Answer:
p(t) = 100%·2^(-t/1.32)
Step-by-step explanation:
The equation for exponential decay is ...
(remaining amount) = (initial amount)·2^(-t/(half-life))
Here, we can represent the percentage remaining by p(t) and the initial amount by 100%. Then, for a half-life of 1.32 minutes, the amount remaining is ...
p(t) = 100%·2^(-t/1.32) . . . . . where t is in minutes
_____
Alternate functional forms are possible, such as ...
p(t) = 100%·e^(-0.525112t)
p(t) = 100%·0.591489^t
Answer:
the slope is 5 i do y feel like doing the work buuut ik im right mark me as brainlyest if im right
Answer:
D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.
Step-by-step explanation:
The Number of boxes = 6
Box containing a prize = 1
Probability of success, p = box containing a price / number of boxes = 1 /6
Number of trials = 5
Probability of success on exactly 2 trials, r = 2
Hence,
P(r = 2) = nCr * p^r * (1-p)^(n-r)
n = 5 ; r = 2 ; p = 1/6
Using a binomial probability calculator :
P(r = 2) = 0.1608
Answer:
His quiz score increased by about 7%.
Step-by-step explanation:
Take the two quiz scores and add them together to get 159.
Take the difference between the two quiz scores to get 11.
Divide the difference by the sum to get 0.0692 or about 7%.
For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°.
1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because
180 - 90 = 90
They do not necessarily have to be both 45 degrees. So your answer would be C, their measure should add up to 90 degrees.
2. There are two angles measured: 100° and 30°. Remember the sum of all angles of a triangle is 180°.
180° = 100° + 30° + X
To get X, you transpose the 100° and 30° to the other equation and it will look like this:
180° - 100° - 30 °= X
Remember when you transpose, you use the opposite operation used.
By following the steps, you can now solve for the missing angle. So your answer to this question is A.
As for number 3, without the figure, it is not possible to solve.
For number 4, just remember that trapezoid angles should sum up to 360°.
Given that m∠A = ?; m∠B = 25°; m∠C = 155°; and m∠D = 117° these should all add up to 360°. Let's write an equation for it:
m∠A + m∠B + m∠C + m∠D = 360°
X + 25° + 155° + 117° = 360°
Add up what you know first then we can derive the missing from what is given:
X + 297° = 360°
Transfer the 297° to the other side of the equation and subtract.
X = 360° - 297°
= 63°
Your answer is then B.
For number 5, without the figure, it cannot be answered.
For number 6, 7 and 8 we can use the Triangle Inequality theorem to determine if the given sides form a triangle. It states that the sum of 2 sides of a triangle should be greater than the other side.
a + b > c b + c > a a + c > b
If all three conditions are met rule then you have a triangle. Now let's use your given.
6. a = 13in b=16in and c= 24 in
Let's do this one after the other:
a + b > c b + c > a a + c > b
13 + 16 > 24 16 + 24 > 13 13 + 24 > 16
29 > 24 30 > 13 37 > 16
Because all three conditions were met, then we can say that a triangle can be found. The answer is A.
7. a = 24.3m b = 7.4m c=5.9m
a + b > c b + c > a
24.3 + 7.4 > 5.9 7.4 + 5.9 > 24.3
31.7 > 5.9 13.3 > 24.3 False
Because b+c is less than a, we can say that the given does not make a triangle. Your answer is B.
8. Using the same theorem and use trial and error to determine which is not plausible.
a = 8 b = 25
if c = 18 if c = 21 if c = 27 if c = 35
8 + 25 > 18 True 8 + 25 > 21 True 8 + 25 > 27 True 8 + 25 > 35 False
25 + 18 > 8 True 25 + 21 > 8 True 25 + 27 > 35 True
8 + 18 > 25 True 8 + 21 > 25 True 8 + 27 > 25 True
18 is possible 21 is possible 27 is possible 35 is not possible
Your answer is then D.
As for questions 9 and 10, it cannot be answered without the figure given.
But just remember that complementary angles are two angles that have a sum of 90° . Supplementary angles are two angles that sum up to 180°.
