Algebra Word Problem Solutions

A woodworker wants to cam at least $$ 20$ an hour making and for materials, Write and solve un inequality that represents how many hours the woodworker can spent building the cabinet.
Given: The price for raw material is $125.
The selling price of cabinet is $500

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or $x_1,x_2,x_3,x_4$  x as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\\ 0& 0& 2\end{array}\right]$

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or $x_1,x_2,x_3,x_4$ x ​ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $\left[\begin{array}{ccccc}1& 0& 0& 0& 1\\ 0& 0& 0& 1& 0\\ 2& 3& 1& 2& 0\end{array}\right]$

Order the following decimals from least to greatest (separated by commas). 0.22, 0.67, 0.33, 0.6, 0.43

Compare the decimals.
8.86_________8.65

The value of expression ${\displaystyle -2{\left(27\right)}^{\frac{2}{3}}}$.

The value of expression ${\displaystyle {(-3)}^{-2}}$

To write and solve the system of linear equations to find the price of 1 cup of dried fruit and 1 cup of almonds.
Given: A small bag of trail mix contains 3 cups of driedd fruit and 4 cups of almonds. A large bag contains ${\displaystyle 4\frac{1}{2}}$ cups of dried fruit and 6 cups of almonds.

On a trip, the total distance (in miles) you travel in x hours is represented by the piccewise function.
$d(x)=\{\begin{array}{ll}55x,& if0\le x\le 2\\ 65x-20,& if2<x\le 5\end{array}$
How far do you travel in 4 hours?

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car.

Antiderivatives of radical function and explain the solution
${\displaystyle \int (3\sqrt{x}+7)dx}$

TD Canada Trust discovers that the estimated proportion of clients defaulting on a loan, if the interest rate is lower than${\displaystyle 15\mathrm{\%}}$ , is 0.34. They also discover that the estimated proportion of clients defaulting on a loan, given the interest is greater than or equal to ${\displaystyle 15\mathrm{\%}}$ , is 0.52.
a) What is the odds ratio of defaulting given the interest rate is greater than or equal to ${\displaystyle 15\mathrm{\%}}$ relative to the interest rate is lower than ${\displaystyle 15\mathrm{\%}}$? Interpret this odds ratio.
b) If we were to analyze this data using the following logistic regression model, what are the estimates of ${\displaystyle {\beta }_0}$ and ${\displaystyle {\beta }_1}$? Showyourwork.
l${\displaystyle \log (\frac{p}{1}-p)={\beta }_0+{\beta }_{1}x}$
(Where p is the probability of defaulting on a loan and x is an indicator variable that is 1 when the interest rate is greater than or equal to ${\displaystyle 15\mathrm{\%}}$ and 0 when the interest rate is less than ${\displaystyle 15\mathrm{\%}}$)

The number of full-time and part-time employees of an online retailer increased exponentially from 69 thousand in 2011 to 306.9 thousand in 2016.
a) Let ${\displaystyle t=0}$ correspond to 2011 and ${\displaystyle t=5}$ correspond to 2016. Then t is the number of years after 2011. Use the data points (0,69) and (5,306.9) to find the exponential growth rate and fit an exponential growth function ${\displaystyle P\left(t\right)=P_0{e}^{kt}}$ to the data, where P(t) is the number of employees, in thousands, t years after 2011.
b) Use the function found in part (a) to estimate the number of employees in 2017.
c) According to this model, when will there be one million employees?
a) P(t)=?

Exponential and Logarithmic Equations Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to two decimals.
${\displaystyle {\log }_8(x+5)-{\log }_8(x-2)=1}$

Find a recurrence relation satisfied by this sequence.
${\displaystyle a_n=3}$

Identify the steeper line. y = 3x + 4 or y = 6x + 11

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

${\displaystyle \tan (t+\pi )=}$___, and ${\displaystyle \cot (t+\pi )=}$___, so the tangent and cotangent functions are___functions.The period of each of these functions is___.

Find the distance between ${\displaystyle (3\sqrt{3},\sqrt{5})}$ and ${\displaystyle (-\sqrt{3},4\sqrt{5})}$ pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.

Evaluate the radical expression, and express the result in the form a + bi.
${\displaystyle \sqrt{\frac{-81}{16}}}$