GuideFoot - Learn Together, Grow Smarter. Logo

Questions in mathematics

📝 Answered - There are five runners in a race. How many different ways can they cross the finish line? [tex] \begin{array}{c} { }_n P_r=\frac{n!}{(n-r)!} \ 0!=1 \end{array} [/tex]

📝 Answered - Given two dependent random samples with the following results: | Population 1 | 24 | 31 | 44 | 31 | 26 | 22 | 25 | |---|---|---|---|---|---|---|---| | Population 2 | 26 | 40 | 48 | 39 | 29 | 18 | 16 | Use this data to find the $80 \%$ confidence interval for the true difference between the population means. Assume that both populations are Step 4 of 4 : Construct the $80 \%$ confidence interval. Round your answers to one decimal place.

📝 Answered - A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by [tex]$M=-2.78(\log P)-1.35$[/tex], where [tex]$M$[/tex] is the absolute magnitude, or brightness, of the star, and [tex]$P$[/tex] is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

📝 Answered - A member of a book club wishes to purchase two books from a selection of eight books recommended for a certain month. In how many ways can she choose them? ${ }_n C_r=\frac{n!}{r!(n-r)!}$

📝 Answered - A scientific calculator is required to answer the following question. A particle [tex]$P$[/tex] is traveling along the [tex]$x$[/tex]-axis with displacement [tex]$s(t)$[/tex] from a fixed origin [tex]$O$[/tex] given by [tex]$s(t)=(t+1) e^{-t}, \quad t \geq 0$[/tex] Find the time at which the acceleration is zero, and find the value of the velocity at this moment. a [tex]$t=2, \quad v=-\frac{2}{e^2}$[/tex] b [tex]$t=1, \quad v=-\frac{1}{e}$[/tex] c [tex]$t=\frac{1}{2}, \quad v=\frac{1}{2 \sqrt{e}}$[/tex] d [tex]$t=\frac{1}{2}, \quad v=-\frac{1}{\sqrt{e}}$[/tex] e [tex]$t=1, \quad v=\frac{1}{e^2}$[/tex]

📝 Answered - Compare $7 / 8$ with $14 / 16$ using ( $<,>,=$ ).

📝 Answered - An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

📝 Answered - This circle is centered at the origin, and the length of its radius is 3. What is the circle's equation? A. $x^2+y^2=9$ B. $x^3+y^3=27$ C. $x^2+y^2=3$ D. $x+y=3$

📝 Answered - Add. $\begin{array}{r} -30+(-45)=\square \\ -26+32=\square \end{array}$

📝 Answered - The general equation for depreciation is given by [tex]$y=A(1-r)^t$[/tex], where [tex]$y=$[/tex] current value, [tex]$A=$[/tex] original cost, [tex]$r=$[/tex] rate of depreciation, and [tex]$t=$[/tex] time, in years. A car was purchased 6 years ago for [tex]$\$25,000$[/tex]. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car? [tex]$y=25,000(0.89)^6$[/tex] [tex]$y=(25,000 \cdot 0.11)^6$[/tex] [tex]$y=(25,000 \cdot 0.89)^6$[/tex] [tex]$y=25,000(0.11)^6$[/tex]