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chubhunter [2.5K]

3 years ago

7

The amount of radioactive uranium changes with time. The abscissas and ordinates of the points given are the time and amoung of

radioactive uranimum, respectively. (0, 100), (0.5, 50) (1, 25). Which exponential function best represents the relationship between f(t) and t? A. f(t) = 100(0.25)t B. f(t) = 0.25(100)t C. f(t) = 100 (0.5)t D. f(t) = 0.25(50)t

1 answer:

kakasveta [241]3 years ago

4 0

The answer is <span>A. f(t) = 100(0.25)t
</span>
This may be solved by inserting all points to your answer and sseeing if they work. Since <span>A. f(t) = 100(0.25)t fits with all points, this best represents the relationship between f(t) and t.
</span>

Thank you for posting your question. I hope you found what you were after. Please feel free to ask me more.

<span> </span>

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wich of the following choices describe the conversion ratio you would use to convert miles to yards check all that apply

Luda [366]

You could do:

1 mile : 1,760 yards.

So, you would multiply 1790 times 2 and get 3520. The closest thing to 4500 yards is 3520.

So you get 2 miles and 980 yards.

5 0

3 years ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago

A drink manufacturer increases the volume of its cans by 25%.They now hold 450ml.How much did they used to hold?

ss7ja [257]

Answer:

562.5ml

Step-by-step explanation:

using percentage multipliers you just have to do:

add 0.25 to 1 because that will make 125%

then multiply it by 450ml

450ml x 1.25 = 562.5ml

7 0

3 years ago

Help I don’t understand this

Ganezh [65]

Answer:

Step-by-step explanation:

they are opposite angles, so we put them equal to each other.

25.

6a+10= 130

6a=120 a=20 so now we plug it in 6(20) +10= 130

26. 4a-4=2a+30

2a=34 a=17 sso now we plug in 4(17)-4= 64 2(17)+30= 64

27. 6y+1=4y+9 2x-5=x+7

2y=8 x=2

y=4

now plug in 6(4)+1=25 4(4)+9=25 2(2)-5= -1 (2)+7=9

5 0

3 years ago

Plzzzzzzzzzzzzzzzzzzzzz help show your work <br><br><br> - 9/2+-8/13

S_A_V [24]

Answer:

-133/26

Step-by-step explanation:

-9/2 + -8/13

First find a common domintor.

26 will be a common domintor.

2 × 13=26 so multiply -9 by 13= -117

13×2=26 so multiply -8 by 2= -16

-117/26 + -16/26 = -133/26

3 0

3 years ago

Read 2 more answers