Improve Your Algebra Skills with Practice Problems

how to convert decimals into fractions

A football team loses 3 yards in 3 consecutive plays. What is the total yardage gained?

Which of the following are assumptions for the Significance Test for the Proportion? Data is from a Normal Distribution nphat and n(1-phat) are both greater than 15 Data is Quantitative. Data is from a convenience sample. Data is Categorical. Data is from a random sample. nPo and n(1-Po) are both the greater than 1

Express the angle as a decimal, to the nearest ten-thousandth of a degree.
${258}^{\circ }{39}^{\prime }{52}^{″}$

For digits before decimals point, multiply each digit with the positive powers of ten where power is equal to the position of digit counted from left to right starting from 0.
For digits after decimals point, multiply each digit with the negative powers of ten where power is equal to the position of digit counted from right to left starting from 1.
1) ${10}^0=1$
2) ${10}^1=10$
3) ${10}^2=100$
4) ${10}^3=1000$
5) ${10}^4=10000$
And so on...
6) ${10}^{-1}=0.1$
7) ${10}^{-2}=0.01$
8) ${10}^{-3}=0.001$
9) ${10}^{-4}=0.0001$

Sharon wants to buy a shirt that costs $45. The sales tax is 5%. How much is the sales tax? What is her total cost for the shirt?

Find an equation of the tangent plane to the given surface at the specified point.
$z=2(x-1{)}^2+6(y+3{)}^2+4,(3,-2,18)$

∣−6∣

You want to invest money for your child's education in a certificate of deposit (CD). You want it to be worth $\$12,000$ in 10 years. How much should you invest if the CD pays interest at a $9\mathrm{\%}$ annual rate compounded
a) Annually?
b) Continuously?

Find the solution of the equation rounded to two decimals.
$2.14(x-4.06)=2.27-0.11x$

Find the solution of the equation rounded to two decimals.
$8.36-0.95x-9.97$

Where does the helix
$r(t)=<\cos (\pi t),\sin (\pi t),t>$
intersect the paraboloid
$z=x^2+y^2$?
(x, y, z) =
What is the angle of intersection between the helix and the paraboloid?

List the first 6 multiples of each number.
a) 6
b) 13
c) 22
d) 31
e) 45
f) 27

Round 2093.33 to the nearest hundredth.

Find the coefficient of$x^7$ in the expression $(x^3+\frac{4}{x^2}{)}^4$

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
$\begin{array}{|ccccccc|}\hline 11.8& 7.7& 6.5& 6.8& 9.7& 6.8& 7.3\\ 7.9& 9.7& 8.7& 8.1& 8.5& 6.3& 7.0\\ 7.3& 7.4& 5.3& 9.0& 8.1& 11.3& 6.3\\ 7.2& 7.7& 7.8& 11.6& 10.7& 7.0\\ \hline\end{array}$
a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. $[Hint.?x_j=219.5.]$ (Round your answer to three decimal places.)
MPa
State which estimator you used.
$x$
$p?$
$\frac{s}{x}$
$s$
$\tilde{\chi }$
b) Calculate a point estimate of the strength value that separates the weakest $50\mathrm{\%}$ of all such beams from the strongest $50\mathrm{\%}$.
MPa
State which estimator you used.
$s$
$x$
$p?$
$\tilde{\chi }$
$\frac{s}{x}$
c) Calculate a point estimate of the population standard deviation ?. $[Hint:?x_{i}2=1859.53.]$ (Round your answer to three decimal places.)
MPa
Interpret this point estimate.
This estimate describes the linearity of the data.
This estimate describes the bias of the data.
This estimate describes the spread of the data.
This estimate describes the center of the data.
Which estimator did you use?
$\tilde{\chi }$
$x$
$s$
$\frac{s}{x}$
$p?$
d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
e) Calculate a point estimate of the population coefficient of variation $\frac{?}{?}$. (Round your answer to four decimal places.)
State which estimator you used.
$p?$
$\tilde{\chi }$
$s$
$\frac{s}{x}$
$x$

Find the solution of the equation rounded to two decimals.
$3.02x+1.48-10.92$

Bethany needs to borrow $\$10,000.$ She can borrow the money at $5.5\mathrm{\%}$ simple interest for 4 yr or she can borrow at $5\mathrm{\%}$ with interest compounded continuously for 4 yr.
a) How much total interest would Bethany pay at $5.5\mathrm{\%}$ simple interest?
b) How much total interest would Bethany pay at $5$ interest compounded continuously?
c) Which option results in less total interest?

To solve:
The equation $x^2-1.800x+0.810=0$ using quadratic formula and a calculator, rounding to three decimals.