Answer:
$26,096
Step-by-step explanation:
property taxes = 31 January + 28 February + 31 March + 30 April + 31 May + 4 June = 155 days
property taxes = (155 days/365 days) x $5,309 = $2,254
agent's commission = 7% x $547,000 = $38,290
seller's net = $547,000 - $480,000 (mortgage) - $38,290 (agent's commission) - $360 (home warranty) - $2,254 (property taxes) = $26,096
Answer:
26,096
Step-by-step explanation:
Proration using 365-day method:
Buyer days are June - December 210 days (June 30 + July 31 + August 31 + September 30 + October 31 + November 30 + December 31 - June 4 days)
Seller days are January - June 155 days (January 31 + February 28 + March 31 + April 30 + May 31 + June 30 - June 26 days)
Formula with closing day to buyer: 210/365 x $5,309 = $3,054.49 --> $5,309 - $3,054.49 = $2,254.51 property taxes
Commission:
$547,000 sale price x .07 commission fee = $38,290 commission
Seller Net:
$547,000 sale price - $480,000 mortgage = $67,000 - $38,290 commission = $28,710 - $360.00 home warranty = $28,350 - $2,254.51 = $26,096
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
Select true or false for each equation
- 48 (134) = 1,608 True or False
- 7.3 • 0.14 = - 1.022 True or Flse
(- 0.28)(- 5.6) = - 1.568 True or False
(3/4)(- 1 1/3) = -1 True or False
Answer:
False
True
False
True
Step-by-step explanation:
Easiest and fastest way is to plug each equation into a calc and see if they match the values given. When you do so, you should get your answers.
Identify the range of the function shown in the graph.
Answer:
B
Step-by-step explanation:
The range is all values of y. Y goes from -1 to 1. Please mark brainliest.
Answer:
see below
Step-by-step explanation:
The domain of the function is the possible x values
The domain is all real values since x can be any number
The range of the function is the possible y value
The values of y go from -1 to 1 so
-1 ≤y≤1
Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce.
Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?
Answer:
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{s}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]X = 17.79, \mu = 17, s = 0.08[/tex]
How many standard deviations is the sample mean from the mean of the distribution of sample?
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.79 - 17}{0.08}[/tex]
[tex]Z = 9.875[/tex]
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
What is the area of the figure below 13 in length, 11 in width, 29 in and 13 in?
Answer:
B. 533in²
Step-by-step explanation:
Step 1: Find the area of the rectangle
A = lw
A = (29)13
A = 377
Step 2: Find the leg of the triangle
13 + 11 = 24
Step 3: Find the area of the triangle
A = 1/2bh
A = 1/2(24)(13)
A = 12(13)
A = 156
Step 3: Add the areas of the 2 figures together
377 + 156 = 533
Help me please I dont understand
Answer:
42°
Step-by-step explanation:
This is right triangle and sum of 2 angles is 90°:
y+48°=90°
so y= 90°- 48°= 42°
What is 66 tens + 24 tens
Answer:
900.
Step-by-step explanation:
66 tens are 660.
and 24 tens are 240.
so, It is 900!
Ten different numbers are written on pieces of paper and thrown into a hat. The sum of all the numbers is 205. What is the probability of selecting four numbers that have a sum greater than 82
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Mr.Chang needs to ship 8 boxes of cookies in a packing carton. Each box is a tight rectangular prism 8 inches long, 5 inches wide, and 3 inches high. What is the volume in cubic inches, of each box?
Answer:
120 inches cubed
Step-by-step explanation:
The formula for finding the volume of a rectangular prism is length * width * height.
In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.
So multiplying all of those together gets you 120 inches cubed.
m−4+m−5 how do i solve this?
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
=m+m-4-5
=2m-9
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
take the like terms
= 2m-4-5
= 2m-9
Sorry if that didn't help
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
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There are two species of plants that live along the ridge line of Old Rag, which is a mountain here in Virginia. The probability of observing the first species is 0.61, while the probability of observing the second species is 0.08. The probability of observing them growing together (i.e. right next to one another) is 0.28. When you go for a hike along this ridge line, what is the probability of observing one species or the other but not both together
Answer:
0.13
Step-by-step explanation:
First let's find the probability of finding the first species or the second species:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.61 + 0.08 - 0.28
P(A or B) = 0.41
Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P(A or B) - P(A and B):
P(A or B) - P(A and B) = 0.41 - 0.28 = 0.13
What is the best description of the transformation shown?What is the best description of the transformation shown?
Answer:
the correct answer is a reflection over the y axis
Step-by-step explanation:
The best description of the transformation shown will be;
''Reflection over the y - axis.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The transformation is shown in figure.
Now,
Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.
So, The best description of the transformation shown will be;
''Reflection over the y - axis.''
Thus, The best description of the transformation shown will be;
''Reflection over the y - axis.''
Learn more about the translation visit:
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The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
Learn more about appropriate domain here:
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Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
The Taylors have recorded their weekly grocery expenses for the past 12 weeks and determined that the mean weekly expense was $.82.55. Later Mrs. Taylor discovered that one week's expense of $74 was incorrectly recorded as $47. What is the correct mean?
Answer:
$84.80
Step-by-step explanation:
find the difference between accurate price and written price: 74 - 47 = 27
find written total (before Mrs. Taylor found mistake) by undoing the mean calculation: 82.55 x 12 = $990.60
the total expenses is $27 more than what they thought: 990.60 + 27 = 1017.60
divide accurate total by 12 to find mean: 1017.60 / 12 = $84.80
hope this helps :)
Convert 100 kilometers to meters.
Answer:
100,000 meters
Step-by-step explanation:
There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.
Answer:
it is 100000 kilometers
Step-by-step explanation:
use the metric system and you get 10000 kilometers.
What is the value of - x^2 -4 x -11 if x =.3
Answer: -32
Step-by-step explanation:
I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend
-(3^2) - (4*3) -11
-(9)- (12) -11
-9 - 12 - 11
-21 -11
-32
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only one number 5 from a total of 8 parts.
1 out of 8.
1/8 = 0.125
P(5) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Spinner divided in parts = 8
Number 5 = 1
P(5) = 12.5%
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
Step-by-step explanation:
t=V100-50/4
t=V50/4=1.76≈1.8 s
when h=0
t=V100/4=10/4=2.5 s
Answer: a) (5√2)/4 ≈ 1.77 seconds
b) 5/2 = 2.5 seconds
Step-by-step explanation:
[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]
Find the value of x for which a ll b
Answer:
x=35
Step-by-step explanation:
. Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito. (a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points) (b) 20% of Chipotle burritos weigh more than what weig
Complete Question
Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.
(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)
(b) 20% of Chipotle burritos weigh more than what weight
Answer:
a
[tex]P(X < 445 )= 0.3085[/tex]
b
[tex]k = 458.42[/tex]
Step-by-step explanation:
From question we are told that
The population mean is [tex]\mu = 450 \ g[/tex]
The variance is [tex]var = 100 \ g^2[/tex]
The consider weight is [tex]x = 445 \ g[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var}[/tex]
substituting values
[tex]\sigma = \sqrt{ 100}[/tex]
[tex]\sigma = 10[/tex]
Given that weight of Chipotle burritos follows a normal distribution the the probability that a Chipotle burrito weighs less than x grams is mathematically represented as
[tex]P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )[/tex]
Where [tex]\frac{X - \mu }{\sigma }[/tex] is equal to z (the standardized values of the random number X )
So
[tex]P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]
[tex]P(X < 445 ) = P (Z <-0.5 )[/tex]
Now from the normal distribution table the value for [tex]P (Z <-0.5 )[/tex] is
[tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]
=> [tex]P(X < 445 )= 0.3085[/tex]
Let the probability of the Chipotle burritos weighting more that k be 20% so
[tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]
From the normal distribution table the value of z for [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is
[tex]z = 0.8416[/tex]
=> [tex]\frac{k - 450}{10 } = 0.8416[/tex]
=> [tex]k = 458.42[/tex]
–9(w + 585) = –360 w = ______
Answer:
w = 15
Step-by-step explanation:
-9(w + 585) = -360w
-9w -5265 = -360w
351w = 5265
w=15
n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
In a basketball shooting competition there are ten balls from 1-10. The number of points earned is based on the number on the ball (I.e shoots a 7 gets 7 points), if a person misses 2 shots what number is not possible
52
44
41
38
35
The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part
3. Maria is a veterinarian. She wants to know how the weight of a puppy is related to its length. To find out, Maria randomly selected 10 puppies that are two months old. She recorded the length and weight of each puppy in the table below. Part A. The data from the table are shown on the scatterplot. Draw an estimated line of best fit through the data points. (3 points) Part B. Use the scatterplot to answer these questions. a. What kind of correlation exists between the length and weight of the puppies? Explain. (2 points) b. Identify two points on the line of best fit that you drew in Part A. Use the two points to find the equation of the line. Write the equation of the best fit line in slope-intercept form. Show your work. (4 points: 1 point for identifying the coordinates of two points, 1 point for slope, 1 point for b-value, and 1 point for showing work)
Answer:
Part A. I chose points (7,1.3) and (48,9.8)
Part B. a. Positive correlation; b. y = 0.21x - 0.2
Step-by-step explanation:
Part A.
I chose the first and last points on the line — (7 in, 1.3 lb) and (48 in, 9.8 lb).
That put three points on the line, three above it, and four below.
Part B
a. Type of correlation
There is a positive correlation between the length of a puppy and its weight.
You would expect a longer dog to be bigger and weigh more than a shorter dog.
b. The equation for the line of best fit
The slope-intercept equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (7,1.3) and (48, 9.8).
(i) Calculate the slope of the line
\begin{array}{rcl}
[tex]m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{9.8 - 1.3}{48-9}\\\\& = & \dfrac{8.5}{41}\\\\& = & \textbf{0.21 lb/in}\\\\\end{array}[/tex]
The slope of the line is 0.21 lb/in.
(ii) Locate the y-intercept
Put the slope and the coordinates of one point into the slope-intercept formula.
[tex]\begin{array}{rcl}y & = & mx + b\\1.3 & = & 0.21\times7 + b\\1.3 & = & 1.47 + b\\b & = & -0.2\\\end{array}[/tex]
The y-intercept is at (0,-0.2)
(iii) Write the equation for the line
y = 0.21x - 0.2
Graph the line y=-1/3x+2
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).