The constant of proportionality in the inverse variation is 79.2
Constant of ProportionalityConstant of proportionality is defined as the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities:
Direct Variation Inverse Variation.This is often determined because of the formula used.
Given that the variation here is an inverse variation.
y ∝ 1/ x
y = k / x
k = y₁x₁ = y₂x₂ = y₃x₃
However, in this question, we can simply represent the constant of proportionality as
k = yx
Substituting the values given into the formula above;
k = 24 * 3.3
k = 79.2
The constant of proportionality is 79.2
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How do you graph a rational function example?
To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).
Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.
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What is a, b, and c in 3x2 + 4 = 5x
Answer:
Subtract
5
x
from both sides of the equation.
3
x
2
+
4
−
5
x
=
0
Once the quadratic is in standard form, the values of
a
,
b
, and
c
can be found.
a
x
2
+
b
x
+
c
Use the standard form of the equation to find
a
,
b
, and
c
for this quadratic.
a
=
3
,
b
=
−
5
,
c
=
4
Step-by-step explanation:
Solve the equation for
x
by finding
a
,
b
, and
c
of the quadratic then applying the quadratic formula.
x
=
5
±
i
√
23
6
A group of friend want to go to the amuement park. They have no more than $80 to pend on parking and admiion. Parking i $14. 75, and ticket cot $11. 25 per peron, including tax. Write and olve an inequality which can be ued to determine xx, the number of people who can go to the amuement park
Using the provided conditions and rule of inequality, The required expression is 11.25x + 14.75 <=80.
What do you mean by inequality equation?Both mathematical phrases, equations and inequalities, are created by connecting two expressions.
What are the different types of equations?The Different Types of Equations are:
Linear Equation.Radical Equation.Exponential Equation.Rational Equation.x= number of friends
Total parking cost = 14.75
Total ticket cost =11.25x
Total money = 80
Since, The total money to be spend can't cross $80, The inequality is given by 11.25x + 14.75 <= 80
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Kaylon shaded the thermometer to represent a temperature of degrees below zero Celsius as shown in the diagram. Is she correct? Therm
Question 5 options:
A: She incorrect because she should have shaded in °
B: She is correct because she shaded a temperature of -°C.
C: She is incorrect because she shaded a temperature of −°.
Using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.
What is logical reasoning?In addition to formal deduction, two more categories of logical thinking are frequently distinguished: induction and abduction.
The following can be explained if one has a precondition or premise, a conclusion or logical consequence, and a rule or material conditional that indicates the conclusion given the precondition.
Mathematical logic and philosophical logic are frequently used to support the claim that "when it rains, objects outside become wet.
The grass is outside, therefore: when it rains, the grass gets wet."
A finding of the rule is supported by inductive reasoning.
So, according to the given, we can easily guess that Kaylon is wrong because the shaded temperature is -°.
Therefore, using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.
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What does AAS and ASA mean?
Here AAS means Angle-Angle-Side whereas ASA means Angle-Side -Angle.
Here AAS stands for Angle-Angle-Side it depicts that when two angles and a non-included side of a triangle are equal to the comparing angles and sides of another triangle, at that point the triangles are said to be congruent. whereas the ASA stands Angle-Side-Angle, where If any two angles and the side included between the angles of one triangle are identical to the comparing two angles and side included between the angles of the second triangle, at that point, the two triangles are said to be consistent by ASA rule.
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Dalvin is 1.85 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 31.35 meters. He stands 27.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer: d
Step-by-step explanation: got itright
Estimate each product to the nearest whole number. Then, find the product. 0.7 x 0.85
The product to the nearest whole number is equivalent to zero.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition.Given is to write the product (0.7 x 0.85) to the nearest whole number.
We have the product as -
0.7 x 0.85
(7/10) x (85/100)
(7/10) x (17/100)
119/1000
0.119
0.12
0.1
0
Therefore, the product to the nearest whole number is equivalent to zero.
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Given the function: f(x) = 1/2 (3x+7) What is the output of the function when the input is x = 9?
Answer:
17
Step-by-step explanation:
1/2(3x+7)
1/2(3(9)+7)
1/2(27+7)
1/2(34)
17
Expand -4(6a - 5)
Please help!!!!
Answer:
-24a+20
Step-by-step explanation:
just use distrubitive property
pls help
Shown below are the scatter plots for four different data sets.
Answer the questions that follow. The same response may be the correct answer for more than one question
3. (6 pts) consider three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong. assume that the average predict accuracy of the dynamic predictor is 90%. which predictor is the best choice for each of the following branches? justify your answers. a. a branch that is take with 5% frequency. b. a branch that is taken with 95% frequency. c. a branch that is taken with 70% frequency.
There are three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong.
In computer architecture, a branch predictor is a digital circuit that attempts to guess which direction a branch (e.g. an if-then-else construct) is going finally announced. The purpose of the branch predictor is to improve the flow of the instruction pipeline. Branch predictors play a key role in achieving high performance in many modern pipeline microprocessor architectures.
1. If the branch is taken 5% of the time, the branch prediction scheme is ``predicted-taken'' because the process must start fetching and then executing at the target address.
2. If a branch is taken 95% of the time, the branch outcome is known with certainty, so the branch prediction scheme is "unpredictable".
3. If the branch is taken 70% of the time, then the prediction scheme is "dynamic prediction" and the branch prediction can change dynamically during program execution.
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A kangaroo hops 9 kilometers in 3 minutes. at this rate how far does the kangaroo travel in 2 minutes
Answer: If a kangaroo hops 9km in 3 minutes, that means he runs 3km every minute, which we can multiply by 2 in order to get 6km in the first 2 minutes. [EXTRA: In one hour, the kangaroo can hop 180km, which means his top speed is 180km/h without accounting for fatigue]
Step-by-step explanation: a
excel grear tire company has produced a new tire with an estimated mean lifetime mileage of 33,500 miles. management also believes that the standard deviation is 3,500 miles and that tire mileage is normally distributed. to promote the new tire, grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. specifically, for tires with a lifetime below 30,000 miles, grear will refund a customer $1 per 100 miles short of 30,000. (a) for each tire sold, what is the average cost of the promotion (in $)? (use at least 1,000 trials. round your answer to two decimal places.) $ (b) what is the probability that grear will refund more than $25 for a tire? (use at least 1,000 trials. round your answer to three decimal places.)
a) The average cost of the promotion is $ 0.01 per liter
b) the probability that Greer will refund more than $25 for a liter is 0.0107.
a.
Mean lifetime mileage : $33,500
Standard deviation of mileage: $3500
Observed miles: 30,000 miles
100 miles failed $1.00
Hence :
= (33,500 – 30,000) / 3500= 1
Cost of production
100 miles = $1.00
= 1* 1 / 100
= $ 0.01 per tire
b.
P (z < 25000 - 36500/5000)
P (z < -11500/5000)
z < -2.3
Hence:
1 - 0.9893
= 0.0107
Therefore, the Probability that gear will refund more than $50.00 per tire is: 0.0107
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If using the method of completing the
square to solve the quadratic equation
2²+3x+37= 0, which number would
have to be added to "complete the
square"?
Answer:
To solve a quadratic equation using the method of completing the square, we need to first write the equation in the form ax² + bx + c = 0, where a, b, and c are constants. In this case, the given equation is 2²+3x+37 = 0, which can be written as 4+3x+37 = 0.
To complete the square, we need to add a number to the constant term (in this case, 37) so that the coefficient of the x² term is a perfect square. In this case, the coefficient of the x² term is 4, which is already a perfect square. Therefore, we do not need to add any number to complete the square.
The correct answer is 0.
Step-by-step explanation:
The gas tank of a car holds 15.9 gallons. If it required 12.2 gallons to fill the tank, how many gallons were still in the car before it was filled up?
Answer: 3.7
Step-by-step explanation: 15.9-12.2=3.7
Solving for proportions
Answer:
1. c=72/15
2. y=4
3. k=-37/4
4.d=6
Step-by-step explanation:
1. c/6=12/15
Cross multiply. 72=15c.
Dividing by 15, we get C=72/15.
2. 21/7=3. So, 12/y=3. Solving for y, we get y=4.
3. -37/24=k/6
24/6=4. So, -37/k must equal 4.
-37/k=4
-37=4k
k=-37/4
4.
40/8=5. That means that 30/d=5
30=5d
d=6
Done!
The circumference of a circle is 20 pi inches, Whats its area
Answer: 100 pi, or 314.15926...
Step-by-step explanation:
The circumference is 2r pi. r is 10. The area is r squared pi. 10 squared in 100, so 100 pi.
A unicycle wheel has a diameter of 30 inches and a radius of 15 inches. How many inches will the unicycle travel in 6 revolutions?
The unicycle wheelof diameter 30 inches travels 282.6 inches in 6 revolution.
What is an inch?An inch can be defined as a unit of length in the customary system of measurement.
To calculate the amount of inches the unicycle will travel in 6 revolution, we use the formula below.
Formula:
R = 6πd.................... Equation 1Where:
The amount of inches the unicycle covered in 6 revolutiond = Diameter of the unicycleπ = PieFrom the question,
Given:
d = 15 inchesπ = 3.14Substitute these values into equation 1
R = 6×15×3.14R = 282.6 inchesHence, the unicycle wheel travels 282.6 inches.
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100 POINTS ILL GIVE BRAINLIEST PICTURE BELOW
Answer:
The correct answer is B. looking for work/total work force.
Unemployment rates are typically calculated by dividing the number of people who are looking for work by the total work force. The work force includes all people who are currently employed or actively looking for work, regardless of whether they are currently employed. The number of people who are looking for work is determined by surveying individuals and asking them whether they are currently seeking employment. The unemployment rate is then calculated by dividing the number of people who are looking for work by the total work force, and expressing this as a percentage.
The other answer choices are not accurate ways of calculating unemployment rates. Dividing the total work force by the number of layoffs (A) would not give an accurate measure of unemployment, as it would not account for people who are looking for work but have not been laid off. Dividing the number of people looking for work by the total population (C) would also not be an accurate way of calculating unemployment, as it would not take into account people who are not part of the work force (e.g. children, retirees, etc.). Therefore, the correct method for calculating unemployment rates is to divide the number of people looking for work by the total work force.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The unemployment rate for any area is the number of area residents without a job and looking for work divided by the total number of area residents in the labor force.
What is the greatest common factor of 78 and 41
Answer:
1
Step-by-step explanation:
41 is prime, so its only factors are 1 and 41.
Since 1 is a factor of 78 but 41 isn't a factor of 78, the greatest common factor is 1.
A model boat i 15 inche long if the boat i bulit to a cale of 1 : 250 inche how long i the real boat
define a variable
write a porortion
olve the porportion
anwer with word
If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.
What does a scale look like in math?The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.
Briefing:The scale of drawing the horse = 1 inch :
Therefore in scale
Horse height in drawing equals one inch
The height of the horse = 250 inche
The original height of the horse = 15 inche
The height in the picture = x inches
To find the height the horse in the picture, we have to use proportion
1 inch : 250 inche = x inches : 15 inche
1 / 250 = x / 15
1 × 15= 250x
250x = 15
x = 15/250
x = 0.06 inches
Therefore, the height of the horse in drawing is 0.06 inches
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What is the slope of a line parallel to the line y =- 3x 10?
To find the slope of a line parallel to a given line, we need to find the slope of the given line. The slope of a line parallel to y = -3x + 10 is -3.
To find the slope of a line parallel to a given line, we need to find the slope of the given line. We can do this by taking the coefficient of x in the equation and making it the numerator of a fraction with a denominator of 1.In the equation y = -3x + 10, the coefficient of x is -3.
Therefore, the slope of a line parallel to y = -3x + 10 is -3.
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A company finds that its advertising costs increased from 72000 to 76680 in a year. What was the rate of increase?
Using the percentage increase formula, we know that the rate of increase in the advertising cost of the company is 93.5%.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
The percent symbol, "%," is widely used to denote it even if the abbreviations "pct," "pct," and rarely "pc" are also employed.
A% is a number that has neither dimensions nor a defined unit of measurement.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, the percentage increase formula:
% increase: original - increase/original * 100
Increase: 76680-72000 - 4680
Now, substitute values as follows:
% increase: original - increase/original * 100
% increase: 72000 - 4680/ 72000* 100
% increase:93.5
Therefore, using the percentage increase formula, we know that the rate of increase in the advertising cost of the company is 93.5%.
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Cadence has a collection of 52 dolls that all have either blue-eyes or green-eyes. Cadence has 16 more blue-eyed dolls than green-eyed dolls. How many green-eyed dolls does Cadence have? How many blue-eyed dolls?
Answer:
18 green eyed dolls and 34 blue eyed dolls
Step-by-step explanation:
Cadence has a total of 52 dolls, either green eyed or blue eyed so lets take the number of green eyed dolls as g and the number of blue eyed dolls as b. So you have
b + g = 52
also we know b is 16 greater than g so
b - 16 = g
transpose 16 & g
b - g = 16
Now we add the equations
b+g = 52
b-g = 16
______
2b = 68
(+g and -g cancel each other out)
so b = 34
If we put 34 into an earlier equation
34 + g = 52
g = 52 - 34
g= 18
What is the smallest whole number that rounds to 80 when rounded to the nearest 10.
Find the value of each expression.
5[(46-14) +4] Note divide by 4.
O 13
O 213
O 227
O 40
By solving the equation 5[(46 - 14) / 4] we will get 40 as the answer
What is BODMAS?
The abbreviation BODMAS is used to assist pupils recall the order of mathematical operations - the right sequence in which to solve maths problems. BODMAS is an acronym that stands for B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction.
Solution:
5[(46 - 14) / 4]
We will solve the round brackets first
5[ 32 / 4 ]
Now we will solve the square bracket
5 * 8 = 40
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I need help with this problem
The expression that represents the chart is 2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
How to determine the expression that represents the chart?From the question, we have the following parameters that can be used in our computation:
The chart
On the chart, we have the following values
Green = x
Purple = 3
Orange = 1 1/2
In terms of the variable x, we have the following equation
2 * Green + 2 * Orange = Purple * (x + Orange)
Substitute the known values in the above equation, so, we have the following representation
2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
The question does not require that the equation be solved
Hence, the required expression is 2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
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Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
-3x + 4y = -5
-6x+8y= -10
a. One Solution
b. No Solutions
c. Infinitely Many Solutions
The system of Linear Equation has Infinitely Many Solutions
What is Linear Equation in Two Variables?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
To check the numebr we need to find the vaules of
a1/a2, b1/b2, c1/c2
a1/a2 = -3/-6 = 1/2
b1/b2 = 4/8 = 1/2
c1/c2 = -5/-10 = 1/2
Since the values of a1/a2 = b1/b2 = c1/c2
Theerefore, the system of Linear Equation has Infinitely Many Solutions
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If the tree grows an additional 10 feet, what is the new angle of elevation from the point 25 feet from the base of the tree to the top of the tree?.
Angle of elevation for the tree grows an additional 10 feet, what is the new angle of elevation from the point 25 feet is angle of elevation 47.1 degree.
Angle of elevation is the elevation in the height of angles from a given points.
Length of tree = 10 feet
Angle of elevation = 25 degreesEquation for the peak of tree=?Let x constitute the peak.We recognize that tan Phi = Perpendicular / B * asetan = peak of tree/ duration of basetan Phi = x / l=>x=I^ * (tan phi)x=10 ^ * tan(25 deg)Now, setting values:x=10 ^ * tan(25 deg)x =10 ^ * 0.4663x = 14.43feetSo, the equation to discover the peak is: x = 10 * tan(25 deg) and the peak is x = 47. 1 degree.Read more about angle;
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Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
The mean of the class is 94.6 and the range of the class is 55.
What is the mean and the range?A dataset's mean is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
The range of a set of numbers is the difference between its highest and lowest values. To find it, subtract the lowest value from the highest in the distribution.
The given data is 45,68,77,90,90,95,100,100,86,90,50,55.
The mean of the data will be calculated as,
Mean = (sum of the data) / ( number of the data)
Mean = ( 45 + 68 + 77 + 90 + 90 + 95 + 100 + 100 + 86 + 90 + 50 + 55)/12
Mean = 94.6
The range of the data will be calculated as,
Range = Highest value - The lowest value
Range = 100 - 45
Range = 55
The mode of the data is 90 because it has three repetitions.
The median of the data is the middlemost value of the data when the data is arranged in increasing order,
(45,50,55,68,77,86,90,90,90,95,100,100)
Median = ( 90 + 90 ) / 2
Median = 45
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