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ser-zykov [4K]
2 years ago
14

A number to the 12th power divided by the same number to the 9th power equals 512.

Mathematics
1 answer:
Mazyrski [523]2 years ago
5 0
Explanation:
Let's call our number
a
. The statement written as a formula is
a
12
a
9
=
125
We can simplify the fraction, and we have
a
3
=
125
To solve for
a
, take the third root of both sides:
a
=
(
125
)
1
3
=
5
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The fox population in a certain region has a relative growth rate of 4% per year. It is estimated that the population in year 20
den301095 [7]

Answer:

a) P(t) = 17900e^{0.04t}

b) The population estimated in 2008 is of 24651.

Step-by-step explanation:

The population growth model may be given by the following exponential function:

P(t) = P_{0}e^{rt}

In which P(t) is the population after t years, P_{0} is the initial population and r is the growth rate.

(A.) Find a function that models the population t years after 2000 (t=0 for 2000)

We have that:

P_{0} = 17900, r = 0.04. So

P(t) = P_{0}e^{rt}

P(t) = 17900e^{0.04t}

(B.) Use the function from part A to estimate the fox population in the year 2008.

2008 is 8 years after 2000. So:

P(8) = 17900e^{0.04*8} = 24650.5

The population estimated in 2008 is of 24651.

3 0
3 years ago
Solve the following problems using 5-D process part 2
svet-max [94.6K]

The two problems are almost identical: you have to set up a system, and then solve it.

In the first case, let g and b be, respectively, the number of girls and boys.

We know that g=2b+4 (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that g+b=61 (there are 61 students in total).

So, we have the system

\begin{cases}g=2b+4\\g+b=61\end{cases}

We can use the first equation to substitute in the second

g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19

And then solve for g:

g=2b+4=2\cdot 19+4=38+4=42

For the second problem, let c and j be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

\begin{cases}c=j+12\\c+j=230\end{cases}

And you can solve it in the very same way we solved the previous one.

5 0
3 years ago
In a poll, 74% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted o
Maksim231197 [3]

Answer:

324

Step-by-step explanation:

given that in a poll, 74% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder?"

i.e. Sample proportion p=0.74\\q =1-p =0.26\\

Margin of error = 4% = 0.04

Confidence level =90%

Z critical value for 90% = 1.645

Margin of error = 1.645 * std error

Hence std error = \frac{0.04}{1.645} \\=0.0243

Std error is also equal to

\sqrt{\frac{pq}{n} } =\sqrt{\frac{0.74(0.26)}{n} } =0.0243\\\sqrt{n} =18..05\\n = 325.83~324

Sample size should be 324.

The formula is sample size = (Z critical value)^2 (pq)/(Margin of error )^2

3 0
3 years ago
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viktelen [127]

Answer:

With Two points is enough to describe this graph

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Step-by-step explanation:

Interception with Y axis (y=0), thus we have the following equation:

0=6*x+4

x=4/6

The point for this is (4/6 , 0)

Interception with x axis (x=0), thus we have the following equation:

Y=4*0-4

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The point for this is (0, -4)

4 0
2 years ago
PLEASE HELP!! 15 POINTS!!!!
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A. Is y=2x+3
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C. Is (1,5) you can graph the slope intercept form equations to show your work :)
7 0
2 years ago
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