Numerade

Questions asked

INSTANT ANSWER

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal. a. In words, define the random variables $X$ and $\overline{X}$ . b. Which distribution should you use for this problem? Explain your choice. c. Construct a 95$\%$ confidence interval for the population mean length of engineering conferences. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound.

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ANSWERED

Dominique Jan Tan

Numerade educator

Agent Bond is standing on a bridge, 13 $\mathrm{m}$ above the road below, and his pursuers are getting too close for comfort. He spots a flatbed truck approaching at $25 \mathrm{m} / \mathrm{s},$ which he measures by knowing that the telephone poles the truck is passing are 25 $\mathrm{m}$ apart in this country. The bed of the truck is 1.5 $\mathrm{m}$ above the road, and Bond quickly calculates how many poles away the truck should be when he jumps down from the bridge onto the truck, making his getaway. How many poles is it?

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ANSWERED

Stephen Ho

Numerade educator

The pH of a 0.10 M HOBr solution is 4.8. a. What is $\left[\mathrm{H}^{+}\right]$ in that solution? b. What is $\left[\mathrm{OBr}^{-}\right] ?$ What is [HOBr]? (Where do the $\mathrm{H}^{+}$ and $\mathrm{OBr}^{-}$ ions come from?) c. What is the value of $K_{\mathrm{a}}$ for HOBr? What is the value of $\mathrm{pK}_{\mathrm{a}} ?$

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ANSWERED

Chandan Gupta

Numerade educator

The speeds of 55 cars were measured by a radar device on a city street: $$\begin{array}{llllllllll} \hline 27 & 23 & 22 & 38 & 43 & 24 & 35 & 26 & 28 & 18 & 20 \\ 25 & 23 & 22 & 52 & 31 & 30 & 41 & 45 & 29 & 27 & 43 \\ 29 & 28 & 27 & 25 & 29 & 28 & 24 & 37 & 28 & 29 & 18 \\ 26 & 33 & 25 & 27 & 25 & 34 & 32 & 36 & 22 & 32 & 33 \\ 21 & 23 & 24 & 18 & 48 & 23 & 16 & 38 & 26 & 21 & 23 \\ \hline \end{array}$$ a. Classify these data into a grouped frequency distribution by using class boundaries $12-18,18-24, \ldots$ $48-54$ b. Find the class width. c. For the class $24-30,$ find the class midpoint, the lower class boundary, and the upper class boundary. d. Construct a frequency histogram of these data.

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ANSWERED

Joshua Trocino

Numerade educator

A 10 ft ladder leans against a wall at an angle $\theta$ with the horizontal, as shown in the accompanying figure. The top of the ladder is $x$ feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at which $x$ changes with respect to $\theta$ when $\theta=60^{\circ} .$ Express the answer in units of feet/degree.

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INSTANT ANSWER

The designer of a sports facility wants to put a quarter-mile (1320 ft) running track around a football field, oriented as in the accompanying figure on the next page. The football field is 360 ft long (including the end zones) and 160 ft wide. The track consists of two straightaways and two semicircles, with the straightaways extending at least the length of the football field. (a) Show that it is possible to construct a quarter-mile track around the football field. I Suggestion: Find the shortest track that can be constructed around the field. $]$ (b) Let $L$ be the length of a straightaway (in feet), and let $x$ be the distance (in feet) between a sideline of the football field and a straightaway. Make a graph of $L$ versus $x$. (c) Use the graph to estimate the value of $x$ that produces the shortest straightaways, and then find this value of $x$ exactly. (d) Use the graph to estimate the length of the longest possible straightaways, and then find that length exactly.

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ANSWERED

Albert Tres

Numerade educator

For the following exercises, write the domain and range of each function using interval notation.

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ANSWERED

Vysakh M

Numerade educator

(I) A diver shines a flashlight upward from beneath the water at a 35.2$^\circ$ angle to the vertical. At what angle does the light leave the water?

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ANSWERED

Darshan Maheshwari

Numerade educator

A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 95.0 $\mathrm{kg}$ . The mass of the rock is 0.300 $\mathrm{kg}$ . Initially the wagon is rolling forward at a speed of 0.500 $\mathrm{m} / \mathrm{s}$ . Then the person throws the rock with a speed of 16.0 $\mathrm{m} / \mathrm{s}$ . Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown directly forward in one case and directly backward in another.

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ANSWERED

Gokul R Nair

Numerade educator

The cube in Fig. $23-31$ has edge length 1.40 $\mathrm{m}$ and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per coulomb, is given by (a) 6.00 $\mathrm{i}$ , (b) $-2.00 \hat{\mathrm{j}},$ and $(\mathrm{c})-3.00 \hat{\mathrm{i}}+4.00 \hat{\mathrm{k}}$ . (d) What is the total flux through the cube for each field?

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Alexis C.