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3 years ago

1. Which shows another way to write 73?

1 answer:

6 0

1. The answer is C. 7 with an exponent of 3 means that you multiply 7 by itself three times, or 7 x 7 x 7.
2. The answer is A. 19 with an exponent of 3 is the same as 19 x 19 x 19.

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A given field mouse population satisfies the differential equation dp dt = 0.5p − 410 where p is the number of mice and t is the

ohaa [14]

Answer:

a) $t = 2 *ln(\frac{82}{5}) =5.595$

b) $t = 2 *ln(-\frac{820}{p_0 -820})$

c) $p_0 = 820-\frac{820}{e^6}$

Step-by-step explanation:

For this case we have the following differential equation:

$\frac{dp}{dt}=\frac{1}{2} (p-820)$

And if we rewrite the expression we got:

$\frac{dp}{p-820}= \frac{1}{2} dt$

If we integrate both sides we have:

$ln|P-820|= \frac{1}{2}t +c$

Using exponential on both sides we got:

$P= 820 + P_o e^{1/2t}$

Part a

For this case we know that p(0) = 770 so we have this:

$770 = 820 + P_o e^0$

$P_o = -50$

So then our model would be given by:

$P(t) = -50e^{1/2t} +820$

And if we want to find at which time the population would be extinct we have:

$0=-50 e^{1/2 t} +820$

$\frac{820}{50} = e^{1/2 t}$

Using natural log on both sides we got:

$ln(\frac{82}{5}) = \frac{1}{2}t$

And solving for t we got:

$t = 2 *ln(\frac{82}{5}) =5.595$

Part b

For this case we know that p(0) = p0 so we have this:

$p_0 = 820 + P_o e^0$

$P_o = p_0 -820$

So then our model would be given by:

$P(t) = (p_o -820)e^{1/2t} +820$

And if we want to find at which time the population would be extinct we have:

$0=(p_o -820)e^{1/2 t} +820$

$-\frac{820}{p_0 -820} = e^{1/2 t}$

Using natural log on both sides we got:

$ln(-\frac{820}{p_0 -820}) = \frac{1}{2}t$

And solving for t we got:

$t = 2 *ln(-\frac{820}{p_0 -820})$

Part c

For this case we want to find the initial population if we know that the population become extinct in 1 year = 12 months. Using the equation founded on part b we got:

$12 = 2 *ln(\frac{820}{820-p_0})$

$6 = ln (\frac{820}{820-p_0})$

Using exponentials we got:

$e^6 = \frac{820}{820-p_0}$

$(820-p_0) e^6 = 820$

$820-p_0 = \frac{820}{e^6}$

$p_0 = 820-\frac{820}{e^6}$

8 0

3 years ago

In the equation 2y=18, determine which property of equality will be used to isolate the variable. Choose the best answer. A. Mul

mixer [17]

Answer:

Step-by-step explanation:

Looking at the equation $2y=18$ , we see that if we want to isolate y, we need to divide it by 2 - because we're multiplying it by 2, and 2 times a number divided by 2 is just the number.

The Division Property of Equality states that if we have an equation, $a=b$ , then $a\div c = b\div c$ .

So, that means $2y\div 2$ will be equal to $18 \div 2$ , which is 9.

Hope this helped!

8 0

2 years ago

Read 2 more answers

81 is 45% of what number

andrew-mc [135]

81 is 45% of 180, all you do is divide 81 by .45 and boom there you go

8 0

3 years ago

Tyesha found that the z-statistic was 2.1 and that the critical z-values were -1.96 and 1.96. Which of the following is a valid

just olya [345]

Answer:

Step-by-step explanation:

If the z statistic does not lie within the critical region, you cannot reject the null hypothesis but neither can you necessarily accept it.

What you can do is reject the alternate hypothesis.

6 0

2 years ago

Read 2 more answers

We’ve shown that matrix multiplication is generally not commutative, meaning that as a general rule for two

ValentinkaMS [17]

Answer:

a) Observe that

$G=\left[\begin{array}{ccc}2&6\\4&0\end{array}\right] =2\left[\begin{array}{ccc}1&3\\2&0\end{array}\right] =2F$

Then, $FG=F(2F)=2FF, \text{ and } GF=(2F)F=2FF$

b) The zero matrix satisfies that for every matrix B such that the product is well defined, $0B=0=B0.$

Since the matrix G is the zero matrix then $FG=F0=0F=GF$

c) The identity(Id) matrix satisfies that for that for every matrix B such that the product is well defined Id*B=B=B*Id. Observe that G is the identity matrix, then FG=F*Id=F=Id*F=GF

d) Observe that

$G=\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right] =3\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =3Id$ .

Then $GF=3Id*F=3F\\FG=F(3Id)=3F*Id=3F$

6 0

2 years ago