My clock chimes two times 15 minutes after the hour, four times 30 minutes after the hour and six times 45 minutes after the hour. the clock also chimes eight times on each hour in addition to chiming the number of times equal to the hour. (so at 2: 00 p. m., the clock chimes $8 + 2 = 10$ times.) starting at 12: 05 a. m., how many times does the clock chime in a 24-hour period?

612 times does the clock chime

Step-by-step explanation:

Given data

two times 15 minutes after the hour

four times 30 minutes after the hour

six times 45 minutes after the hour

clock chimes 8 + 2 = 10 times

to find out

how many times does the clock chime in a 24-hour period

solution

we can say clock chimes from 12:05 - 1:05  is for this 1 hour

2 +4+6+8 = 20 + 1

and clock chimes from 1:05 - 2:05  is for this 1 hour is 20 +2

and we know for 24 hours clock chimes  is 20 × 24 i.e

= 480 + 2 × ( 1 +2 + ...  +11 )     1

we know

2 × ( 1 +2 + ...  +11 ) will be  = 2 × (n) × (n+1) / 2

here n is 11 so

= 2 × (n) × (n+1) / 2

= 2 × (11) × (11+1) / 2

= 132

so now put this in equation 1

we get

clock chime in a 24-hour period = 480 + 132

clock chime in a 24-hour period = 612

so 612 times does the clock chime in a 24-hour period

636

Step-by-step explanation:

Look at the picture for explanation:)

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.

false

step-by-step explanation: