Answer:
There are 604,800 possible permutations.
Step-by-step explanation:
The order in which the digits are chosen is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
7 digits from a set of 10(10 digits to 0-9). So
There are 604,800 possible permutations.
Answer: (-3,-3)
Step-by-step explanation:
(3+-9)/2=-3
(1+-7)/2=-3
2.29lbs + 1.79lbs = 4.08 lbs
4.08 (lbs) / 0.25 (weight of patties) = 16.32 patties
therefor Sonia can make
16 patties
It will take 7.5 hours for only 40% of the caffeine to remain in his body.
Step-by-step explanation:
Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value.
The half-life of caffeine is 5.7 hours.
It means that if we have 10 ounces of caffeine. After 5.7 hours, the remaining caffeine will be equal to 5 ounces and so on.
And the decaying speed depends on the initial amount of the substance.
In the given question.
t1⁄2 = 5.7 hours
Initial amount = N(i) = 16 ounces
Remaining amount after time t = N(t) = 40% of 16 = 6.4 ounces
time t = ?
Using the following formula for remaining amount of substance after time t:
N(t) = N(i)*(0.5)^(t/t1⁄2)
we can find the time t
putting the values in the formula given above, we get:
Taking natural log on both sides:
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First thing to do is to illustrate the problem, Since it was mentioned that work was along the way to training, the order is shown in the picture. Mary's home and workplace are nearer compared to her training center. It is also mentioned that the distance between work and home, denoted as x, is 2/3 of the total distance from home to training. The total distance is (x + 2.5). Thus,
x = 2/3(x+2.5)
x = 2/3 x + 5/3
1/3 x = 5/3
x = 5 km
Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,
Total distance = 2(5km) + 7.5 km
Total distance = 17.5 km