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3 years ago

D.reflection across y=x

Mathematics

1 answer:

AlladinOne [14]3 years ago

6 0

Rotation of 180° about the origin

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he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

elena-s [515]

Answer:

The bones were 12,485 years old at the time they were discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element carbon-14 has a half-life of 5750 years.

This means that $A(5750) = 0.5A(0)$ , and we use this to find k. So

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-5750k}$

$e^{-5750k} = 0.5$

$\ln{e^{-5750k}} = \ln{0.5}$

$-5750k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{5750}$

$k = 0.00012054733$

$A(t) = A(0)e^{-0.00012054733t}$

A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

$A(t) = 0.222A(0)$

Then

$0.222A(0) = A(0)e^{-0.00012054733t}$

$e^{-0.00012054733t} = 0.222$

$\ln{e^{-0.00012054733t}} = \ln{0.222}$

$-0.00012054733t = \ln{0.222}$

$t = -\frac{\ln{0.222}}{0.00012054733}$

$t = 12485$

The bones were 12,485 years old at the time they were discovered.

8 0

3 years ago

Need the answer for my hw

andrew-mc [135]

The answer is (1,1)

5 0

2 years ago

Amélie runs a bakery. She wants to find out whether her cake sales are affected by the weather conditions. She recorded the dail

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

Daily temp(in F) Cakes sold

42 39

45 52

48 31

54 61

59 72

62 35

64 61

65 34

67 58

75 45

84 24

To find whether there is an association between these two let us find the correlation coefficient between these two variables.

r=-0.1975

Since |r|<0.5, correlation is weak.

Let us test the hypothesis r =0

H0:r=0

Ha:r not equals 0

Test statistic = $\frac{r\sqrt{n-2} }{\sqrt{1-r^2} } \\=\frac{-0.1975\sqrt{11-2} }{\sqrt{1-0.1975^2} }\\=\frac{-0.5625}{{0.9803} } \\=-0.5738$

p =0.298

Since p value >0.10, at 90% significance level we accept that there is no association.

6 0

2 years ago

Is 5 3/10 greater than 3 8/10? Please explain as an equation.

riadik2000 [5.3K]

Answer:

53/10 > 38/10

Step-by-step explanation:

4 0

3 years ago

A number increased by two twenty fourths of itself

serious [3.7K]

Answer:

n/12

Step-by-step explanation:

n(2/24)=n(1/12)

n/1 * 1/12 = n/12

n/12

6 0

3 years ago