Kim buys a new shirt for $25.50. She has to pay 8% sales tax. How much tax will be paid?

Mathematics

1 answer:

Ainat [17]2 years ago

4 0

Tax she will pay would be $2.04

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1 point) Are the functions f,g, and h given below linearly independent? f(x)=e3x+cos(5x), g(x)=e3x−cos(5x), h(x)=cos(5x). If the

Fynjy0 [20]

Answer:

Functions are linearly dependent (are not linearly independent.)

Step-by-step explanation:

Remember that two functions f(x), g(x) and h(x) are said linearly independent on an interval I if the only solution to the equation

$\alpha f(x)+\beta g(x)+\omega h(x)=0, \ \text{for all } x\in I$

is the trivial one: α = 0, β = 0, ω = 0. If they are not linearly independent, they are called linearly dependent.

Now, let f(x), g(x) and h(x) be the functions:

$f(x)=e^{3x}+\cos(5x),$

$g(x)=e^{3x}-\cos(5x),$

$h(x)=\cos(5x).$

Then, letting α = 1, β= -1 and ω = -2, we see that:

$\alpha f(x)+\beta g(x)+ \omega h(x)=e^{3x}+\cos(5x)-e^{3x}+\cos(5x)+2\cos(5x)=0.$

Hence, the functions f(x), g(x) and h(x) are not linearly independent, or equivalently, are linearly dependent.

8 0

3 years ago

Gas prices in shelby county are at $3.00 per gallon. if a market scientist predicts a 40% increase in the price of gas in the co

aleksley [76]

Answer-

The price of gas will be $4.2

Solution-

Gas prices in shelby county = $3.00 per gallon

Market scientist predicts a 40% increase in the price of gas in the coming month.

So the new price will be,

$=3+(3\times \dfrac{40}{100})$

$=3+(3\times 0.4)$

$=3+1.2$

$=4.2$

Therefore, the price of gas will be $4.2

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3 years ago

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$\left\begin{array}{ccc}24=3\cdot8\\12=3\cdot4\end{array}\right\}24\cdot12=3\cdot8\cdot3\cdot4\\\\\\\left\begin{array}{ccc}24=144:6\\12=36:3\end{array}\right\}24\cdot12=144:6\cdot36:6\\\\\\\left\begin{array}{ccc}24=96:4\\12=48:4\end{array}\right\}24\cdot12=96:4\cdot48:4\\\\\\\left\begin{array}{ccc}24=16+8\\12=9+3\end{array}\right\}24\cdot12=(16+8)\cdot(9+3)\\sequence\ of\ key:16+18=M+;\ 9+3=\times MR=\\\\\\$