# Pre-Algebra: solving equations with decimals Recent questions in Decimals
Decimals
ANSWERED ### Write an equal decimal having the given number of decimal places. Briefly describe the Decimal Squares for both decimals in the equation. a. $$\displaystyle{0.7}=$$______(hundredths) The Decimal Square for this decimal can be described by A. 7 out of 10 parts shaded, or 70 out of 100 parts shaded. B. 10 out of 7 parts shaded, or 100 out of 70 parts shaded. C. 70 out of 10 parts shaded, or 7 out of 100 parts shaded.

Decimals
ANSWERED ### In 2000. $$\displaystyle{54}\%$$ of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately $$\displaystyle{1.9}\%$$ per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000. $$\displaystyle{P}{\left({x}\right)}=$$____________ (Use integers or decimals for any numbers in the expression.)

Decimals
ANSWERED ### The total percent of individuals aged 16 to 24 enrolled in college as of October of each year who completed high school during the preceding 12 months is $$\displaystyle{f{{\left({x}\right)}}}={66.925}{x}^{{{0.043}}}$$, where x is the number of years after 1999. a) Use this model to estimate the total percent in 2003 and 2007. The total percent in 2003 is __% The total percent in 2007 is __%

Decimals
ANSWERED ### Write an algebraic equation for the following problem and then solve it. When Angela and Walker first started working for the supermarket, their weekly salaries totaled $500. Now during the last 25 years Walker has seen his weekly salary triple. Angela has seen her weekly salary become four times larger. Together their weekly salaries now total$1740. How much did they each make 25 years ago? The algebraic equation is ___$$\displaystyle={1740}$$.

Decimals
ANSWERED ### Write an equation that models the linear situation: A submarine 560 feet below the surface comes up 2.5 feet per second. Instructions: Do not use any spaces between variables, constants, equals signs, and operation signs. For example DO NOT enter $$\displaystyle{f{{\left({x}\right)}}}={2}{x}+{1}$$ DO ENTER: $$\displaystyle{f{{\left({x}\right)}}}={2}{x}+{1}$$ Put parentheses around constants that are fractions like this: $$\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}-{\left(\frac{{1}}{{2}}\right)}$$ You may use decimals if the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4) To write your equation, use the variables: $$\displaystyle{t}=$$ amount of time the submarine rises towards the surface (seconds) $$\displaystyle{L}{\left({t}\right)}=$$ see-level-position of the submarine (feet). Equation _________.

Decimals
ANSWERED ### A roof has a 0.4-inch layer of ice on it from a previous storm. Another ice storm begins to deposit ice at a rate of 0.26 inches per hour. a) Find a formula for a linear function f that models the thickness of the ice on the roof x hours after the second ice storm started. b) How thick is the ice after 3.5 hours? a) $$\displaystyle{f{{\left({x}\right)}}}=$$___ b) The ice is ___ inches thick after 3.5 hours.

Decimals
ANSWERED ### Given that a stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 3.4 ft/sec. Complete parts a through c. a) Find a function for the radius in terms of t. $$\displaystyle{r}{\left({t}\right)}=$$___ (Use integers or decimals for any numbers in the expression.)

Decimals
ANSWERED ### The function that converts the dollars of Country A to the dollars of Country B according to January 13, 2008, values is $$\displaystyle{f{{\left({x}\right)}}}={0.99286}{x}$$, where x is the number of dollars of Country A and f(x) is the number of dollars of Country B. Complete parts a and b below. a. Find the inverse function for f. $$\displaystyle{{f}^{{-{1}}}{\left({x}\right)}}=$$___ (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

Decimals
ANSWERED ### A pendulum swings 80cm on its first swing, 76cm on its second swing, 72.2cm on its third swing, and 68.59cm on its fourth swing. Complete parts a and b below. a. If the pattern continues, what explicit formula can be used to find the distance of the n-th swing? $$\displaystyle{a}_{{{n}}}={80}{\left({0.95}\right)}^{{{n}-{1}}}$$ (Simplify your answer. Use integers or decimals for any numbers in the expression.) b. Use your formula to find the distance of the 10-th swing. $$\displaystyle{a}_{{{10}}}=?{c}{m}$$ (Type an integer or decimal rounded to two decimal places as needed.)

Decimals
ANSWERED ### A person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs$119.96 per month. Write an equation that can be used to determine the total cost, C(t), of this phone plan for t months. Then, find the cost for 22 months, assuming that the number of minutes the person uses does not exceed 2000 per month. An equation that can be used to determine the total cost, C(t), of the phone plan fot t months is $$\displaystyle{C}{\left({t}\right)}=?$$

Decimals
ANSWERED ### In macroeconomic theory, total consumption expenditure on goods and services, C, is assume to be a linear function of national income, I. The table gives the values of C and I for 2004 and 2009 in country A(in billions of dollars). a. Find the formula for C as a function of 1. b. The slope of the linear function is called the marginal propensity to consume. What is the marginal propensity to consume for country A from 2004-2009? a. FInd the formula for C as a function of I. $$\displaystyle{C}=?$$ $$\begin{array}{|c|c|} \hline \text{Year}&2004&2013 \\ \hline \text{Total consumption (C)}&8,289&10,086\\ \hline \text{National income(f)}&9,938&12,027\\ \hline \end{array}$$

Decimals
ANSWERED ### The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. $$\begin{array}{|c|c|}\hline x & 1 & 2 & 4 & 8 & 16 \\ \hline p(x) & 0.05 & 0.10 & 0.30 & 0.45 & 0.10 \\ \hline \end{array}$$ a) Compute E(X). (Enter your answer to two decimal places.) GB b) Compute V(X) directly from the definition. (Enter your answer to four decimal places.) $$\displaystyle{G}{B}^{{{2}}}$$ c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB d) Compute V(X) using the shortcut formula. (Enter your answer to four decimal places.) $$\displaystyle{G}{B}^{{{2}}}$$

Decimals
ANSWERED ### The results of a survey of 39 students and the foreign language they are studying are shown in the two-way frequency table. $$\begin{array}{|c|c|} \hline Gender&Chinese&French&Spanish&Total\\ \hline Girl&3&8&13&24\\ \hline Boy&2&2&11&15\\ \hline Total&5&10&24&39\\ \hline \end{array}$$ What fraction of girls are studying French? Use decimals to answer, and round to 3 places. The fraction of girls that are studying French is ______.

Decimals
ANSWERED ### One way to find the formula of a line passing through (15,16) and (30,25) is by using a table, as shown below. Complete parts (a) and (b) below. a) Complete the box in the first row. $$\begin{array}{|c|c|} \hline x&y\\ \hline 0&\\ \hline 15&16\\ \hline 30&25\\ \hline \end{array}$$ b) Report the formula of the line in slope-intercept form. $$y=$$___$$+x$$___

Decimals
ANSWERED ### Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. $$\displaystyle{5}^{{{x}-{3}}}={3}^{{{2}{x}}}$$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is ______. B. The solution is the empty set.

Decimals
ANSWERED ### The following table shows the tuition for a semester at CBU in dollars for years since 1990. $$\begin{array}{|c|c|} \hline Year & \text{CBU Tuition} \\ \hline 3 & 4440\\ 6&5350\\ 9&6570\\ 12&7895\\ 15&9315\\ 18&11040\\ 21&12760\\ \hline \end{array}$$ A scatter plot for the data and a graph of a linear model in black and a quadratic model in red follows. 3691215182140005000600070008000900010000110001200013000 Use the above scatter plot to decide which model better fits the data. linear quadratic none Let $$C(t)$$ be the cost of tuition at CBU in dollars for t years since 1990. A quadratic model for the data is $$\displaystyle{C}{\left({t}\right)}=$$.Use three decimals in your answer. Estimate the tuition 2015. $Use the model to predict the year in which the tuition will be$15925.

Decimals
ANSWERED ### Write and algebraic equation for the following problem and then solve it. Creekside dormitory just purchased a new sofa on sale $456. The sale price was $$\displaystyle{60}\%$$ of the original price. What was the original price of the sofa? Let $$\displaystyle{x}=$$ original price of the sofa, Write an equation for the statement "the sale price was $$60\%$$ of the original price" .___$$=456$$ (Use integers or decimals for any numbers in the expression.) The original price was$___. (Simplify your answer.)

Decimals
ANSWERED ### A truck rental company rents a moving truck for one day by charging $27 plus$0.10 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 187 miles? 439 miles? Type the linear equation that relates the cost C, in dollars, of renting the truck to the number of x miles driven. $$\displaystyle{C}=$$ What is the cost of renting the truck if the truck is driven 187 miles? $$\displaystyle{C}=\?$$ What is the cost of renting the truck if the truck is driven 439 miles? $$\displaystyle{C}=\$$

Decimals
ANSWERED ### A restaurant mixes sugar and cinnamon together to sprinkle on desserts. The cost of sugar is $$\displaystyle{{1.10}}{{k}}{g}$$ and the cost of cinnamon is $$\displaystyle{{3.60}}{{k}}{g}.$$ What mass of each is needed to make 50 kg of mixture that costs $$\displaystyle{{1.85}}{{k}}{g}?$$ Solve using elimination.

Decimals
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