Algebra Word Problem Solutions

Grandma Betty's recipe makes 6 cupcakes and uses $\frac{1}{3}$ of a cup of sugar. How many cups of sugar will it take to make 2 $\frac{1}{2}$ dozen cupcakes?
${\displaystyle a.1\frac{1}{2}\cup s}$
${\displaystyle b.\frac{2}{3}\cup }$
${\displaystyle c.\frac{3}{5}\cup }$
${\displaystyle d.\frac{1}{9}\cup }$

Andreas buys a new ailboat fo $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of ${25}^{\circ }F$. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to ${25}^{\circ }F$. One frozen food case was equipped with the new thermostat, and a random sample of 21 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a $5\mathrm{\%}$ level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)
(a) What is the level of significance?
State the null and alternate hypotheses.
$H0:{?}_1^2={?}_2^2,H1:{?}_1^2>{?}_2^{2}H0:{?}_1^2={?}_2^2,H1:{?}_1^2\ne {?}_2^{2}H0:{?}_1^2={?}_2^2,H1:{?}_1^2<{?}_2^{2}H0:{?}_1^2>{?}_2^2,H1:{?}_1^2={?}_2^2$
(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)
What are the degrees of freedom?
$d{f}_N=?$
$d{f}_D=?$
What assumptions are you making about the original distribution?
The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.
(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.

Solve ${\displaystyle 2\cos 2x-3\sin x=0f\text{or}{0}^{\circ }\le x\le {360}^{\circ }.}$

Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. ${\displaystyle y=a{\left(\frac{3}{2}\right)}^t}$

The difference of two numbers is 3. Their sum is 13. Find the numbers.

Find each unit rate. Kenny reads ${\displaystyle \frac{5}{8}}$ page in ${\displaystyle \frac{2}{3}}$ minute.

Elleana is planning to join a DVD club and is investigating the options for membership. Option 1 is a $20 membership fee and $1.25 rental charge for each DVD rented. Option 2 has no rental fee and charges $2.50 for each DVD rented. How many DVDs would Elleanna have to rent in order for the total cost of Option 1 to be equal to Option 2?

${\displaystyle \frac{2x-5}{\sqrt{x+5}}}$

Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. ${\displaystyle \sqrt[5]{x^{20}{y}^{-4}}}$

Solve the equations for x and simplify the answer if possible. Indicate which solving technique is used, Linear, Factor, SRP ZPR, QF.
$\frac{1}{6}(\frac{3}{4x}-2)=\frac{-1}{5}$

In 1995 the population of a certain city was 34,000. Since then, the population has been growing at the rate of 4% per year.
a) Is this an example of linear or exponential growth?
b) Find a function f that computes the population x years after 1995?
c) Find the population in 2002

Fill in the bla?

An equation that expresses a relationship between two or more variables, such as $H=\frac{9}{10}(20-a)$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $\left[\begin{array}{ccccc}1& 0& -1& 3& 9\\ 0& 1& 2& -5& 8\\ 0& 0& 0& 0& 0\end{array}\right]$

Solve the following systems of equations.
${\displaystyle x^2+y^2-19x+y+66=0}$
x−y−3=0

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.
${\displaystyle 3y^3+24y^2+9y}$

Consider that math modeling following initial valu problem
${\displaystyle \frac{dy}{dt}=3-2t-0.5y,y\left(0\right)=1}$
We would liketo find an approximation solution with the step size $h=0.05$
What is the approximation of $y(0.1)?$

Franco begins to save for a new Lego set that costs $65. His parents gave him $35 towards the cost and he plans to save $5 per week. Define all unknown variables. Write an equation modeling the total amount he has saved.

Quadratic equation solve $x2+2x-8=0$