problem stringlengths 10 5.15k | answer stringlengths 0 1.23k |
|---|---|
Calculate:<br/>$(1)-3+8-15-6$;<br/>$(2)-35\div \left(-7\right)\times (-\frac{1}{7})$;<br/>$(3)-2^{2}-|2-5|\div \left(-3\right)$;<br/>$(4)(\frac{1}{2}+\frac{5}{6}-\frac{7}{12})×(-24)$;<br/>$(5)(-99\frac{6}{11})×22$. | -2190 |
In triangle $ABC$, let $AB = 4$, $AC = 7$, $BC = 9$, and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. Find $\cos \angle BAD$. | \sqrt{\frac{5}{14}} |
Calculate $\sqrt[4]{\sqrt{\frac{32}{10000}}}$. | \frac{\sqrt[8]{2}}{\sqrt{5}} |
What is the distance, in units, between the points $(-3, -4)$ and $(4, -5)$? Express your answer in simplest radical form. | 5\sqrt{2} |
Calculate: $\left(-2\right)^{0}-3\tan 30^{\circ}-|\sqrt{3}-2|$. | -1 |
Given a hyperbola $x^{2}- \frac {y^{2}}{3}=1$ and two points $M$, $N$ on it are symmetric about the line $y=x+m$, and the midpoint of $MN$ lies on the parabola $y^{2}=18x$. Find the value of the real number $m$. | -8 |
In an arithmetic sequence $\{a_n\}$, $a_{10} < 0$, $a_{11} > 0$, and $a_{11} > |a_{10}|$. The maximum negative value of the partial sum $S_n$ of the first $n$ terms of the sequence $\{a_n\}$ is the sum of the first ______ terms. | 19 |
A special deck of cards contains $49$ cards, each labeled with a number from $1$ to $7$ and colored with one of seven colors. Each number-color combination appears on exactly one card. Sharon will select a set of eight cards from the deck at random. Given that she gets at least one card of each color and at least one c... | 13 |
Let GCF(a, b) be the abbreviation for the greatest common factor of a and b, and let LCM(c, d) be the abbreviation for the least common multiple of c and d. What is GCF(LCM(8, 14), LCM(7, 12))? | 28 |
Two lines with slopes $\dfrac{1}{3}$ and $3$ intersect at $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$. | 8.625 |
A swimming pool is being emptied through a drain at the bottom of the pool and filled by a hose at the top. The drain can empty the pool in 4 hours and the hose can fill the pool in 6 hours. The pool holds 120 liters of water. If the pool starts filled with water, how much water will be left after 3 hours? | It takes the drain 4 hours to empty the pool, so it drains at a rate of 120 liters / 4 hours = <<120/4=30>>30 liters/hour.
After 3 hours, the drain will have removed 3 * 30 = <<3*30=90>>90 liters of water from the pool.
It takes the hose 6 hours to fill the pool, so it fills at a rate of 120 liters / 6 hours = <<120/6=... |
Given that $4:5 = 20 \div \_\_\_\_\_\_ = \frac{()}{20} = \_\_\_\_\_\_ \%$, find the missing values. | 80 |
Given a cone and a cylinder with equal base radii and heights, if the axis section of the cone is an equilateral triangle, calculate the ratio of the lateral surface areas of this cone and cylinder. | \frac{\sqrt{3}}{3} |
The bases \( AB \) and \( CD \) of the trapezoid \( ABCD \) are 155 and 13 respectively, and its diagonals are mutually perpendicular. Find the dot product of the vectors \( \overrightarrow{AD} \) and \( \overrightarrow{BC} \). | 2015 |
If $\displaystyle\frac{m}{n} = 15$, $\displaystyle\frac{p}{n} = 3$, and $\displaystyle \frac{p}{q} = \frac{1}{10}$, then what is $\displaystyle\frac{m}{q}$? | \frac{1}{2} |
Define a **valid sequence** as a sequence of letters that consists only of the letters $A$, $B$, $C$, and $D$ — some of these letters may not appear in the sequence — where $A$ is never immediately followed by $B$, $B$ is never immediately followed by $C$, $C$ is never immediately followed by $D$, and $D$ is never imme... | 8748 |
The number of distinct points common to the curves $x^2+4y^2=1$ and $4x^2+y^2=4$ is: | 2 |
Find the number of integers between 1 and 2013 with the property that the sum of its digits equals 9. | 101 |
Emily wants to know how much it rained last week. She sees that it rained 2 inches on Monday morning and 1 more inch later that day. It rained twice that much on Tuesday. It did not rain on Wednesday but on Thursday it rained 1 inch. The biggest storm was on Friday when the total was equal to Monday through Thursday co... | The total rain was 2 inches + 1 inches = <<2+1=3>>3 inches on Monday.
The total rain was 2 * 3 inches = <<2*3=6>>6 inches on Tuesday.
The total rain was 0 inches + 1 inch = <<0+1=1>>1 inch across Wednesday and Thursday.
The total rain was 3 inches + 6 inches + 1 inch = <<3+6+1=10>>10 inches on Friday.
There were 3 inch... |
If $ rac{1}{2n} + rac{1}{4n} = rac{3}{12}$, what is the value of $n$? | 3 |
At a middle school, 20% of the students are in the band. If 168 students are in the band, how many students go to the middle school? | Let X be the number of students in the middle school. We know that X*20% = 168 students are in the band.
So there are X = 168/20% = 840 students in the middle school.
#### 840 |
The center of a semicircle, inscribed in a right triangle such that its diameter lies on the hypotenuse, divides the hypotenuse into segments of 30 and 40. Find the length of the arc of the semicircle that is enclosed between the points where it touches the legs. | 12\pi |
A rectangular table measures $12'$ in length and $9'$ in width and is currently placed against one side of a rectangular room. The owners desire to move the table to lay diagonally in the room. Determine the minimum length of the shorter side of the room, denoted as $S$, in feet, for the table to fit without tilting or... | 15' |
In a group of five friends, Amy is taller than Carla. Dan is shorter than Eric but taller than Bob. Eric is shorter than Carla. Who is the shortest? | Bob |
We have $n$ positive integers greater than $1$ and less than $10000$ such that neither of them is prime but any two of them are relative prime. Find the maximum value of $n $ . | 25 |
Three distinct vertices of a regular 2020-gon are chosen uniformly at random. The probability that the triangle they form is isosceles can be expressed as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100a+b$. | 773 |
There is a simple pendulum with a period of $T=1$ second in summer. In winter, the length of the pendulum shortens by 0.01 centimeters. How many seconds faster is this pendulum in winter over a 24-hour period compared to summer? (Round to the nearest second).
Note: The formula for the period of a simple pendulum is $T... | 17 |
Find the number of real solutions of the equation
\[\frac{4x}{x^2 + x + 3} + \frac{5x}{x^2 - 5x + 3} = -\frac{3}{2}.\] | 2 |
The ten-letter code $\text{BEST OF LUCK}$ represents the ten digits $0-9$, in order. What 4-digit number is represented by the code word $\text{CLUE}$? | 8671 |
In the sequence \( \left\{a_{n}\right\} \), if \( a_{k}+a_{k+1}=2k+1 \) (where \( k \in \mathbf{N}^{*} \)), then \( a_{1}+a_{100} \) equals? | 101 |
Given the set of vectors \(\mathbf{v}\) such that
\[
\mathbf{v} \cdot \mathbf{v} = \mathbf{v} \cdot \begin{pmatrix} 4 \\ -16 \\ 32 \end{pmatrix}
\]
determine the volume of the solid formed in space. | 7776\pi |
There is a reservoir A and a town B connected by a river. When the reservoir does not release water, the water in the river is stationary; when the reservoir releases water, the water in the river flows at a constant speed. When the reservoir was not releasing water, speedboat M traveled for 50 minutes from A towards B... | 100/3 |
An ellipse has foci at $F_1 = (0,2)$ and $F_2 = (3,0).$ The ellipse intersects the $x$-axis at the origin, and one other point. What is the other point of intersection? | \left( \frac{15}{4}, 0 \right) |
If three standard, six-faced dice are rolled, what is the probability that the sum of the three numbers rolled is 9? Express your answer as a common fraction. | \frac{25}{216} |
A real number $a$ is chosen randomly and uniformly from the interval $[-20, 18]$. The probability that the roots of the polynomial
$x^4 + 2ax^3 + (2a - 2)x^2 + (-4a + 3)x - 2$
are all real can be written in the form $\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$. | 37 |
Given that in triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $\angle BAC = 60^{\circ}$, $D$ is a point on side $BC$ such that $AD = \sqrt{7}$, and $BD:DC = 2c:b$, then the minimum value of the area of $\triangle ABC$ is ____. | 2\sqrt{3} |
A right square pyramid with volume $54$ has a base with side length $6.$ The five vertices of the pyramid all lie on a sphere with radius $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. | 21 |
If the arithmetic mean of $a$ and $b$ is double their geometric mean, with $a>b>0$, then a possible value for the ratio $a/b$, to the nearest integer, is: | 14 |
James is a first-year student at a University in Chicago. He has a budget of $1000 per semester. He spends 30% of his money on food, 15% on accommodation, 25% on entertainment, and the rest on coursework materials. How much money does he spend on coursework materials? | Accommodation is 15% * $1000=$<<15*.01*1000=150>>150
Food is 30% * $1000=$<<30*.01*1000=300>>300
Entertainment is 25% * $1000=$<<25*.01*1000=250>>250
Coursework materials are thus $1000-($150+$300+$250) = $300
#### 300 |
Find the smallest natural number $n$ such that $\sin n^{\circ} = \sin (2016n^{\circ})$. | 72 |
Define a modified Ackermann function \( A(m, n) \) with the same recursive relationships as the original problem:
\[ A(m,n) = \left\{
\begin{aligned}
&n+1& \text{ if } m = 0 \\
&A(m-1, 1) & \text{ if } m > 0 \text{ and } n = 0 \\
&A(m-1, A(m, n-1))&\text{ if } m > 0 \text{ and } n > 0.
\end{aligned}
\right.\]
Compu... | 29 |
Five million times eight million equals | 40,000,000,000,000 |
Find the coefficient of $x^3$ when $3(x^2 - x^3+x) +3(x +2x^3- 3x^2 + 3x^5+x^3) -5(1+x-4x^3 - x^2)$ is simplified. | 26 |
Let $x,$ $y,$ $z$ be positive real number such that $xyz = \frac{2}{3}.$ Compute the minimum value of
\[x^2 + 6xy + 18y^2 + 12yz + 4z^2.\] | 18 |
How many integers between $200$ and $250$ have three different digits in increasing order? | 11 |
If $\frac{4}{3} (r + s + t) = 12$, what is the average of $r$, $s$, and $t$? | 3 |
Eddy draws $6$ cards from a standard $52$ -card deck. What is the probability that four of the cards that he draws have the same value? | 3/4165 |
Determine the number of all positive integers which cannot be written in the form $80k + 3m$ , where $k,m \in N = \{0,1,2,...,\}$ | 79 |
Let $t(x) = \sqrt{3x+1}$ and $f(x)=5-t(x)$. What is $t(f(5))$? | 2 |
Find the sum of all positive integers $n$ such that, given an unlimited supply of stamps of denominations $5,n,$ and $n+1$ cents, $91$ cents is the greatest postage that cannot be formed.
| 71 |
The set of positive even numbers $\{2, 4, 6, \cdots\}$ is grouped in increasing order such that the $n$-th group has $3n-2$ numbers:
\[
\{2\}, \{4, 6, 8, 10\}, \{12, 14, 16, 18, 20, 22, 24\}, \cdots
\]
Determine which group contains the number 2018. | 27 |
Twenty pairs of integers are formed using each of the integers \( 1, 2, 3, \ldots, 40 \) once. The positive difference between the integers in each pair is 1 or 3. If the resulting differences are added together, what is the greatest possible sum? | 58 |
A standard die is rolled eight times. What is the probability that the product of all eight rolls is odd and consists only of prime numbers? Express your answer as a common fraction. | \frac{1}{6561} |
Solve for $x$: $\left(\frac{1}{4}\right)^{2x+8} = (16)^{2x+5}$. | -3 |
If \(100^a = 4\) and \(100^b = 5\), then find \(20^{(1 - a - b)/(2(1 - b))}\). | \sqrt{5} |
Given that a geometric sequence $\{a_n\}$ consists of positive terms, and $(a_3, \frac{1}{2}a_5,a_4)$ form an arithmetic sequence, find the value of $\frac{a_3+a_5}{a_4+a_6}$. | \frac{\sqrt{5}-1}{2} |
Iain has 200 pennies. He realizes that 30 of his pennies are older than he is. If he wishes to get rid of these pennies and then throw out 20% of his remaining pennies, how many will he have left? | Start with taking out the older pennies 200 pennies - 30 pennies = <<200-30=170>>170 pennies
Take the 170 pennies * .20 = <<170*.20=34>>34
170 pennies - 34 pennies = <<170-34=136>>136 pennies.
#### 136 |
Let $f : Q \to Q$ be a function satisfying the equation $f(x + y) = f(x) + f(y) + 2547$ for all rational numbers $x, y$ . If $f(2004) = 2547$ , find $f(2547)$ . | 2547 |
Let $f(x)=\sin\left(2x+\frac{\pi}{3}\right)+\sqrt{3}\sin^2x-\sqrt{3}\cos^2x-\frac{1}{2}$.
$(1)$ Find the smallest positive period and the interval of monotonicity of $f(x)$;
$(2)$ If $x_0\in\left[\frac{5\pi}{12},\frac{2\pi}{3}\right]$ and $f(x_{0})=\frac{\sqrt{3}}{3}-\frac{1}{2}$, find the value of $\cos 2x_{0}$. | -\frac{3+\sqrt{6}}{6} |
Jaron wants to raise enough money selling candy bars to win the Nintendo Switch prize. He needs 2000 points for the Nintendo Switch. He has already sold 8 chocolate bunnies that are worth 100 points each. Each Snickers bar he sells earns 25 points. How many Snickers bars does he need to sell the win the Nintendo Switch... | Jaron has earned a total of 8 * 100 points = <<8*100=800>>800 points.
To win the Switch he needs to earn 2000 - 800 = <<2000-800=1200>>1200 points.
Therefore, he needs to sell 1200 / 25 = <<1200/25=48>>48 Snickers bars.
#### 48 |
A point is randomly thrown onto the segment [3, 8] and let $k$ be the resulting value. Find the probability that the roots of the equation $\left(k^{2}-2 k-3\right) x^{2}+(3 k-5) x+2=0$ satisfy the condition $x_{1} \leq 2 x_{2}$. | 4/15 |
Given a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and the point $(n, \frac{S_n}{n})$ lies on the line $y= \frac{1}{2}x+ \frac{11}{2}$. The sequence $\{b_n\}$ satisfies $b_{n+2}-2b_{n+1}+b_n=0$ $(n\in{N}^*)$, and $b_3=11$, with the sum of the first $9$ terms being $153$.
$(1)$ Find the general formu... | 18 |
In the rectangular coordinate system $(xOy)$, the polar coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of circle $C$ is $ρ=2 \sqrt{2}\cos \left(θ+\frac{π}{4} \right)$, and the parametric equation of line $l$ is $\begin{cases} x=t ... | \frac{10 \sqrt{5}}{9} |
In a magic square, what is the sum \( a+b+c \)? | 47 |
Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\theta = \arg \left(\tfrac{w-z}{z}\right)$. The maximum possible value of $\tan^2 \theta$ can be written as $\tfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$. (Note that $\arg(w)$, for $w \neq 0$, denotes the ... | 100 |
Chewbacca has 20 pieces of cherry gum and 30 pieces of grape gum. Some of the pieces are in complete packs, while others are loose. Each complete pack has exactly $x$ pieces of gum. If Chewbacca loses one pack of cherry gum, then the ratio of the number of pieces of cherry gum he has to the number of pieces of grape ... | 14 |
(1) In $\triangle ABC$, if $2\lg \tan B=\lg \tan A+\lg \tan C$, then the range of values for $B$ is ______.
(2) Find the maximum value of the function $y=7-4\sin x\cos x+4\cos ^{2}x-4\cos ^{4}x$ ______. | 10 |
Find the smallest positive integer $n$ such that there exists a complex number $z$, with positive real and imaginary part, satisfying $z^{n}=(\bar{z})^{n}$. | 3 |
Find the quadratic polynomial, with real coefficients, which has $3 + i$ as a root, and where the coefficient of $x^2$ is 2. | 2x^2 - 12x + 20 |
The matrix
\[\begin{pmatrix} 3 & -1 \\ c & d \end{pmatrix}\]is its own inverse. Enter the ordered pair $(c,d).$ | (8,-3) |
A quarterback steps back to throw 80 times in a game. 30 percent of the time he does not get a pass thrown. Half of the times that he does not throw the ball he is sacked for a loss. How many times is the quarterback sacked for a loss in the game? | No pass thrown:80(.30)=24
Sacked:24/2=<<24/2=12>>12
#### 12 |
Simplify and write the result as a common fraction: $$\sqrt{\sqrt[3]{\sqrt{\frac{1}{4096}}}}$$ | \frac{1}{2} |
Calculate: \( 8.0 \dot{\dot{1}} + 7.1 \dot{2} + 6.2 \dot{3} + 5.3 \dot{4} + 4.4 \dot{5} + 3.5 \dot{6} + 2.6 \dot{7} + 1.7 \dot{8} = \) | 39.2 |
If there are 150 seats in a row, calculate the fewest number of seats that must be occupied so the next person to be seated must sit next to someone. | 37 |
For a certain weekend, the weatherman predicts that it will rain with a $40\%$ probability on Saturday and a $50\%$ probability on Sunday. Assuming these probabilities are independent, what is the probability that it rains over the weekend (that is, on at least one of the days)? Express your answer as a percentage. | 70\% |
Given that \(a - b = 2 + \sqrt{3}\) and \(b - c = 2 - \sqrt{3}\), find the value of \(a^2 + b^2 + c^2 - ab - bc - ca\). | 15 |
What is the positive difference between $\frac{8^2 - 8^2}{8}$ and $\frac{8^2 \times 8^2}{8}$? | 512 |
There are several balls of the same shape and size in a bag, including $a+1$ red balls, $a$ yellow balls, and $1$ blue ball. Now, randomly draw a ball from the bag, with the rule that drawing a red ball earns $1$ point, a yellow ball earns $2$ points, and a blue ball earns $3$ points. If the expected value of the score... | \frac{3}{10} |
Given the expression $\frac{810 \times 811 \times 812 \times \cdots \times 2010}{810^{n}}$ is an integer, find the maximum value of $n$. | 149 |
Given the sets $M={x|m\leqslant x\leqslant m+ \frac {3}{4}}$ and $N={x|n- \frac {1}{3}\leqslant x\leqslant n}$, both of which are subsets of ${x|0\leqslant x\leqslant 1}$, what is the minimum "length" of the set $M\cap N$? (Note: The "length" of a set ${x|a\leqslant x\leqslant b}$ is defined as $b-a$.) | \frac{1}{12} |
A company organizes its employees into 7 distinct teams for a cycling event. The employee count is between 200 and 300. If one employee takes a day off, the teams are still equally divided among all present employees. Determine the total number of possible employees the company could have. | 3493 |
Among the natural numbers from 1 to 100, find the total number of numbers that contain a digit 7 or are multiples of 7. | 30 |
The value of
\[\frac{n}{2} + \frac{18}{n}\]is smallest for which positive integer $n$? | 6 |
In triangle $ABC$, $AB = 3$, $BC = 4$, $AC = 5$, and $BD$ is the angle bisector from vertex $B$. If $BD = k \sqrt{2}$, then find $k$. | \frac{12}{7} |
If $x=18$ is one of the solutions of the equation $x^{2}+12x+c=0$, what is the other solution of this equation? | -30 |
On the side \( BC \) of triangle \( ABC \), points \( A_1 \) and \( A_2 \) are marked such that \( BA_1 = 6 \), \( A_1A_2 = 8 \), and \( CA_2 = 4 \). On the side \( AC \), points \( B_1 \) and \( B_2 \) are marked such that \( AB_1 = 9 \) and \( CB_2 = 6 \). Segments \( AA_1 \) and \( BB_1 \) intersect at point \( K \)... | 12 |
A math teacher had $100 to buy three different types of calculators. A basic calculator costs $8. A scientific calculator costs twice the price as the basic while a graphing calculator costs thrice the price as the scientific. How much change did she receive after buying those three different types of calculators? | A scientific calculator costs $8 x 2 = $<<8*2=16>>16.
A graphing calculator costs $16 x 3 = $<<16*3=48>>48.
So, she spent $8 + $16 + $48 = $<<8+16+48=72>>72 for the three calculators.
Therefore, the math teacher received $100 - $72 = $<<100-72=28>>28 change.
#### 28 |
A circle with center $O$ has radius $5,$ and has two points $A,B$ on the circle such that $\angle AOB = 90^{\circ}.$ Rays $OA$ and $OB$ are extended to points $C$ and $D,$ respectively, such that $AB$ is parallel to $CD,$ and the length of $CD$ is $200\%$ more than the radius of circle $O.$ De... | 5 + \frac{15\sqrt{2}}{2} |
Jeff has a shelter where he currently takes care of 20 cats. On Monday he found 2 kittens in a box and took them to the shelter. On Tuesday he found 1 more cat with a leg injury. On Wednesday 3 people adopted 2 cats each. How many cats does Jeff currently have in his shelter? | Counting the cats he had, the kittens he found, and the injured cat, Jeff had a total of 20 + 2 + 1 = <<20+2+1=23>>23 cats.
3 people took a total of 3 * 2 = <<3*2=6>>6 cats.
After Wednesday, Jeff was left with 23 - 6 = <<23-6=17>>17 cats.
#### 17 |
It takes a butterfly egg 120 days to become a butterfly. If each butterfly spends 3 times as much time as a larva as in a cocoon, how long does each butterfly spend in a cocoon? | Let c be the amount of time the butterfly spends in a cocoon and l be the amount of time it spends as a larva. We know that l = 3c and l + c = 120.
Substituting the first equation into the second equation, we get 3c + c = 120.
Combining like terms, we get 4c = 120.
Dividing both sides by 4, we get c = 30.
#### 30 |
How long should a covered lip pipe be to produce the fundamental pitch provided by a standard tuning fork? | 0.189 |
Find the largest five-digit number whose digits' product equals 120. | 85311 |
Let $\left\{a_n\right\}$ be an arithmetic sequence, and $S_n$ be the sum of its first $n$ terms, with $S_{11}= \frac{11}{3}\pi$. Let $\left\{b_n\right\}$ be a geometric sequence, and $b_4, b_8$ be the two roots of the equation $4x^2+100x+{\pi}^2=0$. Find the value of $\sin \left(a_6+b_6\right)$. | -\frac{1}{2} |
Two distinct numbers a and b are chosen randomly from the set $\{3, 3^2, 3^3, ..., 3^{20}\}$. What is the probability that $\mathrm{log}_a b$ is an integer?
A) $\frac{12}{19}$
B) $\frac{1}{4}$
C) $\frac{24}{95}$
D) $\frac{1}{5}$ | \frac{24}{95} |
Given two intersecting circles O: $x^2 + y^2 = 25$ and C: $x^2 + y^2 - 4x - 2y - 20 = 0$, which intersect at points A and B, find the length of the common chord AB. | \sqrt{95} |
Christina has 3 snakes. 1 snake is 2 feet long. Another snake is 16 inches long. The last snake is 10 inches long. How many inches are all of her snakes combined? | The first snake is 24 inches because there are 12 inches in a foot.
The snakes are 24+16+10= <<24+16+10=50>>50 inches long.
#### 50 |
What is the distance on a Cartesian coordinate plane from $(1, -1)$ to $(7, 7)?$ | 10 |
What is the largest positive integer with only even digits that is less than $10,000$ and is a multiple of $9$? | 8820 |
The polynomial $ax^4 + bx^3 + 32x^2 - 16x + 6$ has a factor of $3x^2 - 2x + 1.$ Find the ordered pair $(a,b).$ | (18,-24) |
Molly got a bike for her thirteenth birthday. She rode her bike 3 miles a day, every day, until she turned 16. How many miles did Molly ride on her bike? | Molly rode for 16 – 13 = <<16-13=3>>3 years.
She rode for 3 years x 365 days = <<3*365=1095>>1,095 days.
She rode a total of 3 miles x 1,095 days = <<3*1095=3285>>3,285 miles.
#### 3,285 |
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