Answer:
123
Step-by-step explanation:
because if its lower than 50 you round down, if its 50 or above you round up
Answer:
If you like to round 123.45 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post. Number:.
Step-by-step explanation:
Crane Corporation is considering purchasing a new delivery truck. The new truck would cost $55,440. The new truck is expected to generate a cost savings of $7,700. At the end of 8 years, the company will sell the truck for an estimated $27,600.
Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company's cost of capital is 8%.
a) Compute the cash payback period and net present value of the proposed investment.
b) Does the project meet the company's cash payback criteria?
c) Does it meet the net present value criteria for acceptance?
A. The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.
B. No, the project does not meet the company's cash payback criteria.
C. Yes, the project does meet the net present value criteria for acceptance.
How do we solve for the net present value of the proposed investment?A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.
$55,440 / $7,700 = 7.2 years
To solve for the net present value, we say
Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.
NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63
+ ($7,700 / (1 + 0.08)²) = 6601.51
+ .($7,700 / (1 + 0.08)³ = 6112.51
+ ($7,700 / (1 + 0.08)⁴) = 5659.73
+ ($7,700 / (1 + 0.08)⁵) = 5240.49
+ ($7,700 / (1 + 0.08)⁶) = 4 852.31
+ ($7,700 / (1 + 0.08)⁷) = 4492.88
+($7,700 / (1 + 0.08)⁸) = 4160.07
+ ($27,600 / (1 + 0.08)⁸)) = 14911.42
- $55,440
We add all these values together and subtract by $55,440
7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440
59160.55 - 55,440
NPV = 3720.55
B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.
C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.
Find more exercises on net present value;
https://brainly.com/question/27557482
#SPJ1
Put these fractions in order from least to greatest.
11/12
1/4
2/6
Answer:
1/4
2/6
11/12
is the correct order <3
Answer:
11/12, 2/6 1/4
Step-by-step explanation:
Find a common denominator.
11/12 4/12 and 3/12
Then solve
Simplify the expression below.
w^2-9
_____
w^2-4w-21
A. 3
_
4w+7
B. -9
—
-4w-21
C. w-3
___
w-7
D. w+3
___
w+7
Answer:
D
Step-by-step explanation:
w² - 9 can be factored as (w + 3)(w - 3) using the difference of squares. To factor w² - 4w - 21, we need to find 2 integers that have a sum of -4 and product of -21; these integers are -7 and 3 so the factored form is (w + 7)(w - 3). Therefore, the expression becomes:
(w + 3)(w - 3) / (w + 7)(w - 3)
Both the numerator and denominator have a factor of (w - 3) so that cancels out, leaving us with (w + 3) / (w + 7).
Simplify this expression . With each step. please (x2 - x - 2)/(x2 + 5x + 4)
Answer:
I hope dis helps
Step-by-step explanation:
Simplify
x2 + 5x + 4
Trying to factor by splitting the middle term
1.1 Factoring x2 - x - 2
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -1 .
-2 + 1 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 1
x2 - 2x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-2)
Which is the desired factorization
Trying to factor by splitting the middle term
1.2 Factoring x2+5x+4
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 4
x2 + 1x + 4x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+1)
Add up the last 2 terms, pulling out common factors :
4 • (x+1)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+1)
Which is the desired factorization
Canceling Out :
1.3 Cancel out (x+1) which appears on both sides of the fraction line.
Final result :
x - 2
—————
x + 4
Pleaseeeeeee help me with this ASAP
Answer:
736
Step-by-step explanation:
25*32=800
16*4=64
800-64
100 Points! Algebra question. Graph the function. Thank you!
The graph of the function is attached
The amplitude and the period are 5 and 2π
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 5cos(θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 5
Period = 2π/1
Evaluate
A = 5
Period = 2π
Hence, the amplitude is 5 and the period is 2π
The graph of the function is attached
Read more about sinusoidal function at
brainly.com/question/21286958
#SPJ1
If the sides of a square measure 9.3 units the.find the length of the diagonal
Answer:
Approximately 13.1521 units.
Step-by-step explanation:
To find the diagonal, we can use the Pythagorean Theorem.
Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:
\(a^2+b^2=c^2\)
Substitute 9.3 for a and b, and let c equal d:
\((9.3)^2+(9.3)^2=d^2\)
Instead of squaring, add the like-terms:
\(2(9.3)^2=d^2\)
Take the square root of both sides:
\(d=\sqrt{2(9.3)^2}\)
Expand:
\(d=\sqrt{2}\cdot\sqrt{(9.3)^2}\)
The right cancels:
\(d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}\)
Amelia rented a dvd and it was due to be returned on 26 november
she actually returned it to the shop on 26 december
the rental shop applies a fine for 9p for every day the dvd is overdue
work out the total fine paid by amelia
give your answer in £?
Anyone help please!!!!!
Answer:
Step-by-step explanation:
I'm not familiar with the conversions from American dollars. I can help you solve it though.
Count how many days from Nov 26 to Dec 26 and multiply that by 9p.
It's 30 days by 9p. Take that total and convert it.
Hopefully this helps you.
...................................
Answer:
D) 28
Step-by-step explanation:
Using my improbable math skills, I calculated that the answer is probably D
Correct me if I'm wrong~
Rewrite the expression as a single logarithm.
The expression \(3log_b(8) - log_b(7)\) written as a single logarithm is \(log_b(\frac{512}{7})\).
How to turn expressions into a single logarithm?Given the logarithmetic expression in the question:
\(3log_b(8) - log_b(7)\)
To rewrite the expression \(3log_b(8) - log_b(7)\) as a single logarithm, we can use the properties of logarithms.
Using the quotient rule property, which states that:
logₙ(a) - logₙ(b) = logₙ(a/b)
Applying the quotient rule:
First, rewrite \(3log_b(8) - log_b(7)\) as:
\(log_b(8^3) - log_b(7)\)
Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).
\(log_b(\frac{8^3}{7})\)
Simplify
\(log_b(\frac{512}{7})\)
Therefore, the single logarithm is \(log_b(\frac{512}{7})\).
Learn more about logarithm here: https://brainly.com/question/29291192
#SPJ1
2. The pesticide DDT was used in the US and later banned. The half-life of DDT is about 15 years.
(a) Write an exponential model for the amount of DDT, A(t), remaining after t years, if the initial
sample is 100 grams.
(b) According to your model, how much of the initial sample will remain after 60 years?
(c) How many years will it take for the sample to decay to 1 gram?
The exponential model is N(t) = \(100(1/2)^\frac{t}{15}\), the remains after 60 years is 6.25 grams, and it will take 2/3 years for the sample to decay to 1 gram.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
Given that, a pesticide DDT was used in the US and later banned. The half-life of DDT is about 15 years, we need to find the exponential model for the amount of DDT, A(t), remaining after t years, if the initial sample is 100 grams, how much of the initial sample will remain after 60 years, how many years will it take for the sample to decay to 1 gram,
The formula for half-life =
N(t) = \(N'(1/2)^\frac{t}{t/2}\)
Where,
N(t) = quantity of the substance remaining
N' = initial quantity of the substance
t = time elapsed
t{1/2} = half life of the substance
a) The exponential model for the amount of DDT, A(t), remaining after t years :-
N(t) = \(100(1/2)^\frac{t}{15}\)
b) The remains after 60 years :-
\(N(t) = 100(1/2)^\frac{60}{15}\)
N(t) = 100(1/2)⁴
= 100×(0.0625)
= 6.25 grams
c) Number of years required for the sample to decay to 1 gram :-
1 = \(100(1/2)^\frac{t}{15}\)
1/100 = \((0.5)^\frac{t}{15}\)
Applying log,
log(0.01) = tlog(0.5)
2/3 = t
t = 2/3 years
Hence, the exponential model is N(t) = \(100(1/2)^\frac{t}{15}\), the remains after 60 years is 6.25 grams, and it will take 2/3 years for the sample to decay to 1 gram.
Learn more about half-life, click;
https://brainly.com/question/24710827
#SPJ9
Write 2 x 10^3 in standard notation.
Answer:
2000
Hope this helps :)
Step-by-step explanation:
Since the exponent of the scientific notation is positive, move the decimal point 3 places to the right.
The standard notation of the expression is 2 x 10³ is 2000.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
2 x 10³
Standard notation means writing an expression without any base and exponents.
Now,
10³ can be written as 1000.
So,
2 x 10³
= 2 x 1000
= 2000
Thus,
The standard notation is 2000.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
F is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. F = (z-x)i + xk r(t) = (sin t)i + (Cost) k, 0 <= t <= 2π
Answer: 177.65
Step-by-step explanation:
its the only accurate answer.........
Label each as a function or not a function.
Answer:
Function, function
Step-by-step explanation:
Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions
how the number e was discover
Answer:
It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients
Find the perimeter of a parallelogram whose base is 8cm and another side is 12cm
A parallelogram
P=2(a+b)
The answer is 64
P=2(a+b)=2·(24+8)=64
How many acres are in an area 3.5 miles long by 30 feet wide?
By using the formula for area of rectangle, it can be calculated that
Total area = 12.73 acres
What is area of rectangle?
Area of rectangle is the total space taken by the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle will be given by
Area of rectangle = \(l \times b\)
Length = 3.5 miles = 3.5 \(\times\) 5280 feet = 18480 feet
Width = 30 feet
Total area = 18480 \(\times\) 30 = 554400 sq. feet
= \(\frac{554400}{43560}\) acres
= 12.73 acres
To learn more about area of rectangle, refer to the link-
https://brainly.com/question/25292087
#SPJ1
PLEASE HELP ME
The function f(x) = -2(4)^x+1 +140
represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
PLEASE SEE PHOTO FOR FUNCTION
The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).
The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.
To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.
For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.
Therefore, the practical domain of the situation is x ≥ 0.
For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.
Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.
Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).
To summarize:
- The practical domain of the situation is x ≥ 0.
- The practical range of the situation is [140, ∞).
Know more about the domain here:
https://brainly.com/question/30096754
#SPJ8
50 POINTS! SHOW WORK OR ILL REPORT! Multiplying mixed numbers
Answer:
15/2 = 7 1/2
Step-by-step explanation:
3 1/3 * 2 1/4 =
= (3 * 3 + 1)/3 * (2 * 4 + 1)/4
= 10/3 * 9/4
= 90/12
= 45/6
= 15/2
= 7 1/2
\(\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}\)
See this attachment
3. Find x and y of both triangles please!!!!
The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.
Given are two right triangles we need to find the missing sides,
We will use Trigonometric ratios to find the same.
We know that,
Sin a = perpendicular / hypotenuse
Cos a = base / hypotenuse
Tan a = perpendicular / base
1) Sin 60° = x / 4√3
x = √3/2 × 4√3
x = 6
Cos 60° = y / 4√3
1/2 × 4√3 = y
y = 2√3
2) Cos 60° = x / 98
x = 1/2 × 98
x = 49
Sin 60° = y / 98
√3/2 = y / 98
y = 49√3
Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.
Learn more about Trigonometric ratios click;
https://brainly.com/question/23130410
#SPJ1
factor please show work
Answer:The answer would be 6a(4b4 +2b3 -3b2)
Step-by-step explanation:All you have to do is take 6a out of each number and put the 6a outside of parenthesis and put the rest of the equation in parenthesis.
The greatest number of elements possible in
Answer:
4
9
Step-by-step explanation:
If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.
If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.
Answer:
4
9
The tickets for the field trip were purchased yesterday for both students and instructors. Children tickets cost $9, adult tickets cost $11. The number of children tickets purchased was three more than ten times the number of adults tickets purchased. How many of each were purchased if all of the tickets cost a total of $936 dollars?
The 9 adult tickets and 93 children tickets were purchased.Let's assume the number of adult tickets purchased is "a" and the number of children tickets purchased is "c."
According to the given information, children tickets cost $9 and adult tickets cost $11. So, the total cost of children tickets is 9c, and the total cost of adult tickets is 11a.
The problem also states that the total cost of all the tickets is $936. Therefore, we can write the following equation:
9c + 11a = 936
Additionally, it is mentioned that the number of children tickets purchased was three more than ten times the number of adult tickets purchased:
c = 10a + 3
We can now solve this system of equations to find the values of "a" and "c." By substituting the value of "c" from the second equation into the first equation, we have:
9(10a + 3) + 11a = 936
90a + 27 + 11a = 936
101a = 936 - 27
101a = 909
a = 909 / 101
a = 9
Substituting this value back into the second equation, we find:
c = 10(9) + 3
c = 90 + 3
c = 93.
For more such questions on Purchased:
https://brainly.com/question/28717901
#SPJ8
Solve for x - y = -3
Answer:
0-3=-3
Step-by-step explanation:
Analyzing a Solution
Mark used a number line to model dividing by 3. He
3
divided the number line from 0 to 1 in 3 equal sections,
and then divided each of those sections into 2 equal
1
parts. Mark says+3 is 3.
Is his answer correct? Explain why or why not.
No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.
Mark's answer is not correct.
When dividing a number line into equal sections, the value of each section represents a fraction of the whole.
In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.
Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.
So far, this is correct.
However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.
So, each of these smaller divisions represents 1/2 \(\times\) 1/3 = 1/6 (one-sixth) of the whole.
Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.
Mark made an error by mistakenly assuming that each smaller division represents the number 3.
In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.
The correct representation for dividing the number line as described is 1/6.
For similar question on smaller divisions.
https://brainly.com/question/29250154
#SPJ8
Which of the b values satisfy the following inequality?
5 < b - 3
choose all answers that apply
A: b=8
B: b=9
C: b=10
Answer:
b and c
Step-by-step explanation:
so to answer this one we just plug in all of the answer choices to see which ones satisfy the inequality
for a we plug in b and get 5<8-3 or 5<5 which is not true so it cant be a
next we plug in 9, 5<9-3 or 5<6 so b is a correct answer
next we plug in 10, 5<10-3 or 5<7 which is correct so c is also a correct answer
hope this helps (:
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
Learn more about Equations here
https://brainly.com/question/29346874
#SPJ1
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
3
Step-by-step explanation:
By going up 3 and right 1 you get 3/1, aka 3
The line of the equation is y=3x+2
ill give you brainlest pls help
Answer:
A. m<R, m<S, m<Q
Step-by-step explanation:
In a triangle, the length of each side determines the size of the angle opposite it. Thus, the longer the side, the bigger the size of the angle opposite it. The shorter the side, the smaller the size of the angle opposite it.
In ∆QRS, we have the following:
✔️The longest side is RS = 16. <Q is opposite to RS, therefore <Q is the largest angle.
✔️The medium side is QR = 15. <S is opposite to QR, therefore <S is the medium angle.
✔️The shortest side is SQ = 9. <R is opposite to SQ, therefore <R is the smallest angle.
From smallest to the largest we would have:
m<R, m<S, m<Q