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2 years ago

The half-life of cobalt-60 (used in

Mathematics

1 answer:

Likurg_2 [28]2 years ago

5 0

Answer:

6.25 gm left

Step-by-step explanation:

Find the number of half lives in 26.3 years

26.3 / 5.26 = 5 half lives

(1/2) ^5 = 1/32 nd of the original will be left

1/32 * 200g = 6.25 gm left

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10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

$p = \frac{4}{6} = 0.6667$

10 normal six sided dice are thrown.

This means that $n = 10$

Find the probability of obtaining at least 8 failures.

This is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951$

$P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867$

$P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174$

Then

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992$

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0

3 years ago

Which set of points below represents a function

vazorg [7]

Answer:

I believe it's the 3rd option:

(-1, 8), (0, 10), (1,12), (2, 14)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Beth is making a rope ladder.each step of the ladder is 2 1/3 feet wide.Beth has a rope that is 21 feet long.how many steps can

Marianna [84]

Answer:

Beth can make 9 2 1/3 foot steps

Step-by-step explanation:

21/2.3=9.1

round to 9

7 0

2 years ago

Read 2 more answers

Given the equation 4x2 − 8x + 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)2 + k =

GenaCL600 [577]

Answer:

The correct option is:

h = 1, k = 16

Step-by-step explanation:

y=4x^2-8x+20 =0

It is a quadratic formula in standard form:

ax^2+bx+c

where a = 4 , b = -8 and c=20

The vertex form is:

a(x − h)2 + k = 0

h is the axis of symmetry and (h,k) is the vertex.

Calculate h according to the following formula:

h = -b/2a

h= -(-8)/2(4)

h = 8/8

h = 1

Substitute k for y and insert the value of h for x in the standard form:

ax^2+bx+c

k = 4(1)^2+(-8)(1)+20

k = 4-8+20

k=-4+20

k = 16

Thus the correct option is h=1, k=16....

8 0

3 years ago

What is a mixed number for 5/2

m_a_m_a [10]

Answer: 2 1/2

Step-by-step explanation: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction. Hope this helps!! PLZ mark me!!!

8 0

3 years ago