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2 years ago

John received $300 for his birthday he buys 4 DVDs at $12.95 each. Sales tax is 6.5% how much birthday money does he have left

Mathematics

1 answer:

joja [24]2 years ago

4 0

Answer: $244.83

Step-by-step explanation:

First find the original amount spent on dvds:

$12.95 * 4 = $51.80

Then, the sales tax (6.5% is converted to decimal form by dividing by 100):

$51.80 * 0.065 = $3.367

Add the sales tax to the original amount to get the total amount spent:

$51.80 + $3.367 = $55.167

Round to the nearest hundredth:

$55.167 -> $55.17

Subtract the total amount from the money received for his birthday:

$300 - $55.17 = $244.83

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Find the mass at time t=0. ANSWER HAS TO BE IN GRAMS

777dan777 [17]

For part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c) 20 years.

<h3>What is exponential decay?</h3>

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an equation for radioactive decay:

$\rm m(t) = 400e^{-0.035t}$

a) Plug t = 0

$\rm m(0) = 400e^{-0.035\times 0}$

m(0) = 400 grams

b) plug t = 20 years

$\rm m(20) = 400e^{-0.035\times 20}$

After solving:

m(20) = 198.63 grams

c) Plug m(t) = m(0)/2 = 400/2 = 200 grams

$\rm 200 = 400e^{-0.035t}$

x = 19.80 years ≈ 20 years

Thus, for part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c) 20 years.

Learn more about the exponential decay here:

brainly.com/question/14355665

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3 0

1 year ago

The first one TO GET IT CORRECT will get brainliest plus 11 points :)

olya-2409 [2.1K]

Answer:

6 x 2.5 = 15

8 x 2.5 = 20

L x W = 300 square units

Step-by-step explanation:

Brainliest?

4 0

2 years ago

I need help with math

aksik [14]

Well what is the problem ?

8 0

3 years ago

Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$