The average of the given 5 equations is; x' = 2x - 1.6
What is the average of the equations?In mathematics, average is also called the mean and it has the formula as;
x' = ∑fx/∑f
Now, we are given the equations as;
x + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.
Thus;
∑fx = x + 3 + 2x - 4 + 3x - 6 + 2x - 5 + 2x
∑fx = 10x - 8
The number of expressions given is 5 and so ∑f = 5
Thus;
x' = (10x - 8)/5
x' = 2x - 1.6
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If I add 5 times a number to 6, I get 80................................
x = 14.8 (OR) x = 74/5.
Step-by-step explanation:
If you add 5 times a number to 6 you will get 80.
We don't know what number is multiplied with five and that number should added with 6. So,
Let, the unknown number be named as x.
The eqⁿ will be
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} → Eqⁿ(1) [/tex]
Shift 6 to the right side.
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{80 - 6}}}[/tex]
[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{74}}}[/tex]
Divide both the sides by 5. then,
[tex]{ \red{ \sf { \cancel{\frac{5}{5}}}}} { \green{ \sf{x}}} = {{ \frac{ \cancel{74} {}^{ \green{ \sf{{ 14.8}}}} }{ \cancel5}}} [/tex]
[tex]{ \red{ \boxed{ \purple{ \sf{x = 14.8}}}}} \: { \tt{(or)}} \: { \red{ \boxed{ \purple{ \sf{x = \frac{74}{5}}}}}} [/tex]
___________________________________
[tex]{ \red{ \sf{ \underline{verification}}}} [/tex]
Let us substitute the value of x in Eqⁿ(1) then,
[tex]{ \red{ \sf{5}}}{ \green{ \sf{(14.8)}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]
[tex]{ \red{ \sf{74}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]
[tex]{ \red{ \sf{80}}} = { \red{ \sf{80}}} [/tex]
Hence, our answer is correct
Seventy-five percent of the players in the basketball program are 5th graders. There are 80 players in the class. How many players are NOT 5th graders?
There are 20 players are not in 5th grades.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Total players in the class = 80
And, 75% of the players in the basketball program are 5th graders.
Now.
Number of players in the basketball program are 5th graders = 75% of 80
= 75/100 x 80
= 60
Thus, Number of players are not in 5th graders = 80 - 60
= 20
Therefore, There are 20 players are not in 5th grades.
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Evaluate the expression when a = 3 and y = -4.
8a - y
(Can someone help ASAP!)
Answer: The answer is 28.
Step-by-step explanation: 8a-y is our problem and we are given two variables, a and y. It is revealed that a=3 and y= -4. So our problem would now look like this: 8*3-(-4). Now see the two minuses (-) next to each other? We have to convert that into a plus (+) sign because two negatives make a positive. So our equation now looks like this: 8*3+4. Now, 8 times 3 (8*3) is equal to 24. Now our equation looks like this: 24+4. Add them together and the sum is 28.
Hope this helps!
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(2a36) (2a²+ 66²) + (6a²b + 12ab² - 76³)
OA. 4a³ - 12a²b 24ab² 116³
B. 4a³+12a²b25b³
O c. 4a³+ 12a²b + 24ab²
O D. 4a³+24ab² - 256³
-
-
1
116³
Reset
Next
the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
what is expression ?
An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It does not have an equal sign, so it cannot be solved.
In the given question,
The correct answer is C.
To simplify the given polynomial expression using the distributive property, we need to distribute the first term (2a³) to each term in the second parentheses, and then add it to the third term.
So, we have:
(2a³) (2a²+ 66²) + (6a²b + 12ab² - 76³)
= 4a⁵ + 132a³ + 6a²b + 12ab² - 76³
Now, we can simplify further by combining like terms:
= 4a³ (a²+ 33) + 6ab (a + 2b) - 76³
Therefore, the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
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let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia. can we conclude, at the 0.01 level of significance, that the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country? perform a two-tailed test. then answer the questions below.
According to the two tailed test, the difference between the first and second country is 40.
Two tailed test:
Two tailed test also means the two-sample t-test is used to determine if two population means are equal.
Given,
Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia.
Here we need to find the the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country.
While we looking into the given question,
For the first country,
Number of samples = 1800
Number of women with iron-deficiency anemia = 392
And for the second country,
Number of samples = 1700
Number of women with iron-deficiency anemia = 352
So, there difference between them is calculated as,
=> 392 - 352
=> 40
And as per the two tailed test both countries doesn't have the same proportion and the sample values is also differs this situation.
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find a number such that 14 less than twice the number is 66
Answer:40
Step-by-step explanation:
so 14 less means that 14 was subtracted. So we need to add that to our main number, 66. When we do that we get 80. Then since 80 is twice the number we are looking for, we divide by 2 (twice is 2 times), and we get 40. Hope this helps
David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?
The choice that best represents David monthly interest rate is 0.625%. The correct option is C.
How to calculate the monthly interest?From the information, David opens a savings account with a 7.5% annual interest rate.
It should be noted that there are 12 months in a year.
Therefore, the monthly interest rate will be:
= Annual interest rate / Number if months in a year
= 7.5% / 12
= 0.625%
The interest is 0.625%.
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Complete question
David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?
A. 7.5%
B. 12%
C. 0.625%
D. 5%
''24 hours per day''
Answer:
Step-by-step explanation:
365 day a year
24 hour per day
60 second in a minute
1440 minutes in a day
86400 second in a day!
rerrange 3g=d with the subject g
Step-by-step explanation:
[tex]3g = d[/tex]
[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]
[tex]g = \frac{d}{3} \\ [/tex]
[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]
Step-by-step explanation:
The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]
In order to get formula for g, let us divide 3 on both the sides.
[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]
Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]
The table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
A) Write an equation that models the amount of storage as a function of the number of songs
B) Interpret the slope and t-intercept of the line of fit
pls include work
From the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
From the table
Choose two points
(242, 14.8) and (519, 14.1)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (14.1 - 14.8) / (519 - 242)
= -0.7 / 277
The slope of the line = - 0.7/277
From the table at x = 0, the value of y = 16
Therefore the y intercept is 16
The slope intercept form is
y = mx + b
Substitute the values in the equation
y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277
The y intercept of the line = 16
Hence, from the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
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given
please help (please state your reason for the answer aswell)
Answer:
m∠C = 30°Step-by-step explanation:
Since the two angles of both triangles are congruent, it makes the remaining angles congruent too:
∠C ≅ ∠FThen we have:
x = 2x - 302x - x = 30x = 30So both C and F are 30°.
The father is 37 years old and his son's age is 5 years.After how many years,the father's age will be five times that of his son?
Answer:Let the age of son be x.
Thus, age of father is 4x.
After 5 years, their ages will be x+5 and 4x+5 years respectively.
As per the question, we have
4x+5=3(x+5)
⇒4x+5=3x+15
⇒x=10
Age of father will be 4x=4×10=40 years.
Thus when son is 10 years old, father is 40 years.
Step-by-step explanation:
After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .
Given,
Present age of father = 37 years.
Present age of son = 5 years.
Now,
Let the number of years be x after which the fathers age will be 5 times the age of his son.
So,
Ages after 3 years ,
Age of father = 40 years
Age of son = 8 years.
Thus age of father is 5 times the age of son.
Therefore after 3 years father's age will be five times that of his son.
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You start with $200 in bank account
and deposit $50 per week. Write an
equation for scenario.
Answer:
y= 50x + 200
Step-by-step explanation:
Find the distance from point A(-1. 7) to the line y = 3x. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
This seems complicated, huh.
So think about the question. They want to know the distance from a line, to a point. first decide if the point could possibly be on the line and there is zero distance. The given point is at (-1, 7) our coordinates of the point are at -1 in the X direction and at 7 in the Y direction. If we were to plug in those two number into the given line equation, y = 3x would it be a true statement? no. 7 = 3(-1) is not true. so our given point is not on the line. Next, find the right angle to the line and point. make your own line equation that does have our given point in it. and is at a right angle to the given line. recall that using a reciprocal can give you a right angle to your line. y = (- 1/3)X . Now we just need the given point to plug into our made up line equation and be true. 7 = (-1/3)(-1) + b . we need to make this equation true by moving a number into "b" that makes it true.
b = 6[tex]\frac{2}{3}[/tex] or [tex]\frac{20}{3}[/tex]
7 = (-1/3)(-1) + [tex]\frac{20}{3}[/tex]
now, when does our made up line, y =(-1/3)x + [tex]\frac{20}{3}[/tex], intersect with the given line, y=3x, that is, set the two equal
3x = (-1/3)x + [tex]\frac{20}{3}[/tex]
3[tex]\frac{1}{3}[/tex] X = [tex]\frac{20}{3}[/tex]
[tex]\frac{10}{3}[/tex]X = [tex]\frac{20}{3}[/tex]
X=[tex]\frac{20}{3}[/tex] * [tex]\frac{3}{10}[/tex]
X = [tex]\frac{20}{10}[/tex]
X=2
our two equations intersect at 2, how handy :)
now we have our two points that are at a right angle from each other and we just need the distance from them
(given) A(-1,7) and (found) B(2,6)
Distance = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
then our given points are A(x1,y1) and B(x2,y2)
Distance = [tex]\sqrt{(2-(-1))^{2}+(6-7)^{2} }[/tex]
Distance =[tex]\sqrt{3^{2}+(-1)^{2} }[/tex]
Distance = [tex]\sqrt{9+1}[/tex]
Distance = [tex]\sqrt{10}[/tex]
Distance = 3.1622
Distance =3.2 (rounded to nearest 10th)
Yes, that was kinda a lot :/
according to 2015 census data, 42.7 percent of colorado residents were born in colorado. if a sample of 250 colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in colorado?
The standard deviation of the number of residents in the sample who were born in Colorado is 7.82
Standard deviation:
The measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists is know as standard deviation.
Given,
According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. if a sample of 250 Colorado residents is selected at random.
Here we need to find the standard deviation of the number of residents in the sample who were born in Colorado.
Here we know that following details,
Number of sample = 250
Estimated proportion for residents born in Colorado = 42.7% which is equal to = 0.427.
Let us consider X be the random variable of interest (number of residents in the sample), on this case we now that:
X ~ (n = 250, p = 0.427)
Now, according to the probability mass function for the Binomial distribution is given as:
E(X) = n x p = 250 x 0.427 = 106. 75.
Now, the standard deviation for the random variable is given by:
SD = √106.75 (1 - 0.427)
SD = √106.75(0.563)
SD = 7.82
Therefore, the standard deviation is 7.82.
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Fill in the blank
According to the Symmetric Property of Equality, if AB = then CD = AB
According to the Symmetric Property of Equality, if AB = CD then CD = AB.
According to the question,
We have the following information:
CD = AB then AB = ?
Now, in order to fill the given blank, we have to use the symmetric property of equality. According to the symmetric property of equality, there is no difference in the final result of an expression if we change the sides of the expression.
For example, if 2 = a then we can also say that a = 2.
So, when CD=AB then we can clearly state that AB = CD.
Hence, according to the Symmetric Property of Equality, if AB = CD then CD = AB.
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IF x=2y and y=1/4 what does x equal
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
replace y with 1/4
x=2(1/4)
x=2/4
x=1/2
Hopes this helps please mark brainliest
A radio station tower was built in two sections. From a point 27 m from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest metre, what is the height of the top section of the tower?
Answer:13234
Step-by-step explanation:
13234 is
5. A line has a slope of zero. Which of the
following points could this line pass through?
A. (12, 9) and (12, 6)
B. (3, -6) and (7,-6)
C. (1, 4) and (2, 5)
D. (-9, 7) and (9, -7)
Answer: The correct answer is B.
Step-by-step explanation:
In a line with a slope of 0 the x can change but the y cannot in a (x, y).
determine whether AB and CD are parallel, perpendicular or neither for A(-1,-1), B(1,5), C(1,2), D(5,4), graph each line to verify your answer.
By finding the slopes of the two segments we can see that the segments are not parallel nor perpendicular.
Are the segments parallel, perpendicular or neither?The slope for a segment whose endpoints are:
(x₁, y₁) and (x₂, y₂) is:
slope = (y₂ - y₁)/(x₂ - x₁)
Two segments are:
parallel if have the same slope.perpendicular if the product of the slopes is -1.Segment AB has endpoints (-1, -1) and (1, 5), so the slope is:
s = (5 + 1)/(1 + 1) = 3
For segment CD the endpoints are (1, 2) and (5, 4), so the slope is:
s' = (4 - 2)/(5 - 1) = 2/4 = 1/2
So the slopes are different and their product is obviously not -1, then the lines are neither parallel nor perpendicular.
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Given: Line A // line B, ∠2≅∠4 Prove: ∠1≅∠3 line 2 and 3 have the same reason
∠1≅∠3 line 2 and 3 have the same reason.
∠1 and ∠3 are vertical angles, so they are formed by intersecting lines. Therefore ang1 and ∠2 are a linear pair, and ∠2 and ∠3 are a linear pair. By the Linear Pair Theorem, ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. So by the Congruent Supplements Theorem, ∠1 ≅ ∠3.
Statements - Reason
1. ∠1 and ∠3 are vertical angles - Given.
2. a and b are intersecting lines - definition of vertical angles
ang1 and ∠2 are a linear pair
3. ∠2 and ∠3 are a linear pair - definition of a line
4. ∠ 1 and 2 are supplementary ang2 and ang3 are supplementary - definition of linear pair.
5. ∠1 ≅ ∠3 - ≅ Supplements theorem
Hence the answer is ∠1≅∠3 line 2 and 3 have the same reason.
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Find the missing angle measures
Answer:
145°
Step-by-step explanation:
Answer: y equals 145 degrees
The mean incubation time of fertilized eggs is 20 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 10th percentile for incubation times. (b) Determine the incubation times that make up the middle 95%.
Using the normal distribution, it is found that:
a) The 10th percentile for incubation times is of: 18.72 days.
b) The incubation times that make up the middle 95% are of: Between 18.04 and 21.96 days.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the incubation times are presented as follows:
[tex]\mu = 20, \sigma = 1[/tex]
The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:
-1.28 = (X - 20)/1
X - 20 = -1.28
X = -1.28 + 20
Z = 18.72 days.
Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.Hence the lower bound is:
-1.96 = (X - 20)/1
X - 20 = -1.96
X = -1.96 + 20
Z = 18.04 days.
The upper bound is:
1.96 = (X - 20)/1
X - 20 = 1.96
X = 1.96 + 20
Z = 21.96 days.
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Least common denominator: the smallest number that both denominator numbers will __ into.
The correct statement is,
''The smallest number that both denominator numbers will include into.''
What is Least common multiple?
The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The statement is,
The smallest number that both denominator numbers will __ into.
Now,
We know that;
The LCM of two or more numbers is divided by the numbers or its include all the numbers.
Thus, The correct statement is,
''The smallest number that both denominator numbers will include into.''
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Select the correct answer from each drop-down menu.
The GCF of the numbers in the expression (32 + 16) is
. The numbers left inside the parentheses after factoring out the GCF are
and
.
Using distributive law and the greatest common factor , the expression (32 + 16) can be factored as 16(2 + 1)
What is GCF(greatest common factor)?The GCF(greatest common factor) is defined as the largest number that is a factor of two or more numbers.
In a simpler term, the greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF.
Using distributive law and the greatest common factor we can factor an expression.
Therefore, let's factor the expression (32 + 16).
The greatest common factor of 32 and 16 is 16.
Therefore, the expression can be express as follows:
(32 + 16) = 16(2 + 1)
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Suppose y varies directly with x, and y = 25 when x = 5. What is the value of y when x = 7 ?
Answer:
35
Step-by-step explanation:
y = 25 and x = 5
When two variable quantities have a constant ratio their relationship is called a direct variation. The formula for direct variation is y = kx, where k is called the constant of variation. If we know k we can find y given x or we can find x given y.
If we solve the equation y = kx for k, we get k = y/x. If we replace the variables x and y with the actual values from the problem we have:
k = 25/5, which is 5.
Now we can substitute this value for k into the equation y = kx to find y when x is 7:
y = (5) (7)
y = 35
NEED ASAP THANKS EXPLANATION WOULD BE APRECIATED
pool empties at a rate of 12 quarts every 2 minutes. how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons? (1 gallon
After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.
As given that pool empties at a rate of 12 quarts every 2 minutes.
In 12 quarts = empties in 2 minutes
As we know that 1 gallon = 4 quarts
So 1 quarts = 1/4 gallon
In 12 quarts = 12/4 gallon
12 quarts = 3 gallon
So 3 gallon = empties in 2 minutes
So 1 gallon = empties in 2/3 minutes
12,000 gallon = empties in 2/3 ×12,000 minutes
Simplifying
12,000 gallon = empties in 2×4,000 minutes
12,000 gallon = empties in 8,000 minutes
Now converting minutes in hours.
As we know that 1 minute = 1/60 hours
So 8000 minute = 8000/60 hours
8000 minutes = 133 hours 33 minutes
133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
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The barge Califa building in Dubai united Arab emirate eighth i one of the tallet building in the world at 2722 feet tall in American football field i 360 feet in length approximately how many football field tall i the Burberry Califa building round to the nearet 10th
The burj khalifa is 7.56 football fields tall .
We have the height of the Burj Khalifa as = 2722 feet
And the given height of one football field is = 360 feet
Now using the Unitary method we can calculate the number football fields that would be equal to the height of the burj khalifa .
So ,
360 feet is equal to football fields = 1
1 feet is equal to football fields = 1/360 fields
therefore
2722 feet will be equal to fields = (1/360) x 2722
= 7.56 fields
So the Burj Khalifa is equal to 7.56 football fields.
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farmer determined the equation "y = "-7/3x" + 72.75" best fits this data when comparing the weight, y, in grams, of strawberries to the average daily mean temperature, x, in °F, each season. Which statement best describes the rate of change of the equation?
The statement that best describes the rate of change of the linear function is given as follows:
For each increase of 1ºF in temperature, the average weight of the strawberries decays by 7/3 grams.
How to obtain the average rate of change of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients are listed as follows:
m is the slope of the linear function, representing the rate of change of the function, that is, by how much the output of the function changes when the input increases by one.b is the y-intercept of the function, which is the value of the output when the input is of zero.The input and the output variables for this problem are given as follows:
Input: Average daily mean tempetature, in ºF.Output: Weight of the strawberries, in grams.The function is defined as follows:
y = -7x/3 + 72.75.
Hence the slope is:
m = -7/3.
And the interpretation, considering the input and output variables, is that for each increase of 1ºF in temperature, which is the input variable, the average weight of the strawberries, which is the output variable, decays by 7/3 grams.
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