Algebra Word Problem Solutions

$$\begin{gathered} 1.17-<!--\; -\; -->5\times <!--\; \times \; -->4+2 \\ 2.40-<!--\; -\; -->32+8+5\times <!--\; \times \; -->-<!--\; -\; -->2 \\ 3.35-<!--\; -\; -->14+2+8^2 \\ 4.(4-<!--\; -\; -->7{)}^2-<!--\; -\; -->6\times <!--\; \times \; -->7+20 \end{gathered}$$

How to convert between Sum Of Products and Product of sums?
Boolean expression.
For instance, $F=a{b}^{\prime }+ad+c^{\prime }d+d^{\prime }$.
I try to get F complement , i.e. F'. But I got: $F^{\prime }=b^{\prime }d+a{c}^{\prime }{d}^{\prime }$.
How tp get the Product of sums form of F?

Find out how many odd prime numbers are between $1$ to $100$ ?

$2^{2x}=2^3$ find value of x

Justin has two times as many books as Rochelle does, and Rochelle has four less than triple the number of books that John does. If John has n books, write an expression for the number of books that Justin has.

Use logarithmic differentiation to find $\frac{dy}{dx}$ for the following function
$y=(x-<!--\; -\; -->2{)}^{x+1}$

Two bicycle tires are set rolling with the same initial speed of 3.10 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes a distance of 18.3 m; the other is at 105 psi and goes a distance of 94.0 m. Assume that the net horizontal force is due to rolling friction only and take the free-fall acceleration to be g 9.80 m/s.

Graph $y=1+\frac{1}{2}\cot <!--\; \; -->(2x-<!--\; -\; -->3\mathrm{\pi <!--\; \pi \; -->})$ over a one-period interval

Simplify the complex fraction
$\frac{\frac{4}{x+3}}{\frac{1}{x}+3}$
A. $\frac{12x+4}{x^2+3x}$
B.$\frac{4x}{3x+9}$
C. $\frac{4x}{3x^2+10x+3}$
D. none of the above

For the equations given below, which statement is true?
$$\begin{gathered} -<!--\; -\; -->2x=14 \\ 6x=-<!--\; -\; -->42 \end{gathered}$$
A. The equations do not have the same solution because the second equation can never be obtained when multiplying the first equation by any value.
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.
C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by 3.
D. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −4.

Why is $f(x+h)=f(x)+h{f}^{\prime }(x)+O(h^2)$ ?

when $x=-<!--\; -\; -->1$, what is the value of y?

Mary wants to have an average of $80$ for his $4$ exams. Each exam is scored on a scale of $0$ to $100$. His first three exam scores are: $87,72,85$. What does Mary need to score on the 4th exam to have a mean of $80$ on all $4$ exams?

Is the fraction $\frac{1}{3}$ equivalent to a terminating decimal or a decimal that does not terminate?

If f(x)=(x^(m)+9)^(2), which statement about f(x) is true?
f(x) is an even furiction for all values of m.
f(x) is an even function for all even values of m.
f(x) is an odd function for all values of m.
f(x) is an odd function for all odd values of m.

Let $X_1,X_2,...,X_{n_x}\sim <!--\; \sim \; -->N({\mathrm{\mu <!--\; \mu \; -->}}_x,{\mathrm{\sigma <!--\; \sigma \; -->}}^2)$ and $Y_1,Y_2,...,Y_{n_Y}\sim <!--\; \sim \; -->N({\mathrm{\mu <!--\; \mu \; -->}}_Y,{\mathrm{\sigma <!--\; \sigma \; -->}}^2)$ where $X_i$ and $Y_j$ are independent for all i and j. Findthe distribution of
$\frac{1}{{\mathrm{\sigma <!--\; \sigma \; -->}}^2}[(n_x-<!--\; -\; -->1)S_x^2+(n_y-<!--\; -\; -->1)S_Y^2]$

The image of the unit circle under the mapping below and is parameterized as $x=\cos <!--\; \; -->(t)$ and $y=\sin <!--\; \; -->(t),t$ element of the real number is?
$f=\{x^{\prime }=4x+2y;y^{\prime }=-<!--\; -\; -->x+2y\}$

Two numbers multiply to -24 and add up to -5

Which formula can be used to describe the sequence $-<!--\; -\; -->2\frac{2}{3},-<!--\; -\; -->5\frac{1}{3},-<!--\; -\; -->10\frac{2}{3},-<!--\; -\; -->21\frac{1}{3},-<!--\; -\; -->42\frac{2}{3}$

28 + 8x = 8(x + 3) + 2
What is x?