Quantitative Reasoning Final
Test 4
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Find the angular size of a circular object with a 3-inch diameter viewed from a distance of 5 yards
0.95 degrees
According to the video, what is the fractal dimension of the given object?
1.1610
In measuring the length of the object, when you reduce the length of your ruler by a factor of 3, the number of length elements increases by a factor of 6.
1.631 - Fractal
The average price of a home in a town was $178,000 in 2007 but home prices are rising by 3% per year.
178,000 x (1 + 0.03) t 1: 183,340 2: 188,840 3: 194,505 4: 200,341 5: 206,351
4^x = 55
2.89
The population of city A is 21% less than the population of city B, so city A's population is _____% of city B's
79%
A slow pitch softball diamond is actually a square 61 ft on a side. How far is it from home to second base?
86.3
Premise: If you live in Los Angeles, then you live in California. Premise: Amanda does not live in Los Angeles. Conclusion: Amanda does not live in California.
California; Los Angeles inside - Invalid Not sound
Why is fractal geometry useful?
It can be used to create shapes that look more like naturally existing shapes
fractal geometry
Study of fragmented geometric irregular shapes, such as those in lining of intestine
The edge of this leaf has a fractal dimension of 1.34.
The statement makes sense.
there are 206 bones in the body
Yes, because the given statement can be either true or false, and it is a complete sentence
You can rent time on computers at the local copy center for a $7 setup charge and an additional $5.50 for every 10 minutes. How much time can be rented for $23?
r = 7 + 0.55t - 29 mins is reasonable
y = 3x + 7
slope = 3 y-intercept = 7
log10(3 + x )= 4.6
x=39807.72
All fault lines are long. Premise: Short Fault is a fault line. Conclusion: Short Fault is long.
'x' inside fault bubble - valid; not sound
122.33 degrees
122 19' 48"
If prices increase at a monthly rate of 1.1%, by what percentage do they increase in a year?
14.0%
The total (after-tax) cost of a laptop computer is $1605.05. The local sales tax rate is 7.2%. What is the retail (pre-tax) price?
1497.25
One hundred twenty five people who grew up in either City A or City B were surveyed to determine whether they preferred country music or blues(both and neither were not acceptableresponses). Of those who grew up in CityB, 48 preferred blues and 19 preferred country music. Of those who grew up in City A 33 preferred country. Answer parts(a) through(d) below.
19; 25 - venn diagram with city B on left (48) and country on right (33) ; 19 in the middle; 25 on the outer right - 48; 73
In measuring the area of the object, when you reduce the length of your ruler by a factor of 5, the number of area elements increases by a factor of 25.
2 - ordinary
In measuring the area of the object, when you reduce the length of your ruler by a factor of 5, the number of area elements increases by a factor of 40.
2.292 - Fractal
Radioactive uranium-235 has a half-life of about 700 million years. Suppose you find a rock and chemical analysis tells you that only 1/16 of the rock's original uranium-235 remains. How old is the rock?
2.8 billion years old
A roof with a pitch of 3 in 10 or a roof with a slope of 2/5.
2/5 is steeper
A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 35 years ago. If the half- life of the substance is 20 years, what was the density of the substance when it was deposited 35 years ago?
23.5 mg
An air duct in a stadium has a circular cross section with a radius of 18 inches and a length of 35 feet and is open at both ends. What is the volume of the duct, and how much paint (in square feet) is needed to paint the exterior of the duct?
247.40 ft^3 - 329.87 ft^2
According to the video, how many times longer is L1 than L0?
4/3
46 N ; 102 W
46 S ; 78 E
2/15 circle
48 degrees
88 meters of fence
484 square meters 616 square meters - The area of the circular enclosure is greater than that of the square enclosure. This suggests that a circle provides a greater area than a square for a fixed perimeter.
The 2015 revenue for Company A was $283 million, compared to $552 million for Company B.
51.3% of the revenue
The figure shows a region to be covered with plywood under a set of stairs. The area of that region is 66 square feet. Suppose that the stairs rise at a shallower angle and are 9 feet tall. What is the area of the region to be covered in this case?
54 ft squared
The water reservoir for a city is shaped like a rectangular prism 250 meters long, 70 meters wide, and 13 meters deep. At the end of the day, the reservoir is 75% full. How much water must be added overnight to fill the reservoir?
56, 875 cubic meters
A circle with a diameter of 23 feet
72.3 ft 415.5 sq ft
Similar Triangles: Larger: (B) 16; (c) 40; missing A
A = 36 B= 30
Consider the graph to the right. a. In words, describe the function shown on the graph. b.Find the slope of the graph and express it as a rate of change. c. Briefly discuss the conditions under which a linear function is a realistic model for the given situation.
According to the function, the distance from home decreases by 600 miles every 8 hours. (- 75) mph It is a good model if the speed is constant for 8 hours.
Australia is in the southern hemisphere.
Australia is not in the southern hemisphere - true; false
The price of a four-star meal, only $180 per couple decades ago, has since increased 400%. The current price of a four-star meal is which of the following?
A four-star meal is $900 because 4×$180=$720, which is added to $180.
1/8
Decimal: 0.13 Percent: 12.5%
peas are vegetables and apples are fruit
Identify P? - Peas are vegetables Identify Q? - Apples are fruit What is the truth value of P? - truth What is the truth value Q? - true > > the entire proposition is true because both p and q are true
p and q; p or q; if p, then q
T,F,T,T - 'if p, then q' is true when both p and q are true. Your answer is correct. 'if p, then q' is true when both p and q are false. Your answer is correct. 'if p, then q' is true when p is false and q is true.
The Flanagans are having their fifth child. All of their children are academically gifted, so the youngest child is bound to be academically gifted as well.
The argument is deductive because the premise is general and the conclusion is specific.
I have read every book released by a particular writer and they have been outstanding. Her next book is bound to be good, so I will certainly read it.
The argument is inductive because the premise is specific and the conclusion is general.
Suppose the value of a home changed by −23% over the past five years. Which of the following is true?
The house decreased in value over the past five years because the relative change is negative
What characterizes a self-similar fractal?
The same pattern repeats under greater magnification
The people who live in Chicago form a subset of those who rent apartments in Chicago
The statement does not make sense because the set of people who live in Chicago also includes home owners which are not part of the set of people who rent apartments in Chicago.
My freeway speed is the rate of change in my distance with respect to time.
The statement makes sense because the slope of a linear function is the change in the dependent variable divided by the change in the independent variable.
The water depth in a lake decreases at a rate of 5 inches per week because of evaporation. How much does the water depth change in 8 weeks? In 13 weeks?
The water depth varies with respect to time with a rate of change of −5 in./week. - Decreased by 40 Decreased by 65
How do fractal dimensions differ from dimensions in Euclidean geometry?
They can have fractional values.
Premise: If prices are increased, then consumers will have less disposable income. Premise: With less disposable income, spending will decrease and the economy will slow down. Conclusion: A price increase will slow down the economy.
Yes, because there is a clear chain from "prices are increased" to "the economy will slow down."
Briefly describe what is meant by the process of iteration in generating fractals. Describe the generation of the Cantor set, the Sierpinski triangle, and the Sierpinski sponge. Describe the fractal dimension of each
a rule; self similar fractal - third; a line segment; less than 1 - equilateral ; black; between 1 and 2 - 27; 2 and 3
Suppose you magically tripled in size. That is, your height, width, and depth increased by a factor of 3. By what factor has the amount of material required for your clothes increased?
factor of 9
Premise: All fish live in water. Premise: Whales live in water. Conclusion: Whales are fish.
fish inside live in water, 'x' on the outline of 'fish' - invalid ; not sound
4/9
rational numbers
square root of 28
real numbers
. Draw a Venn diagram with two circles showing the given relationship between two sets. Let F=fire fighters and C=card players. Choose the correct answer below
standard venn diagram - The diagram correctly shows the two circles overlap because some card players are firefighters
people at the party diagram men: 16 middle: 7 under age 30: 10 women at the party: 23
women under 30: 10 men not under 30: 16 women at party: 33 overall guests: 55
Consider a line with equation y=12x−3. Which of the following lines has the same slope but a different y-intercept? Explain your reasoning
y=12x+3 because the rate of change is thesame, but the initial value is different.
If Jose owns a computer, then he owns a laptop
converse: If Jose owns a laptop, then he owns a computer Inverse: If Jose does not own a computer, then he does not own a laptop contrapositive: If Jose does not own a laptop, then he does not own a computer. - Contrapositive and Conditional Converse and Inverse
If airplanes can fly, then airplanes have wings
airplanes can fly ; airplanes have wings - True
