A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
Future Value:Annuities are a financial instrument that generates a regular stream of cash. They have both a present and future value dependent upon the value of the cash payment, the number of payment periods and the interest rate. This question does not specify the cash inflow amount so an answer will be generated that can be scaled on multiples of $1000.
Let C represent the cash inflow at the end of each year. The future value (FV) of this cash inflow is given by:
FV = [tex]C[((1+i)^n-1)/i][/tex]
where i is the annual interest rate and n is the number of years.
(a) For i = 5% and n = 7
FV = [tex]C [((1+0.05)^7-1)/0.05][/tex]
FV= C[(1.047100-1)/0.05]
FV = C [8.142008]
(b) For i = 8% and n = 7
FV = [tex]C [((1+0.08)^7-1)/0.08][/tex]
FV = C[(1.713824 - 1)/0.08]
FV = C[8.922803]
(c) For i = 17% and n = 7
FV = [tex]C [((1+0.17)^7-1)/0.17][/tex]
FV = C[(3.001242 - 1)/ 0.17]
FV = C[11.772012]
Therefore, A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
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When the car reaches point (A), it has a speed of 25 m/s. If the breaks are applied, its speed is reduced by at= (-1/4t^1/2)m/s^2. Determine the magnitude of acceleration of the car just before it reaches point C
The magnitude of acceleration of the car just before it reaches point C is -0.79 m/s^2.
About magnitude of accelerationThe magnitude of acceleration of the car just before it reaches point C can be calculated using the given formula for acceleration, at= (-1/4t^1/2)m/s^2.
First, we need to determine the time it takes for the car to travel from point A to point C.
Since the speed of the car at point A is 25 m/s, and the speed at point C is 0 m/s, we can use the formula for speed, v=at, to find the time it takes for the car to travel from point A to point C.
Rearranging the formula, we get t=v/a.
Substituting the values for speed and acceleration, we get t=25/(-1/4t^1/2).
Solving for t, we get t^3/2 = -100.
Taking the square root of both sides, we get t=10 seconds.
Now, we can substitute the value of t back into the formula for acceleration to find the magnitude of acceleration just before the car reaches point C.
at= (-1/4t^1/2)m/s^2
= (-1/4)(10^1/2)m/s^2
= (-1/4)(3.16)m/s^2
= -0.79 m/s^2
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pls help asap I need to get this done by tmw
Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
Given that, Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
Simple interest: SI = PRT
P = $5000
r = 5.75% = 0.0575
I = $8,450 - $5000 = $3450
3400 = 5000(0.0575[tex])^t[/tex]
t = 12 years
Thus, Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
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HELP ASAP, WILL GIVE BRAINLIEST TO FIRST ANSWER
A marine biologist was interested in seeing the relationship between a manatee's weight and height. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
Answer:
A - scatter plot; it would show the relationship
Step-by-step explanation:
You want to determine if a scatter plot or line graph is a more appropriate way to represent the relationship between a manatee's weight and height.
VariablesThe variables of concern in the data are weight and height. Time is not involved. (Eliminates choices B and D.)
Functional relationshipIt seems likely there may not be a functional relationship between weight and height. That is, manatees of the same weight may have different height, and vice versa. This suggests a line graph would not be a useful way to represent the relationship
Scatter plotA scatter plot in this case would be used to relate weight on one axis to height on the other axis. Any relationship between them would show up as grouped data points, or data points that generally fall on a line or curve.
Since the "marine biologist [is] interested in seeing the relationship between a manatee's weight and height", ...
A scatter plot [is more appropriate] because it would show the association or relationship between the two variables.
__
Additional comment
As is often the case, the wording of the answer that matches the wording of the problem statement tells you which answer is appropriate.
Answer:A scatter plot, because it would show the association or relationship between two variables
Step-by-step explanation:
An image of a rhombus is shown.
A rhombus with a base of 20 inches and a height of 19.2 inches.
What is the area of the rhombus?
768 cm2
384 cm2
78.4 cm2
39.2 cm2
The area of the rhombus is 384cm²
What is area of a rhombus?a rhombus is a type of quadrilateral. It is a special case of a parallelogram, whose all sides are equal and diagonals intersect each other at 90 degrees. This is the basic property of rhombus. The shape of a rhombus is in a diamond shape.
The area of a rhombus is given as:
PQ/2
Where and q are the diagonals of a the rhombus
A = PQ/2
But in these case the rhombus is a parallelogram, therefore the area = base × height
= 20× 19.2
= 384cm²
The area of the rhombus is 384cm²
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Find the Area of the figure below, composed of a rectangle and a semicircle.
The radius of the circle is shown. Round to the nearest tenths place.
13
6
Answer:
Hi dear !!
area of semicircle = πr²/2
=> 3.14× 6x6 /2
3.14× 6× 3
=> 56.52 cm².
area of rectangle= l x b = 13 x 12 = 169
total area = 169 +56.52 = 225.5 cm²
If an employee earns $550 in 26 hours of work, what is the unit rate at which this employee is paid? Round to the nearest cent.
Answer:
21.15 550 divided by 26 = 21.15.
Step-by-step explanation:
I did the work on my paper. =)
what are the spike regression nonlinear constraints
Spike-and-slab regression is a method used to model the relationship between a response variable and a set of predictor variables, and nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity.
Spike-and-slab regression is a statistical method used to model the relationship between a response variable and a set of predictor variables, where the predictor variables are partitioned into two groups: a set of important predictors (spikes) and a set of unimportant predictors (slabs). Nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity. These constraints can be used to enforce prior knowledge or assumptions about the relationships between the predictor variables, and can help to improve the accuracy and interpretability of the model. Examples of nonlinear constraints that can be used in spike-and-slab regression include the convexity constraint and the total variation penalty.
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Please help quick!!!!
Answer:
19 and 12
Step-by-step explanation:
The rule is y = 2x - 1
If x = 10, y = 19 because 20 - 1 = 19
If y = 23, x = 12 because 24 / 2 = 12
The line passing through the points ( -4, 6) and ( b, 2) has a gradient 1 /2 . Find the value of b.
Answer:
b = - 12
Step-by-step explanation:
calculate the slope of the line passing through the 2 points and equate to [tex]\frac{1}{2}[/tex]
calculate the slope ( gradient ) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )
m = [tex]\frac{2-6}{b-(-4)}[/tex] = [tex]\frac{-4}{b+4}[/tex]
equating gives
[tex]\frac{-4}{b+4}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
b + 4 = - 8 ( subtract 4 from both sides )
b = - 12
use order of operations to simplify 7^2 + [ 81 - (4 x 6)]
Answer:
106.
Step-by-step explanation:
7^2 + [ 81 - (4 x 6)] First work out the exponential:
= 49 + (81 - (4 * 6)] Work out the expression in the inner parentheses:
= 49 + [81 - 24] Work out the expression in the parenthes:
= 49 + 57 Add:
= 106.
For any given event, the probability of that event and the probability of the _______ of the event must sum to one.
For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.
Non occurrence patterns identifies the absence of events when detecting a pattern.
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What is the length of the missing side?
A. 36
B. 37.43
C. 38
D. 39
Answer: I would say B.
Step-by-step explanation: why not pick B…..
Hope this help^^
what is 100.8 f to c?
Using the formula to convert Fahrenheit to Celsius, we get that 100.8°F is 38.22°C.
To convert 100.8°F to °C, we can use the formula:
°C = (°F - 32) x 5/9
Plugging in the value of 100.8°F, we get:
°C = (100.8 - 32) x 5/9
°C = 68.8 x 5/9
°C = 38.22
Therefore, 100.8°F is equal to 38.22°C.
This formula is used to convert temperatures between the Fahrenheit and Celsius scales. It involves subtracting 32 from the Fahrenheit temperature and then multiplying by 5/9 to obtain the equivalent Celsius temperature. The resulting Celsius temperature is then rounded to the nearest tenth. It's important to note that Fahrenheit and Celsius are two different temperature scales, where 0°C is equal to 32°F, and 100°C is equal to 212°F. The Celsius scale is based on the freezing and boiling points of water, whereas the Fahrenheit scale is based on the freezing and boiling points of a solution of salt and water. Knowing how to convert between these two scales can be useful in a variety of settings, including cooking, weather reporting, and scientific research.
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Find the value of X so that the expression X(4-2Y) is equivalent to 2/3 - 1/3Y.
The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
The given expression is c² - 64.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
1) The factorization of c² - 64 is as follows:
Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)
2) 12y² -75 = 3 (4y²-25)
= 3((2y)²-5²)
= 3 (2y+5)(2y-5) (∵ a²-b²=(a-b)(a + b))
3) 9y²-36 = 9(y²-4)
= 9(y²-2²)
= 9(y-2)(y+2) (∵ a²-b²=(a-b)(a + b))
4) -x²+5x-4
= x²-5x+4
= x²-4x-x+4
= x(x-4)-1(x-4) (∵ a²-b²=(a-b)(a + b))
= (x-4)(x-1)
5) ab²-b
=b(ab-1)
Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
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The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
Time (month) Cost
1 $105
3 $165
5 $225
7 $285
What is the slope and y-intercept of the linear function?
The slope is ____ and the y-intercept is ___.
Answer:
The slope is 30, and the y-intercept is 75.
Step-by-step explanation:
Use two points from the table, and find the equation of a line given two points.
Point 1: (1, 105)
Point 2: (3, 165)
y = mx + b
slope = m = (y_1 - y_1)/(x_2 - x_1)
m = (165 - 105)/(3 - 1) = 60/2 = 30
y = 30x + b
Use point (1, 105) for x and y.
105 = 30(1) + b
105 = 30 + b
b = 75
y = 30x + 75
The slope is 30, and the y-intercept is 75.
When data is positively skewed the mean will be?
Round 29.675 to
the hundredths place.
Answer:
29.68
Step-by-step explanation:
If you are rounding to the hundredth place, you take the number in the hundredth place and round it. If it is less than five, for example, if you were rounding 29.674 then it would be 29.67 because 4 is not 5 or more. With 29.675 you will round to 29.68. A saying to remember is, five or above, give it a shove.
Neron Co. Has two derivatives related to two different financial instruments, instrument A and instrument B, both of which are debt instruments. The derivative related to instrument A is a fair value hedge, and the derivative related to instrument B is a cash flow hedge. Neron experienced gains in the value of instruments A and B due to a change in interest rates. Which of the gains should be reported by Neron in its income statement?Gain in value of debt instrument A Gain in value of debt instrument BYes YesYes NoNo YesNo No
Only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
About the reportNeron Co. should report the gains from the fair value hedge related to instrument A in its income statement. This is because fair value hedges are used to offset changes in the fair value of a financial instrument, and any gains or losses from these hedges are recognized in income.
On the other hand, gains from the cash flow hedge related to instrument B should be reported in other comprehensive income, not in the income statement.
This is because cash flow hedges are used to offset changes in the cash flows of a financial instrument, and any gains or losses from these hedges are recognized in other comprehensive income until the hedged item affects income.
Therefore, only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
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please help me find x
Answer:
x = 4.5
Step-by-step explanation:
Using Pythagoras theorem,
Hyp² = Opp² + Adj²
From the question,
Hyp = 9
Adj = Opp
Since Adj = Opp
Let,
Adj = Opp = a
and,
Hyp = b
Therefore,
b² = a² + a²
9² = 2a²
Cancelling equal exponents,
2a = 9
a= 4.5
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.
mLA = 22 degrees
mzB = 75 degrees
Enter your answers as numbers only.
m₂F=
mzH=
degrees
degrees
m² G=
----_ degrees
m₂C= degrees
-----
The missing angle measures are:
m2F = 50 degrees
m2H = 125 degrees
m2G = 5 degrees
m2C = 158 degrees
How to find the missing angle measures?
Since triangle ABC is similar to triangle FGH, the ratios of their corresponding angles are equal. Let's call the missing angles m2F, m2H, m2G, and m2C.
From the given information, we have:
m2F / mLA = m2H / mzB
So, we can find m2H by cross-multiplying and solving for m2H:
m2H = (mzB * m2F) / mLA
Since we don't know m2F, we can use the fact that the sum of the angles in a triangle is 180 degrees:
m2F + m2H + 75 = 180
So,
m2F + ((mzB * m2F) / mLA) + 75 = 180
Expanding and solving for m2F:
m2F + (75 * m2F / 22) + 75 = 180
(22 + 75) * m2F / 22 + 75 = 180
97 * m2F / 22 + 75 = 180
97 * m2F / 22 = 180 - 75
97 * m2F / 22 = 105
m2F = 105 * 22 / 97 = 50
So, the missing angle measures are:
m2F = 50 degrees
m2H = (75 * 50) / 22 = 125 degrees
m2G = 180 - 50 - 125 = 5 degrees
m2C = 180 - 22 = 158 degrees
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The scale of a map is 2 in = 7 feet. If the map distance is 11 inches what is the actual distance.
Answer:
the answer is 38.5 feet
Step-by-step explanation:
divide 7 by two the multiply by 11
Someone help me pls
Answer:
W) 1/18=10/180
N) 2/15=4/30
F) 7/12= 84/144
S) 9/25= 36/100
D) 7/20=35/100
T) 9/10=36/40
M) 19/20=95/100
Step-by-step explanation:
W) is 10/180 as you need to multiply the numerator as the denominator.
N) is 4/30 as you need to multiply the numerator as the denominator.
F) is 84/144 as you need to multiply the numerator as the denominator.
S) is 36/100 as you need to multiply the numerator as the denominator.
D) is 35/100 as you need to multiply the numerator as the denominator.
T) is 36/40 as you need to multiply the denominator as the numerator.
M) is 95/100 as you need to multiply the numerator as the denominator.
On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2, 0) and the y-axis at (0, 0).
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
x-intercepts of the curved line are (-2,0) and (0,0)
What is intercept ?The points where a line or curve intersects the chart's axes are called intercepts. When a point intersects the x-axis it is called the x-intercept. When a point intersects the y-axis, it is called the y-intercept.
A line intercept is a point where it intersects the x-axis or the y-axis. If no axis is specified, the y-axis is normally considered. It is usually represented by the letter 'b'.
Given,
A curved line with a minimum value of (-1 , -2)
it crosses x-axis at (-2,0) and y-axis at (0,0)
We know that, x-intercept is the point where line crosses x-axis, y-coordinate = 0
x-intercepts are (-2,0) and (0,0)
Hence, (-2.0) and (0,0) are x-intercepts of the curved line.
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Answer: (–2, 0), (0, 0)
Step-by-step explanation:
If y varies directly as x, and y is 12 when x is 1. 2, what is the constant of variation for this relation? 1.
The constant of variation for this relation is 10.
If y varies directly as x, we can write it as y = kx, where k is the constant of variation. This constant represents the relationship between x and y, and it determines how much y changes for a given change in x.
To find the constant of variation, we need to know the value of y and x. In this case, we are told that y is 12 when x is 1.2. Using this information, we can solve for k by dividing both sides of the equation by x:
y = kx
12 = k * 1.2
12 / 1.2 = k
k = 10
So the constant of variation is 10. This means that for every change of 1 in x, y will change by 10. In other words, if x increases by 1, y will increase by 10, and if x decreases by 1, y will decrease by 10.
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A concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick, how many cubic metres of concrete are required to make the tank?
Answer:
Step-by-step explanation:
kaboom hope this helps
The volume of concrete is required to make the cylindrical tank is approximately 14 cubic meters.
Given that, external diameter = 10 m and an internal height = 3 m.
We know that, the volume of a cylinder is πr²h.
Volume of a tank with external dimensions = 3.14×5²×3
= 3.14×25×3
= 235.5 cm³
The walls and bottom of the tank are 30 cm thick
So, internal diameter = 1000-30 (10 m =1000 cm)
= 970 cm
= 9.7 m
= 4.85 m
Volume of a tank with internal dimensions = 3.14×4.85²×3
= 3.14×23.5225×3
= 221.58195 cm³
So, volume of concrete = 235.5-221.58195
= 13.91805
≈ 14 cm³
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What is the standard form of the equation of the parabola with focus: (0, 7) and the vertex at the origin?.
The standard form of the equation of the parabola with focus (0, 7) and the vertex at the origin is y = 1/28 x² + 7
A parabola is a symmetrical U-shaped curve that is defined by the set of all points that are equidistant to a fixed point, called the focus, and a straight line called the directrix. In a parabolic equation, the focus and the vertex are important points that determine the shape and position of the parabola.
In the case of the parabola with focus (0, 7) and the vertex at the origin (0,0), we can use the standard form of the equation of a parabola to write its equation. The standard form of a parabola is given by:
y = a(x - h)² + k
Where (h,k) is the vertex of the parabola and a is the coefficient that determines the direction and width of the parabola. To write the equation of this parabola, we need to find the value of a.
Since the focus is (0, 7) and the vertex is (0,0), we can use the formula:
a = 1/(4f)
Where f is the distance from the vertex to the focus. In this case, f = 7. Therefore, a = 1/(4 * 7) = 1/28.
Finally, we can substitute these values into the standard form to get the equation of the parabola:
y = 1/28 x² + 7
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Which graph matches the equation y+6=3/4 (x+4)?
Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:
First, isolate x by subtracting 4 from both sides:
y + 6 - 6 = 3/4 (x + 4) - 6
y = -6 + 3/4 (x + 4)
Next, isolate y by dividing both sides by 3/4:
y = -6 + 3/4 (x + 4) ÷ (3/4)
y = -6 + (x + 4)
y = x - 2 + 10
This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).
Step-by-step explanation:
The odds against winning $1. 00 in the lottery are 19 to 1. What is the probability of winning $1. 00 in the lottery?.
The probability of an event can be calculated from the odds against that event. The formula for converting odds against to probability is:
Probability = 1 / (1 + odds against)
So in this case, the odds against winning $1.00 in the lottery are 19 to 1, and the probability of winning can be calculated as follows:
Probability = 1 / (1 + 19) = 1 / 20 = 0.05
So the probability of winning $1.00 in the lottery is 0.05, or 5%.
the quadrilateral is a trapezoid. what is the value of x? a) 4. b) 5. c) 48. d) 25.
The quadrilateral is a trapezoid. The value of x is 5 by applying midsegment theorem for trapezoids.
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
The side with length 21 units and 27 units are parallel to each other.
From the given diagram, the expression below is true:
5x-1 = (21 + 27)/2
2(5x - 1) = 21 + 27
10x - 2 = 48
10x = 48 + 2
10x = 50
Divide both sides by 10
x = 50/10
x = 5
Hence the value of x is 5
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The image of this question is probably this.
The new shelves in the library can hold a maximum of 12 books each. Molly has 50 books that she wants to place in the new shelves. How many shelves will she need to hold all 50 books
The answer to this is 50/12, which is not a whole number. She would need 5 shelves (you have to round up a number because 4 shelves would only be able to fit 48 books)
Answer: 5 shelves
Step-by-step explanation: you times 12x4 which gives you 48 but you need all 50 so you add a extra shelve so the total shelves is 5