Area Questions and Answers

O Determine which figure has the greater density 9 cm 9 cm 6 cm 400 kilograms 3cm 10 cm 475 kilograms

professional cyclists burn a mean of less than 6900 calories during the annual Monaco Endurance Race This would be an improvement on the previously accepted value of 6900 calories In a sample of 13 randomly selected professional cyclists the sample mean number of calories the cyclists burn during the race is 6833 with a sample standard deviation of 773 calories Assume that the population of numbers of calories burned by professional cyclists during the race is approximately normally distributed Complete the parts below to perform a hypothesis test to see if there is enough evidence at the 0 05 level of significance to support that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 a State the null hypothesis H and the alternative hypothesis H that you would use for the test Ho 0 11 0 The value of the test statistic is given by 1 Jn Student s t Distribution Step 1 Enter the number of degrees of freedom Step 2 Select one tailed or two tailed O One tailed O Two tailed 10 05 is the value that cuts off an area of 0 05 in the right tail Step 3 Enter the critical value s Round to 3 decimal places b Perform a hypothesis test The test statistic has a distribution so the test is a test Here is some other information to help you with your test Step 4 Enter the test statistic Round to 3 decimal places 0 4 03 Since the value of the test statistic lies in the rejection region the null hypothesis is not rejected So there is not enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 0 2 BE Since the value of the test statistic lies in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 H Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is rejected So there is enough evidence to support the claim that the mean number of calories professional cyclists burn during the Monaco Endurance Race is less than 6900 O 0 Osa Since the value of the test statistic doesn t lie in the rejection region the null hypothesis is not rejected So there is not enough evidence to X 0 020 0 0 0 0 X X c Based on your answer to part b choose what can be concluded at the 0 05 level of significance about the claim made by the sports science group O S X 2 A M

Mason is building a 3 D model of a house for a project His model consists of a triangular prism on top of a rectangular prism as shown in the diagram 5 in 8 in 14 in Which measurement best represents the total volume of Mason s model house in cubic inches Answer A 1 218 in 3 3 B 1 323 in 9 in C 1 638 in 3 D 5 040 in 3 X X X

A section of a rectangle is shaded The area of the shaded section is 63 square u What is the value of x O9 units O 11 units 18 units 21 units

In the rectangle below AE 4x 7 CE 6x 1 and mZEDC 54 Find BD and m ZEAD A D E B C BD mZEAD 00

2 Kiran bought a wedge with a central angle radians and radius 3 inches What is the area top surface of this wedge

te the density of a 3D figure any final answer ALL WORK must be shown in order to receive full credit Directions Complete the following questions by showing all work and annotations Keep work residents and the shaded region represents the surrounding water what is the population density of the village 1 The below shape represents a rectangular town with a width b of 6 miles If the circular village has 1 275 in person per square mile a 45 1 b 0 02 C 11 3 d 67 6 b a

2 The town Roundaway NJ can be modeled with a circle with a diameter of 50 miles has a popul 25 504 Blockhead NJ can be modeled with a square with a length of 40 miles has a population of 22 340 Determine which of the two towns has a greater population density

1 A company manufactures cylindrical containers that each have a volume of 6 cubic feet For a new container design the company plans to keep the same height for the container and double the radius V 6 ft

1 point Which expression represents the probability of choosing an item from the intersection of A and B P A U B P ANB An B

Which expression represents the probability of the union of not A and not B A n B P A U B AUB P A B

What does the rational form of the ratio a b look like a a b 01 0 a b b a b

When partitioning a line segment what is the rational form of the ratio 2 3 O 02 10 21 06 3 5

Which point lies on the circle centered at the origin with 5 1 2 1 4 2 3 1 6 O

The balance on a credit card that charges a 28 5 APR interest rate over a 1 month period is given in the following table Days 1 3 150 initial balance Days 4 20 200 50 purchase Days 21 30 50 150 payment What is the finance charge on the average daily balance for this card over this 1 month period Hint First calculate the balance for the 30 days To do this take the number of days and multiply it by the balance What was the balance for the first 3 days

1 point Find the point P that is 2 5 of the way from A to B on the directed line segment AB if A 8 2 and B 6 19 7 2 8 8 2 4 6 4 7 2 8 8 2 4 6 4

I point A triangular pyramid is sliced by a plane parallel to the base What is the shape of the cross section triangle star rectangle square

Which of the following is NOT an equivalent expression to Area of sector Area of sector TT 360 O Area of sector Area of sector area of circle arc measure 360 20 AT 0 360

Find the length of the arc on a circle with a radius of 7 centimeters and a central angle of 74 degrees 7 centimeters 9 04 centimeters 4 52 centimeters 18 08 centimeters

Sector area is a fraction of a circle s radius arc length area circumference

son Posttest Points 1 Find the value of x in the similar right triangles A Question 5 B O 10 O 36 O 12 O 30 45 X CR 15 12 Reset Reset button w comp lent Reset Questions 5 O 7 9

Question 9 Find the measure of MN in the right triangle M O 12 99 cm O 15 cm Points 2 O 7 5 cm O 30 cm 15 cm 30 N

Question 9 The triangles PQR and XYZ are similar What is the length of YZ 8 P 5 O 2 5 4 5 Points 2 O4 9 Y R Z 4 X

d 1 7 4 find the absolute value of d and the absolute value of 6d

17 1 point Which of the following is NOT used in geometric constructions pencil protractor compass ruler

POSSIBLE POINTS each pair of solids determine if their volumes are the same or different If the volumes are different identify the solid with the greatest volume Explai ur reasoning 1 A prism and a pyramid have the same height The pyramid s base has 3 times the area of the prism s base 2 A pyramid and a cylinder have bases with the same area The cylinder s height is 3 times that of the pyramid 3 A cone and a cylinder have the same height The cone s radius is 3 times the length of the cylinder s radius

earthquake intensity measured by 1 lo x 10 m lo is reference intensity and M is magnitude An earthquake measuring 6 1 on the Richter scale is 125 times less intense than the second earthquake What would the Richter scale measure be for the second earthquake

earning Activity 28 Jace Find the surface area of following 4 m 18 m 5 m 6 cm 2 cm 8 cm 4 cm 6 cm

3 the area of each regular polygon Leave your answer in simplest form 2 10 8 8 3 13 12 4 10 6 8 3 11 16

Which of the following exponential functions grows at the slowest rate Select one O a y 2 O b y 0 5 O c y e O d y 5

Determine in which of the four quadrants angle is located given Answer 5 Points csc 0 0 and cos 0 0

13 Given the formula A r find the area A of a circle whose radius is 0 00000607 in O3 32929 x 10 in 9 70 O 3 721 x 10 in 9 3 51649 x 10 9 in 3 68449 x 10 1 in

It is important to limit in a research project because it will give unreliable information When Kora set up the experiment with a group of teenagers who wanted to improve their metabolism she broke them into two groups One group received hot lemon water made with real lemon The other As she asked them and the flavoring would be received hot water with lemon flavoring the second was called the questions about their weight energy etc she chose not to know who was in which group so this was a study

1 A can of soup is full of vegetables and chicken broth The volume of the chicken broth is 141 37 in I can has a height of 5 in and a base area of 30 in What is the volume of the vegetables in the can a 66 37 in b 8 63 in c 291 37 in d 150 in 3

A regular hexagon is shown 10 in What is the length of the apothem rounded to the nearest inch Recall that in a regular hexagon the length of the radius is equal to the length of each side of the hexagon O4 in 5 in O9 in 11 in

7 Determine the volume of the complex figure below Round to the nearest hundredth 6m 5m 50m

Determine the volume the cylinder with a hemisphere scooped out of the top A 487 in 3 7 in C 457 in 3 3 in

d 410 cm 2 Determine the volume of the composite figure Round to the nearest tenth 4m pec 3 m 4 m Z2m 45m in

2 Calculate the volume of a prism with a base area of 45ft2 and a height of 2ft

The polygon below is a regular hexagon 18 cm 18 cm What is the approximate length of the apothem Rou to the nearest tenth O9 0 cm O 15 6 cm 20 1 cm 25 5 cm 0

A regular pentagon has an apothem measuring 20 cm and a perimeter of 145 3 cm 20 cm What is the area of the pentagon square centimeters

2 Find an equation for the plane that contains the line in the ry plane y 2r 1 and the point 3 2 2

In the circle below suppose m GHE 122 and m ZHGF 68 Find the following a m2GHE b mZHEF 0 X

merry go round is rotating at the constant angular speed of 4 3 RPM counterclockwise The platform of this ride is a circular disc of radius 26 feet You jump onto the ride at the location picture elow Impose coordinates as pictured with units in feet a If 31 then what are your xy coordinates after 3 minutes Round your answers to three decimal places x y rotating 4 3 RPM b If 15 then what are your xy coordinates after 15 minutes Round your answers to three decimal places x y c If e x y jump on here X 11 then what are your xy coordinates after 8 seconds Round your answers to three decimal places

7 2 PQRS is a parallelogram S ST and P 120 O DO

Simplify 3 0 X Enter the answer that belongs in the green box for the numerator of the exponent Enter

Complete the missing statements or reasons for the proof Given 21 22 23 44 Prove n Statements PROOF 1 21 22 and 23 24 1 2 2 3 214 4 2 3 4 l Reasons m n If two lines intersect the vertical Zs are 3 4 If two lines are cut by a transversal so that alternate exterior Zs are the lines are

The population of insects in an experiment has been increasing by 9 each week If there were 16 insects at the beginning of the experiment predict how many insects there will be after 8 weeks First complete the equation Future Amount 1 initial amount growth rate time periods

5 Find the surface area of the regular pyramid 9 in 312 12 in

2 Find the exact surface area of a hemisphere that has a diameter of 22 m