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Minchanka [31]
3 years ago
9

Bryant just drank a cup of coffee to help him stay awake. The coffee had 52 milligrams of caffeine in it. If his body processes

20% of the caffeine every hour, how much will be left in 9 hours?
Mathematics
1 answer:
kkurt [141]3 years ago
4 0
Let c be caffeine, h be hours, mg milligrams:

c= 52 mg
1h =.2 (52)= 10.4

x/9h=10.4/1h

x= 93.6 mg

93.6- 52= 41.6 mg of caffeine will be left behind.











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In triangle $ABC$, let angle bisectors $BD$ and $CE$ intersect at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and
Umnica [9.8K]

Answer:

41

Step-by-step explanation:

If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:

... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC

.. = 17+24 = 41

_____

Wow! Thank you for an interesting question with a not-so-obvious answer.

_____

<em>A little more detail</em>

The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.

If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...

... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths

For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.

The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.

Putting these ratios and perimeters together, we get ...

... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s

... = (2/(BC) -1/s) × BC × s = 2s -BC

... perimeter ΔAMN = AB +AC

8 0
3 years ago
The difference of 13 and 5 times a number is 3.
Artemon [7]

Answer:

2

Step-by-step explanation:

13-5x =3  

-13 -13  

-5x = -10  

-5 -5

x=2

3 0
3 years ago
Read 2 more answers
The overhead reach distances of adult females are normally distributed with a mean of 205.5 and a standard deviation of 8.6 . a.
Anastasy [175]

Answer:

a) 0.073044

b) 0.75033

c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

Step-by-step explanation:

The overhead reach distances of adult females are normally distributed with a mean of 205.5 and a standard deviation of 8.6 .

a. Find the probability that an individual distance is greater than 218.00 cm.

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 218

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

For x > 218

z = 218 - 205.5/8.6

z = 1.45349

Probability value from Z-Table:

P(x<218) = 0.92696

P(x>218) = 1 - P(x<218) = 0.073044

b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00

When = random number of samples is given, we solve using this z score formula

z = (x-μ)/σ/√n

where

x is the raw score = 204

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

n = 15

For x > 204

Hence

z = 204 - 205.5/8.6/√15

z = -0.67552

Probability value from Z-Table:

P(x<204) = 0.24967

P(x>204) = 1 - P(x<204) = 0.75033

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

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3 years ago
How can you use a rate to compare the costs of two boxes of cereal that are different sizes?
Rainbow [258]

Answer:

✖ both sides

Step-by-step explanation:

you take both numbers and you multiply it

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3 years ago
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How many 25 cents are there in $10?​
Mashcka [7]

Answer:

40 quarters are in $10

Step-by-step explanation:

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