The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
What is constant of proportionality?When two or more parameters are directly or indirectly proportional to one another, their relationship is expressed as a = kb or a = k/b, where k indicates the nature of the relationship between the two variables. This k is referred to as the proportionality constant.
For example, the number of apples in a crop is proportional to the number of trees in an orchard, with the ratio of proportionality being the average number of apples per tree.
This can be illustrated as:
Let's say y = 4
Let's say x = 2
y = kx
4 = 2k
Divide
k = 4/2
k = 2
The constant is 2.
Note that an overview was given as the information is incomplete.
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Question 10
An electronics retailer purchases a laptop for $430 per unit. Per unit, the expense is 19% of the selling price
and profit is 25% of the selling price. What is the regular selling price per unit?
(rounded to nearest cent)
The regular selling price per unit for the laptop is $298.6.
How to calculate the price?Let the regular price per unit be x.
The expense is 19% of the selling price and profit is 25% of the selling price. This will be illustrated as:
x + (19% × x) + (25% × x) = 430
x + 0.19x + 0.25x = 440
1.44x = 430
Divide
x = 430 / 1.44
x = 298.6
The price is $298.6
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A square shape garden has a side of 6 feet. What is its area?
A manufacturer knows that their items have a normally distributed length, with a mean of 13.6 inches, and standard deviation of 2.4 inches. If one item is chosen at random, what is the probability that it is less than 13.1 inches long?
If one item is chosen at random, the probability that it is less than 13.1 inches long is equal to 0.4176.
How to determine the probability?First of all, we would determine the z-score of this data set. Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:
Z-score = (x - μ)/σ
Where:
x represents the sample score.σ represents the standard deviation.μ represents the mean score.Substituting the given parameters into the formula, we have;
Z-score, z = (13.1 - 13.6)/(2.4)
Z-score, z = -0.5/2.4
Z-score, z = -0.208
If one item is chosen randomly, the probability that it would be less than 13.1 inches long is given by this mathematical expression:
P(x < 13.1) = P(z < -0.208)
P(z < -0.2083) = 0.4176.
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Last year, Lisa opened an investment account with $6600. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year?
Increase in amount:
Year-end amount:
Answer: $429
Step-by-step explanation:
$6600 + 6.5% = $7029
$7029 - $6600 =$ 429
If you have to drink 400 milliliters 4 times a day, how many liters is that for one day?
Answer:
1.6 liters
Explanation:
400x4=1600
1000ml=1l
1600/1000=1.6
The graph of a function g is shown below. Find the following. g(-3)
Answer:
g(- 3) = 3.5Step-by-step explanation:
GivenGraph of the function g(x)To findThe value of g(-3)SolutionTo find the value of g(x), find the point x on the horizontal axis, then find the intersection of the vertical segment from that point to the graph, then trace the corresponding value of intersection on the vertical axis. This is the value of the function at the point x.
This is all done on the attached.
The value of g(- 3) is 3.5.
Write the quadratic equation whose roots are 2 and −6, and whose leading coefficient is 4.
Answer:
4x^2 + 16x - 48
Step-by-step explanation:
A quadratic equation with roots 2 and -6 has to have factors of (x - 2) and (x + 6) since both equal 0 when either 2 or 6 are plugged in. To get a leading coefficient of 4, multiply the product of the two factors by 4. When the 4 is distributed it becomes the leading coefficient:
4(x - 2)(x + 6)
4(x^2 + 4x - 12)
4x^2 + 16x - 48
suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding
It will take about _ years for $36,000 to grow to $51,806.67
It will take about 9.1 years for $36000 to grow with interest to $51806.67 after continuous compounding .
What is continuous compounding?
The process of continuously compounding involves calculating interest and reinvested it into the balance of an account over an infinite number of periods. When they specifically state that the amount is "compounded continuously" in a problem, they should use the continuous compounding formula. The mathematical constant "e" is used in this formula, and its value is roughly equal to 2.7182818. Here is the formula for continuous compounding.
Here the Principal P = $36000 , Total amount A= $39786.15 and
Time t=2.5 yrs.
Now using continuous compounding formula,
=> A = P[tex]e^(rt)[/tex]
=> 39786.15 = 36000*[tex]e^(r*5/2)[/tex]
=> r = 0.04 = 4%
Now A=51806.67 and Again using continuous compounding formula ,
=> A = P[tex]e^(rt)[/tex]
=> 51806.67 = 36000*[tex]e^(0.04*t)[/tex]
=> t =9.1 years.
Therefore it will take about 9.1 years for $36000 to grow to $51806.67 .
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You are driving (too fast) down a straight, country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road tracking vehicle speeds and are in contact with each other. At the first officer’s position, you drive by going 39 miles per hour. At the second officer’s position 63 seconds later, you drive by going 38 miles per hour. The second officer pulls you over and gives you a ticket. Were they justified in giving you a ticket, even though you were not caught speeding?
Hint: refer to the Mean Value Theorem to assist with your justification and reasoning.
Yes, they justified giving us a ticket, even though we were not caught speeding, because we drove at a speed higher than the posted speed limit.
It is given that we are driving down a straight country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road, tracking vehicle speeds, and are in contact with each other. At the first officer’s position, we drive by going 39 miles per hour. At the second officer’s position, 63 seconds later, we drive by, going 38 miles per hour.
The second officer pulls us over and gives us a ticket. We will use the mean value theorem to check whether getting a ticket was justified or not. Let the maximum speed be "v" that we reach between the officers at time "c". Let the function f(t) denote the distance at time "t".
f'(c) = [f(b) - f(a)]/(b - a)
v = (1 - 0)/(63 - 0)
v = 1/63 miles per second
We need to convert the speed into miles per hour.
v = 3600/63 = 57.143 miles per hour
The speed is higher than the posted speed limit. Hence, they justified giving us a ticket, even though we were not caught speeding.
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algebraically manipulating the formula for finding the simple interest find the principal deposited in a savings account which earned $3500 in interest at a simple interest rate of 8.5% for 10 years
34. A six-sided die is thrown three times. What
is the probability of getting a prime number
on all three rolls?
Step-by-step explanation:
The probability of getting prime numbers is =3/6=1/2. So, in 3 throws the probability of getting prime numbers is (1/2)^3=1/8=0.125
Find the coordinates of point P along the directed line segment AB, from A(1,6) to B(-2,-3), so that the
ratio of AP to PB is 5 to 1.
The coordinates are P().
Answer: question
Step-by-step explanation: answer
what is the common denominator of 5, 12, 3 , 8
Answer:
i think the denominator of 5,12,3,8, is 24
Jonathan, Lucas, and Kiley are in a book
club. This past week, Lucas read six less
pages than Kiley read. Jonathan read two
times the amount of pages that Lucas.
read., Altogether, they read 122 pages.
how many pages did each person read? PLS HELP ME
Answer:
Lucas 29
Kiley 35
Jonathan 58
Step-by-step explanation:
Kiley = Lucas + 6
Jonathan = 2 x Lucas
Kiley + Lucas + Jonathan = 122
1. Replace Kiley and Jonathan with information we have
K + L + J = 122
(L+6) + L + (2L) = 122
4L + 6 = 122
4L = 122 - 6
L = 116/4 = 29
2. Replace Lucas with 29, you have
Kiley = 29 + 6 = 35
Jonathan = 2 × 29 = 58
What is the general form of the equation of the line shown?
Answer:
y-2=0
Step-by-step explanation:
Add the 2 to the other side and it would be y=2
Use the function, to match each key feature listed below.
The parabola have a vertex of (-1, -64), it's x-intercept is (3, 0), (-5, 0), it's y-intercept is (0, -60) and it's axis of symmetry is x = -1
ParabolaThis is a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface. It can also be defined as a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. In mathematics, it is a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
f(x) = 4x² + 8x - 60
The vertex = (-1, -64)
The x-intercept = (3, 0), (-5, 0)
The y-intercept = (0, -60)
The axis of symmetry = x = -1
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Divide. Write your answer on the simplest form.
7/15 ÷ 3/10
Answer:
14/9
Step-by-step explanation:7/15 divided by 3/10 equals 14/9
A cyclist cycles for x hours at 12 km/hour and y hours at 18km/hour.All together she cycles 78km in 5 hours.Find x and y 08106764242
The values of x = 2 & y = 3.
A cyclist cycles for x hours at 12 km/hour and y hours at 18km/hour.
To find x and y:
Given kilometers = 78km
Time = 5 hours
So, we know that the
Distance Equation is 12x + 18y = 78 km
Time Equation is x + y = 5 hours
Multiply the equation through the Time Equation by 12:
12x + 18y = 78
12x + 12y = 60
Subtract and solve for "y":
6y = 18
y = 3
So now we have to Solve for "x" using x + y = 5
x + 3 = 5
x = 2
Hence the answer is the values of x = 2 & y = 3.
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Avery is designing a large rectangular sign. They want the sign to have an area of 2 m² and a width of 4/5m.
How tall should the sign be?
The rectangular design should be 2.5 m tall.
What is area of rectangle?
A flat surface of a specific shape can be thought of as the area it occupies in space. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is known as the area of a rectangle. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes. To determine the area that these items occupy, use the formula for a rectangle's area.
Here area of rectangle = 2[tex]m^2[/tex]
And width of the rectangle w= 4/5 m .
Using area of rectangle formula ,
=> A = h*w
=> 2= h*4/5
=> h = 10/4 = 2.5 m.
Therefore the rectangular design would be 2.5 m tall.
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Help pls bro hurry svevd evr
Answer: i believe its B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
because ×=82822929929283838399388
You are on vacation in New York City, and you need to get around town to different locations. Below are the rates for 2 different cab companies, locally dubbed "The Red Cabs" and "The Green Cabs".
How many miles would you travel for the cost to be the same for both cabs and how much will that cost you?
What is the difference in cost between the two companies if you need to travel 8 miles?
After seeing all your vacation photos on S n a p b o o k, your cousin decided they wanted to visit New York City also. They asked for some general advice on traveling around the city. What advice would you give them about which cab company they should use when they travel around the city?
1. When you travel 3 miles in New York City, the cost of The Red Cabs and The Green Cabs would be the same.
2. The difference in cost between the two companies if you need to travel 8 miles is $5.
3. It is cheaper to travel with Red Cabs than Green Cabs if the total distance is more than 3 miles.
How is the difference in cost determined?First, for the costs of both companies to be equal, we set the two cost equations to be equal to each other and solve for the unknown variable (miles).
Based on the equations for the two companies, we can determine the total costs of using any option.
The difference between the total costs is obtained by subtracting.
Let cost of Green Cab = 2 + 2m
Let cost of Red Cab = 5 + m
For the two companies costs to be equal, 2 + 2m = 5 + m
= 2m - m = 5 - 2
m = 3
The costs of traveling 8 miles:Green Cab = 2 + 2m
= 2 + 2(8)
= 18
= $18
Red Cab = 5 + m
= 5 + 8
= 13
= $13
The difference in cost = $5 ($18 - $13)
Thus, based on the solution to the cost equations, cost-conscious travelers should prefer Red Cabs to Green Cabs when they travel in New York City for a distance exceeding 3 miles.
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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.6 years. He then randomly selects records on 28 laptops sold in the past and finds that the mean replacement time is 3 years.
Assuming that the laptop replacement times have a mean of 3.2 years and a standard deviation of 0.6 years, find the probability that 28 randomly selected laptops will have a mean replacement time of 3 years or less.
P(M ≤ 3 years) =
Enter your answer as a number accurate to 4 decimal places.
Based on the result above, does it appear that the computer store has been given laptops of lower-than-average quality? Yes or no question.
Yes- The probability of this data is unlikely to have occurred by chance alone.
No- The probability of obtaining this data is high enough to have been a chance occurrence.
No- The probability of obtaining this data is high enough to have been a chance occurrence.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Test statistic (z) = (sample mean - population mean) ÷ (population sd/√n)
sample mean = 3 years
population mean = 3.2 years
population sd = 0.6 year
n = 28
z = (3 - 3.2) ÷ (0.6/√28) = -0.2 ÷ 0.1134 = -1.764
The cumulative area of the test statistic is subtracted from 1 to obtain the probability that 28 randomly selected laptops would have a mean replacement time of 3 years or less
The cumulative area is 0.9982.
Therefore, the probability is (1 - 0.9982 = 0.0018)
Hence No- The probability of obtaining this data is high enough to have been a chance occurrence.
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William sold 100 tickets for his show.
An adult ticket costs £5.50 and a child ticket costs £1.50.
William's ticket sales totalled £430.
a) How many adult tickets did he sell?
b) How many child tickets did he sell?
Number of ticket sold for adult = 70
Number of ticket sold for child = 30
Given that,
The number of tickets sold = 100
Cost of ticket for adult = £5.50
Cost of ticket for child = £1.50
Total sold amount = £430.
Let number of ticket for adult = x
And number of tickets for child = y
We know that,
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Therefore,
Forming the equation according to the given information,
We get two equation as,
5.50x + 1.50y = 430 ...(i)
x + y = 100 ...(ii)
Now, Subtract equation (ii) with multiplication 1.50 from (i)
4x = 280
x = 70
Now put the values of x in equation (ii)
y = 30
Hence number of ticket for child is 30 and for adult is 70.
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A baseball is hit into the air, and its height h in feet after t seconds is given by h(t)=-16t^2+ 32t+ 1
a What is the height of the baseball when it is hit?
(b) After how many seconds does the baseball reach its maximum height?
(c) Determine the maximum height of the baseball.
a) The ball was struck from a height of one foot.
b) It took the object one second to reach its highest point.
c) The baseball may fly up to a height of 17 feet.
Determining the maximum height of an object using functions.Given the function that represents the height of an object in air expressed as;
h(t)=-16t^2+ 32t+ 1
a) The ball is hit at the point where the time is zero. Equating the function to zero.
h(0) = -16t^2+ 32t+ 1
h(0) = -16(0) + 32(0) + 1
h(0) = 1 feet
Hence the ball was hit at the height of 1 feet
b) At maximum height, the velocity of the object is zero. Hence;
v(t) = -32t + 32
v(t) = 0 = -32t + 32
32t = 32
t = 32/32
t = 1sec
Hence the object reach its maximum height after 1 seconds.
c) Substitute t = 1 into the function to have:
h(1)=-16(1)^2+ 32(1)+ 1
h(1) = -16 + 33
h(1) = 17 feet
The maximum height reached by the baseball is 17 feet.
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Help please i need your help
There are 28 groups of 1/5 are in 5.
And, The solution of the expression 5 ÷ 4/5 will be 25/4.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There is a number line shown in figure.
Now,
In a number line,
The groups of 1/5 in 5 = 28 - 0
= 28
Thus, There are 28 groups of 1/5 are in 5.
And, The expression is,
⇒ 5 ÷ 4/5
Solve aa;
⇒ 5 × 5/4
⇒ 25 / 4
Thus, There are 28 groups of 1/5 are in 5.
And, The solution of the expression 5 ÷ 4/5 will be 25/4.
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How do you do this problem? Show your work
15 x 2 - 8 x 40 + 896 x 2 =
The answer to the arithmetic 15 x 2 - 8 x 40 + 896 x 2 is 1502
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them
Using the PEDMAS rule which states that mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.
15 x 2 - 8 x 40 + 896 x 2 can be solved thus:
Solving the multiplication first;
(15 x 2) - (8 x 40) + (896 x 2)
solving the addition and subtraction
30 - 320 + 1792
1502
Using PEDMAS, the answer to the arithmetic is 1502
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Find the value of x so that the ratios are equivalent.
9:x and 54:8
Answer:
1 1/3
Step-by-step explanation:
9*6=54
So 6x=8
x=1 1/3
The expression 0.12x + (x − 35) models the final price of a scooter with an instant rebate in a state that charges sales tax.
a) Which part of the expression represents the discounted price before tax?
b) Which part of the expression represent the amount of sales tax, in dollars (not the tax rate, the amount of sales tax paid)?
a. The part of the expression that represents the discounted price before tax is (x − 35).
b. The of the expression represent the amount of sales tax, is 0.12x.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the expression 0.12x + (x − 35) models the final price of a scooter.
It should be noted that 0.12x represented the sale tax. In this case, the sales tax is 12% which was depicted as 0.12.
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Triangle DEF, with vertices D(3,-5), E(8,-6), and F(4,-2), is drawn inside a rectangle, as shown below.
The area of triangle DEF, in square units, is given as follows:
4.08 units squared.
What is the area of a triangle?The area of a triangle is given by half the multiplication of it's base by it's height, as follows:
Area = 0.5 x base x height.
We consider the base as the segment DE, hence it's length is given by the distance between these two points, obtained as follows:
[tex]b = \sqrt{(8 - 3)^2 + (-6 - (-5))^2}[/tex]
[tex]b = \sqrt{26}[/tex]
b = 5.1 units.
The midpoint of the base is given as follows:
(5.5, -5.5).
As it is obtained with the mean of the coordinates.
The height is the distance between the midpoint of the base and the other vertex, hence:
[tex]h = \sqrt{(5.5 - 4)^2 + (-5.5 - (-5))^2}[/tex]
h = 1.6 units.
Hence the area of the triangle is obtained as follows:
Area = 0.5 x 5.1 x 1.6 = 4.08 units squared.
Missing InformationThe problem asks for the area of the triangle, as shown in the image given at the end of the answer.
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The perimeter of a quadrilateral (four-sided polygon) is 29 inches. The longest side is twice as long as the shortest side. The other two sides are equally long and are 2 inches longer than the
shortest side. Find the length of all four sides.
The length of the shortest side is ____?
the length of each of the two equal sides is____?
and the length of the longest side is___?
The length shortest side of the quadrilateral is 5 inches
The length longest side of the quadrilateral is 10 inches;
The length of the other two sides of the quadrilateral will be 7 inches.
What is the perimeter of a quadrilateral?
The length of a quadrilateral's boundary, or what remains after joining all four of its sides to form a single line segment, is referred to as the quadrilateral's perimeter. As a result, a quadrilateral's perimeter is measured in the same linear units as its sides, such as meters, inches, centimeters, etc. We are aware that a quadrilateral's perimeter can be calculated by summing all of its side lengths. This can be stated using a straightforward formula. For instance, the formula for a quadrilateral ABCD's perimeter can be written as,
AB + BC + CD + DA = The perimeter
Let the length shortest side of the quadrilateral be x;
So, According to the question,
length longest side of the quadrilateral will be: 2x;
length of the other two sides of the quadrilateral will be (x +2) inches.
We have given that:
The perimeter of the quadrilateral is 29 inches.
So,
⇒ 2x + (x+2) +(x+2)+x = 29
⇒5x + 4 = 29
⇒5x = 29-4
⇒5x = 25
⇒x =5;
Hence,
the length shortest side of the quadrilateral is 5 inches
length longest side of the quadrilateral is 10 inches;
length of the other two sides of the quadrilateral will be 7 inches.
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