Using the concept of exponential function, the exponential decay after
2 months is 13000kwh
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
In this problem, we can model an exponential function to represent the problem.
E = a(1 - r)⁻^d
a = Initial valueE = final valuer = rate d = timea)
This function is an exponential decay function which when we substitute the values, we can easily express E in terms of d.
E = 17500(1 - 75)⁻^d
b) The excess energy left after 2 months ?
Using proportions;
75 kwh/ d = 1 day
x kw/h = 60 days
x = 60 * 75
x = 4500
The amount left will be 17500 - 4500 = 13000 kwh
We will have 13000kwh after 60 days
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jiminy’s cricket farm issued a 30-year, 4.5 percent semiannual bond three years ago. the bond currently sells for 104 percent of its face value. the company’s tax rate is 22 percent.
a) Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = 3.315%
c) After tax cost of debt of 3.135% is more relevant.
Given:
FV = 100
Semiannual bond issued 3 years ago
Maturity = 27
Price, PV = 104
coupon rate = 4.5%
Tax rate = 22%
a) Semiannual bond issued 3 years ago
Maturity, n = 27 years × 2 = 54
Coupon C = 4.5%/2×100 = 2.25
Now,
Pretax cost of debt,
Cost of debt, I = [C+(FV-PV)/n] / (FV+PV)/2
= [2.25 +(100 - 104)/54] / [ 100+1040/2
= 2.12%
= 2.12×2
Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = cost of debt × (1-T)
= 4.25% × (1-22%)
After tax cost of debt = 3.315%
c) After tax cost of debt is more relevant.
Hence we get the required answer.
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Aldo’s art class is 8 hours long. How long is his class in minutes.
Answer:
480 minutes
Step-by-step explanation:
One hour is 60 minutes, so 8*60 will give you your answer.
Answer:
Step-by-step explanation:
Theres 60 minutes in 1 hour, and you are trying to find how many in 8 hours, so you would multiply 60 by 8. The answer would be 480 minutes
The solution of a system of linear inequalities is the intersection of the solutions to each inequality. Every point in the intersection region satisfies all inequalities in the system. Describe how you know which region, if any, represents the solution to a system of linear inequalities
Answer:
To determine which region represents the solution to a system of linear inequalities, you need to graph each inequality on the same coordinate plane and then find the intersection of the regions that satisfy each inequality. This intersection is the solution to the system of linear inequalities, as every point in this region satisfies all of the inequalities in the system.
To graph the solution, you can use a number line for each variable and plot the inequalities as points or lines on the coordinate plane. For example, if the system of linear inequalities is given by the equations y > 2x + 3 and y < -x + 5, you can plot the lines y = 2x + 3 and y = -x + 5 on the coordinate plane and find the intersection of the two lines. This intersection represents the solution to the system of linear inequalities, as every point in this region satisfies both inequalities.
Another way to find the solution to a system of linear inequalities is by using algebra to solve the system. This involves writing the equations in standard form, eliminating variables, and solving for the remaining variable. The solution can then be written as a set of ordered pairs that represent the points on the coordinate plane that satisfy the system of linear inequalities.
In either case, the solution to a system of linear inequalities is the region of the coordinate plane that satisfies all of the inequalities in the system.
Step-by-step explanation:
a hospital needs 0.100 gg of 133 54xe 54133xe for a lung-imaging test. if it takes 10 daysdays to receive the shipment, what is the minimal amount mxemxem xe of xenon that the hospital should order?
In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a minimum amount of 0.4 g of.
Given that:
A hospital needs 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex]
and it takes 10 days for the shipment to arrive:
the half life [tex]t_{\frac{1}{2}[/tex] = 5 days.
So, since the half life = 5 days ;
decay constant [tex]\lambda = \frac{In_{2} }{t_{\frac{1}{2} } } }[/tex]
where:
[tex]No=?[/tex]
[tex]N=0.100\\\\t=10days\\\\N(t)=N_{o} e^{-\lambda\ t} \\\\0.1=N_{o}e^{-In\ 4} \\\\0.1=N_{o}e^{In\ \frac{1}{4} }\\\\0.1=\frac{N_{o}}{4} \\\\N_{o}=01*4\\\\N_{o}=0.4\ g[/tex]
Therefore, In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a minimum amount of 0.4 g of.
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You have a piece of fabric with an area of 32 1/3 ft.² if there are five people in your group what is the area of fabric that each person can use
Answer:6.47 ft^2
Step-by-step explanation:
A rectangular field is to have an area of and is to be surrounded by a fence. The cost of the fence is dollars per meter of length. What is the minimum cost this can be done for?.
The minimum cost for the area can be fenced is $1920
It is given that the area of the rectangular field is 900 m²
Let the length of one side of the field be x m
Therefore, the length of the other side will be
900/x
The perimeter of the rectangular field
= 2(length + breadth)
= 2(x + 900/x)
= 2x + 1800/x m
Therefore, the cost of fencing will be
$(32x + 28800/x )
Let f(x) = 32x + 28800/x
We need to minimize f(x)
Differentiating with respect to x and equating it to 0 gives us
32 - 28800/x² = 0
or, x² = 28800/32
or, x² = 900
or, x = 30
This is because the length cannot be negative hence -30 cannot be a value
Now
f''(x) = 57600/x³
f''(30) = 2/1333
Since f"(x) is positive, x = 30 is the minimum value of x for which the cost is minimum.
Hence, the minimum cost will be
f(30)
= 960 + 960
= $1920
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Complete Question
A rectangular field is to have an area of 900 m² and is to be surrounded by a fence. The cost of the fence is 16 dollars per meter of length. What is the minimum cost this can be done for?
If you take a number, times by 3 then add 5. You get the same as if you took the
number, times by 7 then subtract 8. What is the number?
The number is 4.
If you take a number, times by 3 then add 5, you get (3x + 5).
If you take the same number and times by 7 then subtract 8, you get (7x - 8).
Set the equations equal to each other:
3x + 5 = 7x - 8
Subtract 3x from both sides:
5 = 4x - 8
Add 8 to both sides:
13 = 4x
Divide both sides by 4:
4 = x
Therefore, the number is 4.
how to solve the volume of a frustum with a radius of 15 and height of 4
Answer: 26
Explanation: Well, by using the formula to find volume of frustum. (this can be shown in a easier way or harder i choose my own way)
Step 1: The hight is: h=15h=15
Step 2: The top radius of the frustum is: r=19r=19
Step 3: The lower base radius of the frustum is: R=26R=26
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Given 5.05(−14.6), find the product. 651.11 7.38 −9.55 −73.73
Answer:
Step-by-step explanation: -73.73 D, If its not and its like A,B, or C and one of them is -73.73 its still going to be correct
Use point-slope form to write the equation of a line that passes through the point
(−11,−14) with slope 1.
The equation of the line that passes through the point (−11,−14) is y = x - 3.
What is the slope of the line?
A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
We have,
The line that passes through the point (−11,−14)
With Slope (m) = 1,
The general equation of a straight line is
y = mx + c,
where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
so here,
y = mx + c,
(-14) = 1(-11) + c
c = -14 + 11
c = -3
The equation becomes:
y = x - 3.
Hence, the equation of the line that passes through the point (−11,−14) is
y = x - 3.
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How many times larger is 6.255 × 1010 than 1.5 × 108?
Answer:6,155.55
Step-by-step explanation: 6.255*1010=6,317.55
1.5*108=162
6,317.55-162=6,155.55
Explain how to solve for the volume of a rectangular box if you know the length, width, and height of the box.
Answer:
V= Base X Height X Length
Step-by-step explanation:
Base = 5
Length = 7
Height = 3
Volume = 105
a sample of a radioactive substance decayed to 93% of its original amount after a year. (round your answers to two decimal places.) (a) what is the half-life of the substance?
The half-life of the substance is of 10.31 years.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
a sample of a radioactive substance decayed to 93% of its original amount after a year.
The half-life is t for which:
exp(-0.067 t) = (0.5)
ln(0.5) = -0.067 t
t = 10.31 years.
Hence the half-life of the substance is of 10.31 years.
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How do you represent a linear function?
The linear function can be represented by slope intercept form, point slope form and standard form.
Given,
Linear function;
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
We can represent linear function by;
The slope intercept form, point slope form, and standard form can all be used to express a linear function.
Slope intercept form;
The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Standard form;
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.
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the risk-free return during the sample period was 3%. calculate the jensen measure of performance evaluation for sooner stock fund.
the jensen measure of performance evaluation for sooner stock fund will be 2.6%.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
the risk-free return during the sample period was 3%.
performance evaluation for sooner stock fund.
Expected return of Sooner Stock Fund = E(Rp) = 20%
Beta of stock = 1.8
risk free rate Rf = 3%
Market Return Rm = 11%
So, Jensen measure alpha = E(Rp) - Rf - beta*(Rm - Rf) = 20 - 3 - 1.8*(11-8) = 2.6%
Hence the Jensen measure of performance evaluation for the sooner stock fund will be 2.6%.
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the arguments supplied to the if function, in order, are the condition for execution,
As per the concept of function, the arguments supplied to the IF function, in order, are the condition for execution, the result if condition is true, and the result if condition is false.
What is meant by function?
In math, function refers an expression, rule, or law that defines a relationship between one variable also known as the independent variable and another variable also known as the dependent variable.
Here we need to find the missing term of the given statement the arguments supplied to the if function, in order, are the condition for execution.
Here we have given that, the if function refers decision-making statement that guides a program to make decisions based on specified criteria.
When the IF statement executes one set of code if a specified condition is met (TRUE) or another set of code evaluates to FALSE.
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what order is this in
Considering the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis, the signs for the slope are as follows;
The plane is cruising at an altitude of 37,000 feet above sea level: zero.The plane is descending at rate of 1000 feet per minute: negative.The plane is ascending at a rate of 2000 feet per minute: positive.What is a slope?In Mathematics, a slope is also referred to as gradient and it is typically used to describe both the ratio, direction, and steepness of the function of a straight line.
Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
In this scenario, the sign of the slope of the graph of this plane's equation, with time being represented on the horizontal axis and elevation on the vertical axis are as follows;
The plane is cruising: the slope of the graph would be zero because it is moving at a constant speed.The plane is descending: the slope of the graph would be negative because it is decelerating.The plane is ascending: the slope of the graph would be positive because it is accelerating.In conclusion, the slope of a graph would be positive because there is an increase in the variables on the cartesian coordinate.
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Complete Question:
Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
a. The plane is cruising at an altitude of 37,000 feet above sea level.
b. The plane is descending at rate of 1000 feet per minute.
c. The plane is ascending at a rate of 2000 feet per minute.
A media download store sells songs for $2 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you can purchase. What are three combinations of numbers
of songs and movies you can purchase?
a group of 52 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. the purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. in particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of u.s. college students in general, which is estimated to be 4.73. the group of 52 students in the study reported an average of 5.11 drinks per with a standard deviation of 3.79 drinks. find the p -value for the hypothesis test.
The p -value for the hypothesis test is; 0.4195
What is the p-value of the hypothesis test?Let us first define the hypotheses.
We are told that the mean of u.s. college students in general, is estimated to be 4.73. Thus;
Null Hypothesis; H₀: μ = 4.73
Alternative Hypothesis; Hₐ: μ ≠ 4.73
Since we have the standard deviation for the sample, we will use the t-distribution with the formula;
t = (x' - μ)/(s/√n)
Where;
x' is the sample mean.
μ is the value tested at the null hypothesis.
s is the standard deviation of the sample.
n is the sample size.
We are given;
x' = 5.11
μ = 4.73
s = 3.98
n = 52
Thus;
t = (5.11 - 4.73)/(3.98/√52)
t = 0.688
Using a t-distribution calculator, this p-value is 0.4195
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There were 425 guests at a hotel. 170 guests ordered food. what percentage of the guests ordered food?
There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.
Define percentage.A percentage is a fraction of a whole in mathematics, which is denoted by the symbol per 100. A single unit out of a hundred, or one hundredth of something, is represented as a single percent, such as 1%. The Latin phrase per centum, which means by the hundred, is where the word percent originates. Percentage does really refer to a hundredth or 1/100 of something.
Given,
Total number of guests = 425
Guest who ordered food = 170
For percentage,
Value/ Total × 100%
170/425 × 100%
0.4 × 100%
40%
There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.
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the longest professional tennis match ever played lasted a total of 11 hours and5minutes. how many minutes was this?
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes 665 in minutes or 665 minutes.
Given that:
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes.
Time = 11 hours and 5 minutes
We know that,
1 hour = 60 minutes.
Also, need to know that 1 minute = 60 seconds.
So, multiply hours by 60 to convert hours into minutes and add it with minutes to find the value of time in minutes.
i.e. Time = 11 x 60 minutes + 5 minutes
∴Time = 660 minutes + 5 minutes
= 665 minutes
Hence, 665 minutes was the time the longest professional tennis match ever played lasting a total of 11 hours and 5 minutes.
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I dont understand this. could someone give me step by step what the answer would be If?
Questions: If one solution of a quadratic equation is 7-13i, what would the second solution be?
Question 2: solve these, step by step using indicated operations with work!
1. (4-3i) (-7+21)
2. (-7+6i)+(2-3i)+(4+5i)
3. (-6-i)/4-2i
4. (-2-7i)(-2+7i)
5. (5-3i)-(-2-6i)
Answer:
Below
Step-by-step explanation:
Question 1:
The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. If one solution of the equation is 7-13i, the other solution must be the complex conjugate of 7-13i, which is 7+13i. To find the complex conjugate of a complex number, you simply need to change the sign of the imaginary part of the number. In this case, the complex conjugate of 7-13i is 7+13i.
Question 2:
1. (4-3i) (-7+21)
To add two complex numbers, we need to add their real parts and imaginary parts separately. In this case, we have:
(4-3i) (-7+21)
= (4 - 7) + (-3i + 21)
= -3 + 18i
2. (-7+6i)+(2-3i)+(4+5i)
To add multiple complex numbers, we can add them one at a time using the same procedure as before. In this case, we have:
(-7+6i)+(2-3i)+(4+5i)
= (-7+2) + (6i - 3i) + (4 + 5i)
= -5 + 3i + 4 + 5i
= -1 + 8i
3. (-6-i)/4-2i
To divide two complex numbers, we need to multiply the numerator and denominator by the complex conjugate of the denominator. In this case, we have:
4. (-6-i)/4-2i
= (-6-i)(4+2i)/(4-2i)(4+2i)
= (-24 - 2i + 6i - i^2)/20
= (-24 + 4 -1)/20
= (-21)/20
= -1.05 - 0.05i
5. (-2-7i)(-2+7i)
To multiply two complex numbers, we use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms separately and then adding the results. In this case, we have:
(-2-7i)(-2+7i)
= (-2 * -2) + (-2 * 7i) + (-7i * -2) + (-7i * 7i)
= 4 + (-14i) + 14i + 49
= 4 + 49
= 53
6. (5-3i)-(-2-6i)
To subtract two complex numbers, we need to add the first number to the opposite of the second number. In this case, we have:
(5-3i)-(-2-6i)
= (5-3i) + (2 + 6i)
= 7 + 3i
This is the final answer for each of the problems.
What is Y in the math?
The y is the variable that used in the different situations like to find the unknown variable, graphing, and function
y in the math is usually used as the variable in function, graphing etc.
y variables can be used in the equation to find the unknown values in the equation
Example = 5y + 10 = 15
Similarly in the graphing the y is used in the slope intercept form
The slope intercept form is
y = mx + b
Y can be used in the function as well
Example: y = 2x + 4
Therefore, the y can be used as the variable in the different situation
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One side of a rectangular yard is bounded by the side of a house. The other three sides are to be fenced with 86 ft of fencing. The length of fence opposite the house is 13 ft less than either of the other two sides. Find its length and width.
The length of one side is 20 ft and the other side of the yard is 33 ft.
Let the length of the side opposite to the house be x ft.
We know that the yard to be fenced is rectangular. Hence the opposite sides of the yard are going to be equal.
It is given that the side opposite to the wall is 13 ft less than the length f the other two sides.
Hence the length of the side adjacent to the house will be
(x + 13) ft
The fencing needs to be done on these three sides. We already know that the length that has been fenced is 86 ft.
Hence, we get
x + x + 13 + x + 13 = 86
or, 3x + 26 = 86
or, 3x = 86 - 26
or, 3x = 60
or, x = 60/3
or, x = 20.
Hence the length of one side is 20 ft and the length of the other side is
20 + 13
= 33 ft.
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The value of t is 41 more than 24
Answer:
t=24+41=65
Step-by-step explanation:
The value of t>24 and is 41 more than 24. So 24+41=t.
24+41=65, so t=65.
-Hope this helped & Happy Holidays!
Zoe is starting her own snow plowing business. She will charge $11.00 per hour. If Zoe works 40.25 hours per week, how much money will she earn each week?
Answer:
$442.75
Step-by-step explanation:
40.25 x 11.00= 442.75
the line that passes through (−2, 6) and (−1, 18) in slope-intercept form.
Answer:
To find the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18), we can use the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the coordinates of the points given in the problem, we have:
m = (18 - 6) / (−1 - (−2)) = 12 / 3 = 4
Next, we need to find the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which has an x-coordinate of 0. Substituting the slope and the coordinates of one of the points given in the problem, we can solve for b:
y = mx + b
6 = 4 * (−2) + b
6 = −8 + b
b = 6 + 8 = 14
Therefore, the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18) is y = 4x + 14.
Step-by-step explanation:
Point M lies on AB, AB = 24 , and BM = 13 What is AM?
If Point M lies on AB, AB = 24 , and BM = 13, then the length of AM is; 11 units
What is the length of the line segment?
We are given the following parameters;
Length of line segment AB = 24
Length of line segment BM = 13
Now, we are told that M lies on the line segment AB and as such;
If BM = 13, then it means that;
AM + BM = AB
AM + 13 = 24
AM = 24 - 13
AM = 11 Units
We conclude that the length of AM is 11 units.
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Solve for x given the diagram
Answer:
x=4
Step-by-step explanation:
If we were to perform a reduction, the scale factor would be ½. This means we have to divide by 2. 14÷2=7 and 12÷2=6.
Line segment AB is equal to 7.
Line segment BC is equal to 6.
AB: If you want to double check, 4+3=7
BC: 2×4=8 and 8-2=6
If AGHJ is isosceles,
find the value of x.
G
38°
H
J
(14x + 1)
The value of x from the given isosceles triangle GHJ is 5.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
In the given isosceles triangle GHJ, GJ=GH, ∠G=38° and ∠J=(14x+1)°.
Since, sides GJ=GH
∠J=∠H
Now, ∠G+∠J+∠H=180° (Angle sum property of a triangle)
⇒ 38°+(14x+1)°+(14x+1)°=180°
⇒ 28x+40°=180°
⇒ 28x=140°
⇒ x=140/28
⇒ x=5
Therefore, the value of x is 5.
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"Your question is incomplete, probably the complete question/missing part is:"
If triangle GHJ is isosceles find the value of x.