Evaluate the arise tic
series described:
12. 0,= 300, n = 25 (please help)
Answers
Related Questions
i’ll give lots of points + brainliest
write the equation that represents stretching y=x^2 by a factor of 6
Answers
y=x<2-6 and the answer is -4
on a coordinate plane,point A is located at (7,4), and point B is located at (-8,4). What is the distance between the two points ?
Answers
The distance between the point A and B is 15 units.
How to find the distance between two points?The distance between two points can be found using Pythagoras's principle.
Point A is located at (7,4), and point B is located at (-8,4). Let's find the distance between point A and B as follows:
Therefore,
d = √(y₂ - y₁)² + (x₂ - x₁)²
Hence, using (7, 4) (-8, 4)
x₁ = 7
x₂ = -8
y₁ = 4
y₂ = 4
Hence,
d = √(4 - 4)² + (-8 - 7)²
d = √(0)² + (-15)²
d = √225
d = 15 units
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Rob is saving to buy a new MP3 player. For every $13 he earns babysitting, he saves $9. On Saturday, Rob earned $52 babysitting. How much money did he save?
Answers
4x9=36
He saved $36
Answer:
$36
Step-by-step explanation:
$13 babysitting, $9 saved.
$52 babysitting, $x saved.
Cross multiply
13/13x=468/13
Divide both sides by 13
x=$36
the table below shows the length of the hiking trails at a local park. Aaron hikes half of the blue trail. what distance did he hike?
Answers
Answer:
The answer is B.
Step-by-step explanation:
I was trying to answer ur question a little bit ago, where it had multiple quesitons, but it had gotten deleted. I saved the answers for you
1st one- B(This question lol) , second one- C, third one- ?, fourth one- C, Fifth one- A.
I wasnt sure about the third one but i got the others...
Hope it helps you :)
Pls mark brainleist :P
`
`
`
w/ <3...
Tori
Answer:
Its 0.5 miles
Step-by-step explanation:
A student is deriving the quadratic formula. Her first two steps are shown.
Step 1: –c = ax2 + bx
Step 2:
Which best explains or justifies Step 2?
Answers
Please consider the complete question.
A student is deriving the quadratic formula. Her first two steps are shown. Step 1: \(-c = ax^2 + bx\)
Step 2: \(-c = a[x^2+\frac{b}{a}x]\)
Which best explains or justifies Step 2?
A. division property of equality
B. factoring the binomial
C. completing the square
D. subtraction property of equality
We can see that in step 2 student has factored the right side of equation.
The student factored our a from the right side of equation. To factor our a from right side, student has divide the bx term by a.
We can multiply and divide by same quantity in an equation.
\(-c = ax^2+a\cdot \frac{b}{a}x\)
Now we can factor out a as:
\(-c = a(x^2+\frac{b}{a}x)\)
Therefore, the 2nd step is known as factoring of binomial and option B is the correct choice.
Answer:
it b factoring a binomial on
Step-by-step explanation:
thats on edge
(7th gradish answer please)
Define coordinate in your own words
Answers
Answer:
A specific instead of general place where you can find something
By selling a table for Rs.1,350 a man makes a loss of 10%.What percent would he have gained if he has sold it for Rs. 1,600
Answers
100%= 1500
1% = 15
1600/15 = 106.67
6.67% gain
Determine if the relation shown in the graph is symmetrical with respect to the x-axis, y-axis, or the origin.
Answers
Procter and Gamble (PG) paid an annual dividend of $2.95 in 2018. You expect PG to increase its dividends by 7.4% per year for the next five years (through 2023), and thereafter by 2.6% per year. If the appropriate equity cost of capital for Procter and Gamble is 8.6% per year, use the dividend-discount model to estimate its value per share at the end of 2018.
Answers
The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.
First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)
where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:
PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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There is a 25ft fence, 130 feet away from where the ball was hit. If the ball was hit towards the fence would it be high enough to clear
Answers
If the maximum height of the ball is greater than or equal to the height of the fence, then it would clear the fence.
To determine whether the ball hit towards the fence would clear it, we need to use the laws of projectile motion. Assuming the ball was hit at an angle of 45 degrees, we can calculate the maximum height it would reach using the following formula:
h = (\(v^{2}\) * \(sin^{2} \alpha\)) / (2g)
where h is the maximum height, v is the initial velocity, \(\alpha\) is the launch angle, and g is the acceleration due to gravity (9.8 m/\(s^{2}\)).
Since we know the distance the ball traveled (130 feet), we can use the following formula to calculate the initial velocity:
d = \(v^{2}\) * sin(2\(\alpha\)) / g
where d is the distance, v is the initial velocity, \(\alpha\) is the launch angle, and g is the acceleration due to gravity (9.8 m/\(s^{2}\)).
Converting the distance and height to meters (since the formula uses SI units), we have:
d = 130 * 0.3048 = 39.624 m
h = 7.62 m (assuming a 45 degree launch angle)
Using the second formula, we can solve for the initial velocity:
v = \(\sqrt{dg/sin2\alpha }\) = \(\sqrt{39.624*9.8/sin(90)}\) = 28.07 m/s
To determine whether the ball would clear the fence, we need to calculate the height of the fence in meters:
fence_height = 25 * 0.3048 = 7.62 m
If the maximum height of the ball is greater than or equal to the height of the fence, then it would clear the fence. In this case, since the maximum height is 7.62 m and the fence height is also 7.62 m, the ball would just clear the fence if it was hit directly towards it at a launch angle of 45 degrees. However, if the ball was hit at a different angle or with a different initial velocity, the outcome could be different.
Correct Question:
There is a 25ft fence, 130 feet away from where the ball was hit. If the ball was hit towards the fence, would it be high enough to clear the fence?
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determine whether each statement is true or false. you have one submission for each statement. (a) if p denotes the equilibrium price, then the consumer surplus at any price higher than p must be less than or equal to the consumer surplus at price p. true false (b) if p denotes the equilibrium price, then the producer surplus at any price lower than p must be less than or equal to the producer surplus at price p. true false
Answers
Both statements are false. Consumer surplus decreases when the price is increased above the equilibrium, and producer surplus decreases when the price is decreased below the equilibrium.
(a) False.
The statement is not necessarily true. Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. At the equilibrium price, consumer surplus is maximized. However, if the price is increased above the equilibrium price, consumer surplus will generally decrease.
This is because as the price increases, fewer consumers are willing to purchase the good or service, resulting in a decrease in consumer surplus. T
herefore, at any price higher than the equilibrium price, the consumer surplus will generally be less than the consumer surplus at the equilibrium price.
(b) False.
Similar to the previous statement, the statement is not necessarily true. Producer surplus is the difference between the price producers receive for a good or service and the minimum price they are willing to accept. At the equilibrium price, producer surplus is maximized.
However, if the price is decreased below the equilibrium price, producer surplus will generally decrease. This is because as the price decreases, fewer producers are willing to supply the good or service, resulting in a decrease in producer surplus.
Therefore, at any price lower than the equilibrium price, the producer surplus will generally be less than the producer surplus at the equilibrium price.
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Can you answer please ASAP
Answers
There are 400 fish in a large tank. Model, then write an expression to find thenumber of fish in the tank if the number of fish increases by 23%.
Answers
Let x be the total number of fish in the tank.
We know that at the beggining we had 400 fish and that then the number increased by 23%, this means that the total number of fish are:
\(\begin{gathered} x=400+400\cdot0.23 \\ x=400(1+0.23) \\ x=400(1.23) \end{gathered}\)Therefore the nynumber of fish at the end is:
\(x=400(1.23)\)You walk quickly to your friend’s house, which is half of the way between your house and the school. You wait a few minutes for your friend to get ready. You then walk slowly with your friend the rest of the way to school. Which of the graphs matches this situation?
Answers
Answer:
I think B fits best :)
Step-by-step explanation:
hope this was helpful
(17x + 21)
123
need the answer asap
Answers
plz help me this one is a lil tough
Answers
Answer:
100 degrees
Step-by-step explanation:
It's going through 140 and 40, 180 - 40 = 140
180 cause a flat line is 180 degrees
Answer:
140*
Step-by-step explanation:
the line is pointing through 40* and 100* which makes it that.
hope this helps! have a good day and stay safe!
id like brainliest but if not its ok!
(i got it wrong the first time but once i looked at it more i found it out)
A group of randomly selected Clyde Marketing employees were asked what their most common form of transportation is. The bar graph below shows the results of the survey. There are 275275275 employees at Clyde Marketing.
Answers
Answer:
88 would be the answer maybe.....
Answer:
88
Step-by-step explanation:
6)
Manuel found a wrecked Trans-Am that he could fix. He
bought the car for 65% of the original price of $7200.
What did he pay for the car? (Round to nearest dollar)
Show how you got the answer
Answers
Answer:
$4680
Step-by-step explanation:
65% of 7200 equals 4680.
Answer:
He payed 4,680
Step-by-step explanation:
multiply 7200 by .65
7200 * .65 = 4,680
*Brainliest* What is the value of X?
or how do I solve this equation?
Answers
Answer:
x = 6
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360
69+111+12x-3 +111 = 360
Combine like terms
12x+288=360
Subtract 288 from each side
12x+288-288 = 360-288
12x = 72
Divide by 12
12x/12 = 72/12
x = 6
Answer:
x = 6
Step-by-step explanation:
All angles together equal 360
Us this to set up your formula
360 = 111 + 111 + 69 + 12x-3
360 = 288 + 12 x
360 - 288 = 12x
72 = 12x
72/12 = x
6 = x
You could also use the fact that angle t and r are equal to set your formula up as
69 = 12x-3
69+3=12x
72=12x
72/12=x
6=x
Through: ( -1,5), parallel to y=-2x+1
Answers
Answer:
y = -2x + 3
Step-by-step explanation:
Parallel Lines:Parallel lines are lines with the same slope (m), but a different y - intercept (b).
The basic equation of a line is y = mx + b, where m represents slope, and b represents the y - intercept
Solving for the Line:First solve for the parallel slope of -2
Parallel slope to -2 = -2
Next, input the x and y values given to you by the point to the equation
y = -2x + b
We will input the -1 and 5 for x and y in the equation y = -2x + b
5 = -2(-1) + b
5 = 2 + b
b = 3
The line is y = -2x + 3
-Chetan K
Antonio ate 1/4 of a box of cereal, Jamie ate 1/8 of the box, and Marianna ate 8/16 of it. What is this situation about?
Answers
The box's dimensions are (2/8 + 1/8 + 8/16) = (4/16 + 2/16 + 8/16) = 14/16, which is reduced to 7/8.
what is unitary method ?Mathematicians utilize the unitary approach to solve issues involving direct proportion. Finding the value of a single unit of a quantity and then utilizing that value to calculate the value of any other number of units is what this process entails. If 10 apples cost $5, for instance, you may calculate the price of a single apple by dividing the total cost by the number of apples, which is $0.50. The cost of one unit of apples is defined as $0.50 per apple. We can easily calculate the price of 6 apples by
given
Three persons (Antonio, Jamie, and Marianna) are sharing a box of cereal and each is consuming a specific amount of the box in this scenario. They reported eating 1/4, 1/8, and 8/16 in fractions.
We can see that 1/4 and 2/8 are similar, and 8/16 reduces to 1/2, thus making the fractions easier to understand. The quantity they consumed can therefore be stated as:
Antonio consumed 2/8 of the box, leaving only 1/4 remaining.
Jamie ate a quarter of the box.
Marianna ate 1/2 of the box
The three of them consumed a combined total of:
The box's dimensions are (2/8 + 1/8 + 8/16) = (4/16 + 2/16 + 8/16) = 14/16, which is reduced to 7/8.
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Find domain‼️ look at image
Answers
Based on the given graph, the domain of the function can be expressed as [-5, 2], indicating that the function is defined for x-values within this interval.
The graph described features a straight line segment connecting the points (2, 2) and (0, 4), representing a linear relationship. Additionally, there is a curved line segment passing through (0, 3) and intersecting the x-axis at (-2.5, 0), extending to (-5, -10), indicating a nonlinear relationship.To determine the domain of the function represented by the graph, we need to identify the range of x-values for which the function is defined. In this case, it appears that the graph spans from x = -5 to x = 2, inclusive. This means that any x-value within this interval will have a corresponding y-value on the graph. However, beyond this range, there is no indication of the function's behavior or defined values.Therefore, based on the given graph, the domain of the function can be expressed as [-5, 2], indicating that the function is defined for x-values within this interval.
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The graph of the function 1/67 f(x) can be obtained from the graph of y=f(x) by one of the following actions: horizontally stretching the graph of f(x) by a factor 67 horizontally compressing the graph of f(x) by a factor 67 vertically stretching the graph of f(x) by a factor 67 vertically compressing the graph of f(x) by a factor 67 Question Help: Video D Post to forum
Answers
The graph of the function 1/67 f(x) can be obtained from the graph of y=f(x) by vertically compressing the graph of f(x) by a factor 67.
When we have a function of the form y = k * f(x), where k is a constant, it represents a vertical transformation of the graph of f(x). In this case, we have y = (1/67) * f(x), which means the graph of f(x) is vertically compressed by a factor of 67.
To understand why this is a vertical compression, let's consider an example. Suppose the graph of f(x) has a point (a, b), where a is the x-coordinate and b is the y-coordinate. When we multiply f(x) by (1/67), the y-coordinate of the point becomes (1/67) * b, which is much smaller than b since 1/67 is less than 1. This shrinking of the y-coordinate values causes a vertical compression of the graph.
By applying this vertical compression to the graph of f(x), we obtain the graph of 1/67 f(x). The overall shape and features of the graph remain the same, but the y-values are compressed vertically.
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Please help due tonight.
Answers
Answer
A
Step-by-step explanation:
Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank? (1000 cubic cm = 1 liter).
Answers
The height of the water tank of the air cooler brought by Anu is 40 cm.
What is the meaning of Height?Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.
given,
Length = 50 cm
Width = 20 cm
Maximum tank volume = 40 liters = 40,000 cm3
Tank height?
Steps,
Tank volume = length x width x height
40,000 = 50 x 20 x height
40,000 = 1000 x height
Tank height = 40,000 : 1000
Tank height = 40 cm
So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.
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A diver leaps from the edge of a diving platform into a pool below. The figure shows the initial position of the diver and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver's shoulders is given by xXt and the vertical distance from the water surface to her shoulders is given by t), where x(t) and yt) are measured in meters. Suppose that the diver's shoulders are 11.4 meters above the water when she makes her leap and that d0.8 and dar 3.6 9.8t for Os ts A, where A is the time that the diver's shoulders enter the water. image y0) Note: Figure not drawn to scale Question 1 (3 points) Find the maximum vertical distance from the water surface to the diver's shoulders. Question 2 (2 points) Find A, the time that the diver's shoulders enter the water Question 3 (2 points) Find the total distance traveled by the diver's shoulders from the time she leaps from the platform until the time her shoulders enter the water. Question 4 (2 points) Find the angle e. 0くθ 〈 π , between the path of the diver and the water at the instant the diver's shoulders enter the water.
Answers
A- The maximum vertical distance from the water surface to the diver’s
shoulders are 12.061 meters.
B- The time that the diver’s shoulders enter the water is 1.936 seconds.
C- The total distance traveled by the diver’s shoulders from the time
she leaps from the platform until the time her shoulders enter the water is 12.946 meters.
D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.
A-
\(\frac{dy}{dx} =0\) only when \(t=0.36735\). Let \(b=0.36735\)
The maximum vertical distance from the water surface to the diver’s
shoulders is y(b)=11.4 + \(\int\limits^b_0 \frac{dy}{dT} dt = 12.061\) meters.
B-
\(y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0\)
when A= 1.936 seconds.
C-
\(\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m\)
At time A, dy/dx = \(\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913\)
D- The angle between the path of the diver and the water is \(tan^{-1} (19.21913) = 1.518 or 1.519\)
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what is the x and y intercept of y= -2x - 21 ?
Answers
Answer:
To find the x-intercept of a linear equation in the form y = mx + b, we set y = 0 and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.
For the equation y = -2x - 21, to find the x-intercept, we set y = 0 and solve for x:
0 = -2x - 21
2x = -21
x = -21/2
So the x-intercept is (-10.5, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = -2(0) - 21
y = -21
So the y-intercept is (0, -21).
Step-by-step explanation:
the x-intercept of the equation y = -2x - 21 is (-21/2, 0) and the y-intercept is (0, -21). These two points are important in graphing the line defined by this equation.
How to solve the question ?
To find the x-intercept and y-intercept of the linear equation y = -2x - 21, we need to understand what these intercepts represent.
The x-intercept is the point where the graph of the equation crosses the x-axis, meaning that y is equal to zero. In other words, it is the value of x where the line intersects with the x-axis. Conversely, the y-intercept is the point where the graph of the equation crosses the y-axis, meaning that x is equal to zero. It is the value of y where the line intersects with the y-axis.
To find the x-intercept, we set y equal to zero and solve for x:
0 = -2x - 21
2x = -21
x = -21/2
Therefore, the x-intercept is (-21/2, 0).
To find the y-intercept, we set x equal to zero and solve for y:
y = -2(0) - 21
y = -21
Therefore, the y-intercept is (0, -21).
To summarize, the x-intercept of the equation y = -2x - 21 is (-21/2, 0) and the y-intercept is (0, -21). These two points are important in graphing the line defined by this equation. The x-intercept tells us where the line crosses the x-axis, while the y-intercept tells us where the line crosses the y-axis. Knowing these intercepts allows us to draw the line more accurately and understand its behavior in different regions of the coordinate plane.
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6. The table below represents the number of
donut holes per box at Damon's Donuts. What
is the median number of donut holes?
# OF DONUT
HOLES
22
23
24
25
FREQUENCY
1
2
3
2
A. 23
B. 23.75
C. 24
D. 24.5
Answers
First you add the first frequency with the first number of donut holes then keep adding the frequencies on top of that giving you 48 then divide by 2 giving you 24
solve t^2y'+2ty-y^3=0
Answers
The general solution to the given differential equation is
y = ± √(1 / (2ln|t| + 4/t - C2))
Solution to the differential equationTo solve the given differential equation, we can use the method of separable variables. Let's go through the steps:
Rearrange the equation to separate the variables:
t^2y' + 2ty - y^3 = 0
Divide both sides of the equation by t^2:
y' + (2y/t) - (y^3/t^2) = 0
Now, we can rewrite the equation as:
y' + (2y/t) = (y^3/t^2)
Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:
(1/y^3)dy = (1/t - 2/t^2)dt
Integrate both sides of the equation:
∫(1/y^3)dy = ∫(1/t - 2/t^2)dt
To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.
-1/2 ∫du = ∫(1/t - 2/t^2)dt
-1/2 u = ln|t| + 2/t + C1
-1/2 (y^(-2)) = ln|t| + 2/t + C1
Multiply through by -2:
y^(-2) = -2ln|t| - 4/t + C2
Now, take the reciprocal of both sides to solve for y:
y^2 = (-1) / (-2ln|t| - 4/t + C2)
y^2 = 1 / (2ln|t| + 4/t - C2)
Finally, taking the square root:
y = ± √(1 / (2ln|t| + 4/t - C2))
Therefore, the general solution to the given differential equation is:
y = ± √(1 / (2ln|t| + 4/t - C2))
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What is the final amount if 784 is decreased by 1% followed by a 4% increase?
Give your answer rounded to 2 DP.
Answers
Answer:
The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
Step-by-step explanation:
General Formula
A way to solve this problem is as follows:
The general formula for this is taking into account that:
\( \\ percent\;change = \frac{change}{starting\;point}\)
The starting point is number 784.
The most important key is the solution for this answer is that:
\( \\ change = starting\;point - x\)
Where x is a number that we need to find. Then
\( \\ percent\;change = \frac{starting\;point - x}{starting\;point}\) [1]
Is 784 increased or decreased after all?
We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.
Finding the result
If 784 increases by 3%, we have:
\( \\ 3\% = \frac{784 - x}{784}\)
Which is equal to
\( \\ 0.03 = \frac{784 - x}{784}\)
Solving for x, we first multiply by 784 to both sides of the previous formula:
\( \\ 0.03 * 784 = \frac{784 - x}{784}*784\)
\( \\ 0.03 * 784 = (784 - x)*\frac{784}{784}\)
\( \\ 0.03 * 784 = (784 - x)*1\)
\( \\ 0.03 * 784 = (784 - x)\)
Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.
Subtracting 784 to both sides:
\( \\ (0.03 * 784) - 784 = (784 - 784 - x)\)
\( \\ (0.03 * 784) - 784 = (0 - x)\)
\( \\ (0.03 * 784) - 784 = - x\)
\( \\ 23.52 - 784 = - x\)
\( \\ -760.48 = - x\)
Multiplying by -1 to both sides:
\( \\ -1 * (-760.48) = -1 * (-x)\)
We have to remember that:
\( \\ +*+ = +; - * - = +; - * + = -; + * - = -\)
\( \\ 760.48 = x\)
Then
\( \\ x = 760.48\)
Therefore, using formula [1], an increase of 3% is
\( \\ 3\% = \frac{784 - 760.48}{784}\)
\( \\ change = 784 - 760.48\)
\( \\ change = 23.52\)
Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.
As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
In a more terse way of solving this problem, we can say that:
Increase of 4% = 784 * 0.04 = 31.36.
Decrease of 1% = 784 * 0.01 = 7.84.
Difference = 31.36 - 7.84 = 23.52.
Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).