, D, E, F, G

Slot A can have 8 choices {1,2,3,4,5,6,7,8}

Slot B can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot C can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot D can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot E can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot F can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot G can have 2 choices {7,8}

Multiply out those values: 8*10*10*10*10*10*2 = 1,600,000

In words this value is "one million, six hundred thousand" or we can say it as "1.6 million" as a much shorter more compact format.

3-4

step-by-step explanation:

the answer is 3-4 because both 45 and 60 has a multiple of 15.

45/3=15

60/4=15

therefore the odds against selecting a red is 4-3

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240