Answer:
See below ~
Step-by-step explanation:
What was the rat population in 1992?⇒ t represents the years after 1992
⇒ So, in 1992, t = 0
⇒ Apply in the formula
⇒ n(0) = 89e^(0.02 × 0)
⇒ n(0) = 89e⁰
⇒ n(0) = 89,000,000
The rat population in 1992 was 89,000,000.
===========================================================
What does the model predict the rat population was in the year 2003?⇒ Number of years after 1992 : 2003 - 1992 = 11
⇒ Substitute for t in the formula
⇒ n(11) = 89e^(0.02 × 11)
⇒ n(11) = 89e^(0.22)
⇒ n(11) = 89 × 1.24607673
⇒ n(11) = 110,900,829 rats
The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.
Answer:
(a) 89,000,000 rats
(b) 110,900,829 rats
Explanation:
Given equation:
n(t)=89e^0.02tTo find the initial population (1992):
insert t = 0
n(0) = 89e^0.02(0) = 89 million ≈ 89,000,000To find the rat population in 2003 (after 11 years):
insert t = 11
n(11) = 89e^0.02(11) = 89e^0.22 ≈ 110,900,829What is the midpoint between (8,-5) and (2,-2)?
O (3,-1.5)
O (10,-7)
O (5, -1.5)
O (5,-3.5)
Answer:
O (5,-3.5)
Step-by-step explanation:
Yesterday I ran less than 5 kilometers but more than 1200 meters. How far could I have run?
change 35:14 to a decimal number
Answer:
35/14 as a decimal = 2.5 · 35/14 in decimal form = 2.5 · Thirty-five fourteenths as a decimal = 2.5 · 35 over 14 as a decimal = 2.5
Can someone help me with this math problem?
see attached photo
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
How to determine the value of trigonometric reasons
In this question we must take into accounts the definitions of the trigonometric reasons sine and secant and the Pythagorean theorem as well.
If sec θ < 0 and csc θ > 0, then sin θ > 0 and cos θ < 0, the angle is in the second quadrant (0.5π < θ < π, x < 0, y > 0) and we have the following expression:
sec θ = r/x
[tex]\frac{r}{x}= -\frac{6\sqrt{11}}{11}[/tex]
Then x = - 11, r = 6√11 and the value of y is:
[tex]y = \sqrt{r^{2}-x^{2}}[/tex]
y = 5√11
By trigonometric expressions we have this formula for sin 2θ:
sin 2θ = 2 · sin θ · cos θ
sin 2θ = 2 · (y/r) · (x/r) = (2 · x · y)/r²
sin 2θ = [2 · (- 11) · (5√11)]/396
sin 2θ = - (5/18) · √11
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
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The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8.
Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget
of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of
new-release and classic movies bought?
Answer:
16 new releases and 22 classic movies.
A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 3 1/2 meters deep. What is its volume? in cubic meters
Answer:
761.25 m³
Step-by-step explanation:
l = 15 , w = 14.5 , h = 3.5
Volume of a rectangular prism is given by the formula :
V = lwh
V = 15 × 14.5 × 3.5
V = 761.25
Units will be m³
I am attaching an image for visual understanding
Hope this helped and brainliest please.
Find the surface area of the prism.
mi
8 mi
8/12 mi
The surface area is
square miles.
112
Answer: 433.5 square miles or 433 1/2 square miles
Step-by-step explanation
[tex]SA = 6x^{2}[/tex]
[tex]SA = 6 *(8.5)^{2} \\\\SA = 6*72.25\\\\SA = 433.5[/tex]
If a hot air balloon pilot inflates the balloon at an average wind speed of about 5 miles per hour with an altitude of 35,000 feet, how fast will the radius of the balloon increase as it goes up higher and higher performing certain tricks? Using the differentiation formula applicable for this situation, estimate the speed of inflation and the speed of landing. Will this be able to help the pilot still perform other tricks before making a colorful landing? Give at least two comprehensible reasons and explain your answer.
The speed of landing is 15.69 ft/sec.
What is differentiation ?"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."
Let the length of the rope = r
Height of the balloon = h
we are given dr/dt = 15ft/sec
at any time t we know:
[tex]r = 125 + 15*t[/tex]
By the Pythagoras theorem we know:
[tex]h^2 + 125^2 = r^2[/tex]
We have to find dh/dt at time t = 20 sec
[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]
By chain rule:
[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]
[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2
=15.69 ft/sec
Hence dh/dt = 15.69 ft/sec
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Which number is equivalent to 16 1/2
Answer:
8
Step-by-step explanation:
vertex (3,-2) and y-intercept (0,7).
Write your answer in this form: (X₁,Y1), (X2,2).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answer:
3±√2/3 = x
Step-by-step explanation:
As you already have the vertex, the equation for this is y = a(x – h)^2 + k,
so by plugging all this in using the vertex coordinates, you get y = 3(x - 3)^2-2, so, if you divide everything by three you get 2/3 = (x - 3)^2
This means that the two x-intercepts are:
A restaurant chef wants to install a new floor in her kitchen. The kitchen measures 8 meters wide and 11 meters long, and the flooring costs $8.71 per square meter. How much will the chef's new floor cost?
Answer:
$766.48
Step-by-step explanation:
area = length × width
area = 11 m × 8 m = 88 m²
cost = 88 m² × $8.71/m²
cost = $766.48
What is the return on equity for a firm with 15% return on assets, 10% return on debt, and a .75 debt/equity ratio?
The return on equity for the firm is 18.75%.
Return on equityReturn on equity=Return on assets +[ (Debt/Equity ratio)×(Return on assets-Return on debt)]
Let plug in the formula
Return on equity=.15+ [(.75)× (.15-.10)]
Return on assets=.15+ (.75×0.05)
Return on assets=.15+0.0375
Return on equity=0.1875×100
Return on equity=18.75%
Therefore the return on equity ratio is 18.75%.
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Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
a. $2,416
b. $3,840
c. $2,088
d. $1,740
I couldn't find the answer to this question when I really needed it, so I did the work myself and got D as the answer. I ended up getting it right because you divide 29,000 by 12, then multiply the answer (2416) by 28%, which gives you the answer, D, 1740. Hope that helped!
Answer:
d. $1,740
Step-by-step explanation:
The annual after-tax salary is found by subtracting the tax from the salary. The tax is found by multiplying the tax rate by the salary. The monthly after-tax income is 1/12 of the annual after-tax income.
__
stepsannual tax = 0.28 × $29,000 = $8,120
annual take-home pay = $29,000 -8,120 = $20,880
monthly take-home pay = annual pay / months per year
= $20,880 / 12 = $1,740 . . . . net monthly income
_____
Additional comment
The net pay will be (1 - 0.28) = 0.72 times the nominal salary. The monthly pay will be 1/12 of the annual pay. These combined factors give a monthly net pay of (0.72)(1/12) = 0.06 times the annual pay.
0.06 × $29000 = 6×$290 = $1740
Find the absolute mean deviation of this data set:
8, 8, 4, 12
Answer:
2 is the absolute mean deviation
Step-by-step explanation:
absolute mean deviation is
the average of the differences of the data from the average
8, 8, 4, 12
1. take the average
8+8+4+12=32 -> 32/4 = 8
2. subtract each number from this average
8 - 8 = 0
8 - 8 = 0
4 - 8 = 4 (there are no negative answers)
12 - 8 = 4
3. take the average of these subtractions
0+0+4+4=8 -> 8/4 = 2
4. answer: 2 is the absolute mean deviation
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 1. Rational 2. Irrational
Step-by-step explanation:
remember what a rational number is ?
any number that can be expressed by a/b, with a and b being integer numbers, and b different to 0.
so,
-7 = -7/1 rational
sqrt(10) irrational, because there is no rational number that multiplied by itself is 10.
sqrt(16) = sqrt(4×4) = 4 = 4/1 rational
52% = 52/100 rational
1.235 = 1235/1000 rational
PLEASE HELP 50 POINTS
The total leaf mass of a certain species of young plant saplings is approximately normally distributed with a mean of 14.2 grams and a standard deviation of 0.5 grams.
a. What is the probability of obtaining a randomly chosen plant sapling with a total leaf mass of more
than 15 grams?
b. Identify the leaf mass that would represent the 99th percentile.
Answer:
THE ANSWER IS A
Step-by-step explanation:
CORRECT IF I WRONG
C= 5/9(F-32)
urgent!!! will give 50 points
Answer:
25°
Step-by-step explanation:
hope it helps you solve the question
help me to give answer....
please help!
Thank you.
Answer:
Option A ----> -5
Step-by-step explanation:
Slope of a graph is given by the equation :
[tex]\frac{dy}{dx}[/tex] where d means change in .
Lets take the y-intercept (0,2) and (-1,7)
Change in y = 5
Change in x = -1
5/-1 = -5
Our answer will therefore Option A ---> -5
Hope this helped and brainliest please
area of rectangle 5 7/8km x 18/4km
Answer:
if ur in college then how do u not know this
Step-by-step explanation:
use ur brain
Please help I cannot find this question
Chua Chang & Wu Inc. is planning its operations for next year, and the CEO wants you to forecast the firm's additional funds needed (AFN). Data for use in your forecast are shown below. Based on the AFN equation, what is the AFN for the coming year?
Based on the AFN equation, the AFN for the coming year will be -$16000.
How to calculate the AFN?Last year's sales =$200,000
Sales growth rate = g = 40%
Forecasted sales = S0 × (1 + ) = 280,000
∆S = change in sales = S1 − S0 = $80,000
Last year's total assets = A*0 = A*0 since full capacity $135,000
Forecasted total assets = A*1 = A*0 × (1 + g) = $189,000
Last year's accounts payable = $50,000
Last year's accruals= $20,000
L*0 = payables + accruals = $70,000
Profit margin = M = 20.0%
Target payout ratio = 25.0%
Retention ratio = (1 − Payout) = 75.0%
AFN = (A*0/S0)ΔS – (L*0/S0)ΔS – Margin × S1 × (1 − Payout)
AFN = $54,000 – $28,000 – $42,000
= -$16,000
The complete question goes thus:
Chua Chang & Wu Inc. is planning its operations for next year, and the CEO wants you to forecast the firm's additional funds needed (AFN). Data for use in your forecast are shown below.
Last year's sales = $200,000
Sales growth rate = 40%
Last year's accounts payable = $50,000
Last year's notes payable = $15,000
Last year's accruals = $20,000
Based on the AFN equation, what is the AFN for the coming year?
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I will mark brainliest!
Graph the line that represents a proportional relationship between Y and X where the UNIT RATE of change is Y with respect to X is 4/5. In other words, a change of 1 unit in X corresponds to a change of 4/5 units in Y.
Answer:
see below
Step-by-step explanation:
Just graph y = 4/5 x
what does 7,124 ÷ 26 equal to?
274
hope that helps
:D
btw i used long division
A triangular prism has a height of 10 cm and a base area of 12 cm2. A rectangular prism has a height of 10 cm and base dimensions of 3 cm and 4 cm. Do the solids have the same volume?
The solids have the same volume.
What is Volume?Volume is the measure of the capacity that an object holds.
Volume of triangular prism be
= Base area * height
= 12*10
=120 cm³
Volume of rectangular prism be,
=10*3*4
=120 cm³
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Please pick one of the options.
9880 different possibilities are there in Sally's new combination option second 9880 is correct.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Total unique numbers consists in a Sally locker = 3
From the digits 0 to 39
Total numbers = 40
Apply combination formula:
= C(40, 3)
= 40!/(3!37!)
= 9880
Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.
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I will give you brainlest if you are the first one to answer(and the best)
Answer:
4 kg
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Add to find total mass:
2.5 + 3.5 + 3.5 + 5 + 5.5 = 20
Since there is a total of 5 bags and want to evenly distribute divided by 5,
20 / 5 = 4
I'd appreciate the help!
Answer:
Step-by-step explanation:
Cordell Johnson purchased a snow blower for $237.00 and two bags of rock salt for
$3.15 each. What is the total purchase price if he lives in Maine where the sales tax
rate is 5%?
a. Total cost of all items?
b. Sales tax?
c. Total price with sales tax?
Answer:
a.240.15
Step-by-step explanation:
a.240.15
b.12.0075
c.252.1575
Find the equation of the graphed line.
On a coordinate plane, a line goes through (negative 4, 0) and (0, negative 2).
a.
y = negative one-half x minus 2
c.
y = 4 x minus 2
b.
y = negative 2 x minus 4
d.
y = negative 4 x minus 2
Please select the best answer from the choices provided
A
B
C
D
Answer:
a. y = -1/2x - 2
Step-by-step explanation:
The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.
__
slopeThe x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...
m = rise/run = -2/4 = -1/2
In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.
__
equationThe slope-intercept equation is ...
y = mx +b . . . . . . . slope m, y-intercept b
We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...
y = -1/2x -2 . . . . . matches choice A
_____
Additional comment
When answering multiple-choice questions, you only need to do enough work to tell which answers are not viable.
When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.