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2,400 | Let $i=\sqrt{-1}$. The product of the real parts of the roots of $z^2-z=5-5i$ is | -6 | 75.78125 |
2,401 | 1-2-3+4+5-6-7+8+9-10-11+\cdots + 1992+1993-1994-1995+1996= | 0 | 75 |
2,402 | Mr. J left his entire estate to his wife, his daughter, his son, and the cook. His daughter and son got half the estate, sharing in the ratio of $4$ to $3$. His wife got twice as much as the son. If the cook received a bequest of $\textdollar{500}$, then the entire estate was: | 7000 | 69.53125 |
2,403 | Betty used a calculator to find the product $0.075 \times 2.56$. She forgot to enter the decimal points. The calculator showed $19200$. If Betty had entered the decimal points correctly, the answer would have been | .192 | 94.53125 |
2,404 | Suppose $a$, $b$, $c$ are positive integers such that $a+b+c=23$ and $\gcd(a,b)+\gcd(b,c)+\gcd(c,a)=9.$ What is the sum of all possible distinct values of $a^2+b^2+c^2$? | 438 | 71.09375 |
2,405 | Let $S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1$. Then $S$ equals: | x^4 | 100 |
2,406 | For a certain complex number $c$, the polynomial
\[P(x) = (x^2 - 2x + 2)(x^2 - cx + 4)(x^2 - 4x + 8)\]has exactly 4 distinct roots. What is $|c|$? | \sqrt{10} | 15.625 |
2,407 | The figure below is a map showing $12$ cities and $17$ roads connecting certain pairs of cities. Paula wishes to travel along exactly $13$ of those roads, starting at city $A$ and ending at city $L$, without traveling along any portion of a road more than once. (Paula is allowed to visit a city more than once.)
How many different routes can Paula take? | 4 | 0 |
2,408 | For any positive integer $M$, the notation $M!$ denotes the product of the integers $1$ through $M$. What is the largest integer $n$ for which $5^n$ is a factor of the sum $98! + 99! + 100!$? | 26 | 95.3125 |
2,409 | How many different patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different. For example, the patterns shown below are not considered different. | 8 | 10.9375 |
2,410 | Each morning of her five-day workweek, Jane bought either a $50$-cent muffin or a $75$-cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy? | 2 | 82.03125 |
2,411 | Three men, Alpha, Beta, and Gamma, working together, do a job in 6 hours less time than Alpha alone, in 1 hour less time than Beta alone, and in one-half the time needed by Gamma when working alone. Let $h$ be the number of hours needed by Alpha and Beta, working together, to do the job. Then $h$ equals: | \frac{4}{3} | 27.34375 |
2,412 | The top of one tree is $16$ feet higher than the top of another tree. The heights of the two trees are in the ratio $3:4$. In feet, how tall is the taller tree? | 64 | 99.21875 |
2,413 | Let $E(n)$ denote the sum of the even digits of $n$. For example, $E(5681) = 6+8 = 14$. Find $E(1)+E(2)+E(3)+\cdots+E(100)$ | 400 | 96.09375 |
2,414 | Bridget bakes 48 loaves of bread for her bakery. She sells half of them in the morning for $2.50 each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs $0.75 for her to make. In dollars, what is her profit for the day? | 52 | 80.46875 |
2,415 | Given that $x$ and $y$ are distinct nonzero real numbers such that $x+\frac{2}{x} = y + \frac{2}{y}$, what is $xy$? | 2 | 96.09375 |
2,416 | Margie bought $3$ apples at a cost of $50$ cents per apple. She paid with a 5-dollar bill. How much change did Margie receive? | $3.50 | 0 |
2,417 | A square with area $4$ is inscribed in a square with area $5$, with each vertex of the smaller square on a side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length $a$, and the other of length $b$. What is the value of $ab$? | \frac{1}{2} | 60.9375 |
2,418 | If the markings on the number line are equally spaced, what is the number $\text{y}$? | 12 | 3.90625 |
2,419 | Equilateral $\triangle ABC$ has side length $1$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle. What is the area of hexagon $DEFGHI$? | 3+\sqrt3 | 0 |
2,420 | For how many integers $n$ between $1$ and $50$, inclusive, is $\frac{(n^2-1)!}{(n!)^n}$ an integer? | 34 | 15.625 |
2,421 | All students at Adams High School and at Baker High School take a certain exam. The average scores for boys, for girls, and for boys and girls combined, at Adams HS and Baker HS are shown in the table, as is the average for boys at the two schools combined. What is the average score for the girls at the two schools combined?
$\begin{tabular}[t]{|c|c|c|c|} \multicolumn{4}{c}{Average Scores}\\ \hline Category&Adams&Baker&Adams\&Baker\\ \hline Boys&71&81&79\\ Girls&76&90&?\\ Boys\&Girls&74&84& \\ \hline \end{tabular}$
| 84 | 57.03125 |
2,422 | A geometric sequence $(a_n)$ has $a_1=\sin x$, $a_2=\cos x$, and $a_3= \tan x$ for some real number $x$. For what value of $n$ does $a_n=1+\cos x$? | 8 | 1.5625 |
2,423 | A positive number $x$ satisfies the inequality $\sqrt{x} < 2x$ if and only if | \frac{1}{4} | 0 |
2,424 | Let $n$ be the smallest positive integer such that $n$ is divisible by $20$, $n^2$ is a perfect cube, and $n^3$ is a perfect square. What is the number of digits of $n$? | 7 | 76.5625 |
2,425 | The digits $1$, $2$, $3$, $4$, and $5$ are each used once to write a five-digit number $PQRST$. The three-digit number $PQR$ is divisible by $4$, the three-digit number $QRS$ is divisible by $5$, and the three-digit number $RST$ is divisible by $3$. What is $P$? | 1 | 94.53125 |
2,426 | For how many integers $x$ is the number $x^4-51x^2+50$ negative? | 12 | 46.875 |
2,427 | Exactly three of the interior angles of a convex polygon are obtuse. What is the maximum number of sides of such a polygon? | 6 | 48.4375 |
2,428 | Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other? | \frac{1}{3} | 63.28125 |
2,429 | Kate bakes a $20$-inch by $18$-inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain? | 90 | 97.65625 |
2,430 | Given $2^x = 8^{y+1}$ and $9^y = 3^{x-9}$, find the value of $x+y$ | 27 | 96.09375 |
2,431 | Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a fair coin repeatedly until he gets his first head, at which point he stops. What is the probability that all three flip their coins the same number of times? | \frac{1}{7} | 68.75 |
2,432 | Real numbers between 0 and 1, inclusive, are chosen in the following manner. A fair coin is flipped. If it lands heads, then it is flipped again and the chosen number is 0 if the second flip is heads, and 1 if the second flip is tails. On the other hand, if the first coin flip is tails, then the number is chosen uniformly at random from the closed interval $[0,1]$. Two random numbers $x$ and $y$ are chosen independently in this manner. What is the probability that $|x-y| > \tfrac{1}{2}$? | \frac{7}{16} | 17.1875 |
2,433 | The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is | 0 | 78.90625 |
2,434 | If \(N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\), then \(N\) equals | 1 | 95.3125 |
2,435 | Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand? | \frac{47}{256} | 14.84375 |
2,436 | The ratio of $w$ to $x$ is $4:3$, the ratio of $y$ to $z$ is $3:2$, and the ratio of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y?$ | 16:3 | 59.375 |
2,437 | You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02, with at least one coin of each type. How many dimes must you have? | 1 | 68.75 |
2,438 | Two real numbers are selected independently at random from the interval $[-20, 10]$. What is the probability that the product of those numbers is greater than zero? | \frac{5}{9} | 100 |
2,439 | Alice is making a batch of cookies and needs $2\frac{1}{2}$ cups of sugar. Unfortunately, her measuring cup holds only $\frac{1}{4}$ cup of sugar. How many times must she fill that cup to get the correct amount of sugar? | 10 | 99.21875 |
2,440 | The set of $x$-values satisfying the equation $x^{\log_{10} x} = \frac{x^3}{100}$ consists of: | 10 \text{ or } 100 | 2.34375 |
2,441 | Triangle $ABC$ is inscribed in a circle, and $\angle B = \angle C = 4\angle A$. If $B$ and $C$ are adjacent vertices of a regular polygon of $n$ sides inscribed in this circle, then $n=$ | 9 | 82.8125 |
2,442 | Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $1 more than a pink pill, and Al's pills cost a total of $546 for the two weeks. How much does one green pill cost? | $20 | 0 |
2,443 | The sum of two nonzero real numbers is $4$ times their product. What is the sum of the reciprocals of the two numbers? | 4 | 85.9375 |
2,444 | Three cards, each with a positive integer written on it, are lying face-down on a table. Casey, Stacy, and Tracy are told that
(a) the numbers are all different,
(b) they sum to $13$, and
(c) they are in increasing order, left to right.
First, Casey looks at the number on the leftmost card and says, "I don't have enough information to determine the other two numbers." Then Tracy looks at the number on the rightmost card and says, "I don't have enough information to determine the other two numbers." Finally, Stacy looks at the number on the middle card and says, "I don't have enough information to determine the other two numbers." Assume that each person knows that the other two reason perfectly and hears their comments. What number is on the middle card? | 4 | 49.21875 |
2,445 | Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle? | 8 | 38.28125 |
2,446 | Ten tiles numbered $1$ through $10$ are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square? | \frac{11}{60} | 21.09375 |
2,447 | Positive integers $a$, $b$, and $c$ are randomly and independently selected with replacement from the set $\{1, 2, 3,\dots, 2010\}$. What is the probability that $abc + ab + a$ is divisible by $3$? | \frac{13}{27} | 59.375 |
2,448 | When $7$ fair standard $6$-sided dice are thrown, the probability that the sum of the numbers on the top faces is $10$ can be written as $\frac{n}{6^{7}}$, where $n$ is a positive integer. What is $n$? | 84 | 68.75 |
2,449 | If an angle of a triangle remains unchanged but each of its two including sides is doubled, then the area is multiplied by: | 4 | 84.375 |
2,450 | In the figure, $\triangle ABC$ has $\angle A =45^{\circ}$ and $\angle B =30^{\circ}$. A line $DE$, with $D$ on $AB$
and $\angle ADE =60^{\circ}$, divides $\triangle ABC$ into two pieces of equal area.
(Note: the figure may not be accurate; perhaps $E$ is on $CB$ instead of $AC.)$
The ratio $\frac{AD}{AB}$ is | \frac{1}{\sqrt[4]{12}} | 0 |
2,451 | Reduced to lowest terms, $\frac{a^{2}-b^{2}}{ab} - \frac{ab-b^{2}}{ab-a^{2}}$ is equal to: | \frac{a}{b} | 91.40625 |
2,452 | Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the $13$ visible numbers have the greatest possible sum. What is that sum? | 164 | 0 |
2,453 | If $x-y>x$ and $x+y<y$, then | $x<0,y<0$ | 0 |
2,454 | Lucky Larry's teacher asked him to substitute numbers for $a$, $b$, $c$, $d$, and $e$ in the expression $a-(b-(c-(d+e)))$ and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry substituted for $a$, $b$, $c$, and $d$ were $1$, $2$, $3$, and $4$, respectively. What number did Larry substitute for $e$? | 3 | 78.125 |
2,455 | \(\triangle ABC\) is isosceles with base \(AC\). Points \(P\) and \(Q\) are respectively in \(CB\) and \(AB\) and such that \(AC=AP=PQ=QB\).
The number of degrees in \(\angle B\) is: | 25\frac{5}{7} | 0 |
2,456 | Four balls of radius $1$ are mutually tangent, three resting on the floor and the fourth resting on the others.
A tetrahedron, each of whose edges have length $s$, is circumscribed around the balls. Then $s$ equals | 2+2\sqrt{6} | 2.34375 |
2,457 | A circle of radius $2$ is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?
[asy] size(0,50); draw((-1,1)..(-2,2)..(-3,1)..(-2,0)..cycle); dot((-1,1)); dot((-2,2)); dot((-3,1)); dot((-2,0)); draw((1,0){up}..{left}(0,1)); dot((1,0)); dot((0,1)); draw((0,1){right}..{up}(1,2)); dot((1,2)); draw((1,2){down}..{right}(2,1)); dot((2,1)); draw((2,1){left}..{down}(1,0));[/asy] | \frac{4-\pi}{\pi} | 5.46875 |
2,458 | If $78$ is divided into three parts which are proportional to $1, \frac{1}{3}, \frac{1}{6},$ the middle part is: | 17\frac{1}{3} | 0 |
2,459 | How many positive two-digit integers are factors of $2^{24}-1$?~ pi_is_3.14 | 12 | 91.40625 |
2,460 | Shauna takes five tests, each worth a maximum of $100$ points. Her scores on the first three tests are $76$, $94$, and $87$. In order to average $81$ for all five tests, what is the lowest score she could earn on one of the other two tests? | 48 | 89.84375 |
2,461 | An ATM password at Fred's Bank is composed of four digits from $0$ to $9$, with repeated digits allowable. If no password may begin with the sequence $9,1,1,$ then how many passwords are possible? | 9990 | 80.46875 |
2,462 | The average (arithmetic mean) age of a group consisting of doctors and lawyers in 40. If the doctors average 35 and the lawyers 50 years old, then the ratio of the numbers of doctors to the number of lawyers is | 2: 1 | 18.75 |
2,463 | A rectangular box measures $a \times b \times c$, where $a$, $b$, and $c$ are integers and $1\leq a \leq b \leq c$. The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible? | 10 | 89.0625 |
2,464 | What is the product of the real roots of the equation $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$? | 20 | 65.625 |
2,465 | If $(3x-1)^7 = a_7x^7 + a_6x^6 + \cdots + a_0$, then $a_7 + a_6 + \cdots + a_0$ equals | 128 | 98.4375 |
2,466 | Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43$. Sharona bought some of the same pencils and paid $1.87$. How many more pencils did Sharona buy than Jamar? | 4 | 67.1875 |
2,467 | The diagram shows an octagon consisting of $10$ unit squares. The portion below $\overline{PQ}$ is a unit square and a triangle with base $5$. If $\overline{PQ}$ bisects the area of the octagon, what is the ratio $\dfrac{XQ}{QY}$? | \frac{2}{3} | 2.34375 |
2,468 | Let $\frac {35x - 29}{x^2 - 3x + 2} = \frac {N_1}{x - 1} + \frac {N_2}{x - 2}$ be an identity in $x$. The numerical value of $N_1N_2$ is: | -246 | 80.46875 |
2,469 | If rose bushes are spaced about $1$ foot apart, approximately how many bushes are needed to surround a circular patio whose radius is $12$ feet? | 48 | 0 |
2,470 | Each of two boxes contains three chips numbered $1$, $2$, $3$. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even? | \frac{5}{9} | 84.375 |
2,471 | Jack had a bag of $128$ apples. He sold $25\%$ of them to Jill. Next he sold $25\%$ of those remaining to June. Of those apples still in his bag, he gave the shiniest one to his teacher. How many apples did Jack have then? | 65 | 0 |
2,472 | Shelby drives her scooter at a speed of $30$ miles per hour if it is not raining, and $20$ miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of $16$ miles in $40$ minutes. How many minutes did she drive in the rain? | 24 | 57.03125 |
2,473 | An equivalent of the expression
$\left(\frac{x^2+1}{x}\right)\left(\frac{y^2+1}{y}\right)+\left(\frac{x^2-1}{y}\right)\left(\frac{y^2-1}{x}\right)$, $xy \not= 0$,
is: | 2xy+\frac{2}{xy} | 57.03125 |
2,474 | The product $(1.8)(40.3 + .07)$ is closest to | 74 | 0 |
2,475 | The isosceles right triangle $ABC$ has right angle at $C$ and area $12.5$. The rays trisecting $\angle ACB$ intersect $AB$ at $D$ and $E$. What is the area of $\triangle CDE$? | \frac{50-25\sqrt{3}}{2} | 0.78125 |
2,476 | From among $2^{1/2}, 3^{1/3}, 8^{1/8}, 9^{1/9}$ those which have the greatest and the next to the greatest values, in that order, are | $3^{1/3},\ 2^{1/2}$ | 0 |
2,477 | In the plane figure shown below, $3$ of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry?
[asy] import olympiad; unitsize(25); filldraw((1,3)--(1,4)--(2,4)--(2,3)--cycle, gray(0.7)); filldraw((2,1)--(2,2)--(3,2)--(3,1)--cycle, gray(0.7)); filldraw((4,0)--(5,0)--(5,1)--(4,1)--cycle, gray(0.7)); for (int i = 0; i < 5; ++i) { for (int j = 0; j < 6; ++j) { pair A = (j,i); } } for (int i = 0; i < 5; ++i) { for (int j = 0; j < 6; ++j) { if (j != 5) { draw((j,i)--(j+1,i)); } if (i != 4) { draw((j,i)--(j,i+1)); } } } [/asy] | 7 | 3.90625 |
2,478 | $\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}$ is equal to | 2 | 70.3125 |
2,479 | Circles with radii $1$, $2$, and $3$ are mutually externally tangent. What is the area of the triangle determined by the points of tangency? | \frac{6}{5} | 0 |
2,480 | There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < \dots < a_k$ such that\[\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + \dots + 2^{a_k}.\]What is $k?$ | 137 | 31.25 |
2,481 | Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon, construct a hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?
[asy] defaultpen(linewidth(0.6)); pair O=origin, A=(0,1), B=A+1*dir(60), C=(1,1), D=(1,0), E=D+1*dir(-72), F=E+1*dir(-144), G=O+1*dir(-108); draw(O--A--B--C--D--E--F--G--cycle); draw(O--D, dashed); draw(A--C, dashed);[/asy] | 23 | 2.34375 |
2,482 | Points $A(11, 9)$ and $B(2, -3)$ are vertices of $ riangle ABC$ with $AB=AC$. The altitude from $A$ meets the opposite side at $D(-1, 3)$. What are the coordinates of point $C$? | $\left( -4, 9 \right)$ | 0 |
2,483 | Carl decided to fence in his rectangular garden. He bought $20$ fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly $4$ yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden? | 336 | 67.96875 |
2,484 | For what value of $x$ does $10^{x} \cdot 100^{2x}=1000^{5}$? | 3 | 77.34375 |
2,485 | Paula the painter and her two helpers each paint at constant, but different, rates. They always start at 8:00 AM, and all three always take the same amount of time to eat lunch. On Monday the three of them painted 50% of a house, quitting at 4:00 PM. On Tuesday, when Paula wasn't there, the two helpers painted only 24% of the house and quit at 2:12 PM. On Wednesday Paula worked by herself and finished the house by working until 7:12 P.M. How long, in minutes, was each day's lunch break? | 48 | 69.53125 |
2,486 | Let $S_n$ and $T_n$ be the respective sums of the first $n$ terms of two arithmetic series. If $S_n:T_n=(7n+1):(4n+27)$ for all $n$, the ratio of the eleventh term of the first series to the eleventh term of the second series is: | 4/3 | 63.28125 |
2,487 | In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\triangle ABC$ is $50$ units and the area of $\triangle ABC$ is $100$ square units? | 2 | 20.3125 |
2,488 | One dimension of a cube is increased by $1$, another is decreased by $1$, and the third is left unchanged. The volume of the new rectangular solid is $5$ less than that of the cube. What was the volume of the cube? | 125 | 97.65625 |
2,489 | How many sequences of zeros and ones of length 20 have all the zeros consecutive, or all the ones consecutive, or both? | 382 | 3.90625 |
2,490 | The symbol $|a|$ means $a$ is a positive number or zero, and $-a$ if $a$ is a negative number.
For all real values of $t$ the expression $\sqrt{t^4+t^2}$ is equal to? | |t|\sqrt{1+t^2} | 0 |
2,491 | For $n$ a positive integer, let $R(n)$ be the sum of the remainders when $n$ is divided by $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, and $10$. For example, $R(15) = 1+0+3+0+3+1+7+6+5=26$. How many two-digit positive integers $n$ satisfy $R(n) = R(n+1)\,?$ | 2 | 98.4375 |
2,492 | How many ordered triples $(x,y,z)$ of positive integers satisfy $\text{lcm}(x,y) = 72, \text{lcm}(x,z) = 600 \text{ and lcm}(y,z)=900$? | 15 | 35.15625 |
2,493 | Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D$. The circles intersect at two points, one of which is $E$. What is the degree measure of $\angle CED$? | 120 | 78.125 |
2,494 | If $t = \frac{1}{1 - \sqrt[4]{2}}$, then $t$ equals | $-(1+\sqrt[4]{2})(1+\sqrt{2})$ | 0 |
2,495 | If the arithmetic mean of two numbers is $6$ and their geometric mean is $10$, then an equation with the given two numbers as roots is: | x^2 - 12x + 100 = 0 | 98.4375 |
2,496 | In the addition shown below $A$, $B$, $C$, and $D$ are distinct digits. How many different values are possible for $D$?
$\begin{array}{cccccc}&A&B&B&C&B\ +&B&C&A&D&A\ \hline &D&B&D&D&D\end{array}$ | 7 | 36.71875 |
2,497 | The cost $C$ of sending a parcel post package weighing $P$ pounds, $P$ an integer, is $10$ cents for the first pound and $3$ cents for each additional pound. The formula for the cost is: | C=10+3(P-1) | 6.25 |
2,498 | Six different digits from the set \(\{ 1,2,3,4,5,6,7,8,9\}\) are placed in the squares in the figure shown so that the sum of the entries in the vertical column is 23 and the sum of the entries in the horizontal row is 12. The sum of the six digits used is | 29 | 21.09375 |
2,499 | The number of roots satisfying the equation $\sqrt{5 - x} = x\sqrt{5 - x}$ is: | 2 | 100 |
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