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2 years ago

14

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

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.

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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.

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3 0

3 years ago

Complete the table Y=6x-4

viktelen [127]

Answer:

With Two points is enough to describe this graph

$\left[\begin{array}{ccc}\frac{4}{6} &0\\0&-4\\\end{array}\right]$

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:

$Y=4*0-4$

$y=-4$

The point for this is (0, -4)

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2 years ago

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lozanna [386]

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2 years ago