Coordinate system Questions and Answers

Each problem below refers to a triangle ABC Any answers that involve angles should be rounded to the nearest tenth of a degree 1 If a 100 inches b 60 inches and C 60 find c 2 If a 100 inches b 60 inches and C 120 find c 3 If a 5 yards b 6 yards and c 8 yards find the largest angle 4 If a 10 yards b 14 yards and c 8 yards find the largest angle 5 If b 4 2 meters c 6 8 meters and A 116 find a

Find the circulation and the flux of the field F xi y j around and across the following curves a The circle r t cos t i sin t j 0 t 2 b The ellipse r t cos t i 2 sin t j 0 t 2 a The circulation of F around the circle is Type an exact answer

K Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby This method is designed to increase the likelihood that each baby will be a gir assume that the method has no effect so the probability of a girl is 0 5 Assume that the groups consist of 44 couples Complete parts a through c below a Find the mean and the standard deviation for the numbers of girls in groups of 44 births The value of the mean is u 22 Type an integer or a decimal Do not round The value of the standard deviation is 3 3 Round to one decimal place as needed b Use the range rule of thumb to find the values separating results that are significantly low or significantly high Values of 10 girls or fewer are significantly low Round to one decimal place as needed Values of 26 girls or greater are significantly high Round to one decimal place as needed c Is the result of 31 girls a result that is significantly high What does it suggest about the effectiveness of the method The result Round to significantly high because 31 girls is as needed girls A result of 31 girls would suggest that the method is not

Return on Investment and Residual ome Johnson Company has two sources of funds long term debt and equity capital Johnson Company has profit centers in the following locations with the following net incomes and total assets Las Vegas Net Income Assets 1 310 000 4 000 000 1 550 000 8 000 000 Dallas Tampa 2 390 000 12 000 000 a Calculate ROI for each profit center and rank them from highest to lowest based on ROI Round ROI to the nearest whole percentage Las Vegas Dallas Tampa ROI Rank 0 0 0 b Calculate residual income for each profit center based on a desired ROI of 5 and rank them from highest to lowest based on residual income RI Rank

5 4 3 2 1 13 12 11 10 9 8 7 6 5 4 B A2 1 5 6 7 1 2 3 4 The curve above is the graph of a sinusoidal function It goes through the points 7 0 and 3 0 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits

Divide Write your answer in simplest form 5r 2 5r 2 P 6r 12r30r

Simplify Express your answer as a single fraction in simplest fe 3u 9 10u 4 5 2u 10

Here is a graph of the function g w y 5 4 3 2 1 2 3 4 3 4 Use the graph to find the following If there is more than one answer separate them with commas a All values at which g has a local minimum b All local minimum values of g

Consider the quadratic equation below 22 10x 24 0 Select the phrases that are true about the solutions to this quadratic equation This quadratic equation will have V because the discriminant is

Solve the quadratic equation using the quadratic formula a 10a 21 0 x 2 18 B 10 184 2 x 7 3 Dx 3 7

Input the correct values into the quadratic formula below x 4x 8 0 b b2 4ac Quadratic formula 2a H 2 4

Add the complex numbers 3 4 7 i

Simplify the following complex numbers given in the first column and choose the appropriate result Complex numbers 15i 9i 7i 5 3i 24 1 OOOC 1 HOOOO i C e D

Write a direct variation equation that relates the two variables Then solve Suppose y varies directly as x and y 21 when x 3 Find x when y 42 k equation x

12 Classify the following graphs on the basis of direct and inverse variation Drop the figure under its appropriate variation DRAG DROP THE ANSWER Direct variation Inverse variation

a Part A Give the generic formula for joint variation Answer Part B List restrictions if there are any If not say no restriction

0 0 2 16 7 4 32 a 6 48 8 64 Part A Decide if the value on the table above shows a direct variation inverse variation or neither Part B Write the equation that represents the variation or explain why it is neither b BU

Name the constant of variation k for the equation y 5x

The quantity a varies directly with b and inversely with c and d When b 9 c 3 and d 7 a 3 What is the value of k the constant of variation Write your answer in the form A or or where A and B are constants or variable expressions

Use the binomial series or any other method to find the Maclaurin series for b a 1 n 1 x2n 2n 2 n 1 x2n 1 2n 1 n 0 8 d 1 1 n 0 n 0 f x 1 8 1 2 x2 n 2n 1 e 1 n 0 8 x n c 1 12n 1 2n n x2n 2n 1 n 0

a f x x 3x3 6x 8x is graphed below 9 2 30 20 10 10 Based on the graph how many zeroes does the polynomial haw Answer

Match the following polynomials with their factored form 3x 12x 32 12 3x 12 DRAG DROP THE ANSW 3 x 4 3x 12 3x x 4 3x x 4 3x 12x 3x x 4 3 x 4 3 x 4

4 Consider the following sequence of numbers tn 0 1 2 3 4 5 6 7 23 37 60 14 5 9 14 Find a recursion equation of the type tn formula for t in terms of n btn 1 ctn 2 for this sequence and fin

How many zeros or roots are shown in the image 6

DISTANCE BETWEEN TWO POINTS Given three points which serve as vertices of a triangle a find the perimeter of each triangle and b determine the kind of triangle according to sides and angles A 0 0 B 5 2 C 3 3 D 3 8 E 5 5 F 6 0 G 2 3 4 3 3 4 V 3 1 W 2 3 2 X 2 3 4 EM 11 N 6 2 0 4 3 1 Determine whether the given points are collinear or non collinear P 3 3 Q 0 1 R 9 7 2 S 3 1 7 1 3 U 10 B V 2 2 W 5 2 X 11 2 If point M x 4 is equidistant from A 5 2 and B 3 4 find the value of x IV If point N 3 y is equidistant from P 26 and Q 7 2 find the value of y

Question Determine the equation of the parabola whose graph is given below Write your answer in General Form 7 6 5 4 3 2 3 4 5 6 7

The point P 24 y lies on the unit circle shown below What is the value of y in simplest form P x y Note the figure is not drawn to scale L

The unit circle below shows 85 and 85 Find the values below rounded to three decimal places if necessary 0 087 0 996 85 O 85 0 087 0 996 cos 85 cos 85 cos 85 L

The unit circle below shows 135 and 135 Find the values below rounded to three decimal places if necessary 0 707 0 707 0 707 0 707 135 tan 135 tan 135 tan 135

Complete the following derivation using the following selection of inference rules As you work on the problem think about which derived rules had to be included in order to make possible the patterns of inference embodied by the basic rules that were omitted Rules I EL VIR E I LI DNE Comm CommV DSR DeM MT HS Def I 1 2 n RV S T R S T K Premise Premise Goal

Factor the following polynomial expression completely x3 2x 9x 18 A x 3 x 3 x 2 B x 2 x 2 x 3 C x 3 x 3 x 2 D x 9 x 2

Factor completely 3x 48x

Directions For the following polynomial factor out the GCF Greatest Common Factor then rewrite the new factored polynomial in the space provided 4x 8x 12x GCF Factored Polynomial

Miss Rose teaches three ballet classes Her students data are shown in the relative frequency table Boys Girls Total Beginner 0 15 0 1 0 25 Which statement is true Intermediate 0 2 0 35 0 55 Advanced 0 05 0 15 0 2 OA 20 of her students are in the advanced class OB 40 of her students are girls C 20 of her students are in the intermediate class D 15 of her students are boys Total 0 4 0 6 1 0

A county clerk was supposed to use randomness to assign the order in which candidates names appeared on voting ballots Among 49 different ballots Democratic candidate names were placed on the first line 43 times The probability of a result that high is 0 000000028639 Assuming randomness was used is the result of 43 Democratic candidate names being placed on the first line significantly low significantly high or neither The probability of a result of 43 which is 0 000000028639 is 0 05 The result is 43 49 what is expected with randomness The result of 43 is

The table shows the probability distribution of siblings of students in a high school with 1500 students What is the expected value for the number of siblings of a randomly chosen student Number of siblings Probability OA 2 5 OB 1 08 O C 1 29 OD 1 11 0 1 0 18 0 65 2 3 0 09 0 05 4 0 02 5 0 01

peria Suppose A and B are independent events If P A 0 6 and P B 0 85 wha is P A and B A 0 68 B 0 17 C 0 34 D 0 51

If the following data were transformed and points with the coordinates x log were plotted what points would be plotted Round log y to three decimal places y 81 5 243 6 729 X 4 O A 1 908 81 2 386 243 2 863 729 OB 4 1 908 5 2 386 6 2 863 OC 81 1 908 243 2 386 729 2 863 OD 1 908 4 2 386 5 2 863 6

Which of the following values represents the weakest correlation OA 0 45 OB 0 65 O C 0 55 OD 0 35

The first quartile of a data set is 41 and the third quartile is 57 Which of these values in the data set is an outlier A 39 OB 83 C 19 OD 73

If the formula X 1122X x is used to find the mean of the following sample n1 what is the value of n 51 37 83 44 52 19 99 7 36 88 OA 11 OB 10 OC 9 D 12

What is the mean of the following data values 53 71 89 10 62 OA 52 OB 57 O C 62 D 67

What is the median of the following data values 12 13 16 19 23 27 29 31 32 33 O A 27 OB 24 3 OC 25 OD 23

There are 11 paintings at an art show Four of them are chosen randomly to display in the gallery window The order in which they are chosen does not matter How many ways are there to choose the paintings A 44 B 121 C 330 OD 7920

Name the degree of each of the following polynomials Polynomials 17x 6 27 4x 7 No degree O 1st degree 3rd degree JA 5th degree KITTY KIN

6 Describe the end behavior of the function graphed below N 8 10 12 14 A As a o f x B As a f x o as a As x f x as x x x D As x 00 f x o as x f x o as x x o f x

Select the Quadratic Binom A x 3x B x 8 Cx 7 D 3x 2x 8

In a valid probability distribution each probability must be between 0 and 1 inclusive and the probabilities must add up to 1 If a probability distribution 1 1 and x what is the value of x has probabilities 5 1 12 6 4 O A 1 4 OB 1 3 116 O C OD 1 2

The Wildcats and the Leopards are evenly matched football teams When they play there is a 0 5 probability that the Wildcats will win If they play 9 times what is the probability that the Wildcats will win 2 of the games Round your answer to the nearest tenth of a percent A 7 0 OB 24 6 OC 16 4 O D 0 2

The bar representing which of the following probabilities on a histogram would be the highest O A 1 OB TO 10 O C 1 O D 30