# Write the reciprocal of each of the following: a. frac{1}{8} b. frac{7}{12} c. frac{3}{5} d. 1frac{1}{2} e. 3frac{3}{4} f. 6

Question
Fractions
Write the reciprocal of each of the following:
$$\displaystyle{a}.{\frac{{{1}}}{{{8}}}}$$
$$\displaystyle{b}.{\frac{{{7}}}{{{12}}}}$$
$$\displaystyle{c}.{\frac{{{3}}}{{{5}}}}$$
$$\displaystyle{d}.{1}{\frac{{{1}}}{{{2}}}}$$
$$\displaystyle{e}.{3}{\frac{{{3}}}{{{4}}}}$$
f. 6

2020-11-15
a) 8
$$\displaystyle{b}{)}{\frac{{{12}}}{{{7}}}}$$
$$\displaystyle{c}{)}{\frac{{{5}}}{{{3}}}}$$
For d and e, I would convert them into improper fractions. You would do this by multiplying the denominator by the whole number (in d's case, the whole number is 1), and then add the product by the numerator (2(denominator)*1(whole number) = 2 + 1(numerator)). However, you would keep the denominator the same.
$$\displaystyle{d}{)}{1}{\frac{{{1}}}{{{2}}}}={\frac{{{3}}}{{{2}}}}\rightarrow{\frac{{{2}}}{{{3}}}}$$
$$\displaystyle{e}{)}{3}{\frac{{{3}}}{{{4}}}}={\frac{{{15}}}{{{4}}}}\rightarrow{\frac{{{4}}}{{{15}}}}$$
$$\displaystyle{f}{)}{\frac{{{1}}}{{{6}}}}$$
As you can see, if you multiply each corresponding problem with their reciprocal, they equal 1. In the end, you want the reciprocal of the problem to equal 1.

### Relevant Questions

1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance.
Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c. 10, 14, 16, 16, 8, 9, 11, 12, 3
d. 10, 8, 7, 5, 9, 10, 7
e. 45, 50, 40, 35, 75
f. 15, 11, 11, 16, 16, 9
Given each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
$$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$
For each set of data below, draw a scatterplot and decide whether or not the data exhibits approximately periodic behaviour.
a) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}&{11}&{12}\backslash{h}{l}\in{e}{y}&{0}&{1}&{1.4}&{1}&{0}&-{1}&-{1.4}&-{1}&{0}&{1}&{1.4}&{1}&{0}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
b) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{1}&{2}&{3}&{4}\backslash{h}{l}\in{e}{y}&{4}&{1}&{0}&{1}&{4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
c) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{0.5}&{1.0}&{1.5}&{2.0}&{2.5}&{3.0}&{3.5}\backslash{h}{l}\in{e}{y}&{0}&{1.9}&{3.5}&{4.5}&{4.7}&{4.3}&{3.4}&{2.4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
d) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{0}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}&{12}\backslash{h}{l}\in{e}{y}&{0}&{4.7}&{3.4}&{1.7}&{2.1}&{5.2}&{8.9}&{10.9}&{10.2}&{8.4}&{10.4}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \\ \hline \end{array}$$ b) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \\ \hline \end{array}$$
c) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \\ \hline \end{array}$$
d) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \\ \hline \end{array}$$
In science class, students are learning about organic compounds. An acetic molecule is made of 2 carbon atoms, 2 oxygen atoms, and 4 hydrogen atoms. What is the ratio of carbon atoms to hydrogen atoms?
A 2 : 4
B 4 : 2
C 6 : 2
D 2 : 8
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.
For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
$$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}\backslash{h}{l}\in{e}{f{{\left({x}\right)}}}&{409.4}&{260.7}&{170.4}&{110.6}&{74}&{44.7}&{32.4}&{19.5}&{12.7}&{8.1}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following: Construct a one-sided $$\displaystyle{95}\%$$ confidence interval for the true difference in population means. Test the null hypothesis that the population means are identical at the 0.05 level of significance.
$$S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.$$
Let event $$E={2, 3, 4, 5, 6, 7}, event$$
$$F={5, 6, 7, 8, 9}, event G={9, 10, 11, 12}, and event H={2, 3, 4}$$.