How to solve examples c) d) ?
Factorial sums

Recall the binomial theorem:

a. Let a = b = 1 and n = 8. Then the sum above gives the sum shown here,

so it reduces to (1 + 1)⁸ = 2⁸ = 256.

b. Let a = 1 and b = -1 and k = 8. Then by the same argument, the sum reduces to (1 - 1)⁸ = 0.

c. Notice that

but this is nearly identical to the sum in part a, with a = b = 1 and arbitrary n, but the order of terms is reversed. Then it reduces to (1 + 1)ⁿ = 2ⁿ.

d. Let a = 1 and b = 2. Then the sum is (1 + 2)ⁿ = 3ⁿ.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

15% chance.

step-by-step explanation:

3/10 times, the 5 year old will get a tablet. 5/10 times, the 13 yer old will get a tablet. multiply both fractions to get 15/100 times, both would have a tablet.