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son4ous [18]
3 years ago
5

29847839298273827736+83839302839288383

Mathematics
1 answer:
Nikolay [14]3 years ago
7 0

Answer:292820839382

Step-by-step explanation:

282739282992

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Substance A decomposes at a rate proportional to the amount of A present. ​a) Write an equation relating A to the amount left of
horrorfan [7]

Answer:

Step-by-step explanation:

a) The equation relating A to the amount left of an initial amount Upper A 0 after time t is

A(t) = A0e^(kt)

b) It is found that 18 lb of A will reduce to 9 lb in 4.2 hr. It means that

A0 = 18

A = 9

t = 4.2

Therefore, substituting into the formula, it becomes

9 = 18e^(4.2k)

9/18 = e^(4.2k)

0.5 = e^(4.2k)

Taking ln of both sides of the equation, it becomes

Ln0.5 = ln e^(4.2k)

- 0.693 = 4.2k

k = - 0.693/4.2

k = - 0.165

The equation becomes

A(t) = 18e^(- 0.165t)

For A = 1(1 lb left), then

1 = 18e^(- 0.165t)

1/18 = e^(- 0.165t)

0.056 = e^(- 0.165t)

Taking ln of both sides, it becomes

Ln0.056 = ln e^(- 0.165t)

- 2.88 = - 0.165t

t = - 2.88/-0.165

t = 17.5 hours

After 17.5 hours, 1 lb would be left

7 0
3 years ago
The area of the circle is 78.5 units. What is the radius? Use 3.14 for pi.
irga5000 [103]
The radius is 5
5 x 5 = 25
25 x 3.14 = 78.5
7 0
3 years ago
The red team scored 4 goals. The blue team scored 3 times as many goals.How many goals did the blue team score?
Vinvika [58]
3×4=12 more than the red team
3 0
3 years ago
Read 2 more answers
Denver gets 5/19 of the dog food.
natka813 [3]

Answer:

Fido have \frac{42}{95} of the dog food (44.211 %), Engle have \frac{28}{95} of the dog food (29.474 %) and Denver have \frac{5}{19} of the dog food (26.316 %).

Step-by-step explanation:

If Denver gets \frac{5}{19} of the dog food, then Engle and Fido share \frac{14}{19} of the dog food. If Fido have x of the dog food, then Engle have \frac{4}{3}\cdot x such that:

x + \frac{4}{3}\cdot x = \frac{14}{19}

\frac{5}{3}\cdot x = \frac{14}{19}

x = \frac{42}{95}

Fido have \frac{42}{95} of the dog food (44.211 %), Engle have \frac{28}{95} of the dog food (29.474 %) and Denver have \frac{5}{19} of the dog food (26.316 %).

4 0
3 years ago
A study of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the goalkeeper correctly guessed the dir
vladimir2022 [97]

Answer:

z=-2.09

Step-by-step explanation:

Given that a study  of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the goalkeeper correctly guessed the direction of the kick only 41% of the time.

Set up hypotheses as:

H_0: p=0.50\\H_a: p

(left tailed test at 5% significance level)

Standard error = 0.043

Sample proportion p = 0.41

p difference = 0.41-0.50=-0.09

Test statistic Z = p diff/std error

= \frac{-0.09}{0.043} \\=-2.09

Z = -2.09

4 0
3 years ago
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