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3 years ago

Please help with trend lines

Mathematics

1 answer:

satela [25.4K]3 years ago

3 0

Answer:

$K=-2J+24$

Step-by-step explanation:

Trend line passes through the points (6,12) and (4,16).

Find the slope of the line:

$m=\dfrac{K_2-K_1}{J_2-J_1}=\dfrac{16-12}{4-6}=\dfrac{4}{-2}=-2$

Write the equation of the line in the form $K=mJ+b,$ where the slope $m=-2:$

$K=-2J+b$

This line passes through the point (6,12), then its coordinates satisfy the equation:

$12=-2\cdot 6+b\\ \\12=-12+b\\ \\b=12+12\\ \\b=24\\ \\K=-2J+24$

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3 years ago

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3 years ago

Read 2 more answers

8. A substance has a half life of 2.347 minutes.

mina [271]

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

$A=A_0b^{\frac{t}{c}}$

Where $A$ is the final population

$A_0$ is the initial population

$b$ is the growth factor

$c$ is the time taken for the growth 'b'

$t$ is the amount of time

Here, we are given that:

$A$ = 6. 9 grams

$A_0$ = 110.4 grams

$b = \dfrac{1}{2}$

$c = 2.347$ min

To find:

a.) Number of half lives taken for the decay.

b.) Total time in the decay.

Solution:

a.) Number of half lives taken for the decay is nothing but equal to $\frac{t}{c}$ .

Putting the values in the formula, we get:

$6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4$

Therefore, the answer is:

4 half lives have passed.

b.) Total time of decay. We have to find the value of $t$ here.

From answer of part a.):

$\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}$

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3 years ago

How do we convert kilogram to gram

Sloan [31]

1kg=1000g

7kg*1000=7000g

10kg*1000=10000g

15g*1000=15000g

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3 years ago