Add the following vectors, and convert the resultant vector to polar notation

A baseball is thrown with an initial velocity of 30 m/s at an angle of 30° above the horizontal. What is the highest point the ball will reach?

As part of an athlete’s rehab, you are testing the athlete’s performance on a test called “fly in sprints.” After a running start, you measure how quickly the athlete is able to complete the run. You determine that the athlete has an initial velocity of 5 m/s, and the athlete accelerates at a rate of 2.5 m/s2 over the 3 s it takes to complete the sprint. What was the athlete’s velocity at the end of the test?

QUESTION 1 Multiple Choice Questions   Write only the LETTER of the correct answer.     1.1 Which of the following objects has the shape of a prism?       Right click to open the diagram in a new tab.       A)     Objects A and B B)     Objects B and D C)     Objects B and C D)     Objects C and D   (1)   1.2 Which of the following coloured pictures have shapes that look like trapeziums?       Right click to open the diagram in a new tab.   (1)   1.3 The perimeter of a square is 80 cm. The length of a side is:       A)     20 cm       B)     160 cm       C)    320 cm       D)    640 cm (1)   1.4 Which one of the letters shown below has both parallel and perpendicular lines?       A)      M        B)       T       C)       Z       D)       E (1)   1.5 The figure below is not drawn to scale. AÔB is a straight line. If AÔC is 150°, find the value of CÔB.       Right click to open the diagram in a new tab.       A)      210°            B)      30°       C)      50°        D)      180° (1)     TOTAL [5]   Please draw a line before you start with the next question.

QUESTION 3 AREA AND PERIMETER 3.1 Calculate the perimeter of a rectangle if the length is 15 cm and the breadth is 7 cm. (2) 3.2 Write down the formula for the surface area of a cube. (1) 3.3 The floor of a room 4,5 m by 3,75 m has to be covered with square carpet tiles with sides equal to 750 mm. Calculate:   3.3.1     The area of the floor in m2. (2)   3.3.2     The area of a tile in mm2. (2)   3.3.3     The number of tiles you will need to cover the floor. (2) 3.4 Calculate the area of the following shape. (draw sketches to show how you divided it up):     Right click to open the diagram in a new tab.  (5)   TOTAL [14] Please draw a line before you start with the next question.

QUESTION 2 Properties of 2D shapes Match Column A with Column B. Write only the question number and the correct letter.   Column A Column B 2.1     All sides equal and all angles equal A)     Rectangle 2.2     Two pairs of opposite sides parallel B)     Rhombus 2.3     Two pairs of adjacent sides equal C)     Square 2.4     Only one pair of opposite sides parallel D)     Kite 2.5     Two pairs of opposite sides equal and all interior angles            are equal to 90° E)     Parallelogram F)     Trapezium (5)   TOTAL [5] Please draw a line before you start with the next question.  

QUESTION 5 Similarity and Congruency 5.1 Look at this pair of shapes. Are they similar or congruent? Show all calculations to motivate your answer. (4)   Right click to open the diagram in a new tab.   5.2 Are △ABC and △JKL congruent? Give a reason for your answer. (2)   Right click to open the diagram in a new tab.   5.3 Write down whether each pair of triangles given below is congruent, similar or neither. Give a reason for your answer using calculations if necessary.     Right click to open the diagram in a new tab     5.3.1 Triangles in figure 1 are: __________ (2)   5.3.2 Triangles in figure 2 are: __________ (4)   TOTAL [12] Please draw a line before you start with the next question.

Which of the following is not a known hotspot?

 Suppose that you are interested in examining if it is true that on average men earn more than $30.00 a day more than women in certain entry level positions in technical fields.  If sample data show that 80 men earned on average  $353.78 a day with a standard deviation of $18.03, while 80 women earned on average $315.14 a day with a standard deviation of $21.22 with a standard deviation of $21.33, conduct a hypothesis test at the .01 level of significance. 

A confidence interval for a population mean has a margin of error of  3.4 What is the length of the confidence interval? If the sample mean is 52.8 obtain the confidence interval.