Joshua breeds mice and notices that he can model their population growth with the equation m = 2(3) d/14. He plans to breed them for 100 days. What parameter does the denominator 14 represent in this experiment?

Answers

Answer 1

Answer: A. The population at the start of the experiment
B. The growth factor of the population every two weeks
C. The population after one hundred days
D. How many days it takes for the population to triple

If these were the choices of the above question, the answer would be B.) The growth factor of the population every two weeks.

14 days represents 2 weeks.

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PLEASE DON'T SKIP

Solve.

Answers

(7z - 1) / 2 = 3z - 2

Multiply each side by 2 : (7z - 1) = 2 (3z - 2)

7z - 1 = 6z - 4

Subtract 6z from each side: z - 1 = -4

Add 1 to each side: z = -3

50 POINTS! Vectors u, v, and w are shown in the graph. What are the magnitude and direction of u + v + w? Round the magnitude to the thousandths place and the direction to the nearest degree.

Answers

Answer:

C) 48.786, 152°

Step-by-step explanation:

To add the vectors u, v and w, we first need to rewrite each vector in component form (where vectors are represented using the unit vectors i and j along the x and y axes).

The (x, y) components of a vector, given its magnitude (r) and direction (θ), are (r cos θ, r sin θ), where θ is measured in the anticlockwise direction from the positive x-axis.

Every vector in two dimensions is made up of horizontal and vertical components, so any vector can be expressed as a sum of i and j unit vectors. Therefore, the i + y form of a vector is:

(r cos θ) i + (r sin θ) j

So, the component form of the given vectors are:

$\mathbf{u}=80 \cos 230^(\circ)\textbf{i}+80 \sin 230^\circ}\textbf{j}$

$\mathbf{v}=60 \cos 120^(\circ)\textbf{i}+60 \sin 120^\circ}\textbf{j}$

$\mathbf{w}=50 \cos 40^(\circ)\textbf{i}+50 \sin 40^\circ}\textbf{j}$

Sum the vectors:

$\mathbf{R}=\mathbf{u}+\mathbf{v}+\mathbf{w}\n\n\mathbf{R}=(80 \cos 230^(\circ)+60 \cos 120^(\circ)+50 \cos 40^(\circ))\textbf{i}+(80 \sin 230^\circ}+60 \sin 120^\circ}+50 \sin 40^\circ})\:\textbf{j}\n\n\mathbf{R}=-43.1207866\:\textbf{i}+22.8173493\:\textbf{j}$

$\textsf{For a vector\;\;$\mathbf{a} = x\mathbf{i} + y\mathbf{j}$, its magnitude is\;\;$||\mathbf{a}|| = √(x^2+y^2)$.}$

Calculate the magnitude of the resultant vector ||R||:

$\mathbf{||R||}=√((-43.1207866)^2+(22.8173493)^2)\n\n\mathbf{||R||}=48.7855887...\n\n\mathbf{||R||}=48.786$

The direction θ can be found by finding the angle with the horizontal, which is given by:

$\boxed{\theta=\tan^(-1)\left((y)/(x)\right)}$

As the resultant vector is in quadrant II (since the i component is negative and the j component is positive), we need to add 180° to the value of tan⁻¹(y/x). Therefore:

$\theta=\tan^(-1)\left((22.8173493)/(-43.1207866)\right)+180^(\circ)$

$\theta=-27.8855396+180^(\circ)$

$\theta=152.114460^(\circ)$

$\theta=152^(\circ)\; \sf (nearest\;degree)$

Therefore:

Magnitude = 48.786
Direction = 152°

The answer is c :48.786; 152°

Dylan invested $7200 in an account paying in interest rate of 2.3% compounded quarterly assuming no deposit or withdrawals are made how much money to the nearest dollar will be in the account after 12 years

Answers

idk something you could do is google it then you copy the answer

Write pqqqqrr in exponential form.
p·q^4·r^2

Answers

Answer:

$pqqqqrr = p.q^4.r^2$

Step-by-step explanation:

Write any number or value in exponential form simply means a numeric form involving exponents.

The exponents for each of the number in a value represent the number of times that number or value appears as a factor.

For example, here in this case, we have one p, 4 q's and 2 r's so we can write it in exponential form as:

$pqqqqrr = p.q^4.r^2$

Whats the slope of a line if its plotted (0,0) and (3,6), find the y-intercept of the line. Write an equation for the line using your answers. Find one more point that lies on the line. Explain why that point is also a solution to the function. (Please explain your answers so I could understand it more) thanks guys!

Answers

To find the slope you do the method
Y2-Y1
--------
X2-X1
So you do 6-0=6 and 3-0=3. That would be 6/3 and then, you simplify it. Your slope is 2.
To find the y-intercept you have to do the point slope form, then, you do the slope intercept form
Y-Y1=m(x-x1)
You do y-6=2(x-3)
Y-6=2x+(-6)
You add six to both sides
The equation is y=2x
The y-intercept is -6
One more point on the line would be (4,8). Because if you look at the slope it is 2/1. When plotting a point you look at the slope as rise over run. The two is the rise and the 1 is the run. So you go to (3,6) and add 1 to the 3. Then, you add 2 to the 6 to get (4,8). That's why that point is a solution to the function. You could also do (2,4) if you did the opposite and subtracted the 2 and 1 to make the bottom half of the line.

very simple.

so slope=rise/run so if we plot the points and find how high and how long it went we see that the slope=6/3=2
slope=2

since the line goes through the origin (0,0) the y-intercept=(0,0)
and the equation is
y=mx+b
m=slope
b=how much away from the origin whic is not applicable in this problem. so
y=2x

Write a sentence to represent the equation 4m = -8.Please help my teacher has been bugging me to do this.
(Online schooling)

Answers

Answer: 4 times m is equals to -8.

4 times a number is -8

Step-by-step explanation:

Given algebraic equation: 4m =-8

which is equivalent to 4 times m= -8

Therefore ,the sentence to represent the given algebraic equation will be

4 times m is equals to -8.

OR, you can also write

4 times a number is -8, where m is the number.

4 times a number is equal to negative 8

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