Determine the algebraic modeling Solve for x: displaystyle{32}{left({1.05}right)}^{x}={90}

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.

The function ${\displaystyle y=3.5x+2.8}$ represents the cost y (in dollars) of a taxi ride of x miles.
a. Identify the independent and dependent variables.
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

Marcus rowed 20 miles downstream in 2 hours. The trip back, however, took him 4 hours. Find the rate that Marcus rows in still water and the rate of the current. If x is Marcuss

Verify by direct substitution that the given power series is a solution of the indicated differential equation. $[Hint:\text{For a power}{x}^{2n+1}\text{let}k=n+1.]$

$y=\sum _{(n=0)}^{\mathrm{\infty }}\frac{(-1)}{2^{2n}(n!{)}^2}{x}^{2n},x{y}^{n+y^{\prime }}=xy=0$

A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $145(without tax) and that the calculator cost $20 more than four times the cost of the textbook. What was the cost of each item? Let ${\displaystyle x=}$ the cost of a calculator and ${\displaystyle y=}$ the cost of the textbook.

The corresponding modeling system is $\{\begin{array}{l}x+y=145\\ x=4y+20\end{array}$
Solve the system by using the method of substitution and enter the ordered pair.

Which of the following statements is/are correct about logistic regression? (There may be more than one correct answer) Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.

System of linear equations that the augmented matrix represents