MATHEMATICS COLLEGE

The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q(t) (in g) after t years is given by:Q(t)= 1/2^t/1620

Required:
a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for Q(0), Q(1620), and Q(3240).

Answers

Answer 1

Answer:

Answer:

(a) $e^(-0.000428 t)$

Step-by-step explanation:

We are given that

Half life of radium-226=1620 yr

The quantity left Q(t) after t years is given by

$Q(t)=((1)/(2))^{(t)/(1620)}$

a. We have to convert the given function into an exponential function using base e.

$Q(t)=((1)/(2))^{(t)/(1620)}$

= $(((1)/(2))^t)^{(1)/(1620)$

= $e^(ln(1/2) t/1620)$

$=e^({(ln(1/2))/(1620)t)$

= $e^(-0.000428 t)$

(b)

$Q(0)=e^(-0.000428 * 0)$

From original function

Q(0)=1

$Q(1620)=((1)/(2))^{(t)/(1620)}$

$Q(1620)=(1)/(2)=0.5$

From exponential function

$Q(1620)=e^(-0.000428 * 1620)$

$=0.499\approx 0.5$

$Q(3240)=((1)/(2))^{(3240)/(1620))=0.25$

$Q(3240)=e^(-0.000428 * 3240)$

Q(3240)=0.249= $\approx 0.25$

Hence, verified.

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There are 80 participants in a competition. The average score of each participant is 58.5. The average score of the male participants is 64 and the average score of the female participants is 56. How many male participants are there in the competition?

Answers

Answer:

Step-by-step explanation:

Given

Total number of participants= 80
Male = x
Female = 80 - x
Average = 58.5
Average for male = 64
Average for female = 56

Equation to reflect the sum:

64x + 56(80 - x) = 80*58.5
64x - 56x = 80*(68.5 - 56)
8x = 80*2.5
x = 25

The answer is 25 male participants

Consider random samples of size 40 from a population with proportion 0.15. (a) Find the standard error of the distribution of sample proportions.
Round your answer for the standard error to three decimal places.
mean=______
standard error=_______
(b) Is the sample size large enough for the Central Limit Theorem to apply?
1. Yes
2. No

Answers

The standard error of the distribution of sample proportions is 0.056 and mean is 0.15.

Yes, the sample size is enough for the Central Limit Theorem to apply.

(a). Given that, size of sample, $n=40$

Proportion, $p=0.15$

In the distribution of sample proportions, mean $\mu=p$

and, standard error = $\sqrt{(p(1-p))/(n) }$

So, mean $\mu=0.15$

Standard error = $\sqrt{(0.15(1-0.15))/(40) }=0.056$

(b). The Central Limit Theorem applies if np > 5 .

$np=40*0.15=6>5$

Thus, the Central Limit Theorem is applied.

Learn more:

brainly.com/question/22233199

Answer:

a) The mean is 0.15 and the standard error is 0.056.

b) 1. Yes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportions p, in samples of size n, the mean is $\mu = p$ and the standard error is $s = \sqrt{(p(1-p))/(n)}$ . The Central Limit Theorem applies is np > 5 and np(1-p)>5.

In this question:

$n = 40, p = 0.15$

(a) Find the mean and the standard error of the distribution of sample proportions.

$\mu = 0.15, s = \sqrt{(0.15*0.85)/(40)} = 0.056$

So the mean is 0.15 and the standard error is 0.056.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

np = 40*0.15 = 6 > 5

np(1-p) = 40*0.15*0.85 = 5.1>5

So yes

7x(15+4) = (7x ) + (7+4)

Answers

Add the numbers inside the parentheses
7x(15+4)=(7x)+(7+4)
and you get
7x*19= 7x+11

Calculate the product
133x=7x+11

Move variable to the left hand side & change its sign
133x-7x=11

Collect like terms
126x=11

Divide both sides by 126 & you get
x=11/126

Answer: x= 11/126

Hope this helps ʕ•ᴥ•ʔ

Which point is a solution to the inequality shown in this graph?
(0,4)
(-3,0)

Answers

(-3,0) point is a solution to the inequality shown in this graph.

What is the definition of inequality?

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

There are two solutions os inequality are;

(0,4)

(-3,0)

But only one solution is given in the graph as;

(-3,0)

Hence, the (-3,0) is the point that is a solution to the inequality shown in this graph. Option B is correct.

To learn more about inequility, refer to;

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#SPJ2

Answer:

B.(-3,0)

Step-by-step explanation:

i just finished the test

A quality control inspector has drawn a sample of 15 light bulbs from a recent production lot. Suppose that 60% of the bulbs in the lot are defective. What is the expected value of the number of defective bulbs in the sample

Answers

Answer:

Step-by-step explanation:

Expected number of defective is given as :

N x P = np

Where = number of the sample drawn from the production lot

P= percentage of bulbs In The lot which are defective

N = 15

P = 60% = 0.60

So when we do the multiplication,

We have:

NP = 15x0.60

= 9

So in conclusion the expected value of defective bulbs in the sample is 9.

19 + 11 - 12² ÷ 3 (12 - 9) · 11)) - 7 =Use PEMDAS for this.

Also it's a made up question

Answers

PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

First, subtract the numbers in the parentheses, then multiply by 11.

(12 - 9) = (3)

3 x 11 = 33

19 + 11 - 12^2 ÷ 3(33) - 7

Now, just multiply 33 by 3, and then square 12 (12 x 12).

19 + 11 - 144 ÷ 99 - 7

Now, you can divide 144 by 99, this is an infinite number, so..

144 ÷ 99 = 1.455

19 + 11 - 1.455 - 7

Finally add, then subtract.

30 - 1.455 - 7

28.545 - 7

The final answer is 21.545.

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