Dominics son is 45inches tall
<u>Step-by-step explanation:</u>
Let his sons height be 'h'
If Dominic is 72 inches and casts a shadow of 60 inches. His son casts a shadow of 50 inches.
Then We can say that,
h = 50 x (72/60)
h = 45 inches
Dominics son is 45inches tall
Answer:
x = number of nickels = 127
y = number of dimes = 156
z = number of quarters = 78
Step-by-step explanation:
Let
x = number of nickels
y = number of dimes
z = number of quarters
Total worth of the coins = $41.45
Total number of coins = 361
x + y + z = 361 (1)
dime = $0.1,
nickel = $0.05
quarter = $0.25
0.05x + 0.1y + 0.25z = 41.45 (2)
twice as many dimes as quarters.
y = 2z
Substitute y = 2z into (1) and (2)
x + 2z + z = 361
0.05x + 0.1(2z) + 0.25z = 41.45
x + 3z = 361
0.05x + 0.2z + 0.25z = 41.45
x + 3z = 361 (3)
0.05x + 0.45z = 41.45 (4)
Multiply (4) by 20
x + 3z = 361 (3)
x + 9z = 829 (5)
Subtract (3) from (5)
9z - 3z = 829 - 361
6z = 468
Divide both sides by 6
z = 468 / 6
= 78
z= 78
Recall,
y = 2z
= 2(78)
= 156
y = 156
Substitute the value of y and z into
x + y + z = 361
x + 156 + 78 = 361
x + 234 = 361
x = 361 - 234
= 127
x= 127
x = number of nickels = 127
y = number of dimes = 156
z = number of quarters = 78
1. We need to find how many times John Jogger went to the gym.
He goes 2x weekly for 13 weeks.
13 x 2 = 26 times in the first 3 months.
We still have another 9 months left. He goes twice monthly for each month.
9 x 2 = 18.
We add the total times he went to the gym for the first 3 months to the other 9 months in the year.
26 + 18 = 44 times in one year. If we repeat this for 3 years, you get 44 x 3 = 132 gym visits in three years.
The gym membership is $395 per year. For three years this is 395 x 3 = $1185.
He went to the gym 132 times for a total of $1185. To find the price per visit, divide the total price by the amount of times he went to the gym.
1185/132 = ~$8.98 per gym visit.
2. If 13 weeks = 3 months (1/4 of a year), then there are 52 weeks per year.
If he goes twice every week for 52 weeks, that's 52 x 2 = 104 times per year. If he kept this up for three years, that's 104 x 3 = 312 gym visits in three years.
At the price we found earlier of $1185 for a three-year membership, divide the price by the total number of visits to find the price per visit.
1185/312 = ~$3.80 per gym visit.
Step-by-step explanation:
Since, cos 200°
= 1/sec 200°⇒ cos 200°
= 1/(-1.0641)
= -0.9397
