Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is $95.0 \mathrm{~cm}$ and the eyepiece focal length of both telescopes is $3.80 \mathrm{~cm}$. The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of $10.0 \mathrm{~cm}$ while the lenses of telescope B are scaled up by a factor of two, so that its objective diameter is $20.0 \mathrm{~cm}$. a) What are the angular magnifications of telescopes $A$ and $B$ ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

Choose the correct description of the skin condition.

_______ urticaria

a.an autoimmune skin condition

b.skin cancer that can develop from a mole; the most serious form of skin cancer

c.another name for hives

d.skin lesion caused by a shallow scratch

e.another name for a skin boil

f.a virus-caused skin cancer that sometimes develops in immune-deficient individuals

(a) Prove the result in the earlier example by induction.

(b) Prove the result of the earlier example directly by recursively substituting $(1+x^k )= (1−x^{2k} )/(1−x^k)$ in g*(x).

Organizers of a televised fundraiser know from past experience that most people donate small amounts ($10-$25), some don ate larger amounts ($50-$100), and a few people make very generous donations of $250,$50, or more. Historically, pledges average about $32 with a standard deviation of$54

What assumption did you make in answering the question?

Find each integral by using the integral table on the inside back cover. $\int \frac{x}{\sqrt{1-x}} d x$

Why is the genome of the tube worm symbiont thought to be so much larger than the genomes of insect symbionts?

Above each of the following items, write $C$ if brackets are used correctly or $I N$ if they are used incorrectly.

Example 1. Referring to the "American dream," the writers assert that "The Great Gatsby by F. Scott Fitzgerald [1896 $\overset{C}{-}$ 1940] mirrors both its failures and its promises."

10. I also pointed out that the Great Depression [of the 1930s] extinguished some of this optimism.

Express the answer to the following permutation problem using permutation notation $\left({ }_n P_k\right)$ and numerically. See the earlier examples.

Given 26 building blocks, each with a different letter of the alphabet printed on it, how many different 3-letter "words" can be formed?

A neutral atom of a certain element has 17 electrons. Without consulting a periodic table, write the ground-state electron confi guration of the element.

Circle the letter of each characteristic of birds.
a. feathers
b. four legs
c. wings
d. scales

n each of the following sentences, circle any letter that should be capitalized and draw a slash (/) through any letter that is capitalized but should not be. Example: $\text{\textcircled}{\text{n}}$igetl enjoys stories about $\cancel{\text{T}}$he $\cancel{\text{L}}$egendary $\text{\textcircled}{\text{k}}$ing Arthur of $\text{\textcircled}{\text{b}}$ritain and his knights the letter I found in my Great-Grandmother's papers began, "my dearest mimi."

Rodrigo practiced playing the guitar

$$15\frac{1}{3}$$

hours over the past 3 weeks. He practiced for

$$6\frac{1}{4}$$

hours during the first week and

$$4\frac{2}{3}$$

hours during the second week. How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to write an equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.

$$15 \frac { 1 } { 3 }$$

$$6 \frac { 1 } { 4 }$$

$$4 \frac { 2 } { 3 }$$

$$\times$$

$$=$$

$$+$$

Practice time during third week: ______ hours.

Find the distance between points with the given coordinates. $(3,-3),(7,2)$

Find the distance between points with the given coordinates. $(-5,2),(4,-2)$