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Anuta_ua [19.1K]
2 years ago
12

If the cost of an item increased by a percentage and decreased by the same percentage, what would that percentage be if the new

cost was 84% of the original?
Mathematics
1 answer:
Orlov [11]2 years ago
8 0

The percentage, if the new cost was 84% of the original is 40%

Let the cost of the item be x.

When the price increased by y%, the new price is:

New =x \times (1 + y\%)

When the price decreased by the same percentage (i.e. y%), the new price is:

New =x \times (1 + y\%) \times (1 - y\%)

The cost is said to be 84% of the original price.

So, we have:

x \times (1 + y\%) \times (1 - y\%) =84\% \times x

Divide both sides by x

(1 + y\%) \times (1 - y\%) =84\%

Apply the difference of two squares

1 - (y\%)^2 =84\% \\\\

Subtract 1 from both sides of the equation

- (y\%)^2 =-16\%

Cancel out the common factors

(y\%)^2 =16\%

Take the square root of both sides

y\% =0.4

Multiply both sides by 100

y =40

Hence, the percentage is 40%

Read more about percentage change at:

brainly.com/question/809966

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The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasin
hoa [83]

Answer:

\frac{dI}{dt}=-0.00016 A/s

Step-by-step explanation:

We are given that

By ohm's law

V=IR

R=389 ohm

I=0.03 A

\frac{dV}{dt}=-0.06V/s

\frac{dR}{dt}=0.07ohm/s

We have to find rate of change of current I means \frac{dI}{dt}

Differentiate the equation w.r.t t

\frac{dV}{dt}=\frac{dI}{dt}R+I\frac{dR}{dt}

Substitute the values then we get

-0.06=\frac{dI}{dt}\times 389+0.03\times 0.07

-0.06=389\frac{dI}{dt}+0.0021

-0.06-0.0021=389\frac{dI}{dt}

-0.0621=389\frac{dI}{dt}

\frac{dI}{dt}=\frac{-0.0621}{389}=-0.000160 A/s

Hence, the current I is changing at the rate=-0.00016A/s

4 0
3 years ago
Use a proportion if two cassettes cost $14.50 How much will 15 cost
aev [14]
Cost/(number of cassettes) = $14.50/2 = x/15

Multiply by 15 to solve
   15*($14.50/2) = x = $108.75

15 cassettes will cost $108.75.
8 0
3 years ago
Calvin paints pictures and sells them at art shows. He charges $ 56.25 for a large painting. He charges $25.80 for a small paint
crimeas [40]
He made $ 394.90 because you need to add all the large paintings then the small ones then add them all
6 0
3 years ago
Read 2 more answers
Orwell building supplies' last dividend was $1.75. Its dividend growth rate is expected to be constant at 38.00% for 2 years, af
WITCHER [35]

Answer:

Estimated current stock price is $46.84

Step-by-step explanation:

First we have to find the value of dividend payment t_1, t_2 \& t_3

Given D_0=$1.75

Yearly growth rate for next 2 years( g_1 )=38.00%

D_1=\$1.75\times 1.38=\$2.42

D_2=\$2.42\times1.38=\$3.34

Growth after two years will 6% indefinitely

g_2=6\%=\dfrac{6}{100}=0.06

D_3=\$3.34\times1.06=\$3.54

Estimate of current stock price is

=\dfrac{D_1}{(1+r)}+\dfrac{D_2}{(1+r)^{2}}+\dfrac{\dfrac{D_3}{(r-g_2)}}{(1-r)^{3}}

=\dfrac{\$2.42}{(1.12)}+\dfrac{\$3.34}{(1.12)^{2}}+\dfrac{\dfrac{\$3.54}{(0.12-0.06)}}{(1.12)^{3}}

=$46.84

Estimate of current stock price is =$46.84

3 0
2 years ago
Three-fourths of the tickets had been sold, and there were 420 tickets left. How many tickets were printed?
BabaBlast [244]

Answer: 560 tickets

Step-by-step explanation:

3/4 = 420/x; now cross multiply:

3x = 4(420)

3x = 1,680; now divide both sides by 3, and you get x = 560

3 0
3 years ago
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