Generally, \(\displaystyle{a}^{{n}}\) means that you multiply a by itself n times. Hence, \(\displaystyle{6}^{{2}}\) means \(\displaystyle{6}\cdot{6}={36}\). So, correct answer is choice A.

Question

asked 2021-01-08

Simplify sqrt-54 using the imaginary number i

A) \(\displaystyle{3}{i}\sqrt{{6}}\)

B) \(\displaystyle-{3}\sqrt{{6}}\)

C) \(\displaystyle{i}\sqrt{{54}}\)

D) \(\displaystyle{3}\sqrt{-}{6}\)

A) \(\displaystyle{3}{i}\sqrt{{6}}\)

B) \(\displaystyle-{3}\sqrt{{6}}\)

C) \(\displaystyle{i}\sqrt{{54}}\)

D) \(\displaystyle{3}\sqrt{-}{6}\)

asked 2020-11-10

If \(\displaystyle{s}≥{0}\), then \(\displaystyle√{s}^{{2}}\) is equal to

O A. 0

O B. 1

O c. −s

O D. s

O A. 0

O B. 1

O c. −s

O D. s

asked 2021-03-04

Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. \(a*(1/81)^(-1/4)b*x^(-2)y^(-4)c*(2x)^(-2)(16x^2y)^(1/2)\)

asked 2021-01-31

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

asked 2021-03-11

An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by

\(\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.\)

\(\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)

(A) Complete the table below.

\(\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)

(Round to one decimal place as needed.)

\(A. 20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.

\(B. 20602060xf(x)\)

Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.

Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.

\(C. 20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.

\(D.20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29

\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) and for 35

\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)

The mileage for the tire pressure \(\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) is

The mileage for the tire pressure \(\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}\) in. is

(Round to two decimal places as needed.)

(D) Write a brief description of the relationship between tire pressure and mileage.

A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.

B. As tire pressure increases, mileage decreases.

C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.

D. As tire pressure increases, mileage increases.

\(\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.\)

\(\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)

(A) Complete the table below.

\(\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)

(Round to one decimal place as needed.)

\(A. 20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.

\(B. 20602060xf(x)\)

Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.

Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.

\(C. 20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.

\(D.20602060xf(x)\)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29

\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) and for 35

\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)

The mileage for the tire pressure \(\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) is

The mileage for the tire pressure \(\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}\) in. is

(Round to two decimal places as needed.)

(D) Write a brief description of the relationship between tire pressure and mileage.

A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.

B. As tire pressure increases, mileage decreases.

C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.

D. As tire pressure increases, mileage increases.

asked 2020-10-25

“For any elements @ and b from a group and any integer n, prove thal (a−1ba)n=a−1bna

asked 2021-02-13

Express the fraction \(\displaystyle\frac{{1}}{{6}^{{4}}}\) using negative exponent.

asked 2021-01-15

The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the \(\displaystyle{F}{e}^{{{2}}}\ :\ {H}_{{{2}}}\ {O}_{{{2}}}\) delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article.
\(\displaystyle{b}{e}{g}\in{\left\lbrace{m}{a}{t}{r}{i}{x}\right\rbrace}\text{Initial Concentration (M)}&\text{Delivery Ratio}&\text{Sorption (%)}\ {15}&{1}:{0}&{10.90}\quad{8.47}\quad{12.43}\ {15}&{1}:{1}&{3.33}\quad{2.40}\quad{2.67}\ {15}&{1}:{5}&{0.79}\quad{0.76}\quad{0.84}\ {15}&{1}:{10}&{0.54}\quad{0.69}\quad{0.57}\ {40}&{1}:{0}&{6.84}\quad{7.68}\quad{6.79}\ {40}&{1}:{1}&{1.72}\quad{1.55}\quad{1.82}\ {40}&{1}:{5}&{0.68}\quad{0.83}\quad{0.89}\ {40}&{1}:{10}&{0.58}\quad{1.13}\quad{1.28}\ {100}&{1}:{0}&{6.61}\quad{6.66}\quad{7.43}\ {100}&{1}:{1}&{1.25}\quad{1.46}\quad{1.49}\ {100}&{1}:{5}&{1.17}\quad{1.27}\quad{1.16}\ {100}&{1}:{10}&{0.93}&{0.67}&{0.80}\ {e}{n}{d}{\left\lbrace{m}{a}{t}{r}{i}{x}\right\rbrace}\)
a) Estimate all main effects and interactions.
b) Construct an ANOVA table. You may give ranges for the P-values.
c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.

asked 2020-11-06

A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio \(x_1\)

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

asked 2021-03-09

Simplify: \(\displaystyle{\left({7}^{{5}}\right)}{\left({4}^{{5}}\right)}\). Write your answer using an exponent.

Explain in words how to simplify: \(\displaystyle{\left({153}^{{2}}\right)}^{{7}}.\)

Is the statement \(\displaystyle{\left({10}^{{5}}\right)}{\left({4}^{{5}}\right)}={14}^{{5}}\) true?

Explain in words how to simplify: \(\displaystyle{\left({153}^{{2}}\right)}^{{7}}.\)

Is the statement \(\displaystyle{\left({10}^{{5}}\right)}{\left({4}^{{5}}\right)}={14}^{{5}}\) true?