Answer:
a. Alice
b. Briana
c. 0.51 minutes
Step-by-step explanation:
a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for
2t - 1 > 0
2t > 1
t > 1/2 minutes
b. They finish when their covered distance is equal to 5 kilometers. For Alice:
t/4 = 5
t = 5*4 = 20 minutes
For Briana:
√(2t - 1) = 5
2t - 1 = 5²
2t = 25 + 1
t = 26/2
t = 13 minutes
c. They are side by side when they have covered the same distance, that is:
t/4 = √(2t - 1)
(t/4)² = 2t - 1
t²/16 = 2t - 1
t² = 16*(2t - 1)
t² = 32t - 16
t² - 32t + 16 = 0
Using quadratic formula:
Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.
Answer: The approximate total weight of the grapefruits, using the clustering estimation technique is B. 35 ounces.
Answer:
Step-by-step explanation:
It's given in this question,
m∠2 = 41°, m∠5 = 94° and m∠10 = 109°
Since, ∠2 ≅ ∠9 [Alternate interior angles]
m∠2 = m∠9 = 41°
m∠8 + m∠9 + m∠10 = 180° [Sum of angles at a point of a line]
m∠8 + 41 + 109 = 180
m∠8 = 180 - 150
m∠8 = 30°
Since, m∠2 + m∠7 + m∠8 = 180° [Sum of interior angles of a triangle]
41 + m∠7 + 30 = 180
m∠7 = 180 - 71
m∠7 = 109°
m∠6 + m∠7 = 180° [linear pair of angles]
m∠6 + 109 = 180
m∠6 = 180 - 109
= 71°
Since m∠5 + m∠4 = 180° [linear pair of angles]
m∠4 + 94 = 180
m∠4 = 180 - 94
m∠4 = 86°
Since, m∠4 + m∠3 + m∠9 = 180° [Sum of interior angles of a triangle]
86 + m∠3 + 41 = 180
m∠3 = 180 - 127
m∠3 = 53°
m∠1 + m∠2 + m∠3 = 180° [Angles on a point of a line]
m∠1 + 41 + 53 = 180
m∠1 = 180 - 94
m∠1 = 86°
The equation must equal 84, so you can eliminate B and D.
Chin charges a rate for 2 hours, then charges a reduced rate for 4 hours. There are no discounts present in his rate, so you can eliminate A.
The equation for Chin's charges can be found by the equation C. 2x + 4y = 84.
Given:
Principal value = $12000
Rate of interest = 2.5%
To find:
Total amount after 15 years.
Solution:
Formula for amount discontinuously compounded interest is
where, P is principal, r is rate of interest and t is time in years.
Substitute P=12000, r=0.025 and t=15 in the above formula.
Therefore, the amount after 15 years is $17459.897.
