Answer:
The value is [tex]P_o = \$ 561958.9 [/tex]
Step-by-step explanation:
From the question we are told that
The capacity of the metal tank is [tex]C = 2000 \ gallon[/tex]
The duration usage is [tex]t = 15\ years \ ago[/tex]
The cost of 2000-gallon tank 15 years ago is [tex]P = \$100,000[/tex]
The capacity of the second tank considered is [tex]C_1 = 5,000[/tex]
The power sizing exponent is [tex]e = 0.57[/tex]
The initial construction cost index is [tex]u_1 = 180[/tex]
The new construction after 15 years cost index is [tex]u_2 =600[/tex]
Equation for the power sizing exponent is mathematically represented as
[tex]\frac{P_n}{P} = [\frac{C_1}{C} ]^{e}[/tex]
=> Here [tex]P_n[/tex] is the cost of 5,000-gallon tank as at 15 years ago
So
[tex]P_n = [\frac{5000}{2000} ] ^{0.57} * 100000[/tex]
[tex]P_n = \$168587.7[/tex]
Equation for the cost index exponent is mathematically represented as
[tex]\frac{P_o}{P_n} = \frac{u_2}{u_1}[/tex]
Here[tex]P_o[/tex] is the cost of 5,000-gallon tank today
So
[tex]\frac{P_o}{168587.7} = \frac{600}{180}[/tex]
=> [tex]P_o = \frac{600}{180} * 168587.7[/tex]
=> [tex]P_o = \$ 561958.9 [/tex]
If f(x)=ax²+bx+c and f(1)=6,f(2)=11,f(3)=18 find the value of a,b,c
f(x) = ax² + bx + c
f(1) = 6
f(2) = 11
f(3) = 18
Find:value of a,b,c
Solution:Substitute x = 1 , 2 , 3 in the given polynomial.
★ f(1) = a(1)² + b(1) + c
⟹ 6 = a + b + c -- equation (1)
Similarly,
★ f(2) = a(2)² + b(2) + c
⟹ 11 = 4a + 2b + c -- equation (2)
★ f(3) = a(3)² + b(3) + c
⟹ 18 = 9a + 3b + c -- equation (3)
Subtract equation (1) from (2).
⟹ 4a + 2b + c - (a + b + c) = 11 - 6
⟹ 4a + 2b + c - a - b - c = 5
⟹ 3a + b = 5 -- equation (4).
From equation (3) ,
⟹ 18 - c = 9a + 3b
⟹ 18 - c = 3(3a + b)
Substitute the value of 3a + b from equation (4).
⟹ 18 - c = 3 * 5
⟹ 18 - 15 = c
⟹ 3 = c
substitute the value of c in equation (1).
⟹ 6 = a + b + 3
⟹ 6 - 3 = a + b
⟹ 3 = a + b -- equation (5)
Subtract equation (5) from equation (4).
⟹ 3a + b - (a + b) = 5 - 3
⟹ 3a + b - a - b = 2
⟹ 2a = 2
⟹ a = 1
Substitute a value in equation (5).
⟹ 1 + b = 3
⟹ b = 3 - 1
⟹ b = 2
Therefore,
a = 1
b = 2
c = 3.
I hope it will help you.
Regards.
Chandler wants to start saving money for vacation. She currently has $300 in her bank account and plan to save $100 more each month until she reaches her goal of $1500. How long will chandler have to save until she can afford her vacation.
(write equation in y=mx+b)
At a basketball game, a vender sold a combined total of 222 sodas and hot dogs. The number of sodas sold was 58 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
Probably 169
Step-by-step explanation:
I divided 222 by 2 and got 111 so i added 58 and got 169
111+58=169
If im incorrect please correct me so i can learn as well :D
12x+8y=240
How do I solve for y ?
A relation between a collection of inputs and outputs exists comprehended as a function.
If the equation be 12x + 8y = 240 then the value of y exists 30 - (12x/8).
What is meant by function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A relation between a collection of inputs and outputs exists comprehended as a function.
Let the equation be 12x + 8y = 240
8y = 240 - 12x
simplifying the above equation, we get
y = (240 - 12x) / 8
y = 30 - (12x/8)
Therefore, the value of y = 30 - (12x/8).
To learn more about function refer to:
https://brainly.com/question/11624077
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The first side of a triangle is 2 inches shorter than three times the second side. The third side is 1 inch longer than twice the second side. If the perimeter of the triangle is 101 inches, how long is each side?
(Answer to get brainliest)
Answer:
17in, 49in, 35in
Step-by-step explanation:
I did this in my RSM homwork and it is correct.
First, I added the two inches shorter to the 101, then subtracted 1 longer and got 102.
then divide 102 by how many second lengths, 6. so 102 ÷ 6 = 17
17 is the second length.
3x17-2=49 (another length)
2x17+1=35 (last length)
and there is your answer!
First side : 49
Second side : 17
Third side : 35
What is the perimeter of a triangle?
If triangle has sides a, b, c , then the perimeter of that triangle will be P= a +b +c.
Now, according to the question
Let second side be (b) = x unit
then, First side will be (a)= 3x-2 unit
and Third side will be (c)= 2x + 1 unit
since , perimeter is 101
P = a + b + c
x + 3x -2 + 2x + 1 = 101
6x - 1 = 101
x= 17
hence , b = 17 unit
a= 3*17 - 2 =49 unit
c = 2*17 +1 = 35 unit
Lets learn more about perimeter of a triangle
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When a whole number is multiplied by 10to the 5th power, how does the placement of the decimal point change? a It moves five places to the right. b It moves ten places to the right. c It moves five places to the left. d It moves ten places to the left.
Answer:
The correct option is;
a) It moves five places to the right
Step-by-step explanation:
Multiplying a whole number by 10 raised to a given (positive whole number) power, involves the shifting of the positioning of the decimal places to the right, depending on the value of the positive whole number power to which the 10 is raised
Similarly, multiplying a whole number by 10 raised to a given (negative whole number) power, involves the shifting of the positioning of the decimal places to the left, depending on the value of the negative whole number power to which the 10 is raised.
The reason is because, the number base generally used for arithmetic is in base 10 and multiplying or dividing by 10 is what is required to change a number's place value
Therefore, multiplying a whole number by 10 raised to the 5th power (10⁵) requires shifting the decimal place 5 places to the right
Example:
x.0 × 10⁵ = x00000.0
Where, x is a whole number.
The altitude of a helicopter increase is 1000 feet every four minutes. What is the unit rate of change (feet per minute) of the altitude?
Answer:
250 feet per minute
Step-by-step explanation:
1000 divided by 4 is 250. You divide them by each other because if you multiply 250 feet by 4 minutes, you get 1000.
(brainliest?)
The area of the triangle below is 2/5 square foot.
What is the length, in feet, of the base of the
triangle?
Answer:
B. 2/3
Step-by-step explanation:
The equation for area of a triangle is A=1/2bh
so we can plug in what were given
2/5 =1/2(6/5)b now we solve for b
2/5=6/10 b
2/5 divided by 6/10 =b
2/5 x 10/6 =b
4/6=b
2/3=b
Five cards are numbered 1 through 5. The back of each card is identical. The cards are mixed up and placed faced down. A person randomly flips over three cards and determines the sum of the three exposed cards. What is the probability that the sum is odd?
after walking 15 mins zacharys treadmill displayed 120 calories burned, at this rate how many calories can zach burn in 65 mins
Step-by-step explanation:
520 calories
15 mins = 120 calories
65 mins = 65/15 × 120
= 520 calories
What is the quotient?
(-3)
(-3)2
Og
9
O 9
Answer:
The answer to your problem is negative 9
what is 8.8x10^5 in standard notation?
Answer:
880,000
Step-by-step explanation:
Move the decimal in 8.8 five places to the right.
Use the distributive property to rewrite the following expression.
4(2x - 3)-3(x + 2)
Pls I only have 1 min to get this
Answer:
6x-12-3x+2
Step-by-step explanation:
8x-12-3x-6
5x-18 this is the answer
What kind of transformation is illustrated between the triangle XYZ and XYZ?
2
. translation
O rotation
O reflection
O translation
help i need to pass:/
Answer:
biologists have a 14ft john boat with trolling motor for sale or trade for hipnopotomus
Answer:
false
Step-by-step explanation:
1=-11+n
Please help me
Answer:
n=12
Hope this helps!!!!!
3x + -18x + 26x + -11x
Answer:
0
Step-by-step explanation:
First, you have 3x and subtract 18x from it. This gives you -15x.
Then you have positive 26x, so you add 26x onto -15x.
After doing so, you have a positive 11x.
Now you need to subtract 11x from 11x.
Your final answer is 0! (No need to put x since it is just zero.)
Have a nice day and mark brainliest if you can, I would appreciate it tons!
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
A) d = 20h
B) h = 20d
C) d = 45h
D) h = 45d
First, let's find the amount of money Troy charges per hour.
$30 / 1.5hrs = $20 / hr
d = $20h
A is the correct answer choice.
The product of Greg's height and 5 is 90
Answer:
450
Step-by-step explanation:
is the answer
Elena wants to make a scale drawing of her apartment. Her apartment is a rectangle with length 18cm and width 10m. She decides on a scale of 1cm to 2m. What are the dimensions of the scale drawing of Elena's apartment, using a scale of 1cm to 2m. The answer should look like: __cm and__cm)
Answer:
9cm and 5cmStep-by-step explanation:
Note: The unit of the width in the question is suppose to be in cm
"with length 18cm and width 10m"====>>> "with length 18m and width 10m"
so given that the dimension of the room is
18mx10m
This is a reduction process since we aim to transfer the dimension to paper
we are reducing the dimension by 2
and 1cm---2m
since 2m will represent 1cm
then the dimension will be
9cm and 5cm
Dylan and his friends are going into a bakery. How much would it cost to buy 1 cookie and 5 brownies if each cookie costs $0.50 and each brownie costs $2.25? How much would it cost to buy 11 cookies and 55 brownies if each cookie cost \$c$c and each brownie cost \$b?$b?
Answer:
a)$ 11.75
b) $ 129.25
Step-by-step explanation:
Dylan and his friends are going into a bakery.
Each cookie costs $0.50 and each brownie costs $2.25?
a) How much would it cost to buy 1 cookie and 5 brownies
1 × $0.50 + 5 × $2.25
= $0.50 + 11.25
= $ 11.75
b) How much would it cost to buy 11 cookies and 55 brownies
11 × $0.50 + 55 × $2.25
= $5.5 + $123.75
= $ 129.25
the value of y varies directly with x. If x=13, ten y=65. What is the value of x when y=35?
Answer:
x=7
Step-by-step explanation:
direct variation is in the form y=kx
65 = k 13
by dividing both sides be 13, we see that 5 = k
thus, we can then take the next situation 35 = 5x
dividing both sides by 5 brings us to 7 = x
You flip a coin. What is p(heads)? Write your answer as a percentage rounded to the nearest tenth
Answer:
0.50%
Step-by-step explanation:
the sum of the 2 integers is -112. if one of them is -109 find the other
Answer:
let x and be the two integers
x+y=-112
if one of them is -109
let x be one of the that is substitute-109 to the above equation
-109+y=-112
collect like terms to the left hand side.
-109+112=-y
3=-y
move the sigh to the constant
y=-3
8+($6)+6
Simplify and solve this expression:
Answer:
6+8=14
14 times 6 is 84
Emily decides that 3 pizzas will feed 10 people. How many pizzas will feed 150 people?
Answer:
45 pizzas
Step-by-step explanation:
She has to feed a crowd fifteen times bigger
What is the index in the expression
2
2?
Answer:
2
Step-by-step explanation:
Is it 1 2 3 or 4? I need to know
Answer:
I think it is 1
I'm almost positive
The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap
Sum of 8th & 4th terms of an AP = 24
Sum of 6th & 10th terms = 44
Find:A.P.
Solution:We know that,
nth term of an AP = a + (n - 1)d
Hence,
⟹ a + (8 - 1)d + a + (4 - 1)d = 24
⟹ a + 7d + a + 3d = 24
⟹ 2a + 10d = 24 -- equation (1)
Similarly,
⟹ a + 5d + a + 9d = 44
⟹ 2a + 14d = 44 -- equation (2)
Subtract equation (1) from (2).
⟹ 2a + 14d - (2a + 10d) = 44 - 24
⟹ 2a + 14d - 2a - 10d = 20
⟹ 4d = 20
⟹ d = 20/4
⟹ d = 5
Substitute the value of d in equation (1).
⟹ 2a + 10(5) = 24
⟹ 2a = 24 - 50
⟹ 2a = 24 - 50
⟹ 2a = - 26
⟹ a = - 26/2
⟹ a = - 13
We know,
General form of an AP is a , a + d , a + 2d...
Hence,
⟹ required AP = - 13 , - 13 + 5 , - 13 + 2(5)...
⟹ required AP = - 13 , - 8 , - 3....
I hope it will help you.
Regards.
The average distance from Pluto to the Sun is about 6×109 kilometers. The average distance from Mars to the Sun is about 2×108 kilometers. The average distance from Pluto to the Sun is about how many times greater than the average distance from Mars to the Sun?
Answer:
The average distance from Pluto to the Sun is 30 times greater than the average distance from Mars to the Sun.
Step-by-step explanation:
We have:
- Distance from Pluto to the Sun ([tex]d_{PS}[/tex]) = 6x10⁹ km
- Distance from Mars to the Sun ([tex]d_{MS}[/tex]) = 2x10⁸ km
Now, we can find how many times greater is [tex]d_{PS}[/tex] than [tex]d_{MS}[/tex] as follows:
[tex] \frac{d_{PS}}{d_{MS}} = \frac{6 \cdot 10^{9} km}{2 \cdot 10^{8} km} = 30 [/tex]
Therefore, the average distance from Pluto to the Sun is 30 times greater than the average distance from Mars to the Sun.
I hope it helps you!