Algebra Word Problem Solutions

Ina recipe for tomato sauce, the ratio of fluid ounces of water to fluid ounc. of tomato paste is 3 : 4. You plan to make 35 fluid ounces of tomato sauce. Tow many fluid ounces of tomato paste do you need?

Use Exponential Models in Applications
Elise invests $4500 in an account that compounds interest monthly and earns 6%. How long will it take for her money to double?

Need to calculate:The value of g(5) from the function $g(x)=\{\begin{array}{l}x-5ifx\le 5\\ 3xifx>5\end{array}$

What are two advantages of using meters as a measurement of length than old measurements of length such as hands or steps

Determine whether the statement makes sense or does not make sense, and explain your reasoning : By modeling attitudes of college freshmen from 1969 through 2013, I can make precise predictions about the attitudes of the freshman class of 2040.

Solve the equation:
${\displaystyle 9^x-3^{x+1}+1=0}$

f​ increased by 45 is equal to 88

A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio $x_1$
(in $) and the amount spent advertising in the newspaper $x_2$ (in $) according to $y=a{x}_1+b{x}_2+c$
The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.
$\begin{array}{|ccc|}\hline \text{ Advertising, }{x}_1& \text{ Advertising, }{x}_2& \text{sales, y}\\ \$2400& \$800& \$36,000\\ \$2000& \$500& \$30,000\\ \$3000& \$1000& \$44,000\\ \hline\end{array}$
a) Use the data to write a system of linear equations to solve for a, b, and c.
b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.
c) Write the model $y=a{x}_1+b{x}_2+c$
d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

Sandy is upgrading her Internet service. Fast Internet charges $15 for installation and $56.45 per month. Quick Internet has free installation but charges $58.95 per month. Complete the equation that can be used to find the number of months after which the Internet service would cost the same. Use the variable x to represent the number of months of Internet service purchased.

For the following system of homogeneous linear equations, find the solution if it is unique, otherwise, describe the infinite solution set in terms of an arbitrary parameter k. 4x-2y+6z=0 5x-y-z=0 2x-y+3z=0

Let G be a group. Show that ${\displaystyle G\ne qH\cup KG=H\cup K}$ for any two subgroups ${\displaystyle H\le GH\le G\text{and}K\le GK\le G}$.

Use the two-way table to create a two-way table that shows the joint and marginal relative frequencies.
$\underline{\begin{array}{cc}\text{Class }& \text{Gender}\\ & \text{Male}& \text{Female}& \text{Total}\\ \text{Sophomore}& 26& 54& 89\\ \text{Junior}& 32& 48& 80\\ \text{Senior}& 50& 55& 105\\ \text{Total}& 108& 157& 265\end{array}}$

Given that Domain of the rational function is all real numbers.
So the rational function should not contain denominator part.

Consider that algebraic modeling Identify the decay factor, if any, for each function. If there is no decay factor, type N.
1) ${\displaystyle y={0.8}^x}$
2) ${\displaystyle y=-3x-8}$
3) ${\displaystyle g\left(x\right)={\left(\frac{1}{2}\right)}^x}$

Let P be an approximation of pai accurate to n decimals. Show that $P+\sin P$ gives an approximation correct to 3n decimals.
(Hint: Let $P=p+x$.)

Explain how simple regression modeling can be extended to understand the relationship among several variables?

Express each of the following pairs of signed numbers as absolute values and subtract the smaller absolute value from the larger absolute value.
c.-6,+6