Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give reasons for your answer.

$$f(x)=\left\{\begin{array}{ll}{2 x-3,} & {0 \leq x \leq 2} \\ {6 x-x^{2}-7,} & {2<x \leq 3}\end{array}\right.$$

Divide.Write each answer in simplest form.

$$4\div 1\frac{1}{8}$$

What is suggested, in lines 408-413, about Gilbert's emotional state at this point of the story?

The Hilbert transform of a signal f(t) is defined by $F_{\mathrm{Hi}}(x)=\mathscr{H}\{f(t)\}=\frac{1}{\pi} \int_{-\infty}^{\infty} \frac{f(\tau)}{\tau-x} \mathrm{d} \tau$ Show that the operation of taking the Hilbert transform is equivalent to the convolution $-\frac{1}{\pi t} * f(t)$ and hence deduce that the Hilbert-transformed signal has an amplitude spectrum $F_{\mathrm{Hi}}(j \omega)$ identical with f(t). Show also that the phase of the transformed signal is changed by $\pm \frac{1}{2} \pi$, depending on the sign of ω.

A benefit concert with three performers lasts 8 hours. At this rate, how many hours is a concert with four performers?

Calculate the derivative.

$$y = \left( \sinh ^ { - 1 } \left( x ^ { 2 } \right) \right) ^ { 3 }$$

Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary. $x ^ { 2 } + 14 x - 10 = 0$

Find the English derivative in the sentence and write the corresponding Latin word: All restaurants and public eating places must be sanitary.

Classify each of the following as a strong acid, weak acid, strong base, or weak base in aqueous solution. $a. \mathrm { HNO } _ { 2 }\ b. \mathrm{HNO} _ { 3 }\ c. \mathrm{C H} _ { 3 } \mathrm{N H} _ { 2 }\ { d } . \mathrm { NaOH }\ e. \mathrm { NH } _ { 3 }\ f. \mathrm {HF}$

$$g. \begin{matrix} \text{O}\\ \text{||}\\ {}\ \quad \mathrm{HC-} \mathrm{OH}\\ \end{matrix}$$

$h. \mathrm { Ca } ( \mathrm { OH } ) _ { 2 }\ i. \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 }$

Perform the indicated operations. If possible, reduce the answer to its lowest terms. $-1 \frac{4}{7}-\left(-2 \frac{5}{14}\right)$

A car is traveling on a cement road with a drag factor of 1.1. The speed limit on this portion of the road is 45 mph. It was determined that the brakes were operating at 85% efficiency. The driver notices that the drawbridge is up ahead and that traffic is stopped. The driver immediately applies the brakes and the tires leave four distinct skid marks each 50 feet in length. a. What is the minimum speed the car was traveling when it entered the skid? Round your answer to the nearest tenth. b. Did the driver exceed the speed limit when entering the skid?

Base your answer on the passage below and on your knowledge of Earth science. Some people say Christopher Columbus proved that Earth is round. However, when they say this they are probably confusing Columbus with Ferdinand Magellan, the first captain whose ship sailed all the way around Earth. This was 15 years after the death of Columbus. (Unfortunately, hostile natives killed Magellan before his ship returned to Europe.) Columbus accepted the (incorrect) estimate of Posidonius for Earth's circumference. The Posidonius estimate was only about half Earth's true size. Columbus had an idea how far east Asia was, so he figured that a relatively short trip westward across the Atlantic Ocean would take him to Asia. If he had accepted the correct calculations of Eratosthenes, he would have known that sailing westward to Asia was very foolhardy. Unable to obtain a ship and funding from his Italian countrymen, he convinced the Queen of Spain to finance his voyage of discovery. If only an ocean separated Europe from Asia to the west, Columbus and all his men would have suffered a terrible fate. They could not bring enough food and water with them to sail the true distance to Asia, about 20,000 kilometers. That is roughly half way around Earth. In the late 1400s it was impossible for a sailing ship and crew to make such a long journey. We now know that Columbus landed in the West Indies near modern Cuba and Puerto Rico. They are called the "Indies" because Columbus thought he had sailed to Asia (India). In fact, he made four voyages to the Americas and he died believing he had found a new route to Asia. So we now call this area the "West" Indies because it became apparent later that Columbus had sailed to a previously unknown hemisphere. Being so wrong, Columbus and his men were very lucky to have survived! What incorrect measurement made Columbus think he could sail from Europe west to Asia?

Explain whether $\overline{x}$ or $\mu$, is the correct statistical notation for each mean described.

The mean hours of study per week was 15 hours for a sample of n = 30 students at a college.