Algebra Word Problem Solutions

Use a triple integral to find the volume of the solid bounded by the graphs of the equations. ${\displaystyle z=2-y,z=4-y^2,x=0,x=3,y=0}$

Find the solution ${\displaystyle \log (6x+10)=\frac{\log \left(x\right)}{\log \left(\frac{1}{2}\right)}}$

The table gives the midyear population of Japan, in thousands, from 1960 to 2010.
$\begin{array}{|cc|}\hline \text{Year}& \text{Population}\\ 1960& 94.092\\ 1965& 98.883\\ 1970& 104.345\\ 1975& 111.573\\ 1980& 116.807\\ 1985& 120.754\\ 1990& 123.537\\ 1995& 125.327\\ 2000& 126.776\\ 2005& 127.715\\ 2010& 127.579\\ \hline\end{array}$
Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. [Hint: Subtract 94,000 from each of the population figures. Then, after obtaining a model from your calculator, add 94,000 to get your final model. It might be helpful to choose $t=0$ to correspond to 1960 or 1980.]

Evaluate the line integral ${\displaystyle {\oint }_C\frac{y}{{(x-1)}^2+4y^2}dx+\frac{-(x-1)}{{(x-1)}^2+4y^2}dy}$ where C is circle defined by ${\displaystyle x^2+y^2=27}$

Approximate each expression correct to 4 decimals. ${\displaystyle a)5^{\frac{3}{5}}b)-3^{\sqrt{6}}c)7^{-2.356}}$

For the given fraction and decimals we have to write its equivalent percent. Given fractions are ${\displaystyle a)\frac{3}{25}b)\frac{1}{5}c)\frac{2}{5}}$ And the decimals are, ${\displaystyle d)0.01,e)4.06,f)0.6}$ We have to find its equivalent percent.

Consider the "clock arithmetic" group $(Z_{15},\oplus )$ a) Using Lagrange`s Theotem, state all possible orders for subgroups of this group. b) List all of the subgroups of $(Z_{15},\oplus )$

Solve the Quadratic equation by factorization
${\displaystyle x^2-5x-24=0}$

Use the prime factorizations ${\displaystyle a=2^4\times 3^4\times 5^2\times 7^3\text{and}b=2^2\times 3\times 5^3\times 11}$ to find the prime factorization of the following.
(a) LCM(a, b)
(b) GCF(a, b)

Looking around in your own country, discuss one practical application in which “piecewise functions” are used either explicitly or implicitly.
Example to be used- A paid parking lot based on length of time stayed, up to half an hour cost $1, over half an hour up to an hour cost $2.50 and over an hour and up to 15 hours cost $20.

The terms in the polynomial $-4y^5+7y^2-3y-2.$

1. The graph of a linear equation in two variables is a _____________________line.
2. The general form of linear equation in two variables is _______________________.
3. Linear equations in three variables are expressed as _________________________.
4. The number of variables in is __________________________.
5. The solution of a linear equation always ________________________ the equation.

True or False. The domain of every rational function is the set of all real numbers.

Fill in the bla
. The imaginary unit i is defined as i = _______ , where i2i
= _______ .

To calculate: The least common denominator for the pair of expressions $\frac{x+3}{x^2+20x100}and\frac{3}{2x^2+20x}$

Completely simplify the expression $(2\frac{x}{y^{-1/3}}{)}^{-1}$ Your final answer should contain no negative exponents and no radicals.

factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 70 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
(a) What is the level of significance?
State the null and alternate hypotheses.
$H_0:\sigma =60$

$H_1:\sigma <60H_0:\sigma >60$

$H_1:\sigma =60H_0:\sigma =60$

$H_1:\sigma >60H_0:\sigma =60$

$H_1:\sigma \ne 60$
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
What assumptions are you making about the original distribution?
We assume a binomial population distribution.We assume a exponential population distribution. We assume a normal population distribution.We assume a uniform population distribution.

Radical and Exponents Simplify the expression $(\frac{a{b}^2{c}^{-3}}{2a^3{b}^{-4}}{)}^{-2}$

A certain scale has an uncertainty of 3 g and a bias of 2 g. a) A single measurement is made on this scale. What are the bias and uncertainty in this measurement? b) Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements? c) Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements? d) As more measurements are made, does the uncertainty get smaller, get larger, or stay the same? e) As more measurements are made, does the bias get smaller, get larger, or stay the same?

Insert five arithmetic means between 5 and 21. (Enter your answers from smallest to largest.) Find the sum of the first n terms of the arithmetic sequence. $-9+(-12)+(-15)$ + ... (to 10 terms)