Answers
Answer:
1) Part A
The function that models the situation is P = 8,300·(1 - 0.12)ⁿ
Part B
2626 people
Part C
1575 people
2) Part A
The function that models the situation is A = 342.000·(1 - 0.06)ⁿ
Part B
The value of the hose in 2025 is approximately $208,472.6
Part C
The value of the hose in 2032 is approximately $135,189.8
Step-by-step explanation:
1) Part A
The given parameters are;
Martianville population in 2012, P₀ = 8,300 people
The percentage annual decrease in the population, r = -12% = -0.12
The formula for the growth of a population is presented as follows;
P = P₀·(1 + r)ⁿ
Where;
P = The population amount at a later time
P₀ = The initial amount of the population
r = The rate of the population growth
n = The number of years
Therefore;
The function that models the situation is P = 8,300·(1 - 0.12)ⁿ
Part B
The population that will attend Martianville in 9 years is given as follows;
P₉ = 8,300 × (1 + (-0.12))⁹ = 8,300 × (1 - 0.12)⁹ ≈ 2626.77
Therefore, by rounding down to the next whole person, the population that will attend Martianville in 9 years, P₉ = 2626 people
Part C
The population that will attend Martianville in 13 years is given as follows;
P₁₃ = 8,300 × (1 - 0.12)¹³ ≈ 1575 people
2) Part A
The price at which the house was bought, A₀ = $342,000
The rate of decrease of the value of the house = 6% therefore, r = -0.06
The function that models the situation is presented as follows;
A = A₀·(1 + r)ⁿ
Therefore;
The function that models the situation is A = 342.000·(1 - 0.06)ⁿ
Part B
The number of years between 2025 and 2017 = 2025 - 2017 = 8 years
The value of the hose in 2025, A₂₀₂₅ = 342.000·(1 - 0.06)⁸ = 208,472.576981
The value of the hose in 2025, A₂₀₂₅ ≈ $208,472.6
Part C
The number of years between 2032 and 2017 = 2032 - 2017 = 15 years
The value of the hose in 2032, A₂₀₃₂ = 342.000·(1 - 0.06)¹⁵ = 135,189.795176
The value of the hose in 2025, A₂₀₃₂ ≈ $135,189.8
Related Questions
What is the measure of E in degrees?
Answers
Answer:
c
Step-by-step explanation:
E=10×10+25
but solve it to make sure
the answer is 130° a p e x
A spinner used in a board game is divided into 8 equally sized sectors. Three of these sectors indicate that the player should move his token forward on the board, two of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board. The total area of the sectors that do not allow the player to move his token is 35.9 inches squared. What is the radius of the spinner
Answers
Answer:
5.52 inch
Step-by-step explanation:
Recall :
Area of Sector : θ/ 360 * πr²
Sectors that do not allow movement : (8-3-2) = 3
Total sectors = 8
θ/ 360 = 3/8 ; Area = 35.9
Radius = r
35.9 = 3/8 * π * r²
35.9 / (3/8 * π) = r²
30.472866 = r²
r = √30.472866
r = 5.52 inch
The radius of the spinner is 5.520 inch whose [tex]\frac{3}{8}[/tex] sector area is 35.9 inches square.
It is given that the spinner used in a board game is divided into 8 equally sized sectors. three sectors indicate that the player should move his token forward on the board, two sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board and its area of the sector is 35.9 inches square.
It is required to find the radius of the spinner.
What is the area of the sector?The region enclosed by the two radii of a circle and the arc is known as a sector's area. In other words sector area is a portion of the circle's area.
We know the formula of sector area (A):
[tex]\rm A= \frac{\theta}{360 \°} \pi r^2[/tex] Where 'r' is the radius of the circle and [tex]\rm \theta[/tex] is in degree
The remaining sectors = ( Total sectors - Three sectors - Two sectors)
= ( 8 - 3 - 2) ⇒ 3 sectors indicate the player do not move his token
Total sector = 8
[tex]\rm \frac{\theta }{360 \° } = \frac{3}{8} \ when \ A = 35.9 \ inches^2[/tex]
Putting these values in the above formula, we get:
[tex]\rm 35.9 = \frac{3}{8} \pi r^2\\\rm 35.9\times 8 = 3\pi r^2\\\rm 287.2 = 3\pi r^2\\\\\rm \frac{287.2}{3} = \pi r^2\\\\\rm 95.733= \pi r^2\\\rm 30.4728 = r^2[/tex]Where [tex]\rm \pi[/tex] = 3.14159
[tex]\sqrt{30.4728} = r\\\rm 5.520= r \\\rm or = 5.520 \ inch[/tex]
Thus, the radius of the spinner is 5.520 inch.
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ethan bought 4 packages of pencils. after he gave 8 pencils to his friends, he had 40 pencils left over. how many pencils were in each package? use the drop-down menus to solve the problem arithmetically and algebraically
Answers
Answer:
there was 12 pencil's in each package because 12 ×4=48 48 -8=40
Log 8 1/32 is equaled to
Answers
Answer:
I think the answer wold be -5/3 or -1.666666667 .
The value of the given expression is,
[tex]log_8 \frac{1}{32}[/tex] = -3/5
The given logarithmic expression is,
[tex]log_8 \frac{1}{32}[/tex]
Since we know that,
The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to expressing enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.
We can write the given expression as,
[tex]log_8 \frac{1}{32}[/tex] = [tex]log_8 32^{-1[/tex]
= - [tex]log_8 32[/tex] [ [tex]log_a b^x = x log_a b[/tex]]
= - [tex]log_{2^3} 2^5[/tex]
= - [tex]\frac{3}{5} log_{2} 2[/tex] [ [tex]log_{a^y} b^x = \frac{x}{y} log_a b[/tex]]
= -3/5 [ [tex]log_{a} a = 1[/tex]]
Hence,
[tex]log_8 \frac{1}{32}[/tex] = -3/5
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The possibility of an event happening is its ______.
Answers
Answer:
Probability
Step-by-step explanation:
Answer:
Probability.
Step-by-step explanation: This is the chance of an event or something happening. Like one green, blue, yellow, and a red square have a1/4 chance of happening since there are four. This can go to 1/6 if we add white and purple to the spinner.
Please hurry! This is due soon.
Answers
Hi!
We can see here that this is a composition question.
And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).
To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.
[tex]f(x)=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]y=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]x=\frac{e^7^y+\sqrt{3}}{2}[/tex]
[tex]2x=e^7^y+\sqrt{3}[/tex]
[tex]e^7^y=2x-\sqrt{3}[/tex]
[tex]7y=ln(2x-\sqrt{3})[/tex]
[tex]y=\frac{ln(2x-\sqrt{3})}{7}[/tex]
Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.
[tex]g(f(x))[/tex]
[tex]g(\frac{e^7^x+\sqrt{3}}{2})[/tex]
[tex]\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}[/tex]
2s cancel.
[tex]\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}[/tex]
The natural log and e cancel.
[tex]\frac{7x+\sqrt{3}-\sqrt{3}}{7}[/tex]
[tex]\sqrt{3}[/tex]s cancel.
[tex]\frac{7x}{7}[/tex]
7s cancel.
[tex]x[/tex]
Hope this helps!
A cable that is 42 feet long is divided into lengths in the ratio 3:4. What are the two lengths into which the cable is divided?
Answers
Answer:
18 ft and 24 ft
Step-by-step explanation:
3:4
6:8
9:12
12:16
15:20
18:24, 18+24=42
The two lengths into which the cable is divided is 18 and 24.
Given that,
A cable that is 42 feet long is divided into lengths in the ratio 3:4.Based on the above information, the calculation is as follows:
The first length be
[tex]= 42 \times 3 \div (3 + 4)[/tex]
= 18
And, the second length be
[tex]= 42 \times 4 \div (3 + 4)[/tex]
= 24
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Factor the following...
[tex]9n^2-34n-8[/tex]
Please show work
Answers
Step-by-step explanation:
9x8= 72
therefore 36 x 2 are the products
9 n^2 - 36n + 2 n -8
9 n( n-4) + 2( n- 4)
therefore the two factors are
( 9 n +2) ( n-4)
Identify the volume of the composite figure. Round to the nearest tenth.
Answers
Answer:
474.5 ft ³
Step-by-step explanation:
1) Find the volume of the cube
[tex]A=l^3[/tex] where l is the side length
Plug in 9 ft as l
[tex]A=9^3\\A=729[/tex]
Therefore, the volume of the cube is 729 ft³.
2) Find the volume of the cylinder
[tex]A=\pi r^2h[/tex] where r is the radius of the base and h is the height of the cylinder
Plug in 3 ft as the radius and 9 as the height
[tex]A=\pi (3)^2(9)\\A=\pi (9)(9)\\A=81\pi \\A=254.5[/tex]
Therefore, the volume of the cylinder is approximately 254.5 ft ³.
3) Subtract the volume of the cylinder from the volume of the cube
729 ft³ - 254.5 ft ³
= 474.5 ft ³
Therefore, the volume of the figure is 474.5 ft ³.
I hope this helps!
Answer:
I think It's A
Step-by-step explanation:
HELPPME PLEASE ASAP i will give brainliest
Answers
You do 90-73 = 17
X = 17 degrees
Answer:
don't know but I think these is the answer =
17
Step-by-step explanation:
90 - 73 = 17
The shaded portion of the bar model in Part A shows 38. What percent is equivalent to 38? Enter the correct answer in the box.
Answers
Question:
The shaded portion of the bar model in Part A shows 3/8. What percent is equivalent to 3/8? Enter the correct answer in the box.
Answer:
The equivalent is 37.5%
Step-by-step explanation:
Given
[tex]\frac{3}{8}[/tex]
Required
The equivalent
The model is not shown, but the question can still be solved.
We have:
[tex]\frac{3}{8}[/tex]
Multiply by 100%
[tex]\frac{3}{8} = \frac{3}{8} * 100\%[/tex]
[tex]\frac{3}{8} = 0.375 * 100\%[/tex]
[tex]\frac{3}{8} = 37.5\%[/tex]
Fred's recipe for a smoothie called for 1/3 of an apple, 1/4 of a lemon, and 2/3 of peach to make a single smoothie. A family of 6 arrives and they all want that smoothie.
Answers
Answer:
Recipe for 6 smoothies:
2 apples
3/2 of a lemon
4 peaches
Step-by-step explanation:
Recipe for 1 smoothie:
1/3 of an apple
1/4 of a lemon
2/3 of peach
A family of 6 arrives and they all want that smoothie.
Multiply every recipe for 1 smoothie by 6
Recipe for 6 smoothies:
6 × 1/3 of an apple
= 6/3 = 2 apples
6 × 1/4 of a lemon
= 6/4 = 3/2 of a lemon
6 × 2/3 of peach
= 12/3 = 4 peaches
Recipe for 6 smoothies:
2 apples
3/2 of a lemon
4 peaches
What is the volume of this composite solid?
A. 156 cubic meters
B. 86 cubic meters
C. 136 cubic meters
D. 84 cubic meters
Answers
Answer:
C
Step-by-step explanation:
first cube :
4 × 3 × 6 = 72 m³
second cube :
4 × 4 × 4 = 64 m³
sum of both cubes :
72 + 64 = 136 m³ ( C )
please help me. i have been stuck on this question for the past 10 mins
Answers
Answer:
it's A and C
(4, -8) and (-1,7)
Step-by-step explanation:
y = -3x + 4
A. works
x = 4
y = -8
-3(4) + 4
-12 + 4 = -8
B. doesn't work
x = 2
y = -10
-3(2) + 4
-6 + 4 = -2
C. works
x = -1
y = 7
-3(-1) + 4
3 + 4 = 7
D. doesn't work
x = -3
y = 4
-3(-3) + 4
9 + 4 = 13
it's A and C
(4, -8) and (-1,7)
1. a+b+c+d
2. -a+b-c+d
3. ab+cb
4. ab-bc
5. ba+da
Answers
Answer:
1 a+b+c+d
=(ab + c+ d)
=ab+ a+c+ a+d
5)
A coach is ordering jerseys for the school.
• The coach pays a one-time fee of $10.
• The coach also pays $12 for each shirt ordered.
Which function can be used to find t, the total amount the coach pays in dollars when c shirts
are ordered?
A t = 12c + 10
Bt = 100 - 12
Ct = 120 - 10
D t = 10c + 12
Answers
Answer:
10c + 12
Step-by-step explanation:
I believe that is the answer please let me know if I am wrong
Four numbers are such that their mean is 13 their median is 14 and their mode is 15. Find the 4 numbers
Answers
Answer:
7,5,3,1
Step-by-step explanation:
Solve the system by substitution.
y = 7x – 20
y = 2x
Answers
Answer:
x=4 y=8
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation
Show that (16 1/4)3 and (16 3)1/4 are equivalent
Answers
Answer:
They are both 12
Change 16 1/4 into 4.
4 • 3
12
16 • 3 is 48
1/4 of 48 is 12
Hope this helps
What is the positive solution to this equation?
4x2 + 12 x= 135
Answers
find the value of given expression
[tex] \sqrt{99 - ( - 1)} [/tex]
Answers
Answer:
10
Step-by-step explanation:
Note that when there are two negative signs directly next to each other, you are adding:
[tex]\sqrt{99 - (-1)} = \sqrt{99 + 1} = \sqrt{100}[/tex]
Simplify:
[tex]\sqrt{100} = \sqrt{10 * 10} = 10[/tex]
10 is your value for the given expression
Answer:
± 10Step-by-step explanation:
[tex]\sqrt{99 - (-1)} = \sqrt{99 + 1} = \sqrt{100}[/tex] = ± 10What is z4 + z4 + z4 + z4?
Answers
Answer:
4z
Step-by-step explanation:
a. Write a formula for the area A
of a triangle.
b. Solve the formula for b.
c. Use the new formula to find the
base of the triangle.
A = 36 mm2
h = 6 mm
b
Answers
Answer:
A = 1/2 b * h
b = 2A / h
b = 12
Step-by-step explanation:
Remark
The formula starts out as
A = 1/2 * b * h
You want to rearrange it to show b by itself.
Formula
Multiply by 2
2A = b * h
Divide by h
2A/h = b
Part C
b = 2A / h
A = 36 mm^2
h = 6 mm
b = 2*36 / 6
b = 72 / 6
b = 12 mm
please help as soon as possible and please don’t take advantage of the points
a:1 hour
b:1.5 hours
c:2 hours
d: 3.5 hours
e:5.5 hours
Answers
Answer:
2 hours
Step-by-step explanation:
can someone help with this i don't get it
Answers
Answer:
Lord have mercy thats a bunch of numbers I woud help but i dont know how to start
Step-by-step explanation:
what is the answer to this
Answers
Answer:
IDEK
Step-by-step explanation:
Answer: i d k
Step-by-step explanation:
PLZ HELP ME LOL
A large cheese pizza cost 7.50. Diego has 40$ to spend on pizzas. How many large cheese pizza can he afford . Explais or show your rwasoning
Answers
So Diego can buy 5 pizzas with a little money left over.
On Monday, the baker makes 36 blueberry muffins. What is the total number of muffins that the baker makes on Monday?
Answers
Answer:
90
Step-by-step explanation:
Answer:
am preety sure the total s 40%
Step-by-step explanation:
Which equation demonstrates the multiplicative identity property?
Answers
Answer:
B. (-3+5i)(1)= -3+5i
Step-by-step explanation:
The multiplicative identity property states that any number or polynomial times 1 will be equal to itself. In answer B, a polynomial is multiplied by 1 and then equals itself. None of the other answers have 1 as a term, and therefore cannot be correct.
need help due today .
Answers
Answer:
Radius=7.5cm
Diameter=15cm
Step-by-step explanation:
The radius is half of the diameter which is the length of the circle measured across (or through I guess), so the radius is what is shown 7.5, and the radius doubled (x2) is the diameter so 7.5x2 = 15.
HOPE THAT HELPS AND MAKES SENSE! :)