Flagged question review

A triangle with angle measures 30°, 60°, and 90° has a perimeter of $18 + 6 \times \sqrt{3}$. What is the length of the longest side of the triangle?

In the figure above, $BD = 6$ and $AD = 8$. What is the length of $\overline{DC}$ ?

In the figure above, $\overline{BD}$ is parallel to $\overline{AE}$. What is the length of $\overline{CE}$ ?

The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?

In the right triangle shown above, what is the length of  ?

Points $A$ and $B$ lie on a circle with radius 1, and arc $A B$ has length $\dfrac{\pi}{3}$. What fraction of the circumference of the circle is the length of arc $A B$ ?

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

In the $xy$-plane above, points $P$, $Q$, $R$, and $T$ lie on the circle with center $O$. The degree measures of angles $P O Q$ and $R O T$ are each 30°. What is the radian measure of angle $Q O R$ ?

In above, what is the length of  ?

Triangle $ABC$ and triangle $DEF$ are shown. The relationship between the side lengths of the two triangles is such that $\dfrac{AB}{DE} = \dfrac{BC}{EF} = \dfrac{AC}{DF} = 3$. If the measure of angle $BAC$ is 20°, what is the measure, in degrees, of angle $EDF$ ? (Disregard the degree symbol when gridding your answer.)

In triangle $RST$ above, point $W$ (not shown) lies on $\overline{RT}$. What is the value of $\cos\left(\angle RSW - \sin\left(\angle WST\right)\right)$ ?

The area of triangle $ABC$ above is at least 48 but no more than 60. If $y$ is an integer, what is one possible value of $x$ ?

In the $xy$-plane, the graph of $2 x^2 - 6 x + 2 y^2 + 2 y = 45$ is a circle. What is the radius of the circle?

In the figure above, $R T = T U$. What is the value of $x$ ?

At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 300 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet long. Given that the Washington Monument is approximately 555 feet tall, which of the following is closest to the height, in feet, of the cherry tree?

The number of radians in a 720-degree angle can be written as $a \times \pi$, where $a$ is a constant. What is the value of $a$ ?

In the figure above, $\tan\left(B\right) = \dfrac{3}{4}$. If $B C = 15$ and $D A = 4$, what is the length of $\overline{DE}$ ?

The equation $\left(x + 6\right)^2 + \left(y + 3\right)^2 = 121$ defines a circle in the $xy$‑plane. What is the radius of the circle?

In the figure above, what is the length of $\overline{NQ}$ ?

Triangle $A B C$ above is a right triangle, and $\sin\left(B\right) = \dfrac{5}{13}$. What is the length of side $B C$?

What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

In the figure above, $\overline{MQ}$ and $\overline{NR}$ intersect at point $P$, $N P = Q P$, and $M P = P R$. What is the measure, in degrees, of $\angle QMR$ ? (Disregard the degree symbol when gridding your answer.)

Intersecting lines $r$, $s$, and $t$ are shown below.

What is the value of $x$ ?

For a certain computer game, individuals receive an integer score that ranges from 2 through 10. The table below shows the frequency distribution of the scores of the 9 players in group A and the 11 players in group B.

The median of the scores for group B is how much greater than the median of the scores for group A?

A random sample of 400 town voters were asked if they plan to vote for Candidate A or Candidate B for mayor. The results were sorted by gender and are shown in the table below.

The town has a total of 6,000 voters. Based on the table, what is the best estimate of the number of voters who plan to vote for Candidate A?

Thomas installed a new stove in his restaurant. At the time of installation, the stove had a value of $800. Thomas estimates that each year the value of the stove will depreciate by 20% of the previous year’s estimated value. What is the estimated value of the stove exactly 2 years after Thomas installed it?

Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of $x$ ?

A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?

The mean of the list of numbers above is what fraction of the sum of the five numbers?

During a sale, the original prices of all the items in a clothing store have been reduced by 20%. What is the sale price of a jacket with an original price of $50 ?

Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. According to the line of best fit, what is the number of people, rounded to the nearest 10, predicted to visit this beach on a day with an average temperature of 32°C?

To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

If $a$ is the mean and $b$ is the median of nine consecutive integers, what is the value of $\left|a - b\right|$ ?

Which of the following statements about the means and medians of data set A and data set B is true?

Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. The line of best fit for the data has a slope of approximately 57. According to this estimate, how many additional people per day are predicted to visit the beach for each 5°C increase in average temperature?

On May 10, 2015, there were 83 million Internet subscribers in Nigeria. The major Internet providers were MTN, Globacom, Airtel, Etisalat, and Visafone. By September 30, 2015, the number of Internet subscribers in Nigeria had increased to 97 million. If an Internet subscriber in Nigeria on September 30, 2015, is selected at random, the probability that the person selected was an MTN subscriber is 0.43. There were $p$ million MTN subscribers in Nigeria on September 30, 2015. To the nearest integer, what is the value of $p$?

Which of the following statements correctly compares the means of data set A and data set B?

The scatterplot above shows a company’s ice cream sales $d$, in dollars, and the high temperature $t$, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

Jeremy deposited $x$ dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of $x$?

An inspector begins a day of work with a large sample of shirts that need to be checked for defects. The inspector works at a constant rate throughout the morning. What type of model is best to model the number of shirts remaining to be checked for defects at any given time throughout the morning?

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

Which of the following is true about the values of $2^{x}$ and $2 x + 2$ for $x > 0$?

Human blood can be classified into four common blood types—A, B, AB, and O. It is also characterized by the presence $\left(+\right)$ or absence $\left(-\right)$ of the rhesus factor. The table above shows the distribution of blood type and rhesus factor for a group of people. If one of these people who is rhesus negative $\left(-\right)$ is chosen at random, the probability that the person has blood type B is $\dfrac{1}{9}$ . What is the value of $x$ ?

The line graph shows the total amount of snow, in inches, recorded each year in Washington, DC, from 2003 to 2015. If $p\%$ is the percent decrease in the annual snowfall from 2003 to 2007, what is the value of$p$?

Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of $x$?

Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company?

A city has 50 city council members. A reporter polled a random sample of 20 city council members and found that 6 of those polled supported a specific bill. Based on the sample, which of the following is the best estimate of the number of city council members in the city who support the bill?

A group of monarch butterflies migrated from Chicago, Illinois, to Michoacán, Mexico, flying a total of 2,100 miles. It took a single butterfly in the group 120 days to travel this route one way. On average, how many miles did the butterfly travel per day?

A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?

What is the median of the seven data values shown?

A researcher interviewed 411 randomly selected US residents and asked about their views on the use of nuclear energy. The table above summarizes the responses of the interviewees. If the population of the United States was 300 million when the survey was given, based on the sample data for the 411 US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it? (Round your answer to the nearest whole number.)

For a person m miles from a flash of lightning, the length of the time interval from the moment the person sees the lightning to the moment the person hears the thunder is k seconds. The ratio of m to k can be estimated to be 1 to 5. According to this estimate, the person is how many miles from a flash of lightning if the time interval is 25 seconds?

The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station’s average speed in miles per hour?

What value of $x$ satisfies the equation above?

Let the function $p$ be defined as $p(x) = \dfrac{\left(x - c\right)^2 + 160}{2 c}$, where $c$ is a constant. If $p(c) = 10$, what is the value of $p(12)$ ?

If $a$ and $c$ are positive numbers, which of the following is equivalent to $\sqrt{\left(a + c\right)^3} \times \sqrt{a + c}$?

The function $h$ is defined above, where $a$, $b$, and $c$ are integer constants. If the zeros of the function are $-5$ 6, and 7, what is the value of $c$?

Which of the following is equivalent to  ?

The total distance $d$, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of $t$, where $t$ is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when $t = 0$, then what is the total distance traveled, in meters, by the object after 30.0 seconds?

If the given expression is rewritten in the form $\left(2 x - 3\right) \times \left(x + k\right)$, where $k$ is a constant, what is the value of $k$ ?

The expression above can be written in the form $a \times y^2 + b$, where $a$ and $b$ are constants. What is the value of $a + b$ ?

In the$xy$-plane, the graph of $y = 3 x^2 - 14 x$ intersects the graph of $y = x$ at the points $\left(0, 0\right)$ and $a, a$. What is the value of $a$ ?

If $a$ is a solution of the equation above and $a > 0$, what is the value of $a$ ?

According to Moore’s law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based on this information, in which of the following years does Moore’s law estimate the number of transistors to reach 1.1 million?

The surface area of a cube is $6 \times \left(\dfrac{a}{4}\right)^2$, where $a$ is a positive constant. Which of the following gives the perimeter of one face of the cube?

A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?

If one solution to the system of equations above is $\left(x, y\right)$, what is one possible value of $x$ ?

The expression above is equivalent to $a x^2 + b x + c$, where $a$, $b$, and $c$ are constants. What is the value of $b$?

The sum of $-2 x^2 + x + 31$ and $3 x^2 + 7 x - 8$ can be written in the form $a x^2 + b x + c$, where $a$, $b$, and $c$ are constants. What is the value of $a + b + c$ ?

A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

The graph of the function $f$, defined by $f(x) = -\dfrac{1}{2} \times \left(x - 4\right)^2 + 10$, is shown in the $xy$-plane above. If the function $g$ (not shown) is defined by $g(x) = -x + 10$, what is one possible value of $a$ such that $f(a) = g(a)$ ?

In the equation above, $a$ is a constant and $a > 0$. If the equation has two integer solutions, what is a possible value of $a$ ?

In the expression  , $p$ is a constant. This expression is equivalent to the expression $6 x^2 - 155 x + 24$. What is the value of $p$ ?

In the $xy$-plane, what is the $y$-coordinate of the point of intersection of the graphs of $y = \left(x - 1\right)^2$ and $y = 2 x - 3$ ?

If the ordered pair $x, y$ satisfies the system of equations above, what is one possible value of $x$ ?

During a 5-second time interval, the average acceleration $a$, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation $a = \dfrac{v_{f} - 12}{5}$, where $v$_$f$ is the final velocity of the object in meters per second. If the equation is rewritten in the form $v_{f}$ = $xa$ + $y$, where $x$ and $y$ are constants, what is the value of $x$ ?

If $\dfrac{\sqrt{x^{5}}}{\sqrt[3]{x^{4}}} = x^{\dfrac{a}{b}}$ for all positive values of $x$, what is the value of $\dfrac{a}{b}$?

Which of the following is equivalent to the given expression?

The function $f$ is defined by $f(x) = m x + b$, where $m$ and $b$ are constants. If $f(0) = 18$ and $f(1) = 20$, what is the value of $m$ ?

Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, what is the maximum number of hours for which Maria can rent the boat?

In the solution $x, y$ to the system of equations above, what is the value of $x$ ?

How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?

In the given equation, $k$ is a constant. If the equation has infinitely many solutions, what is the value of $k$ ?

A librarian has 43 books to distribute to a group of children. If he gives each child 2 books, he will have 7 books left over. How many children are in the group?

If $\left(x, y\right)$ is the solution to the given system of equations, what is the value of $y$ ?

The line with the equation $\dfrac{4}{5} x + \dfrac{1}{3} y = 1$ is graphed in the $xy$‑plane. What is the $x$-coordinate of the $x$‑intercept of the line?

If $3 x + 2 = 8$, what is the value of $9 x + 6$ ?

Megan’s regular wage at her job is p dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Megan worked for 10 hours, and her total earnings for that day were $137.50. What is Megan’s regular hourly wage?

Store A sells raspberries for $\$ 5.50$ per pint and blackberries for $\$ 3.00$ per pint. Store B sells raspberries for $\$ 6.50$ per pint and blackberries for $\$ 8.00$ per pint. A certain purchase of raspberries and blackberries would cost $\$ 37.00$ at Store A or $\$ 66.00$ at Store B. How many pints of blackberries are in this purchase?

On January 1, 2015, a city’s minimum hourly wage was $9.25. It will increase by $0.50 on the first day of the year for the next 5 years. Which of the following functions best models the minimum hourly wage, in dollars, $x$ years after January 1, 2015, where ?

The table above shows the coordinates of three points on a line in the $xy$-plane, where $k$ and $n$ are constants. If the slope of the line is 2, what is the value of $k + n$ ?

In the system of equations above, $c$ is a constant. If the system has no solution, what is the value of $c$ ?

The formula above is Ohm’s law for an electric circuit with current $I$, in amperes, potential difference $V$, in volts, and resistance $R$, in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by $n$ six-volt batteries that produce a total potential difference of $6 n$ volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, $n$, of six-volt batteries that can be used?

The function  is defined as $g(x) = 5 x + a$, where $a$ is a constant. If $g(4) = 31$, what is the value of $a$ ?

What value of $p$ is the solution of the equation above?