Answer: 45T + 55S +102 + 96= Combined income
Step-by-step explanation:
Using the MACRS rates from the following table, what is the book value of a $2,500 computer after 3 years? Ro Year MACRS Rate 1 2 3 4 5 20.0 % 32.0% 19.2% 11.52 % 11.52% book value = [?]
Using MACRS rates, the book value of the $2,500 computer after 3 years is $720.
What are MACRS rates?MACRS (Modified Accelerated Cost Recovery System) rates are prearranged percentages used for the purposes of tax.
They compute how much an asset depreciates each year based on its class and expected lifespan.
Using MACRS rates, we shall calculate the book value of a $2,500 computer after 3 years in this way.
First, we shall apply the respective depreciation rates to the initial cost and subtract the accumulated depreciation each year.
Year 1:
Depreciation = Year 1 MACRS Rate x Initial Cost
Depreciation = 20.0% × $2,500 = $500
Year 2:
Depreciation = Year 2 MACRS Rate x Initial Cost
Depreciation = 32.0% × $2,500 = $800
Year 3:
Depreciation = Year 3 MACRS Rate x Initial Cost
Depreciation = 19.2% × $2,500 = $480
Next, subtract the accumulated depreciation from the initial cost to have the book value for each year:
Year 1:
Book Value = Initial Cost - Depreciation
Book Value = $2,500 - $500 = $2,000
Year 2:
Book Value = Year 1 Book Value - Year 2 Depreciation
Book Value = $2,000 - $800 = $1,200
Year 3:
Book Value = Year 2 Book Value - Year 3 Depreciation
Book Value = $1,200 - $480 = $720
Therefore, the book value of the $2,500 computer after 3 years is $720.
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Help please
Write an equation for a function that has a graph with the given characteristics.
The shape of y= |x| that has been shrunk vertically by a factor of 2/9.
----------------------.
The required equation of the function with the given characteristics is y = (2/9)|x| whose height will be compressed to 2/9 of the original height.
As per the question, the absolute value function y = |x| looks like a "V" shape with its vertex at the origin and opening upward.
To shrink it vertically by a factor of 2/9, we need to multiply the function by this factor.
Thus, the equation of the function with the given characteristics is:
y = (2/9)|x|
The resulting graph will still have a "V" shape, but its height will be compressed to 2/9 of the original height.
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a) On the occasion of Teej, the principal of a school organized a Teej program for her female staffs. She distributes 90 bangles and 108 sweets equally to the staffs including herself. If there are 20 male staffs in the school, find the maximum number of staffs of her school.
The maximum number of staff at the school, given the distribution of bangles and sweets, is 38 staff.
How to find the number of staff ?The principal has distributed 90 bangles and 108 sweets equally among her female staff includng herself. This means that the total number of female staff in the school is a number that can divide both 90 and 108 evenly, as each staff member must receve an integer number of bangles and sweets.
Find the greatest common divisor (GCD) of 90 and 108. The GCD of 90 and 108 is 18.
So, the princpal's school has 18 female staff including herself. In addition to the 20 male staff, this implies a maxmum of:
18 (female staff) + 20 (male staff) = 38 staff in total
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A survey of the people who like the films made in Nepali, English or Hindi languages reported that 50 liked Nepali, 40 liked English, 30 liked Hindi, 24 liked Nepali and 11 English, 19 liked Nepali and Hindi, 13 liked Hindi and English, 6 liked all three and people were found not intended in any films.
To solve this problem, we can use the formula:
Total = n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)
where:
n(A) = number of people who liked Nepali
n(B) = number of people who liked English
n(C) = number of people who liked Hindi
n(A and B) = number of people who liked both Nepali and English
n(A and C) = number of people who liked both Nepali and Hindi
n(B and C) = number of people who liked both English and Hindi
n(A and B and C) = number of people who liked all three languages
From the given information in the problem, we have:
n(A) = 50
n(B) = 40
n(C) = 30
n(A and B) = 11
n(A and C) = 19
n(B and C) = 13
n(A and B and C) = 6
We can now substitute these values into the formula:
Total = 50 + 40 + 30 - 11 - 19 - 13 + 6
Total = 73
ANSWER: Therefore, there were a total of 73 people who liked at least one of the three languages.
How do I approximate √329 to the nearest integer? show work and explain on a piece of paper. i will mark you brainliest
The approximate value of √329 to the nearest integer is 18.
How to approximate √329 to the nearest integer?Approximation is the process of using rounded values when presenting numerical data and making rough calculations.
To approximate √329 to the nearest integer, we can find the perfect squares that are less than or equal to 329.
The perfect squares less than or equal to 329 are 16, 25, 36, and 49. But the nearest perfect square to 329 is 324, which is the square of 18 (i.e. 18² = 324).
Therefore, the nearest integer to √329 is 18.
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Which value is a solution to the inequality 9 – y >12?
A) 2
B) –6
C) 8
D) –1
Answer:
To find the solution to the inequality 9 - y > 12, we need to isolate the variable y.
9 - y > 12
Subtract 9 from both sides:
-y > 12 - 9
-y > 3
Since we have a negative coefficient for y, we need to flip the inequality sign when multiplying or dividing by a negative number. In this case, we can multiply both sides of the inequality by -1 to simplify it further:
y < -3
The inequality states that y is less than -3.
Now let's check which value among the given options satisfies this inequality:
A) 2: 2 is not less than -3. It is greater.
B) -6: -6 is less than -3. It satisfies the inequality.
C) 8: 8 is not less than -3. It is greater.
D) -1: -1 is less than -3. It satisfies the inequality.
Based on the given options, the values that satisfy the inequality y < -
Step-by-step explanation:
Find the probability that a randomly
selected point within the square falls in the
red-shaded square.
1
1
3
P = [?]
3
Enter as a decimal rounded to the nearest hundredth.
The probability that a randomly selected point within the square falls in the red-shaded square is 0.11
Finding the probabilityFrom the question, we have the following parameters that can be used in our computation:
Red square of length 1White square of length 3The areas of the above shapes are
Red square = 1² = 1
White square = 3² = 9
The probability is then calculated as
P = Red square/White square
So, we have
P = 1/9
Evaluate
P = 0.11
Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11
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when given angle measures of 25,65,and 90,is it possible to draw a triangle,possible to draw only one triangle,or possible to draw more than one triangle?explain.
The total angle measurement of a triangle sum above is 180°. So yes, it is possible to only make a right angle triangle but impossible to draw a triangle
What is the triangle?To check if a triangle can be drawn with 25°, 65°, and 90° angles, we use the Triangle Angle Sum Theorem stating that all triangle angles add up to 180 degrees.
If you add all the angles together (25 + 65 + 90 = 180°), We can draw a triangle based on this sum, but we only consider the angles' nature. The triangle has angles of 25°, 65°, and 90°, making it a right triangle. It only applies to right triangle and not others triangle .
Note that based on the given angle measures of 25°, 65°, and 90°, it is impossible to draw a triangle as it does not follow the triangle inequality property.
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round 12.083 to the neatest tenth
Answer: 12.1
Step-by-step explanation: rounding 12.083 to the nearest tenth will leave you with- 12.1
hope this helps!
What is the measure of GEF?
OA. 50°
OB. 60°
OC. 160°
OD. 110°
110°
G
✓
The measure of angle CDE is 70°.
Option C) 70° is correct.
Angle BAC measures 80°.
Point D is located on side BC such that BD = CD.
Angle ADE measures 30°.
To find: Measure of angle CDE.
Since angle BAC measures 80° and angle ADE measures 30°, we can determine the measure of angle CDE by subtracting the sum of these two angles from 180° (the total measure of angles in a triangle).
Measure of angle CDE = 180° - (80° + 30°)
= 180° - 110°
= 70°
Therefore, the measure of angle CDE is 70°.
The correct answer is:
C) 70°
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The complete question may be like;
In the diagram below, triangle ABC is shown. Angle BAC measures 80°. Point D is located on side BC such that BD = CD. Angle ADE measures 30°. What is the measure of angle CDE?
A) 50°
B) 60°
C) 70°
D) 80°
Please let me know if you have any specific requirements or if there's anything else I can assist you with.
The w of a golden rectangle is 30cm. Find the lengths to the nearest centimeter
The length of the golden rectangle is 49 cm.
A rectangle is a quadrilateral (a polygon with four sides) in which each angle is a right angle (90 degrees). It is a type of parallelogram in which opposite sides are parallel and congruent (equal in length). Rectangles have four sides and four vertices (corners).
The length of a rectangle is the distance between its two longer sides, while the width is the distance between its two shorter sides. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width.
A golden rectangle has sides in the proportion of the golden ratio, which is approximately 1:1.618. Therefore, if the width is 30cm, the length can be found by multiplying 30 by 1.618.
Length ≈ 48.54 cm
The length of the rectangle is 49 cm.
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A 4-digit number has the digits 0,5,9 and 3.To the nearest thousand,it rounds to 10,000. What is the number? Explain.
Answer: 9530
Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0
In LMN point P in the centroid, and AN = 18. Find AP and NP
The measures of NP and AP equals 8
How to determine the valuesFirst, it is important to note that;
The center of any shape is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. The median is a line that connects the middle of a side to the triangular opposite vertex.From the information given, we have that;
The centroid of the triangle divides AN in the ratio of 1: 2
Hence, the length of AN is twice that of line NP
So;
AN = 2NP
Substitute the value
18 = 2NP
Divide by the coefficient
NP = 9
But;
AN = NP + AP
Substitute the values, we get;
AP = 18 - 9
AP = 9
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.will give brainless
Step-by-step explanation:
OK, 'Brainless'.... the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...
42 + 20 > x then 12 , 20, 22, 32, 42, 50 will work here
42+x > 20 all of the possibles work here
20 + x > 42 32, 42, 50, 62 and 70 work here
so 32 and 42 are in all of the lists ....that is your answer
Please help with this 4-5
In ⊙C, DE≅FG. Select all the statements that must be true.
A. △DCE≅△FCE
B. arcDE arcFG
C. △FCE≅△FCG
D. ∠DCE≅∠GCF
E. EF≅ED
In a circle with congruent line segments DE and FG, statements A is true, B is false, C and D are false, and E may or may not be true.
In the given circle ⊙C, DE and FG are two line segments that are congruent. The following statements must be true:
A. △DCE≅△FCE: This statement is true because both triangles share the same side lengths of DE and FG and the common angle ∠DCE = ∠FCE.
B. arcDE = arcFG: This statement is false since congruent line segments do not necessarily correspond to congruent arcs in a circle.
C. △FCE≅△FCG: This statement is false since there is no given information to suggest that the line segment CG is congruent to CE.
D. ∠DCE≅∠GCF: This statement is false since there is no given information to suggest that ∠GCF is congruent to ∠DCE.
E. EF≅ED: This statement may or may not be true since we are not given any information about the length of either of these line segments.
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Graph the function f(x) = -(1/5)^x+5 +7 on the axes below. You must Plot the asymptote and any two points with the integer coordinates
The graph of the function is added as an attachment
The asymptote: y = 7 and the points are (-5, 6) and (-7, -18)
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = -(1/5)ˣ ⁺ ⁵+ 7
The above function is an exponential function that has been transformed as follows
Reflected over the x-axisDecay factor of 1/5Shifted left by 5 unitsShifted up by 5 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment, where we have the following points
Asymptote: y = 7
(-5, 6) and (-7, -18)
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Chau is cooking a roast. The table below gives the temperature of the roast (in degrees Celsius), at a few times (in minutes) after he removed it from the oven.
Time
(minutes) Temperature
0 184.3
20 140.3
30 109.3
50 51.3
60 28.3
(a) Find the average rate of change for the temperature from 0 minutes to 20 minutes.
(b) Find the average rate of change for the temperature from 30 minutes to 60 minutes.
a. The average rate of change for the temperature from 0 minutes to 20 minutes is 2.2.
b. The average rate of change for the temperature from 30 minutes to 60 minutes is 2.7.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(t) over the interval [0, 20]:
a = 20; f(a) = 140.3
b = 0; f(b) = 184.3
By substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (184.3 - 140.3)/(20 - 0)
Average rate of change = 44/20
Average rate of change = 2.2
Part b.
a = 30; f(a) = 109.3
b = 60; f(b) = 28.3
By substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (109.3 - 28.3)/(60 - 30)
Average rate of change = 81/30
Average rate of change = 2.7
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Given that events A and B are independent with P(A) = 0.68 and
P(A and B) = 0.544, determine the value of P(B), rounding to the nearest
thousandth, if necessary.
The value of P (B) = 0.8
The probability of event A, P (A) = 0.68
The probability of events A and B, P (A ∩ B) = 0.544
The probability of event B, P (B) = ?
We know that Independent events are those where the probability of A event occurring doesn't affect the probability of B event. In other words, they don't depend upon each other and are independent.
By formula;
P (A ∩ B) = P (A) . P (B)
By substituting the values to the above equation, we get;
0.544= 0.68 * P (B)
P (B) = 0.8
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What is the solution of 3√x+8 = -4? X =√72 O x=-66 O x = 58 O no solution
Answer: add image
Step-by-step explanation:
janice wants to book a holiday
the holiday will cost £ 1754
janice will pay a deposit of £350
she will then pay the rest od the cost in 6 equal monthly payments
how much is each monthy paymwnt
Answer: £234
Step-by-step explanation:
First, we need to subtract the deposit (£350) from the total cost of the trip (£1754):
£1754 - £350 = £1404
Then we need to divide the remaining amount of money (£1404) by the number of months Janice will be on holiday (6 months):
£1404 ÷ 6 months = £234 each month
Hope this helps!
If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
OC) 3 years
D) 308 years
Answer:
31 years
Step-by-step explanation:
A = P(interest rate)^number of years (n)
if the money is to quadruple, A = 4 X 22,000 = 88,000.
P = investment amount = 22,000.
interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.
n is number of years.
22,000 (1.045)^n = 88, 000
divide both sides by 22, 000:
(1.045)^n = 4
take logs for both sides:
log (1.045)^n = log 4
simplify using log laws (by bringing down the n):
n log (1.045) = log 4
divide both sides by log (1.045):
n = (log 4) / log (1.045)
= 31.49 (31 years to nearest year)
Given rhombus ABCD, find the area if mZABC = 60° and AE = 2.
The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;
Area = 8·√3
What is the area of a plane figure?The area of a plane figure is the two dimensional space occupied by the figure on a plane.
The measure of the angle ABC, m∠ABC = 60°
The length of the segment AE = 2 units
The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;
BE = ED, m∠AEB = 90°
m∠ABE = 30°
sin(30°) = AE/AB
sin(30°) = 2/AB
AB = 2/(sin(30°)) = 4
AB = 4
BE = √(4² - 2²) = √(12) = 2·√3
Therefore; AC = 2 + 2 = 4
BD = 2·√3 + 2·√3 = 4·√3
The area of a rhombus = (1/2) × The product of the length of the diagonals
Therefore;
Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3
The area of the rhombus = 8·√3
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un auto parte de reposo y se desplaza con una aceleración de 1m/s2 durante 1s. luego se apaga el motor y el auto desacelera debido al rozamiento durante 10s a un promedio de5 cm/s2. entonces se le aplica los frenos y se detiene 5s despues ¿ calcular la distancia total recorrida?
After considering all the given data we conclude that the total distance traveled by the car is 285m, under the condition that the given car starts from rest and moves with an acceleration of 1m/s2 for 15.
The distance traveled during this time can be evaluated using the formula
[tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (0),
a = acceleration (1m/s2)
t = time (15s).
Placing in these values we get
s = 0 + (1/2) × 1 × 15²
= 112.5m .
After this, the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. The distance traveled during this time can be evaluated applying the formula
[tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (the final velocity of the previous step),
a = acceleration (-0.05m/s2)
t = time (10s).
Placing in these values we get
s = 112.5 + (1/2) × (-0.05) × 10²
= 87.5m.
Finally, brakes are applied and it stops after 5s. The distance traveled during this time can be evaluated using the formula [tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (the final velocity of the previous step),
a = acceleration (-0.05m/s2)
t = time (5s).
Placing in these values we get s = 87.5 + (-0.05)× 5² = 85m.
Therefore, total distance traveled by car can be calculated by adding all three distances together which gives us
112.5m + 87.5 + 85
= 285m.
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The complete question is
A car starts from rest and moves with an acceleration of 1m/s2 for 15. Then the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. then the brakes are applied and it stops 5s after calculating the total distance traveled?
Find domain and range thank you for the help have a great afternoon
Step-by-step explanation:
Domain : (-5,4]
Range [-2,0)
rate of change between (-4,-12)and (2,4)
Answer: 2.667
Step-by-step explanation:
Answer:
Can you mark me brainiest.
Step-by-step explanation:
Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.
Or 2.667
Give the coordinates of the point in the graph below.
-5
A
32
-3 -2
-1
-4
-3-
2-
0
-1-
--2-
-3-
-4
-5
-N-
2
3
4
5.
The coordinates of the point in the graph is (3, 2)
How to determine the coordinates of the point in the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following
The point is 3 units to the right of the x-axisThe point is 2 units above the y-axisRepresent the point with x
So, we have
X = (3, 2)
Hence, the coordinates of the point in the graph is (3, 2)
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Goran bought 8 pounds of rice for $4.
How many pounds of rice did he get per dollar?
PLEASE HELP ME
Answer:
Step-by-step explanation:
32
Bookwork code: K27
,Calculator
allowed
A pendulum of length 18 cm is swinging from a fixed point, as shown.
Calculate the distance that the end of the pendulum travels when it swings
through an angle of 87°.
Give your answer in centimetres (cm) to 1 d.p.
87°
18 cm
The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm
Given data ,
A pendulum of length 18 cm is swinging from a fixed point
Now , it swings through an angle of 87°
So , Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
Now , D = ( θ/360 ) x 2πr
On simplifying , we get
D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )
D = ( 0.241667 ) ( 113.04 )
D = 27.3 cm
Hence , the pendulum travels a distance of 27.3 cm
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Write the equation of the conic section shown below.
The vertex form of the equation of a parabola is equal to y + 1 = - (1 / 12) · (x - 2)².
How to determine the equation of a parabola in vertex form
In this problem we need to determine the equation of a parabola, this can be done by knowing the distance between vertex and focus and the coordinates of the focus. The vertex form of the equation of the parabola is:
y - k = [1 / (4 · p)] · (x - h)²
Where:
h, k - Coordinates of the vertex.p - Distance of the focus with respect to vertex.If we know that (h, k) = (2, - 1) and p = - 3, then the equation of the parabola in vertex form is:
y + 1 = - (1 / 12) · (x - 2)²
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Answer:
[tex](x-2)^2=-12(y+1)[/tex]
Step-by-step explanation:
From observation of the given diagram, we can see that the graphed conic section is a vertical parabola that opens downwards, with a vertex at (2, -1) and a focus at (2, -4).
The equation of a vertical parabola in standard form is:
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a vertical parabola}\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k + p)$\\\end{minipage}}[/tex]
Given the vertex is (2, -1):
[tex]h = 2[/tex][tex]k = -1[/tex]Given the formula for the focus is (h, k+p), then:
[tex]\begin{aligned}(h, k+p)&=(2, -4)\\(2,-1+p)&=(2,-4)\\\\\implies -1+p&=-4\\p&=-4+1\\p&=-3\end{aligned}[/tex]
To write the equation of the graphed conic section, substitute the found values of h, k and p into the standard formula:
[tex](x-2)^2=4(-3)(y-(-1))[/tex]
[tex](x-2)^2=-12(y+1)[/tex]
Therefore, the equation of the graphed conic section is:
[tex]\boxed{(x-2)^2=-12(y+1)}[/tex]
