The square root of a number is between 7 and 8. Which could be the number? *

Question
Quadratics
asked 2020-12-17
The square root of a number is between 7 and 8. Which could be the number? *

Answers (1)

2020-12-18
Let x be the number. If the square root of the number is between 7 and 8, then \(\displaystyle{7}{<}\sqrt{{{x}}}{<}{8}\)</span>.
Squaring all sides of the inequality gives \(\displaystyle{7}^{{{2}}}{<}\sqrt{{{x}}}^{{{2}}}{<}{8}^{{{2}}}\)</span>, which simplifies to \(\displaystyle{49}{<}{x}{<}{64}\)</span> x can then be any number such that \(\displaystyle{49}{<}{x}{<}{64}\)</span>.
0

Relevant Questions

asked 2020-12-25
Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
1
6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
asked 2021-02-06
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September: \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}&{C}{r}{a}{w}{l}\in{g}\ {a}\ge\backslash{h}{l}\in{e}{B}{i}{r}{t}{h}\ {m}{o}{n}{t}{h}&{M}{e}{a}{n}&{S}{t}.{d}{e}{v}.&{n}\backslash{h}{l}\in{e}{J}{a}\nu{a}{r}{y}&{29.84}&{7.08}&{32}\backslash{M}{a}{y}&{28.58}&{8.07}&{27}\backslash{S}{e}{p}{t}{e}{m}{b}{e}{r}&{33.83}&{6.93}&{38}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\) Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below. \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{o}{u}{r}{c}{e}&{S}{u}{m}\ {o}{f}\ \boxempty{s}&{D}{F}&{M}{e}{a}{n}\ \boxempty\ {F}\backslash{h}{l}\in{e}{G}{r}{o}{u}{p}{s}&{505.26}\backslash{E}{r}{r}{\quad\text{or}\quad}&&&{53.45}\backslash{T}{o}{t}{a}{l}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\) What are the degrees of freedom for the groups term?
asked 2021-02-25
sqrt5 is between which two integers? Explain your reasoning.
asked 2020-12-12
Which of the following is/are always false ?
(a) A quadratic equation with rational coefficients has zero or two irrational roots.
(b) A quadratic equation with real coefficients has zero or two non - real roots
(c) A quadratic equation with irrational coefficients has zero or two rational roots.
(d) A quadratic equation with integer coefficients has zero or two irrational roots.
asked 2021-02-27
The table to the right has the​ inputs, x, and the outputs for three​ functions, f,​ g, and h. Use second differences to determine which function is exactly​ quadratic, which is approximately​ quadratic, and which is not quadratic.

The functon
f(x) is _______ quadratic,
g(x) is _____ quadratic,
h(x) is _______ quadratic.
asked 2021-01-22
Explain how to complete the square for an expression of the form x²+bx.
Add __ to \(\displaystyle{x}²+{b}{x}.\)
asked 2020-10-23
The equation \(\displaystyle{m}^{{\frac{{2}}{{3}}}}+{10}{m}^{{\frac{{1}}{{3}}}}+{9}={0}\) is said to be in __________form, because making the substitution u = __________results in a new equation that is quadratic.
asked 2020-11-30
A quadratic has an axis of symmetry of x=m, and the quadratic hax an x-intercept at (m,0). The quadratic has a vertical compression as a approaches infinty y approaches negative infiniy. What is a possible equation of the quadratic?
asked 2020-12-25
A quadratic function has its vertex at the point (1,6). The function passes through the point (-2, -3). Find the quadratic and linear coefficients and the constant team of the function.
- The quadratic coefficients is
- The linear coefficients is
- The constant term is
asked 2021-03-01
Find the vertex of the qudratic function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{6}{x}+{42}\), then express the qudratic function in standart form \(\displaystyle{f{{\left({x}\right)}}}={a}{\left({x}-{h}\right)}^{{2}}+{k}\) and state whether the vertex is a minimum or maximum. Enter exat answers only, no approximations.
...