Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that the initial value and the growth rate are given as follows:
A(0) = 31124, r = 0.06.
Hence the profit function is given by:
[tex]P(t) = 31124(1.06)^t[/tex]
Then, the total profit over the first 10 years is given by:
[tex]\int_{0}^{10} P(t) dt[/tex]
[tex]\int_{0}^{10} 31124(1.06)^t dt[/tex]
[tex]\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72[/tex]
Thus, her total profit for the first ten years is of $422,426.72.
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The population in the United States was roughly 161,000,000 in 1950. By 2000, it had grown to roughly 291,000,000. Assume that the population in the United States grew linearly during that period. Find a linear equation which models the population in the United States during the period 1950 to 2000
to get the equation of any straight line, we simply need two points off of it, so let's use the ones provided in the table above.
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{millions}{population}&year\\ \cline{1-2} 161&1950\\ 291&2000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{161}~,~\stackrel{y_1}{1950})\qquad (\stackrel{x_2}{291}~,~\stackrel{y_2}{2000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2000}-\stackrel{y1}{1950}}}{\underset{run} {\underset{x_2}{291}-\underset{x_1}{161}}} \implies \cfrac{ 50 }{ 130 }\implies \cfrac{5}{13}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1950}=\stackrel{m}{\cfrac{5}{13}}(x-\stackrel{x_1}{161}) \\\\\\ y-1950=\cfrac{5}{13}x-\cfrac{805}{13}\implies y=\cfrac{5}{13}x-\cfrac{805}{13}+1950\implies y=\cfrac{5}{13}x+\cfrac{24545}{13}[/tex]
I NEED HELP ASAP PLEASE I WILL GIVE BRAINLIEST
Simplify:
| -1/2 - 1/8| + ( -3/4 + 5/6)
A. 1/12 B. -5/8 C. -13/24 D. 17/24
Answer:
0.705
Step-by-step explanation:
| -1/2 - 1/8| + ( -3/4 + 5/6)
| -1/2 - 1/8| + ( -0.75 + 0.83)
| -1/2 - 1/8| + 0.08
| -0.5 - 0.125| + 0.08
|-0.625| +0.08
0.625+0.08
0.705
hope it helps
Can you guys pls help me with this math question
Answer:
Dimensions: 150 m x 150 m
Area: 22,500m²
Step-by-step explanation:
Given information:
Rectangular fieldTotal amount of fencing = 600mAll 4 sides of the field need to be fencedLet [tex]x[/tex] = width of the field
Let [tex]y[/tex] = length of the field
Create two equations from the given information:
Area of field: [tex]A= xy[/tex]
Perimeter of fence: [tex]2(x + y) = 600[/tex]
Rearrange the equation for the perimeter of the fence to make y the subject:
[tex]\begin{aligned} \implies 2(x + y) & = 600\\ x+y & = 300\\y & = 300-x\end{aligned}[/tex]
Substitute this into the equation for Area:
[tex]\begin{aligned}\implies A & = xy\\& = x(300-x)\\& = 300x-x^2 \end{aligned}[/tex]
To find the value of x that will make the area a maximum, differentiate A with respect to x:
[tex]\begin{aligned}A & =300x-x^2\\\implies \dfrac{dA}{dx}& =300-2x\end{aligned}[/tex]
Set it to zero and solve for x:
[tex]\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 300-2x & =0 \\ x & = 150 \end{aligned}[/tex]
Substitute the found value of x into the original equation for the perimeter and solve for y:
[tex]\begin{aligned}2(x + y) & = 600\\\implies 2(150)+2y & = 600\\2y & = 300\\y & = 150\end{aligned}[/tex]
Therefore, the dimensions that will give Tanya the maximum area are:
150 m x 150 m
The maximum area is:
[tex]\begin{aligned}\implies \sf Area_{max} & = xy\\& = 150 \cdot 150\\& = 22500\: \sf m^2 \end{aligned}[/tex]
What is the y-intercept of f(x) = 3x 2? a. (9,0) b. (0,9) c. (0,-9) d. (9,-9)
Answer:
f(x) = 3x + 9: y - intercept is option c. (0,-9)
f(x) = 3x - 9: y - intercept is option b. (0, 9)
Step-by-step explanation:
option a and d cant be correct since y = 0 in those answer when the y - intercept is when x = 0
If the function f(x) = 3x + 9
than x = 0
f(x) = 3(0) + 9
f(x) = 0 + 9
f(x) = 9
x = 0 and y = 9 (0, 9)
If the function f(x) = 3x - 9
than x = 0
f(x) = 3(0) - 9
f(x) = 0 - 9
f(x) = -9
x = 0 and y = -9 (0, -9)
Which of the following shapes have faces? Select two options.
cube
rectangle
hexagon
octagon
pyramid
circle
Answer:
Objects mostly have one or more geometrical shapes like the following. These types of shapes are called three dimensional (3-D) shaped solids. All these geometrical shapes have faces. We have learned about faces like triangular faces, rectangular face, square face and circular face.
What is the slope of a line perpendicular to the line whose equation is 5x - y = -7.
Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so a line perpendicular to that one above will have a slope of
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}[/tex]
What is the area of triangle ABC?
Answer: The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height
Step-by-step explanation:
Area of ΔABC= 1/2 × Base × Height = 1/2 × h × BC
If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.
Thus, we have seen the formula and definition of the area of triangle ABC.
Helpppp asap : two non-vertical lines are parallel if they have the same slope and different y-intercepts.
true
false
help me please i still struggle
Answer:
59 degrees
Step-by-step explanation:
Angles on a straight line add up to 180 degrees
Angles in a triangle add up to 280 degrees
180 minus 149 is 31
31 add 90 is 121
180 minus 121 is 59
4. You are packing clothes for vacation and don't want to take any t-shirts. You randomly choose 3 shirts from a drawer containing 4 t-shirts, 3 polo shirts, and 3 button-downs.
a. What is the probability that the first 3 shirts are t-shirts when you replace each shirt before choosing the next one?
b. What is the probability that the first 3 shirts are t-shirts when you do not replace each shirt before choosing the next one?
*I know this is a lot, but it would really help me out if someone could help me out, I don't know how to describe it, but thanks.*
Answer:
A. 3/10
B.1/7
Step-by-step explanation:
Which step is the same when constructing an inscribed regular hexagon and an inscribed equilateral triangle?.
Step is the same when constructing an inscribed regular hexagon and an inscribed equilateral triangle is shown below:
What is construction?Geometric construction is the process of drawing a geometrical figure using two geometrical instruments, a compass, and a ruler.
Construction of an inscribed regular hexagon
1) Set compass width to the radius of the circle
2) Make an arc on the circle with the set radius.
3) From the previous arc draw another arc with the same radius.
4) Continue this process for the other vertex.
5) Connect all the vertices.
Construction of an inscribed equilateral triangle
1) Set compass width to the radius of the circle
2) Make an arc on the circle with the set radius.
3)From the previous arc draw another arc with the same radius.
4)Continue this process for the other vertex.
5) Connect the every other vertices point by drawing a line between every other adjacent vertex point to form an inscribed equilateral triangle.
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Liam has 4 ½ cups of sugar. He uses 2 ½ cups to bake bread, then borrows another 1 cup from his neighbor. He wants to bake cookies, which take 2 ½ cups of sugar. Does he have enough? How much will he have left over,or how much more does he need?
Answer:
1/2
Step-by-step explanation:
1. 4 1/2- 2 1/2= 2
2. 2+1=3
3. 3-2 1/2= 1/2
He has enough
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting a bird?
express the probability as a reduced fraction
15 and 12 are the two longest side lengths of a right triangle. What should the shortest side length
be in order to form a Pythagorean Triple?
Answer:
9 units
Step-by-step explanation:
Using Pythagorean Theorem
12^2 + x^2 = 15^2
144 +x^2 = 225
x^2 = 81
x = 9
This set of points is on the graph of a function.
{(-3, 9), (-1, 1), (0, 0), (2, 4)}
Which points are on the graph of the inverse?
Select each correct answer.
(-9, 3)
(1, − 1)
(4,2)
(0, 0)
Answer:
Points on the inverse are [tex](1,-1), (4,2), \text{and } (0,0)[/tex]
Step-by-step explanation:
When writing the inverse function of a set of points, you simply switch the coordinates:
[tex]\text{Function}: (x,y)\\\text{Inverse}: (y,x)[/tex]
We are given the points
[tex](-3,9), (-1,1), (0,0), \text{and } (2,4)[/tex]
Using our rule for function, our new points will be
[tex](9,-3), (1,-1), (0,0), \text{and } (4,2)[/tex]
From the list, the points we have for the graph of the inverse are
[tex](1,-1), (4,2), \text{and } (0,0).[/tex]
It takes a bird 6 minutes to fly with a 10 mph tailwind from its nest to a bird
feeder. It takes 30 minutes for the bird to get back to its nest. What is the bird's
speed in still conditions? How far away is the bird feeder?
Answer:
The bird's speed is 50mph.
The bird's feeder is 25 miles away.
Step-by-step explanation:
10/6=x/30
6*x=30 is 6/30=x
x=5
6*5=30 so 10*5=50
x=50
mph/time=distance per hour
50/(1/2)=25 miles
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
[tex]x = 2, y = -3[/tex]
Step-by-step explanation:
Add the 2 equations together, then solve for x.
[tex](2x + 2y) + (3x - 2y) = (-2) + (12)\\ 2x + 3x + 2y - 2y = -2 + 12\\5x = 10\\x = 2[/tex]
Now that we know the value of x, we can easily find y by substitution.
[tex]3x - 2y = 12\\3(2) - 2y = 12\\6 - 2y = 12\\-2y = 6\\y = -3[/tex]
These are the answers
- Kan Academy Advance
f(7) if f(x) = x + 10.
Answer:
17
Step-by-step explanation:
at f(7) means x is 7
7+10 is 17
Please help me with this one.
Answer:
V = 16W = 48Step-by-step explanation:
The triangles are congruent when corresponding sides are congruent.
__
ΔFGH ≅ ΔABC means corresponding sides are ...
(GH, BC) = (V, 16)
(HF, CA) = (48, W)
Corresponding sides being congruent means ...
V = 16
W = 48
Find the surface area of the square pyramid. Enter your answer in the box.
A square pyramid. The side length of the base is 11 centimeters. The height of each of the 4 triangular faces is 10 centimeters.
cm2
Answer:
341 cm²
Step-by-step explanation:
Formula :
Surface area = Area of 4 triangle faces + Area of square base
===============================================================
Solving :
⇒ Surface area = 4 × 1/2 × 11 × 10 + 11²
⇒ Surface area = 2 × 110 + 121
⇒ Surface area = 220 + 121
⇒ Surface area = 341 cm²
The surface area of the square pyramid is 341 square centimeter.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The surface area of a square pyramid is calculated by the equation S = B + 1/2 × P × S
where B is the area of the base,
P is the perimeter of the base, and
S is the slant height of the pyramid.
the area of the base =11×11
B=121 square centimeter
The perimeter of the base = 2(11+11)
P= 44 cm
Slant height (S) is 10 cm.
Surface Area = 121 + 1/2 (44×10)
=121+220
=341 square centimeter
Hence, the surface area of the square pyramid is 341 square centimeter.
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A veterinarian finds that weights for the population of each dog breed tend to be approximately normally distributed. The mean weight of beagles is 25 pounds with a standard deviation of 3 pounds. The mean weight for Great Danes is 150 pounds with a standard deviation of 20 pounds. About 68% of beagles weigh between 22 and 28 pounds. Consider these values in terms of the mean and standard deviation only. The interval that would represent a similar percentage of Great Danes would fall between
Using the Empirical Rule, it is found that the interval that would represent a similar percentage of Great Danes would fall between 130 and 170 pounds.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.68% fall within 1 standard deviation of the mean, hence for the Great Danes, the values are given as follows:
150 - 20 = 130 pounds.150 + 20 = 170 pounds.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 680 grams, how much of the element would remain after 19 years, to the nearest whole number?
Answer:
410 g
Step-by-step explanation:
Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).
y = a(1/2)^(t/h)
__
We can use this equation with the given values to find the amount remaining.
y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)
y ≈ 410 g
About 410 grams of element X will remain after 19 years.
How many 4 letter arrangements can be made by using different letters from the word hexagon
Answer:
I can find at least 10 4-letter words out of hexagon.
Step-by-step explanation:
1.) Hexa (means 6)
2.) gone
3.) nage (a type of bullion)
4.) gane (to yawn)
5.) hage (a frightening old woman; a witch)
6.) hane (ghostly)
7.) axon (a part of a nerve cell)
8.) hang
9.) oxen
10.) hoax
The water in a fish tank is treated by using 5 millilitres of AquaGuard for every 10 litres of
water in the tank.
Write down the ratio of the volume of AquaGuard used to the volume of water in the tank.
Give your answer in the form 1 : n
What can you conclude about the population density from the table provided? Population Area (km²) Region A 20,178 521 Region B 1,200 451 Region C 13,475 395 Region D 6,980 426
Answer:
A got it right
Step-by-step explanation:
got it right
Show problem set up for full credit.
Answer:
∠ QPR = 125°
Step-by-step explanation:
the angles subtended by 2 congruent arcs are congruent , that is
5x = 4x + 25 ( subtract 4x from both sides )
x = 25
Then
∠ QPR = 4x + 25 = 4(25) + 25 = 100 + 25 = 125°
4x - 1 < 11
solve the inequality
Answer:
12
Step-by-step explanation:
127491733816383827i 9273
Answer question 6 for me thanks
Answer: its c
Step-by-step explanation: im a smarty boy i hope u its right or not
What is the slope of the line that is parallel to the line whose equation is 4x + y2 = 0?
We know the slope formula
m=-a/bm=-4/2m=-2Parallel lines have equal slope so it has m=-2
A random sample of 81 items is taken,producing a sample of 47.the population standard deviation is 5.89.construct a 90% confidence interval to estimate the populations mean.
The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. The confidence interval for the given sample is 48.07656, 45.9234.
What is a confidence interval?The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. The percentage is used to represent the location of a population mean between an upper and lower interval.
Given the random sample is 81, while the sample means is 47, the standard deviation is 5.89. Therefore, the confidence interval for 90% of the population mean is,
[tex]CI = \bar{x} \pm z \dfrac{s}{\sqrt{n}}\\\\CI = 47 \pm 1.645 \dfrac{5.89}{\sqrt{81}}\\\\CI= 47 \pm 1.07656\\\\CI = 48.07656, 45.9234[/tex]
Hence, the confidence interval for the given sample is 48.07656, 45.9234.
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