Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?
Piedmont Hotels is an all-equity company. Its stock has a beta of 1.29. The market risk premium is 7.2 percent and the risk-free rate is 3.0 percent. The company is considering a project that it considers riskier than its current operations so it wants to apply an adjustment of 2.2 percent to the project's discount rate. What should the firm set as the required rate of return for the project?
The firm set 14.49% as the required rate of return for the project.
What is the required rate of return for Piedmont Hotels' riskier project?We will first calculate the Project's discount rate which can we calculated using the formula that:
= Rf rate + Beta*risk premium
= 3.0% + 1.29*7.2%
= 3.0% + 0.09288
= 0.12288
= 12.29%
The required rate of return for the project will be:
= Project's discount rate + Adjustment rate
= 12.29% + 2.2%
= 14.49%
Thus, the firm set 14.49% as the required rate of return for the project.
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Selena took a pizza out of the oven, and it started to cool to room temperature (68°F). She will serve the pizza when it reaches 130°F. She took the pizza out at 5:00 P.M. Use regression to find when she can serve it.
Selena can serve the pizza at around 6:40 P.M.
How to explain the regressionThe regression line should have the equation y = -1.7x + 300, where y is the temperature, x is the time in minutes since the pizza was taken out of the oven, -1.7 is the slope of the line, and 300 is the y-intercept.
Set y (the temperature) to 130°F, and solve for x (the time).
130 = -1.7x + 300
-170 = -1.7x
x ≈ 100
According to the regression model, the pizza will reach 130°F after about 100 minutes after it was taken out of the oven. Therefore, Selena can serve the pizza at around:
= 5 + 1:40
= 6:40 P.M.
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What is the surface area of the figure below
The surface area of the triangular prism is 108 km².
Given is a triangular prism we need to find the surface area of the prism,
SA = perimeter × length
= (3 + 4 + 5) × 9
= 12 × 9
= 108
Hence, the surface area of the triangular prism is 108 km².
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(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
Find the equation of the ellipse with foci at (+-3,0) and major axis of length 12.
The equation of the ellipse with the foci is x²/36 + y²/(27) = 1.
What is the equation of the ellipse?
The distance between the foci of an ellipse is calculated using the following formula;
c² = a² - b²
Where;
a is half the length of the major axisb is half the length of the minor axisc is the distance between the fociFor this question, a = 6 and c = 3, the value of b is calculated as;
c² = a² - b²
3² = 6² - b²
9 = 36 - b²
b² = 27
b = √27
b = 3√3
The equation of the ellipse is calculated as;
x²/a² + y²/b² = 1
x²/36 + y²/(27) = 1
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Simplify: 9-4x³ +2x² +8x³ +1+6x²
Answer:
it can be simplify as follows:
Put the quadratic into vertex form
The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.
How to find the vertex formTake a look at the quadratic function:
f(x) = 2x^2 + 8x + 7
In this situation, a = 2 and b = 8, yielding:
f(x) = 2(x^2 + 4x) + 7
It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:
f(x) = 2(x^2 + 4x + 16 - 16) + 7
The expression inside the parenthesis can now be written as a perfect square:
f(x) = 2((x + 2)^2 - 16) + 7
Finally, the phrase is simplified by spreading the 2:
f(x) = 2(x + 2)^2 - 32 + 7
f(x) = 2(x + 2)^2 - 25
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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7
the scatter plot shows the relationship between the number of chapters and the total number of pages for several books.Use trend line to predict how many oages there would be in a book with 19 chapters?show work.
A)180pages
B)170pages
C)200 pages
D)190 pages
There are 190 pages would be in a book with 19 chapters.
We have to given that;
The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.
Now, We get;
For 19 chapters at x - axis,
The value of pages at y - axis is, 190
Thus, There are 190 pages would be in a book with 19 chapters.
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A student is using wooden blocks to build two towers of different heights. All of the blocks are the same size and have a height of 3/4inch. The short tower is 5 blocks high and the tall tower is 9 blocks high. What is the difference in height, in inches, between the short tower and the tall tower?
The difference in height of short and tall tower is 3 inch.
We have,
length of each block = 3/4 inch
So, the length of 5 block
= 5 x 3/4
= 15/4 inch
and, the length of 9 blocks
= 9 x 3/4
= 27/4 inch
So, the difference in height of short and tall tower is
= 27/4 - 15/4
= 12/4
= 3 inch
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The table below shows the U.S. National Debt (in trillions of dollars) by year
Year 1960 1970. 1980 1990 1995 2000 2005 2010 2014
Debt .29 .37 .91 3.23 4.97 5.67 7.93 13.96 17.82
Find an exponential model for the national debt. Use the model to estimate the National Debt for the year 2015. Compare it with the actual value found in the table
The terms given in US national debt in standard form when converted to scientific notation form will be 2.86 * 10^11, 3.70 * 10^11, 9.07 * 10^11, 3.23 * 10^12, 5.67 * 10^12 and 1.35 * 10^13 respectively.
Scientific notation if the process of conversion of very large numbers which are otherwise inconvenient to read into decimal form raised to some power of 10.
During this conversion, the numbers in standard form are written such that only one place value before decimal is left and written as coefficient and all other numbers are then counted and written in the form of base 10 raised to some exponent value.
The coefficient value must be such that its value lies between 1 and 9 and less than 10. Thus, the following numbers can be written as follows in scientific form.
286330760848.37 = 2.86 * 10^11
370918706949.93 = 3.70 * 10^11
907701000000.00 = 9.07 * 10^11
3233313451777.25 = 3.23 * 10^12
5674178209886.86 = 5.67 * 10^12
13561623030891.79 = 1.35 * 10^13
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Determine the measure of angle Q.
Not possible
20°
30°
25°
The angle that is marked as Q has a value of 30°
What is cosine rule?The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.
Cosine rule useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.
By the use of the cosine rule, we have that;
7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q
49 = 144 + 196 -336CosQ
49- 340 = -336CosQ
-291= -336CosQ
Q = Cos-1 (-291/-336)
Q = 30
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What are the coordinates of point A?
(4.5,1)
(4.5, 0.5)
(5, 0.5)
(5,1)
Which ordered pair is a solution to the system? X>4 Y≥12
Some solutions for the given system of inequalities are:
(5, 12)
(6, 12)
(7, 13)
And so on.
Which ordered pair is a solution for the system?Here we have the following system of inequalities:
x > 4
y ≥ 12
We want to see which ordered pair, of the form (x, y), is a solution for the system.
A solution is a pair that makes both inequalities true.
So, x must be larger than 4.
y can be equal to 12, or larger than 12.
Then some solutions are:
(5, 12)
(6, 12)
(7, 13)
And so on.
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the altitude of bombay beach is -60.96 meters. The altitude of salton city is -38.1. which is true. A. Bombay has a lower altitude because -60.96 is less than -38.1 meters. B. Bombay has a lower altitude because -60.96 is greater that -38.1. C. Salton City has a lower altitude because -60.96 meters is less that -38.1 meters. D. Salton City has a lower altitude because -60.96 meters is greater than -38.1
Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.
Option C is the correct answer.
We have,
The altitude of Bombay Beach is -60.96 meters.
The altitude of Salton City is -38.1 meters.
Altitude is the height of a location above sea level, and a negative value indicates that the location is below sea level.
Therefore, we can see that Salton City has a higher altitude than Bombay Beach because -38.1 meters is a higher altitude than -60.96 meters.
Thus,
Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
144π = (1/2)(4/3)π(r^3)
144 = (2/3)(r^3)
r^3 = 216, so r = 6 mm, meaning the diameter is 2 × 6 mm = 12 mm.
You want to purchase a new bike that costs $125.99. To save for the bike, you mow your neighbor's yard for $40 each week. How much money will you have left over if you buy the bike after saving for 4 weeks?
Answer: $34.01
Step-by-step explanation:
To get the answer, we must first add up the entire amount of money saved after four weeks of mowing the neighbor's lawn, then subtract the bike's price.
Since we get $40 a week, after 4 weeks we will have saved the following:
40 × 4 = 160
We will therefore have $160 to spend on the bike. The bike costs $125.99, so we will have the following amount of money after purchasing the bike:
160 - 125.99 = 34.01
Therefore, after purchasing the bike, we will have $34.01 leftover.
Use the given circumference to find the surface area of the spherical object. a pincushion with C = 24 cm
Answer:
approximately 183.4 square centimeters.
Step-by-step explanation:
We can use the formula for the circumference of a sphere, which is:
C = 2πr
where C is the circumference and r is the radius.
We know that the circumference of the pincushion is 24 cm. We can use this to find the radius:
C = 2πr
24 = 2πr
r = 24/(2π)
r ≈ 3.82 cm
Now that we know the radius, we can use the formula for the surface area of a sphere, which is:
A = 4πr^2
Substituting the value we found for the radius, we get:
A = 4π(3.82)^2
A ≈ 183.4 cm^2
Therefore, the surface area of the pincushion is approximately 183.4 square centimeters.
Alicia bitman,age
30,plans to purchase a $50,000 whole-life policy what is the annual premium
The annual premium is $192.5.
We have,
Number of units to be purchased by Alicia:
= 50,000 / 1,000
= 50 units
At age 30, the cost per $1,000 unit of insurance is $3.85 for a female.
= Number of units purchased x Premium per $1,000
= 50 x 3.85
= $192.5
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for a new customer top golf charges $10 for a player card and $2 per hour.
The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.
Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.
We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.
So, the equation for the cost "x" can be written as
x = 10 + 2(6)
The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us
x = 10 + 12
Now, we can combine like terms to find the final cost
x = 22
Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.
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--The given question is incomplete, the complete question is given
" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--
Linear or exponential interest
The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]
The fox population in 2008 is 9722.
What is the fox population in 2008?The equation that would represent the population of the foxes is an exponential equation.
The form of the exponential equation would be
Future population = present population x [tex](1 + r)^{t}[/tex]
Where:
r = interest rate = 6%t = number of years after 2000P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]
P(t) = 6100 x [tex]1.06^{t}[/tex]
Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722
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Convert 300° to radians.
O A. 3T
7T
OB. T
O C.
11T
ike
O D. ST
3
A conversion of 300 degrees to radians is equal to 5.24 radians.
How to determine the angle in radians?In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = rθ
Where:
r represents the radius of a circle.θ represents the central angle measured in degrees.Next, we would convert degrees to radians;
300 = rads × 180/π
Radians = 300π/180 = 5.24 radians.
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Find the component form of the indicated vector
Answer:
(d) (12, -34)
Step-by-step explanation:
You want the component form of the vector sum -3u +5v where u=(1,3) and v=(3,-5).
Vector sumAdd the corresponding parts of the scaled vectors. The scale factor applies to both vector components. (It works the same way as "dilation".)
-3u +5v = -3(1, 3) +5(3, -5)
= (-3, -9) +(15, -25) = (-3 +15, -9 -25)
= (12, -34)
£1 = $1.41
£1= €1.15
$1= €?
We can use unit conversion to find the value of $1 in Euros:
\begin{aligned}
£1 &= $1.41 \\
\frac{£1}{1.15} &= \frac{$1.41}{x} \\
x &= \frac{$1.41}{\frac{£1}{1.15}} \\
&= $1.7278
\end{aligned}
Therefore, $1 is equal to €1.7278.
rancher wants to enclose a rectangular plot of land, but have a divider in the middle. There is 240 feet of fencing available. What dimension will produce the largest area the rancher can make? What is the max area? Dimensions: __________________ Area:___________ --------------------------------------------------------------------------------------------------------- 2. (10 points) From a thin square piece of cardboard 20 in. per side, square corners (x) are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Dimensions: __________________ Volume:___________ ----------------------------------------------------------------------------------------------------------- 3. (10 points) During a recent oil spill in the gulf, the radius of the spill was increasing at a rate of 10 feet per second. How fast is the circular area of the spill increasing at the moment that the radius is 80 feet? dA = dt __________
The solution is, the two dimensions will be 2121.32 by 1414.2.
Here, we have,
let X and Y be the two dimensions.
Area will be X times Y.
XY = 3000000
Y = 3000000 / X
Perimeter = 2x + 3y
substituting the values:
Perimeter = 2x + 3*3000000 / x
= 2x + 9000000 / x
so, we get,
2 = 9000000 / x^2
x^2 = 9000000 / 2 = 4500000
x = sqrt(4,500,000)
= 2121.32
= 1000 sqrt (4.5)
y = 3000000 / 2121.32
= 1414.2
= 1000 sqrt(2)
so the dimensions will be 2121.32 by 1414.2 .
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complete question:
A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
4,12,44,176,890
which is odd one ?
Answer:
890 as it is not divisible by 4
help!!!
.............
The evaluated form of the factorial expression 5! / 3! 2! is 10.
How to solve factorial ?Let's evaluate the factorial expression as follows:
The factorial function (!) says to multiply all whole numbers from our chosen number down to 1.
Therefore,
5! / 3! 2!
Hence,
5! = 5 × 4 × 3 × 2 × 1 = 120
3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
Hence,
5! / 3! 2! = 120 / 6 × 2
120 / 6 × 2 = 120 / 12 = 10
Therefore,
5! / 3! 2! = 10
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f(x)=3x-15 g(x)=1/3x+15
find f(g(x))
g(f(x))
are they inverses if do, why?
The values for the composition of functions are:
a. (f o g)(x) = -x³ - x + 1
b. (g o f)(x) = -x³ - x - 1
Here, we have,
to Determine the Value of Composite Functions:
The value of composite functions are determined by first finding the output of the inner function, which would be used as the input of the outer functions to derive the value of the composite functions.
Given the following:
f(x) = x³ + x + 1
g(x) = -x
a. To find (f o g)(x), substitute g(x) as the inner function for x into f(x):
(f o g)(x) = (-x)³ + (-x) + 1
Simplify
(f o g)(x) = -x³ - x + 1
b. To find (g o f)(x), substitute f(x) as the inner function for x into g(x):
(g o f)(x) = -(x³ + x + 1)
Distribute by -1
(g o f)(x) = -x³ - x - 1
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complete question:
If f(x)=x³+x+1 and g(x)=-x, find (f°g)(x) and (g°f)(x).
(f°g)(x)=
Determine whether the pairs of vectors is orthogonal
No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.
What is the dot product of the pair of vectors?The dot product will help us to determine if the pair of vectors are orthogonal or not.
If the dot product is equal to zero, then the pair of vectors are orthogonal.
The dot product of the vectors is calculated as follows;
(3i - 8j).(8i - 3j)
= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)
= (24) - (0) - (0) + (24)
= 24 + 24
= 48
So the pairs of vectors are not orthogonal.
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Can someone help me pleasee
Answer:
The answer is 50% or 1/2
Step-by-step explanation:
There are four outcomes on that chart: 1,2,3,3
There are two threes which means 2/4=.5 or 1/2
Answer:
1/2 chance of landing on a 3.
Step-by-step explanation:
Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.
What function does this table make
Answer:
f(n) = 3^(n -1)
Step-by-step explanation:
You want a function that describes the relation shown in the table.
AnalysisThe values under Steps are sequential, which makes determining the function a lot easier.
The values listed under Black Triangles don't have a common difference, but they do have a common ratio:
r = 3/1 = 9/3 = 27/9 = 3
Exponential functionFor this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.
For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...
f(n) = b·r^(n -a)
With r=3 and (a, b) = (1, 1), this becomes ...
f(n) = 1·3^(n -1)
The multiplier 1 isn't really needed, so we can use ...
f(n) = 3^(n -1)