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Cradlepoint E3000 5G (BF01-30005GB-GN) vs Cradlepoint E300 5G (BF01-03005GB-GN)
Cradlepoint E3000 5G (BF01-30005GB-GN) vs Cradlepoint E300 5G (BF01-03005GB-GN)
Looking for a reliable and high-performance 5G router? Look no further than the Cradlepoint E3000 5G and Cradlepoint E300 5G. These two routers offer lightning-fast speeds and advanced features to keep your network running smoothly. With the E3000 5G, you can enjoy the latest 5G technology for faster downloads, streaming, and gaming. The E300 5G, on the other hand, offers a compact and cost-effective option for small businesses or home use. Compare the two routers side by side and choose the one that best fits your needs. Upgrade to 5G with Cradlepoint and experience the future of connectivity.<|endoftext|><|endoftext|>
# 2017 AMC 12A Problems.
2017 AMC 12A (Answer Key)Printable versions: Wiki • AoPS Resources • PDF
Instructions
This is the first of two AMC 12 exams, both of which are 75 minutes long and contain 25 multiple-choice questions. The problems on this exam are relatively difficult; for example, fewer than 5% of all worldwide test-takers scored a 15 or higher on this exam in 2016. Calculators are not allowed.
The first link contains the full set of test problems. You can also see the 2017 AMC 12A Problems page for the full list of problems and solutions, or the 2017 AMC 12A Problems on the AoPS Wiki. The second link contains video solutions to the problems, and the third link contains video explanations to each problem. Finally, the fourth link contains the test answers.
2017 AMC 12A Problems
2017 AMC 12A (Problems • Answer Key • Resources)
2017 AMC 12A Problems (Problems • Answer Key • Resources)
2017 AMC 12A Problems (Problems • Answer Key • Resources)
2017 AMC 12A Answer Key
2017 AMC 12A (Answer Key) (Problems • Answer Key • Resources)
Problem 1
A tiling in the shape of an isosceles right triangle is made up of three horizontal rows of small congruent isosceles right triangle tiles as shown. The tile in the bottom row has legs of length $1$ and the tile in the top row has legs of length $3$. What is the area of the shaded trapezoidal region?
[asy] draw((0,0)--(1,0)--(1,1)--(0,1)--cycle); draw((1,0)--(2,0)--(2,2)--(1,2)--cycle); draw((2,0)--(3,0)--(3,3)--(2,3)--cycle); fill((1,0)--(1,1)--(2,1)--(2,0)--cycle, mediumgray); fill((1,1)--(1,2)--(2,2)--(2,1)--cycle, mediumgray); fill((1,2)--(1,3)--(2,3)--(2,2)--cycle, mediumgray); [/asy]
$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ \frac{7}{3} \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ \frac{8}{3} \qquad \textbf{(E)}\ 4$
Solution
Problem 2
A charity sells $140$ benefit tickets for a total of $$2006$. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?
$\textbf{(A)}\ 922 \qquad \textbf{(B)}\ 934 \qquad \textbf{(C)}\ 946 \qquad \textbf{(D)}\ 958 \qquad \textbf{(E)}\ 970$
Solution
Problem 3
A point $P$ is chosen at random in the interior of the unit square whose sides are parallel to the coordinate axes. What is the probability that the slope of the line determined by $P$ and the point $(4,3)$ is positive?
$\textbf{(A)}\ \frac{1}{4} \qquad \textbf{(B)}\ \frac{1}{3} \qquad \textbf{(C)}\ \frac{1}{2} \qquad \textbf{(D)}\ \frac{2}{3} \qquad \textbf{(E)}\ \frac{3}{4}$
Solution
Problem 4
A large cube is assembled from $125$ unit cubes. The outside of the large cube is then painted. How many of the unit cubes have exactly one face painted?
$\textbf{(A)}\ 54 \qquad \textbf{(B)}\ 64 \qquad \textbf{(C)}\ 74 \qquad \textbf{(D)}\ 98 \qquad \textbf{(E)}\ 108$
Solution
Problem 5
A set of $25$ square blocks is arranged into a $5 \times 5$ square. How many different combinations of three blocks can be selected from that set so that no two are in the same row or column?
$\textbf{(A)}\ 300 \qquad \textbf{(B)}\ 350 \qquad \textbf{(C)}\ 600 \qquad \textbf{(D)}\ 650 \qquad \textbf{(E)}\ 700$
Solution
Problem 6
A circle of radius $1$ is externally tangent to a circle of radius $2$. The sides of $\triangle ABC$ are the tangent lines to the circles, as shown, and the sides $\overline{AB}$ and $\overline{AC}$ are congruent. What is the area of $\triangle ABC$?
[asy] unitsize(5mm); defaultpen(linewidth(.8pt)+fontsize(8pt)); dotfactor=4; pair O1=(0,0), O2=(3,0); pair A=O1+2*dir(110), B=O1+2*dir(200), C=O1+2*dir(-20); pair[] dotted={A,B,C}; draw(Circle(O1,2)); draw(Circle(O2,1)); draw(A--B--C--cycle); dot(dotted); label("$A$",A,NW); label("$B$",B,SW); label("$C$",C,E); [/asy]
$\textbf{(A)}\ \frac{\sqrt{3}}{2
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