Questions in mathematics

Questions in mathematics

📝 Answered - Minimize [tex]z=6 x_1+8 x_2[/tex] subject to [tex] 2 x_1+3 x_2 \geq 7 [/tex] [tex] 4 x_1+5 x_2 \geq 9 [/tex] [tex]x_1, x_2 \geq 0[/tex] Solve by the simplex method.

📝 Answered - Estimate the quotient: [tex]$6.31 \times 10^5+2.085 \times 10^3$[/tex]

📝 Answered - Factor the quadratic $5 x^2+9 x-2$. List ONLY ONE of the factors with parentheses and no spaces. Example: $(x+1)$

📝 Answered - The graph of which of the following equations is a line perpendicular to the graph [tex]4x - 7y = 17[/tex]? A. [tex]y = -\frac{7}{4}x + \frac{17}{4}[/tex] B. [tex]y = \frac{7}{4}x + \frac{17}{4}[/tex] C. [tex]y = \frac{4}{7}x + 17[/tex] D. [tex]y = \frac{4}{7}x - \frac{17}{4}[/tex]

📝 Answered - The prices of a pound of butter for several different years are shown below. Calculate the price of a pound of butter in 2010 dollars. Enter results in the table below. Round answers to the nearest penny. | Year | 1970 | 1980 | 1990 | 2000 | 2010 | | --- | --- | --- | --- | --- | --- | | Price of butter (lb) (unadjusted) | $1.33 | $1.80 | $2.11 | $2.43 | $2.78 | | Price in 2010 dollars | $7.33 | $ | $3.46 | $ | 2.78 Enter an exact number. | | | | | | | | Inflation rates between the indicated years and 2010 are shown in the table below. | Time span | 1970-2010 | 1980-2010 | 1990-2010 | 2000-2010 | | --- | --- | --- | --- | --- | | Inflation rate | 451% | 154% | 64% | 26% |

📝 Answered - Find all relative extrema of the function. Use the second derivative test where applicable. (If an answer does not exist, enter DNE.) [tex]f(x)=x^4-8 x^3+1[/tex] relative maximum (x, y) = ( relative minimum (x, y) = ( )

📝 Answered - A probability experiment is conducted in which the sample space of the experiment is $S=\{1,2,3,4,5,6,7,8,9,10,11$, $12,13,14,15\}$. Let event $A=\{2,3,4,5\}$ and event $B=\{13,14,15\}$. Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually exclusive? Select one: a. $\{2,3,4,5,13,14,15\}$; yes b. $\{\}$; no c. $\{2,3,4,5,13,14,15\}$; no d. $\{\}$; yes

📝 Answered - A sports store sells basketballs and soccer balls. Basketballs cost $15, and soccer balls cost $20. If the store sells 25 items and earns $400, what system of equations represents the situation? a. $20 x+15 y=25, x+y=400$ b. $15 x+20 y=25, x+y=400$ c. $20 x+15 y=400, x+y=25$ d. $15 x+20 y=400, x+y=25

📝 Answered - For each pair of polar coordinates below, select the correct conversion into rectangular coordinates. 1. M([tex]8,30^\circ[/tex]) A. ([tex]4\sqrt{3}, 4[/tex]) B. ([tex]-4\sqrt{3}, 4[/tex]) C. ([tex]4, 4\sqrt{3}[/tex]) D. ([tex]-4, 4\sqrt{3}[/tex]) 2. N([tex]7,\frac{5\pi}{6}[/tex]) A. ([tex]7 \sqrt{3}, 7[/tex]) B. ([tex]-7, 7 \sqrt{3}[/tex]) C. ([tex]7,-7 \sqrt{3}[/tex]) D. ([tex]-7 \sqrt{3},-7[/tex]) E. ([tex]7,7 \sqrt{3}[/tex])

📝 Answered - How many pastries are needed for 50 guests if they take a long break?