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3 years ago

Mike buys breakfast for $8.23. If sales tax is 9%, how much does he pay in tax? How much does he pay in total?

Mathematics

1 answer:

Lina20 [59]3 years ago

4 0

Answer:

9% of $8.23=

0.09x$8.23=$0.74 (tax)

$8.23+$0.74=$8.97 (total)

Step-by-step explanation:

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What is 1 1/3 as a improper fraction

Mumz [18]

Okay so for this all you have to do is add 1 to 1/3.

However, to do this you first need to convert 1 into a fraction.

1 = 3/3
3/3 + 1/3 = 4/3

Hope this helps :)

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3 years ago

Solve the system. -3x-y=10; y-4z=-13; x-4y+z=4

kvasek [131]

9514 1404 393

Answer:

(x, y, z) = (-3, -1, 3)

Step-by-step explanation:

Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.

Use the last equation to write an expression for z.

z = 4 -x +4y

Substitute this into the second equation:

y -4(4 -x +4y) = -13

y -16 +4x -16y = -13

4x -15y -3 = 0

In genera form, the first equation can be written as ...

3x +y +10 = 0

Now, the solution to these two equations can be found to be ...

x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"

y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation

z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z

The solution to the system is (x, y, z) = (-3, -1, 3).

_____

<em>Additional comment</em>

Written as an augmented matrix, the system of equations is ...

$\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]$

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3 years ago

Select the correct answer.

Alex73 [517]

C. 7.2°F is warmer than 7.0°F but colder than 7.6°F.

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3 years ago

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

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2 years ago

A radioactive isotope that was originally 275 grams has decayed to 150 grams. the equation shown can be used to calculate the nu

k0ka [10]

Answer: 4.4 years

Step-by-step explanation:

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3 years ago

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