Write 3n/9n-1 as a power of 3

Colin is painting figurines. He spends 20 minutes painting each figurine. After painting for 60 minutes, he still has 9 more fig

miss Akunina [59]

Answer:

$f(t) = -0.05t +12$

Step-by-step explanation:

To solve this problem we must pay attention to the following data supplied:

- f It is the number of figurines that remain to be painted.

- t amount of time, in minutes, that Colin spends painting

- Colin takes 20 minutes painting each figurines.

- After painting 60 min, he still has 9 figurines left. f (60) = 9

If he takes 20 minutes painting 1, it means that in 60 minutes he has painted 3 and he has 9 left.

Then, at the beginning he has 9 +3 figurines to be painted.

$f (0) = 3 + 9\\f (0) = 12$

With these two points we can find the function:

If m is the slope of the line, then:

$m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{9-12}{60-0}\\\\m = -0.05\\\\f (t) = -0.05t + c$

Where by definition $c = f(0) = 12$

Finally the formula is:

$f(t) = -0.05t +12$

3 0

2 years ago

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Ashley plants a tree 45cm tall it grows by 10 cm each year. Find the amount ashley gets in the 5th year?

Genrish500 [490]

Answer:

95cm

Step-by-step explanation:

45cm is the initial height

each year grow 10cm

growing time 5 years

45+(10 × 5)=95 cm

4 0

2 years ago

A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every ba

Ahat [919]

Answer:

$z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68$

Step-by-step explanation:

Information provided

n=100 represent the random sample taken

X=21 represent the number of bags overfilled

$\hat p=\frac{21}{100}=0.21$ estimated proportion of overfilled bags

$p_o=0.15$ is the value that we want to test

z would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to test if the true proportion of overfilled bags is higher than 0.15.:

Null hypothesis: $p =0.7$

Alternative hypothesis: $p > 0.15$

The statistic for this case is:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And replacing the info given we got:

$z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68$

5 0

2 years ago

The radius of the circular lens of a magnifying glass is 4 centimeters.

Nadusha1986 [10]

Answer: 50.24 square centimeters.

Step-by-step explanation:

Given: The radius of the circular lens of a magnifying glass = 4 centimeters

The area of a circle is given by :-

$\text{Area}=\pi r^2$ , where r is the radius of the circle.

Then the area of the circular lens of a magnifying glass is given by :-

$\text{Area}=\pi (4)^2=(3.14)(16)=50.24\text{ square centimeters }$

Hence, the area of the circular lens of a magnifying glass = 50.24 square centimeters.

5 0

2 years ago

PLEASE HELP!!!!!!

jek_recluse [69]

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\
-----------------------------\\\\

\begin{cases}
a=12\\
b=10\\
D=90+50
\end{cases}\implies d = \sqrt{{{ 12}}^2+{{ 10}}^2-2(12)(10)cos(140^o)}
\\\\\\
d\approx \sqrt{427.851}\implies d\approx 20.684551$

5 0

2 years ago

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