Kari had a page of stamps. She used some of the stamps from the center of the page. The picture below shows the stamps Kari has left. How much of the page of stamps did Kari use?
Abby, Zach, and Beth had a jump rope contest. The chart below shows the length of time each child jumped rope. Based on this information, which statement is true?
The table shows the possible food choices for lunch. How many different lunches can be made that include 1 type of soup, 1 type of sandwich, and 1 type of salad?
Mr. Jacob's class is going on a field trip. They need to split into groups of 4 students. If there are 24 students in Mr. Jacob's class, how many groups will there be?
Jackie's mom baked cookies. Jackie wants to share the cookies equally with five friends. What information is needed to determine how many cookies each person could get?
Ms. Ryan asked her student in her class if they have any pets. Her results are shown below.
4 students have only cats
12 studetns have only dogs
5 students have a dog and a cat
8 students have fish
No students have pet gerbils
Based on the information from Ms. Ryan's class, which statement is most likely true?
Martha is going to make bracelets to sell for a fundraiser. She bought 8 meters of yarn. She wants to cut it into pieces that are 16 centimeters long for each bracelet. How many bracelets can Martha make?
The table below shows the number of baseball cards Tika collected during four months. What is the best estimate for the number of baseball cards Tika collected in all?
John has 10 pairs of white socks and 1 pair of blue socks in his drawer. There are no other socks in the drawer. Without looking, he takes 1 pair out of the drawer. What are his chances of choosing a white pair of socks?
Nicki's class needs to raise $89.45 in order to have a pizza party. So far, she has collected $62.90. How much more money does Nicki's class need to buy the pizza party?
On Monday, Joel had 17 treats to give his puppy. He gives his puppy 2 or 3 treats each day. The table below shows the number of treats Joel has left at the end of each day. Based on the information in the table, which prediction will most likely to happen if Joel continues to give his puppy 2 or 3 treats each day?
Jim has $7.00 that he uses to purchase school lunch. He spends the same amount of money each day. Which expression can be used to show how much Jim can spend on lunch each day?
Lizeth is having a birthday party. She invited 19 people. She will buy enough juice boxes so each person can have at least 1. If the juice boxes come in packs of 6, how many packs should Lizeth buy?
Marcus bought a pet frog. He went to a pet store to buy some supplies for the frog's home. He found a list of frog rules in the pet store. Small sized frogs need to live in a 10 gallon tank. All frogs need warm light or sunshine. All frogs need water to keep their skin moist. Frogs eat 5 bugs and worms per day. What information should the pet store owner ask Marcus before he sells him the supplies?
Logan Academy students take part in four field trips during the school year. They visit a library, a museum, a park, and a zoo. How many different ways can the four trips be ordered for the school year?
A dolphin was swimming at 20 feet below sea level. Then it dove to 45 feet below its original position. Which integer represents the depth of the dolphin's dive?
Grace measures a bean plant at the end of every week. At the end of week 1, the plant is 4 inches tall. It grows 1/2 inch each week for 5 more weeks. How tall is Grace's bean plant at the end of week 5?
Ms. Cook's class bought 2 bags of concrete and some bricks to build a border for their class garden. The bricks cost $51. The total cost of the bricks and the concrete was $57. Which equations can be used to find the cost, b, of 1 bag of concrete?
Sheri asks 83 students at school to choose the sports that they most enjoy watching. The students can choose from baseball, basketball, football, and soccer. The results are shown in the table. Which statement is a reasonable conclusion to make from the information in the table?
To place 0.67, 3/4, and 34% in order from least to greatest. John changes 3/4 to 0.75 and 34% to 0.34. Then he uses the three decimals to correctly place the original numbers in order from least to greatest: 34% , 0.67, 3/4. Which problem is best solved by using this same strategy?
The diagram below shows the length and width of the wall that Tara is going to cover with wallpaper. What is the least amount of wall paper Tara will need to cover the entire area of the wall?
Samantha and Pedro each have 2 fair number cubes. The faces of each cube are numbered 1 through 6. They each rolled their 2 number cubes 50 times and recorded the sum of the numbers rolled. Based on the data in the tables, which statement is not true?
Erika is baking cupcakes. The recipe calls for 1 1/4 cups of sugar for the batter, and 1 2/3 for the frosting. About how many total cups of sugar will Erika need for her recipe?
Sand Dollar Elementary is planning a school field trip for its fourth and fifth grade students. The location that the students visit will depend on their names. The chart below shows the options for the field trip locations. Based on the information in the chart, which statement is not true?
There are 3 classes of 22 students making ice cream sundaes. A sundae can be made using one of 3 syrups and one of 3 candy toppings. Each student makes one sundae. Which expression can be used to find the total number of sundaes made by the students.
Each stem-and-leaf plot shows the number of points scored by a team in basketball tournament. How many total scores are represented by all stem-and-leaf plots?
Each stem-and-leaf plot shows the number of points scored by a team in basketball tournament. What is the greatest number of points scored by any team in one game?
Kara plans to carpet the entire floor in each of the two rooms shown below. What is the best estimate of the total amount of carpet, in square feet, needed to completely cover both floors?
Vincent's baseball coach suggested that he dirnk one-half gallon of water daily. If Vincent drinks one-half gallon of water, how many 8-ounce glasses will he drink?
On the grid below, points Q, R, and S represent three vertices of a rectangle. What are the coordinates of point T, the vertex that will complete rectangle QRST?
Rafael performed an experiment by spinning the arrow on a spinner 200 times. His results are recorded in the table below.
Which is closest to the number of times he should expect the arrow to land on red section?
The scatter plot shows the relationship between the amount of time Casey was at the mall and the amount of money she spent there. Which statement best describes the relationship between the amount of money Casey spent and the amount of time she was at the mall?
Lauren wants to put a brick border around her garden. A drawing of her garden is represented by the shaded section on the grid below. What is closest to the number of meters of brick border Lauren will need to put around her garden?
Valerie has 35 students in her art class. She asked each student what types of activities they like to do and made a Venn diagram of the results. How many students in Valerie's class told her that they only like to draw and sculpt?
Jim and Don are playing darts. Jim has scored 16, 12, and 2 points. Don's turn is after Jim's. Don has scored 12, 10, and 2 points. They have taken the same number of turns. Who is ahead at this time? Which statement does Kelly need for solving the problem?
Scott delivers the 6th grade newsletter to five rooms at his school. He must find the quickest route. The vertex-edge graph shows the rooms that Scott must deliver to and the time, in seconds, it takes him to get from room to room. If Scott begins and ends at his Homeroom, what is the quickest route for him to take and to make sure he visits each room only once?
The number of students (class size) in each of 7 classes is shown as 15, 25, 25, 29, 31, 32, 37 Which class size affects the range of all 7 classes the most?
Becky created the line graph below to show the distance she traveled during one day. Which activity could be represented by the circled portion of the line?
The Venn diagram below shows the number of students in a class who have visited the Grand Canyon, Carlsbad Caverns, or both. There are 34 students in the class, and all of the students have visited at least one of the locations. What is the number of students, x, who have only visited the Grand Canyon?
The graph below shows the increase in average gasoline prices from Jan. through May. If the gasoline prices continue to increase at the same rate, what will be the average gasoline price in July of that same year?
Max, Owen, Elise, and Cara went to a school carnival. They each played the dart throw, ring toss, water shoot, and basketball throw. Each student won a different game. Clues: Max didn't score any points at the dart throw. Elise correctly tossed 2 rings, but did not win the ring toss. Cara won a bear for outscoring everyone at the water shoot. Owen score more than anyone at the basketball throw. Based on the clues, which game did Max win?
On a winter Monday in Prescott, the temperature at 8 a.m. was -8°F. At 1 p.n. it was 27°F. By how many degrees did the temperature change from morning to afternoon?
Dave's neighbors are going on a trip to Japan. He wants them to bring him a souvenir t-shirt, but Japan has its own unit of currency. Conversion 1 US dollar = about 94.73 Japanese yen. Dave gives his neighbors $20.00. About how many Japanese yen will Dave's neighbors be able to spend on his t-shirt?
Karen wants to visit all of the points of interest near her home. She will leave from her home and then visit each place on her vertex-edge graph only once. What is the shortest distance that Karen will travel to each site and then return home?
Ken will conduct a probability experiment by removing a cube from a bag of colored cubes that are all the same size and shape. Ken will use the following procedure. Without looking, remove a cube. Record its color. Put it back in the bag. Repeat the experiment. The probability of drawing a green cube is 1/2. What is the probability that the first 3 cubes that Ken removes will be green?
Ramon wants to graph his science test scores each week. He will use the graph to determine a trend for his scores based on the days of the week he takes the test. What is the best type of graphic display he should use for this?
Jose is having a party and will invite all of his friends. He will supply the following items for each person. 3 slices of pizza, 2 bottles of sports drink, and 1 piece of cake. What information is needed to make sure that Jose has pizza, sports drink, and cake for each person?
Cece scored a 78 on her first math test. She scored an 84 on her second test. What is the percent increase, rounded to the nearest tenth, from Cece's first score to her second score?
Gary has 10 coins in his pocket 2 quarters, 5 dimes, and 3 nickels. Without looking, Gary pulls one coin from his pocket and put it on a table. Then, he pulls one more coin from his pocket. What is the probability that the first coin is a dime and the second coin is a nickel?
A tower is 160 feet tall and cast a shadow 34 feet long. A person standing next to the tower casts a shadow 1.5 feet long. Which equation will find the height of the person, x?
Melissa earned a score of 75% on her first test. She wants to earn an 85% on her second test. What is the percent increase, rounded to the nearest whole number, from 75% to 85%?
A box contains 4 red pencils, 3 blue pencils, and 3 yellow pencils. What is the probability that a student randomly selects a blue pencil, keep it, and then a second student randomly selects a yellow pencil?
Emily, Zeke, Harry, and Brook each conducted surveys on the number of books people in their homes. Then they each answered the question below. "Must all measures of central tendency appear as a number in the set of data collected?" Which student's statement is true?
Students submitted pictures for the school yearbook. Only 4/5 of the submitted pictures fit in the yearbook. There were 105 pictures that did not fit. Approximately how many total pictures were submitted for the yearbook?
Joe is creating a number pattern. He begins the pattern with the number 3. Each number after 3 is twice the number before it, plus 1. Which pattern fits Joe's rule?
The student council is making gift bags for a fund raiser. They have 105 bags, 150 pens, 115 notebooks, 330 pencils, and 190 highlighters. If each gift bag consists of one bag, 2 pens, 1 notebook, 3 pencils, and 2 highlighters, what is the greatest number of gift bags that can be made?
Joe needs to find the midpoint of a line segment on a coordinate plane. Given the coordinates of the endpoints, what is the best way for him to find the midpoint of the line segment?
Martin is buying a fish tank. For the tank, he wants 10 clownfish, a few plants, and some stones for the bottom. He wants to make sure that the tank is large enough for the fish to swim comfortably. What does he need to ask the salesman in order to make sure he buys a large enough tank?
A team has twelve 15-year-old players and eight 16-year-old players. The coach of the team is 43 years old. Which measure of central tendency best represents the ages of the team, including the coach and why?
Jessica deposits $300 into a savings account that pays an annual interest rate of 2% compounded twice a year. How much money will Jessica have in her account at the end of one year?
A telephone company wants to create as many 7-digits phone number as possible without changing the first 3 digits. How many phnoe numbers can be created?
The data below represents the scores for a soccer team in seven games. Which measure of central tendency best represents the overall performance of the soccer team, and why?
Figure EFGH has a perimeter of 40 cm and an area of 96 cm2. It is dilated by a factor of 1/4 to create figure E'F'G'H'. What statement about the perimeter (p) and the area (A) of figure E'F'G'H' is true?
The area of a larger square is 16 times the area of a smaller square. How many time as long is the base of the larger square than the base of the smaller square?
Six differently colored balls (red, blue, green, orange, purple, and white) are placed in a basket. Without looking, three balls are removed. What is the total number of combinations that include a red ball?
The coordinates (2,2) and (-3,1) are two of the vertices of the figure on the coordinate plane.
What are the coordinates of the midpoint of the two vertices?
Debbie and Jamal each performed an experiment in which they spun a fair spinner 12 times. They recorded their results. What outcome has a probability of 0?
Chords line segment NP and line segment MQ intersect at point S in circle R. If line segment MS = 3, NS = 2, and SQ = 8, what is the length of line segment SP?
The table shows a sequence of figures, the number of squares in each figure, and the perimenter of each figure. Based on the pattern shown, which conjecture is valid?
In the diagram below, line segment RT intersects line segment QU at point S. Which postulate should be used to
prove that triangle ∆ RQS is congruent (approximately equal to) written mathematically ≅ triangle ∆ TUS?
The statements below are out of order.
Statement W: If blitz, then kerd.
Statement X: If mot, then det.
Statement Y: If kerd, then mot.
Statement Z: If toc, then blitz.
Which list shows the if...then statements in logical order?
Janelle's cell phone company charges a monthly fixed rate for the first 1,000 minutes, and then charges for each additional minute. Which graph best represents Janelle's monthly cell phone plan?
Earth's mean temperature is 59°F, and it is 9.3 x107 miles from the sun. Mar's mean temperature is -85° F, and it is 141.6 x 106
miles from the sun. Which matrix represents these data?
The coach wants to introduce each of the starting players at Tuesday's game in how many different order can each of the the 5 starting players be introduced?
A committee consisting of 5 teachers will be chosen from a staff of 25 teachers. To find the number of different possible 5-teacher committees, which should be used?
Bob created a number pattern beginning with 3. He created the next term by doubling the previous term and subtracting 1. The first 5 terms of the number pattern are shown below.
3, 5, 9, 17, 33, . . .
What is the 7th term in Bob's number pattern?
Student council members plan to sell shaved-ice cones to raise funds. They will spend $200.00 for supplies and whill charge $1.00 for each shaved-ice cone. Which graph
represents P, their profit, as a function of n, the number of cones sold?
The rule for a particular number pattern is to multiply the immediately preceding term by 2 then add 1. The first four terms of this number pattern are given below.
-2, -3, -5, -9, . . .
The table below shows information about the members of a concert choir at a high school. Which of the following graphs best describes the
choir's membership data?
The number cube shown is numbered 1 through 6 on its faces. When the cube is tossed once, what is the probability a number divisible by three will be on the top face?
The diagram below shows a building, a nearby flagpole, and their shadows. Based on the information in the diagram, what is x, the length of the shadow of the building?
In the pattern below, each term is found by doubling immediately the preceding term and adding 1
3, 7, 15, 31, 63, . . .
What is the 7th term in the pattern?
Sam began a pattern with 4 and 7. He added them to get 11, the third term. To get each term after the third, he added the two preceding terms.
4, 7, 11, 18, 29, . . .
What is the 9th term in this sequence?
The graph below shows the percent of the moon's face illuminated for the month of April. On What day in April did the moon reach its maximum illumination?
The Palmdale High School varsity basketball team's total points per game for this year's season is shown below.
Which stem-and-leaf plot could be used to correctly display the data?
The first two terms in a sequence are shown below. Each term after the first is found by rotating the arrow 45° clockwise. What will be the 7th term in the sequence?
In a cafeteria survey, 300 students chose one favorite lunch from 4 choices. The probability that a randomly selected student chose pizza was 0.25. Which data set support this conclusion?
A pattern is defined by the following rules. The first term is 4. The second term is 7. Each term after the second is found by adding 3 to the immediately preceding term.
What is the fifth term in this pattern?
Vectors A, B, and C satisfy the vector equation Vector A + Vector B = Vector C and their magnitude are related by the scalar equation A2 + B2 = C2. How is vector A oriented with respect to Vector B?
Assuming a car has gasoline consumption of 6 km/liter of gasoline. Its average speed is 60 km/hour. How far can a car travel in one and one half hours?
A straight track is 1600 meter in length. A runner begins at the starting line, runs due east for the full length of the track, turns around, and runs halfway back. The time for this run is five minutes. What is the runner's average velocity, and what is the average speed?
A plane starts from rest. The plane accelerates down the runway and at T=29 seconds attains a velocity of -260 km/hour. Determine the average acceleration of the plane in m/s2 ?
The spacecraft shown below has an initial velocity component of Vox = - 22 m/s and an acceleration component of A x = -24 m/s 2 and Voy = + 14 m/s and A y = + 12 m/s 2. Calculate the final displacement in x and y axis and the final velocity component, V x and V y after 7 seconds the spacecraft was initially observed.
An airplane moving horizontally with a constant velocity of -115 m/s at an altitude of 1050 meter. The direction of airplane to the right have been chosen as the positive direction. The plane release a crate box that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the crate box to hit the ground.
A projectile is launched from and return to ground level as shown below. Air resistance is neglected. The horizontal range of the projectile is R= 1200 meters and the horizontal component of the launch velocity is Vox = 25 m/s. Find the vertical component of Voy of the launch velocity.
Two people pushing a stalled car. The mass of the car is 1850 kg. One person applies a force of 300 Newton (N) to the car, while the other applies a force of 200 Newton (N). Both forces act in the same direction. A third force of 400 N also acts on the car, but in a direction opposite to that in which the two people are pushing. This third force is due to road frictional force. Find the acceleration of the car.
A man is paddling his boat (mass of man and boat = 1500 kg). By paddling, he causes an average force designated as variable letter P (paddling force) of 17 Newton (N) to applied to the boat in a direction due east. The wind also exerts a force W (wind force) on the boat. This wind force, W has a magnitude of 15 Newton (N) and points 60 degree north of east. Ignoring any resistance from the water, find the x and y component of the boat's acceleration.
An astronaut exerts a force of P = 40 N on the spacecraft. The mass of the spacecraft is 11,500 kg and the mass of the astronaut is 90 kg. Find the acceleration of spacecraft and the astronaut.
A traction device is use in a foot injury. The weight of 3 kg. object creates a tension in the rope that passes around the pulleys. The foot pulley is kept in equilibrium because the foot also applies a force, F to it. This force arises due to the Newton's 3rd law of motion, opposite reaction to the pulling effect of forces T1 and T2. Ignoring the weight of the foot, find the magnitude of force, F.
The engine weight is 3,150 Newton (N). This engine is being raised to certain height. Find the tension T-1 in the supporting cable and the tension T-2.
A jet plane is flying with a constant speed a long a straight line, at an angle of 30° above the horizontal. The plane has a weight of W = 87,200 Newton (N) and its engines provide a forward thrust T = 105,000 Newton (N). In addition, the lift force, L (directed perpendicular to the wings) and the force R, air resistance (directed opposite to the motion) act on the plane. Find the lift force, L, and the air resistance force, R.
The achilles tendon exerts a force of magnitude, F = 750 Newton (N). Determine the torque (magnitude and direction) of this force about the ankle joint, which is located 0.03 meter (m) away from the heel point, P.
A square, 0.50 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. The axis is perpinducular to the plane of the square. A force, F 15 N
lies in this plane and is applied to the square. What is the magnitude of the maximum torque that such force could produce?
You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has magnitude of 45 N*m. Use the sketch below to determine the force, F, that
you must exert on the wrench.
A 1,200 kg car starting form rest, accelerates for 5 s. The magnitude of the acceleration is a = 4.6 m/s2. Determine the average power generated by the net force that accelerate the car in horspower, hp.
The space probe was launched and its mass was 500 kg. Consider the probe is traveling at initial speed of Vo = 270 m/s. No forces act on it except the 56 m N thrust of its engine.
The external engine thrust force, T, is directed parallel to the displacement of 3 x 109 m. Determine the final speed of the probe, assuming that the mass remains constant.
A baseball (mass, m=0.15 kg) has an initial velocity, Vo = -38 m/s as it approaches a bat. Selected the direction of the baseball approach as the negative direction. The bat applies an
average force, Fave, that is much larger than the weight of the baseball, and the ball departs from the bat with a final velocity of Vf = +58 m/s.
Car 1 has a mass of m1 = 70 x 103 kg and moves at a velocity of V01 = +0.80 m/s. The freight operator decided to couple a Car 2 to Car 1 at the switching yard. Car 2 has a mass
m2 =90 x 103 kg and it is running at velocity of V02 = +1.3 m/s to overtakes Car 1 and to couple to it. Neglecting friction, find the common velocity, V, of the cars after
they become coupled.
Starting from rest, two skater "push off" against each other on smooth ice, where friction is negligible. The woman mass, m1 = 50 kg. and the man mass, m2 = 90 kg.
After their "push off" the woman moves away with a velocity of Vf1 = +2.5 m/s (velocity to the right is selected as positive). Find the recoil velocity of the man.
Suppose the pressure acting on the back of a swimmer is 1.4 x 105 Pa near the bottom of the pool. The surface area of the swimmer's back is 0.85 m2.
Determine the magnitude of the force that acts on the swimmer's back.
Blood in the arteries can be treated as a static fluid. Estimate how much blood pressure, P2, at the foot in the anterior tibial artery exceeds the blood pressure, P1, in the aorta at the heart;
a) when the body is reclining horizontally - see sketch 1 below.
b) when the body is standing. see sketch 2 below.
A concrete sidewalk is constructed between two building on a day when the temperature is 25 ° C. The sidewalk consists of two slabs, each three meters in length and of negligible thickness.
As the temperature rises to 40 ° C, the slabs expand, but no space is provided for thermal expansion. The building do not move, so the slabs buckle upward. Determine the change in length of each slab associated with this temperature change.
In half hour, a 50 kg jogger can generate 9.0 x 105 J of heat. This heat is removed from the jogger's body by a variety of means, including the body's own temperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase?
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