The antiderivative of e^(kx), where k is any constant, is (1/k)e^(kx) + C, where C is the constant of integration.
1. As we can see, you are asked to find the antiderivative of the function e^(kx).
2. Recall that the antiderivative of a function is the function that, when differentiated, gives you the original function.
3. The derivative of the function (1/k)e^(kx) is e^(kx), as the constant k in the exponent gets multiplied by the (1/k) factor, canceling each other out.
4. So, the antiderivative of e^(kx) is (1/k)e^(kx) + C, where C is the constant of integration.
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Roxie plans on purchasing a new desktop computer for $1250. Which loan description would result in the smallest amount of interest she would have to pay?
12 months at 6. 25% annual simple interest rate
18 months at 6. 75% annual simple interest rate
24 months at 6. 5% annual simple interest rate
30 months at 6. 00% annual simple interest rate
For a purchase of a new desktop computer for $1250, loan description that would result in the smallest amount of interest she would have to pay is 12 months at 6. 25% annual simple interest rate. Therefore, the correct option is option 1.
To determine which loan description results in the smallest amount of interest for Roxie, we'll calculate the interest for each option using the simple interest formula:
Interest = Principal × Rate × Time.
1. 12 months at 6.25% annual simple interest rate:
Interest = $1250 × 6.25% × (12/12)
Interest = $1250 × 0.0625 × 1
Interest = $78.13
2. 18 months at 6.75% annual simple interest rate:
Interest = $1250 × 6.75% × (18/12)
Interest = $1250 × 0.0675 × 1.5
Interest = $126.56
3. 24 months at 6.5% annual simple interest rate:
Interest = $1250 × 6.5% × (24/12)
Interest = $1250 × 0.065 × 2
Interest = $162.50
4. 30 months at 6.00% annual simple interest rate:
Interest = $1250 × 6.00% × (30/12)
Interest = $1250 × 0.06 × 2.5
Interest = $187.50
Comparing the interest amounts, the smallest interest is for the first option, 12 months at 6.25% annual simple interest rate, with an interest amount of $78.13.
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√x+3
a.3x^1/2
b.(x+3)^1/2
c.x^1/2+3
d.(3x)^1/2
Answer:
b
Step-by-step explanation:
The expression √x+3 means the square root of x+3. We can rewrite this as (x+3)^(1/2), using the exponent rule that says taking the square root is the same as raising to the power of 1/2.
So the options become:
a. 3x^(1/2)
b. (x+3)^(1/2)
c. x^(1/2) + 3
d. (3x)^(1/2)
None of the other options match the given expression. So the correct answer is (b) (x+3)^(1/2).
Find the volume of a pyramid whose base is a square with side lengths of 6 units and height of 8 units.
Answer:
i think the answer is 96
Step-by-step explanation:
If a person takes 125 milligrams of a drug, whose concentration
decreases by 30% each hour. how long will it take for the concentration of
the drug in the bloodstream to be 1 milligram?
It takes approximately 10 hours for the drug concentration to decrease.
What is the quadratic formula?We can use exponential decay to model the concentration of the drug in the bloodstream. Let C(t) be the concentration of the drug in milligrams at time t in hours since the person took the drug. Then we have:
[tex]C(t) = 125(0.7)^t[/tex]
where 0.7 is the factor by which the concentration decreases each hour.
We want to find the time t such that C(t) = 1. Substituting this into the equation above, we get:
[tex]1 = 125(0.7)^t[/tex]
Dividing both sides by 125, we get:
[tex]0.008 = (0.7)^t[/tex]
Taking the logarithm of both sides with base 0.7, we get:
[tex]t = log(0.008) / log(0.7)[/tex]
Using a calculator, we can evaluate this expression to get:
t ≈ 10.07
Therefore, it will take approximately 10.07 hours for the concentration of the drug in the bloodstream to be 1 milligram.
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Ac is a diameter of d. if mbdc = 150°, what is the measure of ab?
this is due today so if anyone can answer this in the next 5-15 minutes that would be great!
We know that the measure of AB is 240°.
Given that AC is a diameter of D and MBDC = 150°, we know that angle ABC is a right angle (90°) because it is inscribed in a semicircle.
Using the fact that the sum of angles in a triangle is 180°, we can find angle MBC:
MBC + 150° + 90° = 180°
MBC = -60°
Since angle MBC is negative, we know that it must actually be 360° - 60° = 300°.
Finally, using the fact that angles on a straight line add up to 180°, we can find angle ABM:
ABM + MBC = 180°
ABM + 300° = 180°
ABM = -120°
Again, since angle ABM is negative, we know that it must actually be 360° - 120° = 240°.
Therefore, the measure of AB is 240°.
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Simplify m^8m^−6.
one over m to the forty eighth power
m^2
one over m squared
−m^14
It should be noted that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².
How to calculate the valueUsing the product of powers rule for exponents, we can simplify m⁸m as follows:
m⁸m⁻⁶ = m⁸⁻⁶) = m²
Therefore, m⁸⁻⁶ is equal to m².
Now, we can further simplify by expressing m² as (m²)¹. Multiplying the exponents, we get:
(m²)¹ = m²
We can say that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².
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Zachary says that the equation 0 = (x – 4)(x – c) has one unique real number solution. What must be the value of c for his statement to be true?
c = 4
Answer:
c=4
Step-by-step explanation:
as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0
Gloria buys last year's best-selling novel, in hardcover, for $18.70 . This is with a 15% discount from the original price. What was the original price of the novel?
The original price of the novel is $21.5
How to calculate the original price of the novel ?The first step is to write out the parameters given in the question
Last year, Gloria buys a novel for $18.70
This price is with a discount of 15% form the original price
The original price of the novel can be calculated as follows
15/100 × 18.70
= 0.15 × 18.70
= 2.805
The next step is to add 2.805 to the price of the novel last year($18.70)
= 18.70 + 2.805
= 21.5
Hence the original price of the novel before the addition of the discount is $21.5
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Question 2 < Σ Use integration by parts to evaluate the integral: + 10x – 9)e *dx = 4.1 f(x²
The value of integral ∫(x^2+10x-9)e^-4x dx is (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.
To evaluate the integral ∫(x^2+10x-9)e^-4x dx using integration by parts, we need to choose two functions to multiply together, one of which we differentiate and the other we integrate. A common choice is to let u = x^2+10x-9 and dv = e^-4x dx, which gives du = (2x+10) dx and v = (-1/4)e^-4x.
Using the formula for integration by parts, we have:
∫(x^2+10x-9)e^-4x dx = uv - ∫v du
= (-1/4)(x^2+10x-9)e^-4x - ∫(-1/4)(2x+10)e^-4x dx
= (-1/4)(x^2+10x-9)e^-4x + (1/2)∫(x+5)e^-4x dx.
Now we can use integration by substitution to evaluate the second integral on the right-hand side:
(1/2)∫(x+5)e^-4x dx = (-1/8)(x+5)e^-4x - (1/32)e^-4x + C,
where C is the constant of integration.
Substituting this back into our previous equation, we get:
∫(x^2+10x-9)e^-4x dx = (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.
Thus, we have found the antiderivative of the integrand using integration by parts, up to a constant of integration.
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Complete question is:
Use integration by parts to evaluate the integral: ∫(x^2+ 10x – 9)e ^-4x dx
A cylinder has a radius of 2 ft and a hight of 6 ft. What is the total surface area using 3.14 as pi.
The total surface area of a cylinder is the sum of the areas of its top and bottom circles, along with the area of its lateral surface (the curved surface that connects the two circles).
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
The formula for the area of a circle is:
Area of circle = πr^2
Using these formulas, we can calculate the total surface area of the cylinder as follows:
Area of top and bottom circles = 2 × π × r^2
= 2 × 3.14 × 2^2
= 25.12 square feet
Lateral surface area = 2 × π × r × h
= 2 × 3.14 × 2 × 6
= 75.36 square feet
Total surface area = Area of top and bottom circles + Lateral surface area
= 25.12 + 75.36
= 100.48 square feet
Therefore, the total surface area of the cylinder is 100.48 square feet.
SPEEDBOAT RACE Speedboats race around four buoys in the lake on a rectangular course. If the total length of the course is 2.4
kilometers and the ratio of the length to the width is 2:1, what are the length and width of the course?
length:
width:
Let's represent the width of the rectangular course as $w$. Then the length of the rectangular course can be represented as $2w$, since the ratio of the length to the width is given as 2:1.
We know that the total length of the course is 2.4 kilometers, so we can write an equation:
$\sf\implies\:2w + 2(2w) = 2.4$
Simplifying the equation:
$\sf\implies\:6w = 2.4$
$\sf\implies\:w = \frac{2.4}{6}$
$\bigstar\implies\sf{\textbf{\boxed{w = 0.4}}}$
Therefore, the width of the course is 0.4 kilometers.
The length of the course is $\sf\:2w = 2(0.4)=$
${\boxed{\sf{0.8 kilometers.}}}$
Hence, the length of the course is 0.8 kilometers and the width of the course is 0.4 kilometers.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
7. The Key West Lighthouse is 86 feet tall. What is the height of the lighthouse in meters?
The height of the Key West Lighthouse in meters is approximately 26.21 meters.
Here's how you can calculate it:
- There are 3.28 feet in a meter.
- Divide the height of the lighthouse in feet by the number of feet in a meter: 86 ÷ 3.28 = 26.21 meters (rounded to two decimal places).
- Therefore, the height of the Key West Lighthouse in meters is approximately 26.21 meters.
Part B: If GA = 29 and a major arc mDUG = 185°, then determine the minor arc length of
GD.
The length of the minor arc GD is approximately 0.196π units.
To get the length of the minor arc GD, we need to subtract the measure of the major arc mDUG from the circumference of the circle, and then divide by 360° to find the length of one degree of arc.
First, we need to find the circumference of the circle. Since GA = 29, we know that the radius of the circle is also 29. The formula for the circumference of a circle is C = 2πr, so for this circle we have: C = 2π(29) = 58π
Next, we need to subtract the measure of the major arc mDUG from the circumference of the circle. Since mDUG = 185°, we have:
58π - (185/360)(58π) = (175/360)(58π)
Simplifying this expression, we get: (175/360)(58π) = 29(175/72)π ≈ 70.48π
Finally, we divide this value by 360° to find the length of one degree of arc:
(70.48π)/360 ≈ 0.196π
Therefore, the length of the minor arc GD is approximately 0.196π units.
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Line m is represented by the equation
y +2=
3/2(x + 4). select all equations that represent lines perpendicular to
line m.
oa.
y= -3/2x + 4
oь.
y= -2/3x + 4
oc.
y= 2/3x + 4
od.
y= 3/2x + 4
oe.
y+1= -4/6(x+5)
of.
y + 1= 3/2(x+5)
The equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.
The equation of line m is given as y + 2 = (3/2)(x + 4). To determine the equations that represent lines perpendicular to line m, we need to find the negative reciprocal of the slope of line m and use it as the slope in the perpendicular lines.
The slope of line m is (3/2), so the negative reciprocal is -2/3. We can eliminate options oa, oб, and of because they do not have a slope of -2/3.
Now, let's check the remaining options:
oc: y = (2/3)x + 4
This equation has a slope of 2/3, which is not the negative reciprocal of -2/3. Therefore, it is not perpendicular to line m.
od: y = (3/2)x + 4
This equation has the same slope as line m, which means it is not perpendicular to line m.
oe: y + 1 = (-4/6)(x + 5)
Simplifying the equation, we get y + 1 = (-2/3)(x + 5), which has a slope of -2/3. Therefore, this equation represents a line that is perpendicular to line m.
Therefore, the equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.
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How to find the area of a tier
_________________________________
A = L × B × H = 22ft × 4ft × 6ft = 528ft²_________________________________
Find the missing point of the following parallelogram. (2,4) (6,5) (7,5) (5,3)
Answer:
The missing point of this parallelogram is (6, 5).
1.Number graph
2.Graph the line using the equation y=1/2x
The equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.
What is number graph?In mathematics, a graph is a visual representation of a mathematical relationship. The equation y=1/2x is a linear equation, which means that it describes a straight line. This equation can be graphed using the number graph.
To graph the equation y=1/2x, one must first plot points on the graph. To do this, one can use the given equation to calculate the x and y values of the points. For example, if x is equal to 1, then y is equal to 1/2. Therefore, the point (1, 1/2) can be plotted on the graph. This process can be repeated for other values of x, such as 2, 3, and 4. The result is a straight line that passes through the points (1, 1/2), (2, 1), (3, 1 1/2), and (4,2).
The equation y=1/2x can also be graphed using the slope-intercept form of the equation. This form of the equation is written as y=mx + b, where m is the slope of the line and b is the y-intercept. For the equation y=1/2x, the slope is 1/2 and the y-intercept is 0. To graph the line, one must first plot the y-intercept, which is the point (0,0). Then, one must calculate the slope and draw a line through (0,0) in the direction of the slope. The result is a straight line that passes through the points (0, 0), (1, 1/2), (2,1), (3, 1 1/2), and (4, 2).
In conclusion, the equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.
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The slope-intercept form or a number graph can both be used to visualise the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.
What is number graph?A graph in mathematics is a picture of a mathematical connection. A linear equation is one that describes a straight line, such as y=1/2x. The number graph can be used to graph this equation.
The graph must first have points drawn on it before the equation y=1/2x can be graphed. To do this, one can compute the x and y values of the points using the above equation. For instance, y is equal to 1/2 if x is equal to 1. As a result, the graph's point (1, 1/2) can be drawn. You can repeat this procedure for x values of 2, 3, and 4. Consequently, a straight line that traverses the coordinates (1, 1/2), (2, 1), (3, 1 1/2),and (4,2).
The slope-intercept form of the equation can also be used to graph the equation y=1/2x. Y=mx + b, where m is the line's slope and b is its y-intercept, is how this form of the equation is expressed. The slope and y-intercept of the equation y=1/2x are 1/2 and 0, respectively.
Plotting the y-intercept, or the point, is required before the line can be graphed. (0,0). The next step is to determine the slope and draw a line through (0,0) in the slope's direction. A straight line is created as a result, passing through the points (0, 0), (1, 1/2), (2, 1), (3, 1 1/2), and (4, 2).
In conclusion, the slope-intercept form or a number graph can both be used to graph the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.
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For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting. How much will Nicole make after babysitting for 8 hours?
Answer:
Sure. Here is the equation for the cost, C, after h hours of babysitting:
```
C = 3 + 5h
```
This equation can be found by combining the flat fee of $3 with the hourly rate of $5. For example, if Nicole babysits for 2 hours, she will make $3 + (2 * $5) = $13.
To find how much Nicole will make after babysitting for 8 hours, we can simply substitute h = 8 into the equation. This gives us:
```
C = 3 + 5(8) = 3 + 40 = $43
```
Therefore, Nicole will make $43 after babysitting for 8 hours.
Answer:c= 3 + 5(8)
Step-by-step explanation:
3 is flat fee, and then plus $5 and hour. you know she's going for 8 hours, so you multiply hourly rate by the number of hours plus flat fee and you get your answer
Can someone how to use a TI-84 Plus to do the following:
Normal Distribution: Finding Values
Normal Distribution: Finding Probibilities
Sampling Distributions and the Central Limit Theorem
!!!!I have a test on this tmr please help!!!!
Normal Distribution: Finding Values
Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "Normalcdf" and press enter.
Enter the lower bound, upper bound, mean, and standard deviation. For example, if you want to find the probability that X is between 60 and 70, given that the mean is 65 and the standard deviation is 5, you would enter "60, 70, 65, 5".
Press enter to get the result. The calculator will give you the probability that X falls between the two values you entered.
Normal Distribution: Finding ProbabilitiesPress the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "InvNorm" and press enter.
Enter the probability you want to find. For example, if you want to find the z-score that corresponds to the 90th percentile, you would enter "0.9".
Enter the mean and standard deviation. For example, if the mean is 65 and the standard deviation is 5, you would enter "65, 5".
Press enter to get the result. The calculator will give you the z-score that corresponds to the probability you entered.
Sampling Distributions and the Central Limit Theorem: Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "1-PropZTest" or "2-PropZTest" and press enter, depending on the type of test you want to perform.
Enter the sample statistics and the population parameters, if known. The calculator will use these values to calculate the test statistic and p-value.
Press enter to get the result. The calculator will give you the test statistic and the p-value, which you can use to make inferences about the population.
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Help please I’ve been sick all week so I’m very behind
Answer:
Angle 1 is 77
Angle 2 is 103
Angle 4 is 103
Step-by-step explanation:
Angles that are vertical to each other like 2 and 4, 1 and 3
will always equal each other
since 3 is = to 77, 1 is also = to 77
You can also find the angles by thinking of supplementary angles (180 degrees) Straight angle basically
You see that 3 is 77 and 4 is part of the straight line so it needs to equal 180
so 180-77 it will equal 103.
Hope this helps
Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive? Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families. Use Scratchpad to illustrate both studentsâ solutions
This will show that each family gets 5/16 of a pizza.
Sure, I'd be happy to help you with your question!
So, Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive?
Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families.
To illustrate both students' solutions, we can use Scratchpad. For Savannah's solution, we can draw 5 rectangular pizzas and then divide them into 4 equal parts each. Then, we can shade in 1 whole pizza and divide the remaining pizza equally among the 4 families. This will show that each family gets 1 whole pizza and a quarter of a pizza.
For Josiah's solution, we can draw 5 rectangular pizzas and then divide each pizza into fourths. Then, we can divide the fourths equally among the 4 families.
This will show that each family gets 5/16 of a pizza.
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Angad adds 20 to it, then doubles it and gets an answer of 53. what was the original number?
The original number was 17 to which when Angad adds 20, then doubles it and gets an answer of 53.
To solve this problem, we need to work backwards from the final answer. If Angad added 20 to the original number, we can subtract 20 from 53 to get 33. This means that after Angad doubled the number, he had 33.
To find the original number, we need to undo the doubling process. If Angad had 33 after doubling the number, we can divide 33 by 2 to get the original number.
33 divided by 2 equals 16.5. However, we know that the original number must be a whole number since we cannot add 20 to a decimal. Therefore, we can round up to the nearest whole number to get 17.
So, the original number was 17.
In summary, to find the original number, we worked backwards from the final answer and undid the steps that Angad took. We subtracted 20 to undo the addition, then divided by 2 to undo the doubling. We rounded up to the nearest whole number since the original number must be a whole number.
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solve the equation sin theta equals to Cos 35
Answer:
55 degrees
Step-by-step explanation:
sin Φ = cos 35
sin Φ = .81915
Φ = arc sin (.81915) = 55 degrees
Or you could just know that the cos of an angle is equal to the sin of its comeplement
Qn in attachment . ..
Answer:
Step-by-the answer is (a) 16
You should always measure your following distance in.
You should always measure your following distance in seconds. The correct answer for measuring following distance is A.
It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.
The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.
Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.
The correct answer for measuring following distance is A.
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Complete question is:
You should always measure your following distance in __________
A. seconds. B. car lengths. C. feet.
A bunch of flowers originally cost $32. It goes on sale at 25% off the original price.
Fill in the blanks.
Original percentage:
Percentage off:
Percentage left over:
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = ----------% x $32
Original percentage: 100%
Percentage off: 25%
Percentage left over: 75%
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = (100% - 25%) x $32 = 75% x $32 = $24
a popular TV series is running for 10 seasons. You are buying the seasons from an online DVD service. If each season arrives at random, what is the probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order?
The probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order is given as follows:
p = 1/30240.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
5 seasons are going to be shown from a set of 10, and the order is relevant, hence the permutation formula is used to obtain the total number of outcomes, as follows:
P(10, 5) = 10!/5!
P(10, 5) = 30240.
Only one of the outcomes has the correct seasons and order, hence the probability is given as follows:
p = 1/30240.
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Milan bought a table for rs 3600 he sells it to kirtim at a profit of rs 205 kritim sells it at rs 4968 to aayush find the percentage profit of kritim
Kritim's percentage profit is 8.5%.
Milan bought the table for Rs 3600 and sold it to Kritim at a profit of Rs 205. Hence, Kritim paid Rs 3600 + Rs 205 = Rs 3805 for the table. Kritim then sold the table to Aayush for Rs 4968.
To find Kritim's profit percentage, we need to calculate the profit percentage on the cost price. The cost price for Kritim is Rs 3805, and the selling price is Rs 4968. Hence, the profit earned by Kritim is Rs 4968 - Rs 3805 = Rs 1163.
Profit percentage = (Profit / Cost price) x 100%
Profit percentage = (1163 / 3805) x 100%
Profit percentage = 0.3055 x 100%
Profit percentage = 30.55%
Therefore, Kritim's profit percentage is 8.5%.
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Required: prepare adjusting journal entries on the book
close the book
open a new set of books for the partnership
record the contributions of both partners
prepare balance sheet of the partnership
1. Old stocks of merchandise has appraised its value to 12,000. 00
2. Allowance for bad debts in understated by 200. 00
3. Unrecorded accrued interest on notes receivables dated November 1, 2019 at 5% should be recorded
4. Accrued interest on notes payable issued on July 31, 2019 at 10% should be recognized
5. Net furniture and fixtures is understated by 1,000. 00
N. Lustre will contribute cash and delivery truck the truck was originally valued by N. Lustre as 30,000. 00 but J. Reid estimated it at 20,000. 00 to which N. Lustre agreed N. Lustres capital should be exactly equal to reid capital of 62,200
Prepare adjusting journal entries, close the book, open a new set of books for the partnership, record the contributions of both partners, and prepare the balance sheet of the partnership.
How to prepare adjusting journal entries and balance sheet for the partnership?Adjusting Journal Entries:
Debit Merchandise Inventory: 12,000Credit Allowance for Inventory Appraisal: 12,000Debit Bad Debt Expense: 200Credit Allowance for Bad Debts: 200Debit Interest Receivable: (calculate accrued interest amount based on notes receivable and interest rate)
Credit Interest Revenue: (same amount as above)
Debit Interest Expense: (calculate accrued interest amount based on notes payable and interest rate)
Credit Interest Payable: (same amount as above)
Debit Furniture and Fixtures: 1,000
Credit Accumulated Depreciation - Furniture and Fixtures: 1,000
N. Lustre's Contribution:
Debit Cash: (amount contributed by N. Lustre)
Debit Delivery Truck: 20,000
Credit N. Lustre's Capital: (total contributed amount)
J. Reid's Capital:
Credit J. Reid's Capital: 62,200
Balance Sheet of the Partnership:
Include the capital balances of N. Lustre and J. Reid
List the current assets, fixed assets, current liabilities, and long-term liabilities of the partnership
Calculate the total assets, total liabilities, and partners' equity
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A funnel is in the shape of a cone with a radius of 4 inches and a height of 10 inches.
a. Find the volume of the funnel. Round your answer to the nearest tenth.
b. The funnel is filled with oil. How many quarts of oil are in the funnel? (1 qt ≈ 58 in. ³) Round your answer to the nearest tenth
a. The volume of the funnel is 167.6 in³.
b. The amount in quarts of oil are there in the funnel is approximately 2.9 quarts.
a. To find the volume of a cone, you can use the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting in the values given, we get V = (1/3)π(4 in)²(10 in) ≈ 167.6 in³. Rounded to the nearest tenth, the volume of the funnel is 167.6 in³.
b. To convert cubic inches to quarts, we need to divide by the conversion factor of 58 in³/qt. So, V = 167.6 in³ ÷ 58 in³/qt ≈ 2.9 qt. Rounded to the nearest tenth, there are approximately 2.9 quarts of oil in the funnel.
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