Answers
Answer:
x = 7 , y = 4
Step-by-step explanation:
the triangle on the right has 3 congruent angles and is therefore equilateral with 3 congruent sides, so
3x - 5 = 5y - 4 → (1)
the triangle on the left has 2 congruent angles and is therefore isosceles with the 2 legs being congruent, so
3x - 5 = y + 12 → (2)
we have 2 equations with 3x - 5 on the left side so equate the right sides
5y - 4 = y + 12 ( subtract y from both sides )
4y - 4 = 12 ( add 4 to both sides )
4y = 16 ( divide both sides by 4 )
y = 4
Then
5y - 4 = 5(4) - 4 = 20 - 4 = 16 , so
3x - 5 = 16 ( add 5 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Related Questions
Four students set up a lemonade stand. At the end of the day,their profit is $17. 52. How much money do they have when the profit is split equally?
Answers
Answer:
$4.38
Step-by-step explanation:
17.52/4=4.38
the proportion of defective electronic items in a shipment has the beta distribution. find the probability that at least 30% of the items in the shipment are defective (round off to second decimal place).
Answers
The probability that at least 30% of the items in the shipment are defective is 0.7360.
The beta distribution with parameters (3,3) is the conjugate prior for the binomial distribution with a probability of success of p, where 0<p<1.
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of Bernoulli trials. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. In the context of the problem you presented, success would be a defective item, and failure would be a non-defective item.
To find the probability that at least 30% of the items in the shipment are defective, we can use the cumulative distribution function (CDF) of the beta distribution. The CDF of the beta distribution is given by:
F(x;a,b) = (x^(a-1) * (1-x)^(b-1)) / B(a,b)
where x is the proportion of defective items, a and b are the shape parameters, and B(a,b) is the beta function.
We want to find P(X >= 0.3) where X is the proportion of defective items. Substituting the values for a, b, and x we get
P(X >= 0.3) = 1 - P(X < 0.3)
= 1 - F(0.3;3,3)
= 1 - ((0.3^(3-1) * (1-0.3)^(3-1)) / B(3,3))
= 1 - ((0.3^2 * 0.7^2) / (1/6))
= 1 - ((0.09 * 0.49) / (1/6))
= 1 - (0.044/0.1666)
= 1 - 0.2640
= 0.7360
Therefore, The probability that at least 30% of the items in the shipment are defective is 0.7360.
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let and let be a random sample from a probability distribution with probability density function , zero elsewhere. is the maximum likelihood estimator an unbiased estimator of ? let and let be a random sample from a probability distribution with probability density function , zero elsewhere. is the maximum likelihood estimator an unbiased estimator of ? true false
Answers
The statement "the maximum likelihood estimator is an unbiased estimator of " is False.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.
It depends on the specific probability density function (pdf) of the distribution. An estimator is unbiased if its expected value is equal to the true value of the parameter being estimated. For a given pdf, the maximum likelihood estimator (MLE) may or may not be an unbiased estimator of the true parameter value.
The MLE is the value of the parameter that maximizes the likelihood function, which is the probability of the observed sample under the assumed pdf. In general, the MLE is a consistent estimator, meaning that as the sample size increases, the MLE will converge to the true parameter value with probability 1. However, it may not always be unbiased.
The statement "the maximum likelihood estimator is an unbiased estimator of " is False.
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Which statements are true? Check all that apply.
On a coordinate plane, point A is (2, 3), point B is (3, 2), point C is (negative 2, 2), point D is (negative 3, negative 3), point E is (0, 3), point F is (2, 0), and point G is (0, 0).
A is in Quadrant I.
B is on the x-axis.
C is in Quadrant I.
D is in Quadrant III.
E is on the x-axis.
F is on the x-axis.
G is on the y-axis.
Answer is A, D, F, G
Answers
Answer: On a coordinate plane, the quadrants are defined as follows:
Quadrant I: x-coordinate is positive, y-coordinate is positive
Quadrant II: x-coordinate is negative, y-coordinate is positive
Quadrant III: x-coordinate is negative, y-coordinate is negative
Quadrant IV: x-coordinate is positive, y-coordinate is negative
Based on this information, the following statements are true:
A is in Quadrant I, because its coordinates are (2, 3) and both x and y are positive.
D is in Quadrant III, because its coordinates are (negative 3, negative 3) and both x and y are negative.
F is on the x-axis, because its y-coordinate is 0.
G is on the y-axis, because its x-coordinate is 0.
The other statements are not true:
B is not on the x-axis, because its y-coordinate is not 0.
C is not in Quadrant I, because its x-coordinate is negative.
E is not on the x-axis, because its y-coordinate is not 0.
Step-by-step explanation:
a fictional country has a population of 5 million people and a net immigration rate of 1 person per 1000 people. the population is only increasing due to immigration. how long will it take the country's population to double?
Answers
The time it takes for the country's population to double is 1000 years. The total population would be 10 million people.
How to calculate the population growth?We can calculate the population growth by
P = P₀ × r × t
Where
P = population growthP₀ = current populationr = growth raten = number of periodsSuppose that immigration is the only factor of population growth. We have
Net immigration rate, i = r = 1/1000The current population, P₀ = 5 million peopleFind the time that takes the country's population to double!
To make the country's population double, the population growth should be also 5 million people.
The formula would be
5,000,000 = 5,000,000 × 1/000 × t
t = 1,000/1
t = 1,000 years
Hence, the country's population will be double after 1,000 years.
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The revenue (R) made on the sale of tickets is a function of the price (p) of each
ticket, where R(p) = -40p^2 +400p-640
Pls help 60 points
Answers
To earn at least $640 in revenue, the ticket prices should be $8 or $2
What is an Equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Revenue = number of tickets sold * price per ticket R(p) = -40p^2 +400p-640
p² -10p +16
Factorizing the function to have
(p²-8p)-(2p+16)
p(p-8)-2(p-8)
p-2 = 0 or p-2=0
This implies that
p=8 or p=2
p = $8 or p = $2
To earn at least $640 in revenue, the ticket prices should be $8 or $2.
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Scale model A toy manufacturer sells a 0.9-m tall model of the CN Tower. The
model casts a shadow 0.2 m long. At the same time of day, the CN Tower casts a
shadow 123.3 m long. Find the height of the CN Tower, to the nearest metre.
Include a diagram in your explanation.
Answers
The height of the CN tower found using the trigonometric function to the nearest metre is 555m.
What are the different trigonometric functions?
Trigonometric functions are used to determine the relationship between
angles and sides of a triangle.
The basic functions are sine, cosine and tangent.
sine = perpendicular/hypotenuse
cosine = base/hypotenuse
tangent = perpendicular/base
From the figure, we can see the right-angled triangles made by both the model and real CN towers.
Since the shadow is cast at the same time of the day, we can say that the angles θ and Φ formed are the same angles.
So from the figure,
tan θ = tan Φ
0.9/0.2 = h/ 123.3
h = 554.85 m
Therefore the height of the CN Tower to the nearest metre is 555m.
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Solve each trigonometric function IN THE INTERVAL [0, 2)
3 sec2x − 2 tan2x − 4 = 0
Answers
The intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric function is given below.
3 sec2x − 2 tan 2x − 4 = 0
Simplify the equation, then we have
3 sec2x − 2 tan 2x − 4 = 0
3 / cos 2x − 2 sin 2x / cos 2x = 4
3 − 2 sin 2x = 4 cos 2x
(3 − 2sin 2x)² = 16 cos² 2x
The graph of the functions is drawn below.
From the graph, the intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.
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A hockey player scores 27 goals over a 22 game season. State the goals per game for this situation and round your answer to the nearest tenth if necessary.
Answers
subtract 22 from 27 the results is=5
Claire has no more than $45 to spend on a new dress. If x represents the amount Claire can spend, which inequality represents the possible prices of the new dress?
Answers
The possible prices of the new dress must be any value less than or equal to $45.
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Start with the inequality x ≤ 45
This inequality states that x must be less than or equal to 45.
Therefore, the possible prices of the new dress must be any value less than or equal to $45.
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Suppose your friend's parents invest $10,000 in an account paying 6% compounded annually. What will the balance be after 7 years?
The account balance will be $
(Round to the nearest cent as needed.)
Answers
The balance will be $15,036.30 after 7 years.
What is Compound Interest?Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.
We have,
P = $10,000
R= 6%
T= 7 years
r = R/100
r = 6/100
r = 0.06 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt[/tex]
A = 10,000.00(1 + 0.06/1)⁷
A = 10,000.00(1 + 0.06)⁷
A = $15,036.30
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how to simplify 6(1+10m)
Answers
Answer:
0.1
Step-by-step explanation:
1.distribute the 6 to 1 and 10
2.now its 6+60m
3. divide 60 on both sides
4. 60/60 cancels out.
5. 6/60 =0.1
A desk is on sale for $480 , which is 50% of the regular price.
What is the regular price?
Answers
Answer: $960
Step-by-step explanation:
Regular Price = x
x*0.5 = 480
x = 960
Answer:
$960
Step-by-step explanation:
Since 480 dollars is half (50%) of the regular price...
you can find the total price by dividing 480 by 0.50 (50%)
or multiplying 480 by 2. You end up getting an answer of $960.
Please help I really need it
Answers
Kelly's brothers age after 4 2/3 is 23 12/24 years.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
We have ;
Kelly's Brother is 18 7/8 year old.
We have to calculate;
His age after 4 2/3 years.
So,
⇒ 18 7/8 + 4 2/3
⇒ 151/8 + 14/3
⇒151 x 3 + 14 x 8/24
⇒453 + 112 /24
⇒565/24
⇒23 13/24 year old
Hence , his age after 4 2/3 is 23 13/24 years.
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a crane has a 200-foot arm whose lower end is 5 feet off the ground. the arm has to reach the top of the dome 80 feet high. at what angle x should the arm be set?
Answers
Using the trigonometry ratio, at angle 50.81° should the arm be set.
We have to determine the angle x should the arm be set.
A crane has a 200-foot arm whose lower end is 5 feet off the ground.
The arm has to reach the top of the dome 80 feet high.
The length of crane arm = 200ft
The height of building = 160ft
The initial height of the crane = 5ft
As a result, the height of the building in relation to the crane can be expressed as;
h = 160ft - 5ft
h = 155ft
The angle x the crane makes with the horizontal can be expressed mathematically as;
sin x = opposite/hypothesis
sin x = 155ft/200ft
sin x = 0.775
Taking [tex]\sin^{-1}[/tex] on both side, we get
x = [tex]\sin^{-1}[/tex](0.775)
Using the calculator
x = 50.81°
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A car rental company charges a service fee and then a daily rate when it rents out a car.
The total cost for the rental can be modelled by the following function.
C = 45d + 25
What statement is true about the rental company’s charges?
Answers
The statement that is true about the rental company’s charges is A. The deposit fee is $ 25 and the rental fee per day is $ 45.
How to find the true statement ?The total cost function is given as C = 45d + 25. This means that the slope is 45 and the y - intercept is 25.
This also means that the rental per day is $ 45 because the slope is the amount that the total cost changes by per day which must be the daily rental cost.
The $ 25 would be the cost that a person pays as a down payment when they rent the car because this amount does not change.
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Options for this question include:
A. The deposit fee is $ 25 and the rental fee per day is $ 45.
B. The deposit fee is $ 45 and the rental fee per day is $ 25.
C. The car can be rented for $ 45 and then given back to the company at $ 25
Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden how many packs of seeds were planted in each garden
Answers
If Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden then the number of packs of seeds were planted is 2.74 pack for each garden .
the number of packs of seed planted by Jason is = 11 packs ;
the number of gardens in which the seeds are planted is = 4 garden ;
the amount of packs planted in each garden can be calculated by the expression on dividing "number of seed packs" by "number of gardens" ;
⇒ (number of seed packs)/(number of gardens) ;
Substituting values of number of seed pack and number of garden ,
we get ;
= 11/4 = 2.74 .
Therefore , Jason planted 2.74 packs of seed in each garden .
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in the following equation , what happens to the value of y when the value of x is divided by 6 y=3/x
Answers
The value of y is multiplied by 6 when x is divided by 6
How to determine what happens to yFrom the question, we have the following parameters that can be used in our computation:
y = 3/x
Also, from the question we understand that
x is divied by 6
This means that the new equation is
y = 3/(x/6)
Evaluate
y = 6 * 3/x
This means that the new value of y is multiplied by 6
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eight rooks are placed in distinct squares of an 8 x 8 chessboard, with all possible placements being equally likely. in how many different ways can all the rooks be placed so that they are safe from each other i.e, that there is no row or column with more than one rook?
Answers
There are 5040 ways to place 8 rooks on an 8 x 8 chessboard.
A permutation is a systematic grouping of objects or numbers. Combinations allow you to select objects or numbers from a group of items without having to worry about the order in which they were collected. Contrary to permutations, when selecting components from a collection using the combination method, the order of selection is unimportant.
There are 8! ways to place 8 rooks on an 8 x 8 chessboard such that no two rooks are in the same row or column.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
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6 Total || Part Total 100 John has walked 15% of the way home from school. If he has walked 200 meters so far, how far does he walk home from school? Percent 100
Answers
John will walk 1,333.33 meters home from school.
What is percentage?Percentage is a mathematical concept used to express a number as a fraction of 100. It is generally used to compare one number to another, in terms of its relative size. For example, if 30 out of 100 people have voted for a certain candidate, then the percentage of those who voted for that candidate is 30%.
Percentage can also be used to express a change in a value over time.
For instance, if the price of a product has increased from $10 to $15, then the percentage increase in the price is 50%.
Percentage can also be used to compare different groups of data. For instance, if an organization has ten male employees and five female employees, then the percentage of male employees is 66.67%.
Percentage is an important concept in the field of mathematics and is used to calculate the percentage of a whole or part of a whole.
To find the total distance John will walk home from school, you need to multiply 200 meters, which is the distance he has already walked, by 100%, which is the total amount of the journey home from school, and then divide that answer by 15%, which is the percentage of the journey he has already walked.
200 x 100/15 = 1,333.33
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fx=4(3)^(x)
The function represents exponential growth.
The function represents exponential decay .
The y-intercept is _______
Answers
The function represents exponential growth and the y-intercept is 4
How to determine the type of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 4(3)^x
An exponential function is represented a
f(x) = ab^x
Where
y-intercept = a
rate = b
This means that
y-intercept = 4
b = 3
Since the value of b is greater than 1, then the function is a growth function
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please help i’m so bad at geometry
Answers
Answer:
what is the question the website is blocked
Step-by-step explanation:
11. The range of a cellular phone service area is a circular region bounded by the equation: x² +
y² = 400. A fire road represented by y-3x = 20 runs through the service area. Find the
point(s)) where the fire road intersects the outer boundary of the service area.
Answers
The point(s)) where the fire road intersects the outer boundary of the service area is found using the equation of circle which is (0,20) and (-12,-16).
What is the equation of circle?
A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:
(x-h)² + (y-k)² = r²
The equation of the circle is given as - x² + y² = 400 .... (1)
The equation of the fire road is given as - y - 3x = 20 .... (2)
Write the equation of fire road in slope-intercept form - y = mx + b
y = 3x + 20
Substitute the value of y in equation (1) -
x² + y² = 400
x² + (3x + 20)² = 400
Follow the (a + b)² rule, (a + b)² = a² + 2ab + b²
x² + (3x + 20)² = 400
x² + 9x² + 120x + 400 = 400
10x² + 120x + 0 = 0
x² + 12x = 0
x(x+12) = 0
x = 0, x = -12
Substituting the values of x in equation (2).
First calculate for x = 0.
y - 3x = 20
y - 3(0) = 20
y = 20
Now, calculate for x = -12.
y - 3x = 20
y - 3(-12) = 20
y + 36 = 20
y = 20 - 36
y = -16
Therefore, the points of intersection are (0,20) and (-12,-16).
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A company buys a digital scanner for $12,000 the value of the scanner is $12,000 (1-n/5) after n years. The company has budget to replace the scanner when the trade-in value is 2400. After how many years should the company plan to replace the machine in order to receive this trade in value?
Answers
For the given distance the time taken for the company plan to replace the machine in order to receive this trade in value is 4 years.
The term called distance is defined as the two points lie on the same horizontal or same vertical line and it is the distance can be found by subtracting the coordinates that are not the same.
Here we have know that the company buys a digital scanner for $12,000 the value of the scanner is $12,000 (1-n/5) after n years.
And here we also know that the company has budget to replace the scanner when the trade-in value is 2400.
By Using the given expression for the value of scanner after n years, we equate it to $2400 and solve for n is written as,
=> 12000 (1 - n/5) = 2400
When we simplify this one then we get,
=> 1 - n/5 = 2400/12000
=> 1 - n/5 = 0.2
=> n/5 = 0.8
=> n = 4.
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Select a counter-example that makes the conclusion false. 7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1 Conclusion: the difference of two positive numbers is always positive. Counterexample:
Answers
A counter example to the statement that the difference of two positive numbers is always positive is 4 - 7.
How to illustrate the counter example?Any exception to a generalization is a counterexample. A counterexample refutes the generalization in logic, and it does so firmly in the disciplines of math and philosophy.
A formal proof is necessary to establish the veracity of a mathematical assertion. Finding just one instance where a mathematical assertion is incorrect suffices to disprove it, though. An example like this is referred to as a counterexample because it contradicts or goes against the conclusion of the statement.
Here, a counter example to the statement that the difference of two positive numbers is always positive is:
= 4 - 7.
= -3
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Pleaseeee help meeee
Answers
Answer:
h = [tex]\frac{S-2\pi r^2}{2\pi r}[/tex]
Step-by-step explanation:
S = 2πr² + 2πrh ( subtract 2πr² from both sides )
S - 2πr² = 2πrh ( isolate h by dividing both sides by 2πr )
[tex]\frac{S-2\pi r^2}{2\pi r}[/tex] = h
students are conducting an experiment to determine if the amount of sunlight affects the size of clover leaves. they plant clover in two identical pots, placing one next to a window and one inside a cupboard. they water each pot daily with 10 ml of water. which is the independent variable?
Answers
In the experiment, the independent variable is the amount of sunlight received by the clover plants.
The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.
The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.
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The distance between 2 cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers.
Write you answer as a number without units.
Answers
Answer: 70
Step-by-step explanation:
70 kilometers if 3.5 centimeters is the distance and each centimeter represents 20 kilometers, 3.5 times 20 is equal to 70
6. Four friends are going into business together and have agreed to evenly
split the rental cost of their new company's office space. Each friend
wants to pay no more than $80 per month for their share of the rental
cost. What inequality represents the situation, where x is the total cost of
renting the office space?
Answers
Answer: C.
Step-by-step explanation:
since the four friends are SPLITTING the rental cost, it would be dividing.
Then, since it says NO MORE THAN it would be less than or equal to as the symbol for the inequality.
Need help please I’m stuck on this
Answers
The average rate of rain displayed in the graph is 2.5 inches per day.
1. The C.R.O.C is 2.5.
2. The equation that can be used to find y, is y = 2.5x.
3. Yes, this is a proportional relationship.
4. Yes there is a C.O.P of 2.5.
5. The unit rate is 2.5 inch rain in 1 day.
6. The amount of rain that would fall in 15 days is 37.5 inches.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
In the graph the x-axis represents the number of days.
In the graph the y-axis represents the rain in inches.
The first point is (2,5) which tells that in 2 days the rain fell 5 inches.
So, the average rain will be 5/2 = 2.5 inches.
CROC stands for constant rate of change. The formula for constant rate of change is -
= (y2 - y1)/(x2 - x1)
= (10 - 5)/(4 - 2)
= 5/2
= 2.5
Therefore, the constant rate of change is 2.5
The first point in the graph is (2,5), the x-intercept being 2 and y-intercept being 5. The CROC is obtained as 2.5.
So the equation for y can be given as -
y = 2.5 x
A proportional relationship between two variables x and y is when one variable is always some constant value multiplied by the other.
So, yes the relationship between the x and y value in this graph is proportional.
The “constant of proportionality” is the name given to this constant. All proportional relationships can be represented by the equation y =kx , where k is the proportionality constant.
Since, the equation is y = 2.5x.
Therefore, the constant of proportionality is 2.5.
The unit rate is 2.5 inches of rain in one day.
The amount of rate that would fall in 15 days is -
y = 2.5 x
y = 2.5 (15)
y = 37.5
Therefore, the amount of rain will be 37.5 inches.
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