You want to put a fence around your large yard. There are two companies that you have found to do the work. They have each given
you a quote for how much the work will cost. Of course, you want to find out which company will be the cheapest. The boundary of your yard is determined by five trees. The lines connecting them form the edge of your property. Shown below are the descriptions for the positions of the trees relative to your house.
TREE Position (relative to your house)
1 100 ft. east 2 40 ft east, 80 ft south 3 40 ft west, 120 ft south 4 90 ft west, 60 ft north 5 20 ft east, 110 ft north
STEP 1: On graph paper, mark the position of each of the trees on your land. Let each block of the graph paper represent a 10-foot by 10-foot square. Using a straightedge, connect Tree 1 to Tree 2, Tree 2 to Tree 3, Tree 3 to Tree 4, and so on.
STEP 2: Use the Pythagorean Theorem to find the length of each side of your property. Round
each answer to the nearest hundredth, if necessary.
STEP 3: Determine the perimeter of your property by adding up all of the sides.
STEP 4: Company 1 says that they will complete the job for $12 per foot of fencing. Company 2
says that they will charge you $250 for the first 100 feet of fencing and $15 for each additional foot. Determine the cost of fencing for both companies.
TREE Position (relative to your house)
1 100 ft. east 2 40 ft east, 80 ft south 3 40 ft west, 120 ft south 4 90 ft west, 60 ft north 5 20 ft east, 110 ft north
STEP 1: On graph paper, mark the position of each of the trees on your land. Let each block of the graph paper represent a 10-foot by 10-foot square. Using a straightedge, connect Tree 1 to Tree 2, Tree 2 to Tree 3, Tree 3 to Tree 4, and so on.
STEP 2: Use the Pythagorean Theorem to find the length of each side of your property. Round
each answer to the nearest hundredth, if necessary.
STEP 3: Determine the perimeter of your property by adding up all of the sides.
STEP 4: Company 1 says that they will complete the job for $12 per foot of fencing. Company 2
says that they will charge you $250 for the first 100 feet of fencing and $15 for each additional foot. Determine the cost of fencing for both companies.
1 answer:
Answer:
STEP 1: See attached drawing on graph paper
STEP 2:
Length of segment 1 - 2 = 100 feet
Length of segment 2 - 3 = 89.44 ft.
Length of segment 3 - 4 = 186.82 ft.
Length of segment 4 - 5 = 120.83 ft.
Length of segment 5 - 1 = 136.01 ft.
STEP 3:
The perimeter of the property is 633.103 ft.
STEP 4:
The cost of fencing by Company 1 is $7597.24
The cost of fencing by Company 2 is $8246.55
Therefore, the company that provides the cheapest quote for fencing the property is Company 1
Step-by-step explanation:
STEP 1: See attached drawing on graph paper
STEP 2:
Therefore, we have
Length of segment 1 - 2 = √(8² + 6²) = 10 × 10 = 100 feet
Length of segment 2 - 3 = √(4² + 8²) = 4·√5× 10 = 40·√5 feet = 89.44 ft.
Length of segment 3 - 4 = √(5² + 18²) = √349 = 10·√349 feet = 186.82 ft.
Length of segment 4 - 5 = √(11² + 5²) = √146 = 10·√146 feet = 120.83 ft.
Length of segment 5 - 1 = √(11² + 8²) = √185 = 10·√185 feet = 136.01 ft.
STEP 3:
Therefore, the perimeter of the property = 100 + 89.44 + 186.82 + 120.83 + 136.01 = 633.103 ft.
STEP 4:
Hence the cost of fencing the property by Company 1 = $12 × 633.103 = $7597.24
The cost of fencing the property by Company 2 = $250 + $15 × 533.103 = $8246.55.
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Answer:
Step-by-step explanation:
Hello!
The variable of interest is X: chest circumference of a Scottish man.
X≈N(μ;δ²)
μ= 40 inches
δ= 2 inches
The empirical rule states that
68% of the distribution lies within one standard deviation of the mean: μ±δ= 0.68
95% of the distribution lies within 2 standard deviations of the mean: μ±2δ= 0.95
99% of the distribution lies within 3 standard deviations of the mean: μ±3δ= 0.99
a)
The 58% that falls closest to the mean can also be referred to as the middle 58% of the distribution, assuming that both values are equally distant from the mean.
P(a≤X≤b)= 0.58
If 1-α= 0.58, then the remaining proportion α= 0.42 is divided in two equal tails α/2= 0.21.
The accumulated proportion until "a" is 0.21 and the accumulated proportion until "b" is 0.21 + 0.58= 0.79 (See attachment)
P(X≤a)= 0.21
P(X≤b)= 0.79
Using the standard normal distribution, you can find the corresponding values for the accumulated probabilities, then using the information of the original distribution:
P(Z≤zᵃ)= 0.21
zᵃ= -0.806
P(Z≤zᵇ)= 0.79
zᵇ= 0.806
Using the standard normal distribution Z= (X-μ)/δ you "transform" the values of Z to values of chest circumference (X):
zᵃ= (a-μ)/δ
zᵃ*δ= a-μ
a= (zᵃ*δ)+μ
a= (-0.806*2)+40= 38.388
and
zᵇ= (b-μ)/δ
zᵇ*δ= b-μ
b= (zᵇ*δ)+μ
b= (0.806*2)+40= 41.612
58% of the chest measurements will be within 38.388 and 41.612 inches.
b)
The measurements of the 2.5% men with the smallest chest measurements, can also be interpreted as the "bottom" 2.5% of the distribution, the value that separates the bottom 2.5% of the distribution from the 97.5%, symbolically:
P(X≤b)= 0.025 (See attachment)
Now you have to look under the standard normal distribution the value of z that accumulates 0.025 of the distribution:
P(Z≤zᵇ)= 0.025
zᵇ= -1.960
Now you reverse the standardization to find the value of chest circumference:
zᵇ= (b-μ)/δ
zᵇ*δ= b-μ
b= (zᵇ*δ)+μ
b= (-1.960*2)+40= 36.08
The chest measurement of the 2.5% smallest chest measurements is 36.08 inches.
c)
Using the empirical rule:
95% of the distribution lies within 2 standard deviations of the mean: μ±2δ= 0.95
(μ-2δ) ≤ Xc ≤ (μ+2δ)=0.95 ⇒ (40-4) ≤ Xc ≤ (40+4)= 0.95 ⇒ 36 ≤ Xc ≤ 44= 0.95
d)
The measurements of the 16% of the men with the largest chests in the population or the "top" 16% of the distribution:
P(X≥d)= 0.16
P(X≤d)= 1 - 0.16
P(X≤d)= 0.84
First, you look for the value that accumulates 0.84 of probability under the standard normal distribution:
P(Z≤zd)= 0.84
zd= 0.994
Now you reverse the standardization to find the value of chest circumference:
zd= (d-μ)/δ
zd*δ= d-μ
d= (zd*δ)+μ
d= (0.994*2)+40= 41.988
The measurements of the 16% of the men with larges chess are at least 41.988 inches.
I hope this helps!
Answer:
Step-by-step explanation:
Points are said to be collinear if they all lie on a line .
Let points L , M, N be collinear i.e they all lie on a line .
Consider the following figure :
Given :
LN = 54 units
LM = 31 units
To find : MN
Solution :
Clearly we can see LM + MN and LN coincides each other and we know that two things which coincide are equal to each other .
Therefore , LM + MN = LN
31 + MN = 54
On transposing 31 to RHS , we get MN = 54-31 = 23 units
{ Transposition is basically a process of taking one number from side to the other with the opposite operation }
