A man walking his dog along a Straight road spots a friend a mile away. They wave at one another and the dog sprints to greet he
1 answer:
The distance the dog runs is given by the time it takes the man and the
girl to meet multiplied by the speed of the dog.
Correct response:
- The total distance the dog runs is <u>1.5 miles</u>
Given parameters;
Initial distance of the friend away = 1 mile
Speed of the man = 3 mph
Speed of the girl = 3 mph
Speed of the dug = 9 mph
Required:
The total distance the dog runs
Solution:
The time it takes the man and the girl to meet, <em>t</em>, is given as follows;
Therefore;
Learn more about velocity and speed here:
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Part I: Scale Drawing
<span>Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.</span>
a) Scale Factor: 1 in/ 2 ft
Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patiob) see the picture attached
Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft
<span><span>c) What are the dimensions of Mrs. Johnson’s patio? </span>
</span>the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft
<span><span>d) Calculate the area of Mrs. Johnson’s patio. Show all work.
</span> </span>
area of the square=b²
where b is the length side of the square
b=10 ft
so
Area=10²-----> area =100 ft²
<span><span>e) How many pavers will be needed? Show all work. </span>
</span>
we know that
1 paver is 16 in x 16 in dimensions
convert to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²
if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers
if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed
<span><span>f) What will it cost to build the patio? Show all work.
</span> </span>
the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95
the cost to build the patio is $499.95
Part II: Bigger Design
<span>There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs. After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”</span>
<span>a) What would be the new dimensions of Mrs. Johnson’s patio?
</span>the new dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft
<span>b) Calculate the new area of Mrs. Johnson’s patio. Show all work.
</span>area of the square=b²
where b is the length side of the square
b=20 ft
so
Area=20²-----> area =400 ft²<span>
</span>
<span><span>c) How many pavers will be needed for the new design? Show all work.
</span> </span>
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²
if one paver has an area of----------------> 16/9 ft²
x pavers-----------------------> 400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers
if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed
<span>d) What will it cost to build the bigger patio? Show all work.
</span>the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81
<span><span>e) Is Khianna right? Will doubling the size of the patio, double the cost?</span>
</span>
<span>Khianna is wrong to double the dimensions the cost quadruples</span>
The correct question is
<span>Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation
</span>see the picture in the attached figure N 1
we know that
The formula for Sample Standard Deviation is indicated in the attached figure N2
in this problem
n=4 and Yuri had to divide in the formula by 3
therefore
the answer is Yuri divided by n instead of n -1
<span>Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation
</span>see the picture in the attached figure N 1
we know that
The formula for Sample Standard Deviation is indicated in the attached figure N2
in this problem
n=4 and Yuri had to divide in the formula by 3
therefore
the answer is Yuri divided by n instead of n -1