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Questions in mathematics

[Done] Use long division to find the quotient below. $\left(15 x^3+2 x^2-75\right)-(3 x-5)$ A. $5 x^2+9 x+15$ B. $5 x^2+12 x+15$ C. $5 x^2-12 x+15$ D. $5 x^2-9 x+15$

[Done] $2 \frac{1}{4} \cdot 3 \frac{5}{9}$

[Done] Simplify the following expression: [tex]x^7-\frac{27 x^4}{x^3}[/tex]

[Done] Solve the following: 1625 x 10 25836 x 100 93645 x 1000 34658 x 28 9875 x 45 4839 x 645 46575 x 23 54392 x 374 30395 x 723 4700 ÷ 10 23400 ÷ 100 8000 ÷ 1000 6342 ÷ 76 93634 ÷ 86 84500 ÷ 83

[Done] Maximize P = 7x + y Subject to the following constraints: 2x + y ≤ 150 4x + 3y ≤ 350 x + y ≥ 80 x, y ≥ 0

[Done] Shania is buying a car. She has narrowed her choice down to three cars: a sedan, a hatchback, and a wagon. She uses a spinner divided into three colored sections to decide which car to buy. She first spins the spinner 75 times to check the frequencies that it produces. Her results are shown in the table. | Car | Spinner Color | Times Result Occurred | | --------- | ------------- | ----------------------- | | sedan | red | 11 | | hatchback | blue | 22 | | wagon | green | 42 | Which statement is true based on the results in the table? A. All the outcomes are equally likely because their relative frequencies are similar. B. All the outcomes are equally likely because the relative frequencies of landing on at least two colors are similar. C. All the outcomes are not equally likely because there is a variation in their relative frequencies. D. All the outcomes are not equally likely because the spinner color is not a valid representation of the car color. E. All the outcomes are not equally likely because the relative frequency of landing on red is the least.

[Done] If [tex]g(x)=\frac{5 x-3}{2 x+1}, x \neq \frac{-1}{2}[/tex], find [tex]g^{-1}(x)[/tex] and [tex]g^{-1}(2)[/tex].

[Done] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Done] Solve the equation: [tex]$\frac{5-6 y}{3}+\frac{y}{8}=0$[/tex]

[Done] Use the chain rule to solve: [tex]y=\sqrt{3 x^2+4 x-1}[/tex]