D128 Mathematics for Elementary Educators 2023 with verified questions and answers

What is the length of the missing leg in a right triangle with a hypotenuse of 25 in. and a leg of 9 in.? 4√34 in. A scalene Triangle has no congruent sides Find the distance between points (0, 4) and (15, 0) by applying the Pythagorean theorem. 15.52 A circle has a diameter of 12.8 ft. What is the area of this circle? 128.61 ft. A circle has a circumference of 12.65 cm. Assuming π = 3.14, what is the measure of this circle's diameter? 4.03 cm A directional sign can be best described as which type of polygon? rectangle A quadrilateral has four congruent sides and diagonals that are perpendicular. Rhombus Points P (−2, 1), R (−2, −5), and Q (−6, −5) create triangle PQR, which is then translated 1 unit down and 3 units to the right. What is the new x-coordinate of R? A23 What is the triangle rotated 90 degrees about the origin? The triangle now sits in the upper left corner Which shows a dilation of the figure below? Enlargement by scale factor of one half Triangle ABC is congruent with triangle DEF. Which of the following angles in DEF is congruent to m BCA in the first triangle? EFD A square with vertices A(2, 6) B(4, 8) C(4, 6) and D(2, 4) is dilated by a scale factor of 3 with reference to the origin. Which of the following is the coordinate of B'? (12,24) Given ABCD ~ WXYZ, which of the following is true? BC~ XY Which of the following theorems proves that two figures are similar, but not congruent? Angle Angle Which transformation will map (2, 5) onto (-2, 5) (-x, y) Two triangles are drawn in the coordinate plane. The vertices of the first triangle are (5, 4), (−4, 6), (−8, 9). The vertices of the second triangle are (1, 6), (−8, 8), ( x, y). Find the value of x and y that allow these two triangles to be congruent. (−12, 11) An octagon in the coordinate plane is transformed.Which of the following transformations would result in a similar figure? (-5x, -5y) Which type of transformation are these figures an example of? Dilation A circle has an area of approximately 615.75 in 2. What is the circumference of the circle? 87.96 inches What is the area of this figure? 63 square units A triangular window has an area of 600 in 2. The base of the window is three times its height. What is the length of the base of the window? 60 in. A gardener has a rectangular garden with an area of 374 yd 2. The length of the garden is 17 yd. The gardener wants to enlarge the garden by doubling only the width of the current garden. How much fencing will the gardener need to enclose the new garden? 122 yd A teacher is making a game of ring toss for her class. She starts by using a circle with a diameter of 10 in. and then cuts out a smaller circle with a diameter of 6 in., leaving a ring as shown in the given image. 50.27 sq. cm What is the approximate capacity of a spherical water tank with a radius of 7 ft? 1,436 ft 3 A cylinder has a volume of 484π in. 3 and a height of 4 in. What is the radius of the cylinder? 6.21 inches A cylinder has a volume of 600 in 3. Find the volume of a cone with the same radius and height as the cylinder. 200 cubic inches How many square centimeters of sheet metal are required to manufacture a can with a radius of 3.5 cm and a height of 8 cm without overlapping? 252.77 cm 2 What is the surface area of a sphere with a diameter of 14 in.? 615.44 in 2 Find the surface area of a rectangular prism with a length of 3 in., a width of 4 in., and a height of 5 in. 94 in 2 What device would you use to measure the volume of a liquid? Graduated Cylinder What should a student use to measure the length and width of a textbook? Ruler A runner runs in a park for 110 minutes.What time did the runner finish running if the runner started at 8:10 a.m.? 10:00 AM An individual wants to buy a house worth $500,000, but only has $350,000 in a bank account. What is the deficit? 150,000 A pen is 12 cm long. A pencil is 4 cm longer than the pen. What is the total length of the pencil and the pen? 12 cm+ 16 cm=28 cm What is 15 in. in meters, given 1 in. equals 0.0254 m? 0.381 m There are two weeks and three days remaining until the final exam. How many hours are there until the exam? 408 hours A tank can hold 3 gal. of water. The tank currently has 2.5 gal. of water inside. How many liters of water need to be added to fill the tank, given that 1 gal. equals 3.79 L? 1.895 L How many hours in a week? 168 hours An individual is paying $50 per day for a rental car. How much will it cost to rent that car for two weeks? $700 A car is traveling at 50 mph. How far will the car travel in 30 minutes? 25 miles How many students want to take art based on the given diagram? 20 What type of graph is depicted? box and whisker plot Find the mean of this data set:1, 3, 4, 9, 8, 5, 12 6 A student in a statistics class scored an 80%, 85%, and 92% on the first three tests. What must the student score on the last test to have at least an 87% in the class? [ 91% Given this data set:6, 2, 9, 0, 1, 5, 9, 4, 3, 2Which value could be added to the data set so that the median is 3? 0 Which of the following terms would best describe the given data distribution?{40, 50, 60, 60, 60, 70, 70, 70, 70, 70, 70, 80, 80, 80, 90, 100} symmetrical Which of the following is a true statement based on the given histogram of black cherry tree heights? Black cherry trees have heights between 60 and 90 ft. A student's average score after the first three quizzes is 88%. What does the student need to score on the fourth quiz to raise the average to 90%? 96% A deck of playing cards has 52 total cards. There are four jacks and four aces. Assuming the jack is not replaced, what is the probability of drawing a jack and then an ace from the deck of cards? 4/663 A jar has 8 black marbles and 8 white marbles. Two marbles are drawn. Assuming the first marble is not replaced, what is the probability of drawing two black marbles? 7/30 In an experiment, each member of a population is replaced after it is picked.Which of the following terms best describes these events? Independent There are 40 students in a summer cohort. Of those students, 20 are taking an accounting course, and 25 are taking a Spanish course. A total of eight students are taking both courses. How many students are not taking either course? 3 For a test in a math class, 60 students arrive and take out their supplies. Of those students, 22 bring pens, and 48 bring pencils. Only one student arrives without a pen or pencil. How many students brought both a pen and a pencil? 11 Suppose the probability of winning a game is 2/6. If you lose, you pay $1. If you win, another player pays you X dollars. If the game is to be fair, which of the following should be X? $2 A company makes bobblehead dolls. One out of every five is faulty, but the company does not know which dolls are faulty until a buyer complains. Suppose the company makes a $2.50 profit on the sale of any working doll, but suffers a $10 loss for every faulty one because they have to repair the doll.Which of the following is the company's expected profit or loss per doll in the long term? $0.00 A coin is flipped three times and lands on heads each time. What is the probability of it landing on tails on the fourth flip? 1/8