The proportional relationships for each case are described as follows:
I. Direct proportional relationship.
II. Inverse proportional relationship.
III. Direct proportional relationship.
How to classify proportional relationships?There are two ways to classify proportional relationships, and these two ways are listed as follows:
Direct proportional relationship.Inverse proportional relationship.These two classifications are described as follows:
Direct proportional relationship: as the input increases, the output also increases.Inverse proportional relationship: as the input increases, the output decreases.Then the only inverse proportional relationship is given by item ii, where it is said that the time decreases and the number of workers increases.
Missing InformationThree relationships are described below: I. The cost of hiring a mover is based on the distance traveled and the total weight of the objects moved. II. The amount of time needed to paint a house decreases as the number of painters increases. III. The income of a worker who gets paid an hourly wage depends on the number of hours worked. What type of variation describes each relationship?
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Select the correct answer.
Solve the following compound inequality.
2x − 2 > -8 or -4x ≤ -36
The solution to the compound inequality is x > -3. The correct option is the third option x > -3
Solving compound inequalitiesFrom the question, we are to solve the given compound inequality
2x - 2 > -8 or -4x ≤ -36
Solving the first inequality
2x - 2 > -8
Add 2 to both sides of the inequality
2x -2 + 2 > -8 + 2
2x > -6
Divide both sides by 2
2x/2 > -6/2
x > -3
Solving the second inequality
-4x ≤ -36
Divide both sides of the inequality
-4x/-4 ≤ -36/-4
x ≥ 9
From the two solutions, we can conclude that x > -3
Hence, the solution is x > -3
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Solve the inequality
[tex]16 - < 6k + 2 < 0[/tex]
The answer of the inequality is [tex]-3 < k < -\frac{1}{3}[/tex]
What does algebraic inequality mean?
An inequality in maths shows the relationship between the two values in an uneven algebraic expression. A sign of inequality can be employed to indicate that one of the two variables is less than, greater than or equal to, less than, or equal to another value.
Given That:
-16<6k+2<0
Now to solve this equation we will subtract 2 from all the side
-16-2<6k<-2
now we will divide by 6 on all the side
-18/6<k<-2/6
[tex]-3 < k < -\frac{1}{3}[/tex]
Hence this the answer to the question
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The measures of the angles of a triangle are shown in the figure below. Find the
measure of the largest angle.
(6x+17)°
105°
(5X+14)°
Answer:
56
Step-by-step explanation:
What is the probability that a standard normal random variable will be between. 3 and 3. 2?.
Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.
In the given question,
We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .
We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.
Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .
So The probability should be
P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)
From the standard value of z
P(0.3<z<3.2)=0.9993−0.6179
Simplifying
P(0.3<z<3.2)=0.3814
Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.
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In the process of milling grain, 3% of the original is lost because of spillage, and another 5% of the original is lost because of mildew. If the mill starts out with 490 tons of grain, how much (in tons) remains to be sold after milling?.
If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton.
In the question ,
it is given that ,
the percent of grain that is lost due to spillage = 3%
the percent of grain that is lost due to mildew = 5%
the total percent of grain lost = grain lost due to spillage + grain lost due to mildew
= 3% + 5%
= 8% of total grain
given that amount of grain = 490 tons .
amount of grain lost = 8% of 490
= 0.08 * 490
= 39.2 ton ,
So , 39.2 ton of grains is lost .
the amount of grain remain to be sold = 490 - 39.2 = 450.8 ton
Therefore , If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton .
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1. If y is directly proportional to x and y = 6 when
x = 2,
(i) express y in terms of x,
(ii) find the value of y when x = 11,
(iii) calculate the value of x when y = 12,
(iv) draw the graph of y against x
If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.
What is direct proportion?The definition of "direct proportion" uses the phrase "when the relationship between two quantities is such that if we increase one, the other will likewise grow, and if we lower one, the other quantity will also drop."Take the scenario where x and y are two quantities, where x is the quantity of candy and y is the total amount of money paid, as an example.If we buy more sweets, we will spend more money, and if we buy less candies, we will pay less money. We can therefore say that x and y are directly proportional to one another in this situation. The symbol for it is x y. Additionally, direct proportion and direct variation are used.[tex]&y \propto x \\[/tex]
[tex]&y=k x[/tex]
When x = 2, y = 5
[tex]&5=k(2) \\[/tex]
therefore
[tex]k=\frac{5}{2}[/tex]
When x = 16,
[tex]&y=\left(\frac{5}{2}\right) \\[/tex]
y = 40
Hence, If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.
The complete question is:
If y is directly proportional to x and y=5 when x=2, what is the value of y when x=16?
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What property is 3x5 5x3?.
The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.
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;
The expression is,
⇒ 3 x 5 = 5 x 3
Now,
We know that;
The commutative property is defined as;
⇒ a x b = b x a
Hence, In the expression,
⇒ 3 x 5 = 5 x 3
The commutative property is used.
Thus, The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.
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order these from lease to gratest, 1/3, 0.3, 33%,
8/25, 33.6%
Rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3].
As per the question statement, we are provided with a set of values [1/3, 0.3, 33%, 8/25, 33.6%],
And we are required to rearrange the above mentioned set in the ascending order of magnitude.
To answer this question, we will have to convert all the values into fractions with a common denominator, and then arrange the fractions in an ascending order of magnitude of their numerators to obtain our desired answer, that is,
[(1/3) = 0.33333333...]
[(0.3) = (3/10) = (30/100)],
[(33%) = (33/100) = 0.330],
[(8/25) = (32/100) = 0.320]
And, [33.6% = (33.6/100) = 0.336]
Since (0.336 > 0.333 > 0.330 > 0.320 > 0.300),
Therefore, rearranging [1/3, 0.3, 33%, 8/25, 33.6%] in the ascending order of magnitude, we get, [33.6%, (1/3), 33%, (8/25), 0.3]
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Find the equation (in terms of x) of the line through the points (-4,3) and (2,-4)
The equation of the line (-4,3) and (2,-4) is y = -7/6x -5/3.
What is equation of line?
The equation of a line is the algebraic representation of a line using cartesian coordinates. The general form of the equation of a straight line is written as y = mx + c. Where m is the gradient of the straight line and c is the y y-intercept of the straight line.
Given, the points are (-4,3) and (2,-4)
m = -4-3/2+4
m = -7/6
The equation we get
y = -7/6x +b
the point (-4,3), we get
3 = -7/6(-4) +b
3 = 14/3 +b
3-14/3 = b
b = -5/3
Hence, the equation of line is y = -7/6x -5/3.
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Find the value of f(5) for the function.
f(a)=3(a+2)−8
Answer:
f(5) = 3(5+2) - 8
f(5) = 15+6 -8
f(5) = 21 - 8
f(5) = 13
Bao i the oldet of four ibling whoe age are conecutive even integer. If the um of their age i 60, find Bao' age
Thus, Bao age is 27.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Let the ages of the four siblings be;x , x + 1 , x + 2, x + 3(Ashley's age)If the sum of their ages is 100We have;x + x + 1 + x + 2 + x + 3 = 100collect like terms4x + 6 = 1004x = 100 - 64x = 96Make 'x' the subjectx = 96/ 4x = 24But Bao age is x + 3 = 24 + 3 = 27Thus,Bao's age is 27hence,Thus, Bao age is 27.
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The distance of 2 laps around a park is 2.5 miles. Walking 5 laps around the same park is 6.25 miles.
Complete the table to show the relationship between the number of laps and the number of miles. Enter the answers in the boxes.
Hence the complete table is ,
=> laps Miles
3 3.75
7 8.75
8 10
13 16.25
What is miles ?
A mile is a unit of length that is exactly equal to 5280 feet, or 1760 yards, and was standardised as exactly 1609.344 metres by an International agreement in 1959. It is the largest unit commonly used to measure the distance between distant locations.
Here the distance 2 laps = 2.5 miles. Then ,
=> 1 laps = 2.5/2 = 1.25 miles.
Now 3 laps = 3*1.25 = 3.75 miles
Here n laps = 8.75 miles .
=> n* 1.25 = 8.75
=> n = 7 laps .
Now 8 laps = 8*1.25 = 10 miles.
And n laps = 16.25
=> n = 16.25/1.25 = 13 laps. miles
Hence the complete table is ,
=> laps Miles
3 3.75
7 8.75
8 10
13 16.25
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I need help on question 1 and 2. I really am stuck on it and it will be a lot of help if you help me. Thank you! :)
Jimmy is eating sandwiches at a constant rate the number of sandwiches y that he can eat in a hour x is represented by the linear equation y = 8x how many sandwiches does jimmy eat in 1 hour? 2 hours? 3 hours?
8,16,24
Given:
the relation between number of sandwiches and time is :
y = 8x
where, y is number of sandwiches
x is time
For 1 hour,
y = 8*1
y = 8.
For 2 hour,
y = 8*2
y = 16.
For 3 hour,
y = 8*3
y = 24.
#123
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sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.
Given info;
Jimmy consistently consumes sandwiches. The linear equation y = 8x represents the number of sandwiches(y) that he can consume in an hour(x).
To know how many sandwiches he ate in consecutive hours;
Case(1):
y = 8x
x = 1 hour
y = 8*1
= 8
Case(2):
y = 8x
x = 2 hours
y = 8*2
= 16
Case(3):
y = 8x
x = 3 hours
y = 8*3
= 24
Therefore, sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.
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Suppose that shoe sizes of american women have a bell shaped distribution with a mean of 8.21 and a standard deviation of 1.49. using the empirical rule what percentage of american women have shoe sizes that are less than 11.19
97.5% of American women have shoe sized less than 11.19 according to standard deviation of 1.49 .
What is standard deviation?
It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
Main Body:
Here, we want to use the empirical rule to find the percentage of women with shoe sizes less than 11.19
The first thing we shall do here is to find the z-score
Mathematically, that will be calculated using the formula;
z = (x-mean)/SD
z = (11.19-8.21)/1.49
z = 2
We can see that the given value is 2 standard deviation away to the right of mean
So, we want to get the percentage that is between the mean and two standard deviations away from it using the empirical rule
So according to the empirical rule
The percentage will be
= 100-2.35-0.15
= 100-2.5 = 97.5%
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Look at the graph of a function below.
Which set builder notation represents the domain of the function in the graph?
The domain of the function in the graph is {yl1≤y≤9}. Option b is the correct answer.
Graph:
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables.
A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.
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Three runners are training for a marathon. one day, they all run about ten miles, each at their own constant speed. which of the three runners has the fastest pace?
You did not post enough information.
A mountain climber starts at sea level and descended down a cliff. Her elevation can be represented by -75 feet. How many feet did the mountain climber travel?
Answer:75 ft
Step-by-step explanation:sea level is represented as 0. going from 0 to -75 is 75 ft
A landscaping crew can mulch 3 flower gardens in 1 and one over two hours. At this rate, how long will it take the crew to mulch 12 flower gardens?
The crew will take 6 hours to mulch 12 flower gardens.
Given, that
A landscaping crew can mulch 3 flower gardens in 1(1/2) hours i.e. 3/2 hours.
so, 3 flower gardens mulch = 3/2 hours
Now, we are asked that how long will it take the crew to mulch 12 flower gardens.
As, 3 flower gardens mulch = 3/2 hours
1 flower garden mulch = (3/2)×(1/3) hours
1 flower garden mulch = 1/2 hour
12 flower gardens mulch = (1/2)×12 hours
12 flower gardens mulch = 6 hours
So, it will take 6 hours by the crew to mulch 12 flower gardens.
Hence, the crew will take 6 hours to mulch 12 flower gardens.
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For each direct variation, find the constant of variation. Then find the value of y when x = -0.5.
21. y =4 when x = 0.5
22. y =2 when x = 3
When x = -0.5, the value of y is -0.33. When y varies directly with respect to x, the equation y = kx is used. where k is the constant of proportionality
What is meant by variation?A variation is a relationship between one set of values for one variable and another set of values for another variable. Variation in direct. If m is a nonzero constant and b = 0, then the function y = mx (often written y = kx) is a direct variation of the equation y = mx + b. Variation is defined as differences in an individual's genetic constituents that result in differences in the physical appearance of individuals living in a population. Individuals differ in their physical appearance, fertility, metabolism, and mode of reproduction.The average of the squared deviations from the mean is defined as variance.Therefore,
When X equals 3, Y equals 2.
We solve for k by plugging in 3 for x and 2 for y.
y = kx \s 2 = k(3) (3)
Subtract 3 from both sides.
2/3 = k
Now we plug in 2/3 for k
y = 2/3 x
Given x = -0.5 simplifying we get,
y = 2/3 (-0.5)
y = -0.33
Hence, the value of y is -0.33 when x = -0.5
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What is mean by amplitude in maths?.
The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient.
What is amplitude?The distance that a function's graph moves above and below its midline is referred to as its amplitude. When graphing a sine function, the amplitude's value corresponds to the sine function's coefficient. The height between the center line and the peak is known as the amplitude (or to the trough). Alternatively, we might multiply the height from highest to lowest places by 2. The Phase Shift is the horizontal displacement of the function from its initial point.
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What is the average of first 50 numbers?.
The average of first 50 numbers is 25.5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.
Why do you use the word "average"?The average of a list of data is a mathematical expression for the central value of a set of data. The ratio of all the data points to all the units in the list is how it is mathematically defined. The average of a specific set of numerical data is also referred to as the "mean" in statistics.
Which four sorts of averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
The first 50 natural numbers are 1,2,3,...,50
The sum of first n natural numbers = n(n+1)/2
Sum of first 50 natural numbers is 50(51)/2
=25(51)/2=1275
Hence, average of first 50 natural numbers is
1275/50
=25.5
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Simplify the expression to a + bi form:
(-4+9i)²
Explain in layman's terms for brainiest please
The simplified form of the expression ( -4 + 9i )² such that it takes the form a + bi is; -65 - 72i.
What is the simplified form of the expression?It follows from the task content that the simplified form of the expression is to be determined.
Hence, since the given expression is; ( -4 + 9i )², we have;
( -4 + 9i ) ( -4 + 9i )
= 16 -36i - 36i + 81i²
However, recall that the i² = -1 which follows from the fact that i = √-1.
On this note, the expression can be written as;
= 16 - 72i + 81 (-1)
= 16 - 72i - 81
= -65 - 72i.
Hence, the required simplified form of the expression is; -65 - 72i.
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if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can:
If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can increase the sample size.
The margin of error refers to the statistic measurement that expresses the level of random sampling error in the outcomes of a survey. If the margin of error of the result is high, the confidence level would be low that a result reflects the census of the entire population. It indicated the difference between the actual and estimated results in a random survey sample. The margin of error is generally used in non-survey contexts to show observational error in reporting measured quantities. In order to minimize the margin of error associated with a confidence interval estimate for a population mean, the researchers can increase the sample size to capture the actual trend of the population more accurately.
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Given f (x) = 5x - 12, find the value of x when f (x) = 13.
Answer:
53
Step-by-step explanation:
if x is 13, you would simply do the following:
multiply 5 by 13 which is 65.
then subtract 65 by 12 which is your final answer, 53!
What comes after a pilot project?.
According to question, project managers can assess the outcomes to identify any hazards the project might encounter after it is completely executed.
These risks are frequently examined by project managers and stakeholders to decide whether they are controllable and whether it is worthwhile to move on with the entire project. An organization can control the risk of a novel concept and spot any flaws through a pilot project before significant resources are spent.
On the other hand, a trial is a limited implementation before you launch the pilot project broadly. All the advantages of a pilot project are present, but they are more thorough, and the team is frequently able to test out more features and observe the results on a wider scale.
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Jude deposited 550$ into an account that earns simple interest, and after 11 years, the interest in the account was 484. What was the simple interest rate? Pls give proper explanation and not just answer, Thank u!
Answer: 8%
Step-by-step explanation: Rate = Interest 484 ÷ Principle (550) x Time (11), with this formula the answer is 8%.
If P = (-1,-1) and Q = (5, 3) are the
endpoints of the diameter of a circle,
find the equation of the circle.
(x - 2)² + (y - [?])² = [ ]
Answer:
The equation of the circle is (x-2)^2+(y-1)^2=13
Step-by-step explanation:
∠A and \angle B∠B are supplementary angles. If \text{m}\angle A=(4x-16)^{\circ}m∠A=(4x−16) ∘ and \text{m}\angle B=(x+1)^{\circ}m∠B=(x+1) ∘ , then find the measure of \angle B∠B.
The measure of angle B is 40 degrees.
In this question, we have been given angle A and angle B are supplementary angles.
m∠A=(4x−16)°
and m∠B=(x+1)°
since angle A and angle B are supplementary angles,
angle A + angle B = 180°
So we get an equation,
(4x − 16)° + (x + 1)° = 180°
5x - 16 + 1 = 180
5x = 180 + 15
5x = 195
x = 39
So, x + 1 = 39 + 1
= 40°
Therefore, the measure of angle B is 40 degrees.
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Helpppppp!!!!Given vector v = (-4,4), find 2.5v.
Multiplying vector v we get 2.5v = (-10, 10).
What is the vector?
A vector is a quantity or phenomenon with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.
The magnitude of a vector indicates the vector's length. It is typically represented by an arrow pointing in the vector's direction. A vector a is defined as a1 ^ii^ + b1 ^jj^ + c1 ^kk^, where a1, b1, and c1 are its constituents.
We have,
v = (-4,4)
2.5v = ?
Multiplying vector v by 2.5 we get,
2.5v = (-10, 10)
Hence, by Multiplying vector v we get 2.5v = (-10, 10).
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