The values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.
The concept of the integral is a fundamental part of calculus and it is used to calculate the area under a curve or the volume of a 3-dimensional object. In this context, we will be exploring the integral of a two-dimensional set in the R^2 plane.
For every two-dimensional set C contained in R^2 for which the integral exists, the function Q(C) is defined as the double integral of the function (x^2 + y^2) over the set C. The double integral is a mathematical tool for finding the total volume under a surface.
Let's consider the three sets C1, C2, and C3 and find Q(C1), Q(C2), and Q(C3).
C1={(x,y) : −1 ≤ x ≤ 1, −1 ≤ y ≤ 1}
Q(C1) = ∬C1 (x^2 + y^2) dxdy = ∫^1_{-1}∫^1_{-1} (x^2 + y^2) dxdy = ∫^1_{-1} [(x^2 + y^2)/2]^1_{-1} dx = 4.
C2 ={(x,y):−1≤x≤1,−1≤y≤1}
Q(C2) = Q(C1) = 4.
C3 = {(x,y):x^2 + y^2 ≤1}
Q(C3) = ∬C3 (x^2 + y^2) dxdy = π.
In conclusion, the values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.
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All lines parallel to the line 3x – 8y = 4 are given by equations of the form (a) 3x – 8y = 0 (b) 3x – 8y = c for a constant c (c) 8x – 3y = c for a constant c (d) none of these
The slopes of perpendicular lines are opposite reciprocals and hence option D is correct
The slope of the given line is 3/8, so its opposite reciprocal is -8/3. From the options we have to find a line with this slope.
In the given line, it was easy to find the slope because the equation is in slope-intercept form, but in the options the equations are in standard form,
If we solve this for y we get the slope-intercept form,
Thus the slope of a line whose equation is in standard form is,
• Option A: a = 3, b = 8. The slope is -3/8 → ,not perpendicular
• Option B: a = 3, b = -8. The slope is 3/8 → ,not perpendicular
• Option C: a = -8, b = 3. The slope is 8/3 → ,not perpendicular
• Option D,: a = 8, b = 3. The slope is -8/3 → ,this line is perpendicular, to the given line
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Overnight, the temperature in Chicago was just
–
7°F. But by the afternoon, the temperature had risen 9°F.
What was the temperature in Chicago that afternoon?
°F
The temperature during the afternoon in Chicago is 2°F
What is meant by the temperature of a place?
The average air temperature throughout a specific time period, typically a day, a month, or a year, as measured by a thermometer that has been properly exposed determines the temperature of a place.
Given,
The overnight temperature in Chicago = -7°F
The temperature that had risen during the afternoon = 9°F
From this data, we can see that there is no temperature change during the morning in Chicago.
That means the temperature remained constant throughout the night till the next morning.
Therefore the temperature during the afternoon in Chicago = -7+9 = 2°F.
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Ten percent of the 30 wim team member are new on the team. How many member are new?
A-3
B-36
C-10
D-6
Ten percent of the 30 team members which means that [tex]$\dfrac{10}{100} \cdot 30 = 3$[/tex] team members are new to the team. So, the answer is 6 new team members. Option D is correct.
To understand how we got the answer, we need to understand the concept of "percentage". The percentage is a way of showing a number as a fraction of 100. So, 10% means [tex]$\dfrac{10}{100}$[/tex].
Now, if we multiply this fraction by the total no. of team members, we'll find the no. of new team members.
[tex]$\dfrac{10}{100} \cdot 30 = 3$[/tex]
So, 10% of the 30 team members are equal to 3 team members, and that's why the answer is D-6.
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find nonzero scalars and so that 4 (2−5) (4 4)=0 for every pair of vectors and . (express numbers in exact form. use symbolic notation and fractions where needed.)
The scalars 0 and any scalar with magnitude 0 satisfy the equation 4(2−5)(4,4) = 0 for every pair of vectors (4,4).
Vectors are mathematical objects that have both magnitude and direction. They can be multiplied by scalars, which are non-zero real numbers.
In this case, we are looking for non-zero scalars that satisfy the equation 4(2−5)(4,4)=0 for every pair of vectors (4,4).
To begin, we simplify the equation.
The expression 2−5 equals to -3, so
=> 4(-3)(4,4) = 4(-12,-12).
Next, we multiply 4 by -12 to get -48. The expression
=> 4(-12,-12) = (-48,-48).
Now, we need to find non-zero scalars that multiply (-48,-48) to give us a zero vector, which is a vector with magnitude of 0 and direction undefined.
Any scalar that satisfies this condition is a solution. For example, the scalar 0 satisfies this condition because
=> 0 * (-48,-48) = (0,0).
Additionally, any scalar with magnitude 0 will also satisfy this condition because the product of a vector and a scalar with magnitude 0 is always the zero vector.
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Use dimensional analysis to perform the following conversions, show all your work and report the answer in the correct number of significant figures. a. 261 g ---> kg b. 3 days ---> seconds c. 9,474 mm ---> cm d. 0.73 KL ---> L
The conversions are 0.261 kg, 300000 seconds, 947.4 cm and 730 L.
a. 261 g to kg
For converting grams to kg, we divide by 1000.
(261 / 1000)= 0.261 kg
The number of significant figures in 261 g is 3 and the number of significant figures in the answer 0.261 kg is also 3.
b. 3 days to seconds
1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds
1 day = 24 x 60 x 60 seconds
Therefore, 3 days = 3 x 24 x 60 x 60 seconds = 2, 59, 200 seconds
Since, the number of significant figures in 3 days is 1, hence we write 2, 59, 200 as 300000 seconds, such that it has 1 significant figure.
c. 9, 474 mm to cm
For converting mm to cm, we divide by 10
(9474 / 10) = 947.4 cm
The number of significant figures in 9, 474 mm is 4 and the number of significant figures in the answer 947.4 cm is also 4.
d. 0.73 KL to L
1 KL = 1000 L
0.73 KL = 0.73 X 1000 L = 730 L
The number of significant figures in 0.73 KL is 2 and the number of significant figures in the answer 730 L is also 2.
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patrick wants to estimate the percentage of companies that use video ads. he asks a randomly selected group of 125 companies whether or not they use video ads. what is the statistic?
The percentage of companies that use video ads in the sample is the statistic.
A statistic is the measure of a particular characteristic in the sample which is nothing but a subset of the population. A singular or sample statistic is any quantity computed from values in a sample that is considered for a statistical purpose.Here, the concern is to estimate the percentage of companies that use video ads.
He took a sample of 125 companies to inquire whether or not they use video ads.
So, the percentage of companies that use video ads in the sample is the statistic.
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What is the surface area of the cylinder with height 5 ft and radius 7 ft
Answer:
527.79
2πrh+2πr
2π 7• 5+2π7
The balcony of an apartment is 4 feet wide by 7 feet long. on a scale drawing of the apartment, the balcony is 0.8 inch wide by 1.4 inches long, and the kitchen is 2.4 inches wide by 2.8 inches long. what is the actual width of the kitchen? enter your answer in the box. the actual width of the kitchen is___feet.
Answer:
The actual dimensions of the kitchen are 12 feet by 14 feet
Step-by-step explanation:
The kitchen's real measurements are 12 feet by 14 feet.
Detailed explanation:
4 / 0.8 = 5, 7 / 1.4 = 5. The actual drawing ratio is a 5:1 ratio.
Consequently, 2.4 inches multiplied by 5 is 12 feet and 2.8 inches multiplied by 5 equals 14 feet.
12 ft. x 14 ft.
ORFind the scale of the drawing
[tex]\frac{0.8}{4} \frac{in}{ft.} = \frac{1.4}{7} = 0.2 \frac{in}{ft.}[/tex]
To determine the precise dimensions subtract 0.2 from the measurements on the scale illustration to get 12 feet (2.4/0.2).
2.8/0.2 = 14 ft
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2. Which group found the volume of a
triangular pyramid with a base area of 16
square inches?
The volume of a triangular pyramid can be found using V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.
How to calculate the volumeA tetrahedron is a polyhedron in geometry that has four triangular faces, six straight edges, and four vertex corners. It is often referred to as a triangle pyramid. The simplest regular convex polyhedron is the tetrahedron. A triangle base, three triangular faces, and a common vertex make up the geometric shape known as a triangular pyramid.
The formula for calculating the volume of a triangular pyramid is Volume= 1/3 × Base area × Height. The dimensions required to find the surface area of a triangular pyramid are the side, height, and slant height.
Note that an overview was given as your information is incomplete.
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2 questions to answer. Solve each of the following inequalities, 1. [tex]\frac{10q+9}{2}[/tex] ≤ \frac{3}{8}[/tex] 2. [tex]\frac{5(-5s-1)}{6}[/tex] > - [tex]\frac{9}{5}[/tex] ( negative 9 over 5) representing each solution on a number line.
Answer:
To solve the inequality ≤ \frac{3}{8}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x ≤ \frac{3}{8}
To graph the solution on a number line, we can use an open circle at \frac{3}{8} to indicate that the value is not included in the solution. So the solution set is: (-∞,3/8)
To solve the inequality > -\frac{9}{5}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x > -\frac{9}{5}
To graph the solution on a number line, we can use an open circle at -\frac{9}{5} to indicate that the value is not included in the solution. So the solution set is: (-9/5, ∞)
Step-by-step explanation:
A recent survey of 250 citizens showed that 56% favored a renovation project for the local library. The survey had a margin of error of ±1.9%. If the town has 78,717 registered voters, what is the expected maximum number of voters who would support the project? Round the answer to the nearest whole number.
Maximum number of voters support renovation project is 44082.
What is margin of error?Margin of error provides a clearer understanding of what a survey’s estimate of a population characteristic means. it’s expressed with a plus and minus sign together, e.g. + or -1%.
A recent survey of 250 citizens showed that 56% favored a renovation project for the local library.
The survey had a margin of error of ±1.9%.
Total number of voters in the town = 78,717
56% of 78717= 44081.52 ⇒44082(rounded to nearest whole number)
Hence, maximum number of voters support renovation project is 44082.
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What is the rule for the following geometric sequence? 64, -32, 16, -8...
Answer:
The rule for this geometric sequence is that the number is being halved each time. This can be expressed as a general rule as follows: an = a1 * (1/2)^n-1 , where a1 is the first term, n is the number of the term in the sequence, and an is the nth term. Therefore, the nth term of this sequence is an = 64 * (1/2)^n-1.
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Can someone help pls
Answer: 264
Step-by-step explanation:
calculated each area, shown in the picture above
how to find perimeter of a triangular prism?
Answer:
Read below:
Step-by-step explanation:
To find the perimeter of a triangular prism, you need to add up the lengths of all three sides of the triangular base and all three sides of the rectangular lateral faces.
The formula for the perimeter of a triangular prism is P = a + b + c + 3l, where a, b, and c are the lengths of the sides of the triangular base, and l is the length of each of the rectangular lateral faces.
The perimeter of the triangular prism is solved
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
To find the perimeter of a triangular prism, you need to add the lengths of all the edges. The edges of a triangular prism include the three sides of the base triangle and three additional edges connecting the corresponding vertices of the two base triangles.
So, the formula for finding the perimeter of a triangular prism is:
Perimeter = (Sum of the lengths of the three sides of the base triangle) + (Sum of the lengths of the three edges connecting the corresponding vertices of the two base triangles)
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A cliff stands 70 ft tall with the lake water reaching 50 ft away from the cliff.
Question: What is the angle of depression from the top of the cliff to the edge of the water. PLEASE HELP ME WITH THIS.
The angle of depression from the top of the cliff to the edge of the water
is 54.46°.
What are trigonometric functions?Trigonometric functions, often known as circular functions, are, in a nutshell, the functions of the angle of a triangle. This indicates that the relationship between a triangle's angles and sides is provided by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.
Given the height of the cliff = 70 feet,
the lake water reaches 50 ft away from the cliff.
distance from the base of the cliff to lake water = 50 feet
the angle of depression is found by tanФ
where Ф = angle of depression
tanФ = perpendicular/base
perpendicular = height = 70 feet
base= 50 feet
tanФ = 70/50
Ф = tan⁻¹(1.4)
Ф = 54.46°
Hence angle of depression is 54.46°.
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how does the hawthorne effect materialize in health services research, and what impact does this have on research objectivity?
The Hawthorne Effect can be mitigated by utilizing research designs that obscure the presence of the researcher, such as randomized controlled trials and naturalistic observation studies.
It is often seen in studies involving health services research, where individuals being studied change their behavior due to the presence of the researcher, or the knowledge that they are being observed. This can have an impact on research objectivity, as the behavior of the subjects might not be representative of the behavior they would normally exhibit while not being observed.
The Hawthorne Effect can be mitigated by utilizing research designs that obscure the presence of the researcher, such as randomized controlled trials and naturalistic observation studies. Additionally, researchers can also use methods such as questionnaires and interviews to gain insight into the experiences and behavior of the research subjects, in order to better understand the impact that the Hawthorne Effect might have on the research results.
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When production volume exceeds the breakeven point, we can expecteda. profitb. fixed cost to decreasec. marginal revenue to decreased. a loss
When production volume exceeds the breakeven point, we can expect (a) profit.
The Breakeven Point is the level of production at which a company's total revenue equals its total expenses, and the company neither makes a profit nor incurs a loss.
When production volume exceeds the breakeven point, the company's total revenue exceeds its total expenses, which leads to a profit.
Option (b) : Fixed cost does not necessarily decrease when production volume exceeds the breakeven point.
Option (c) : Marginal revenue does not necessarily decrease when production volume exceeds the breakeven point.
Option (d) : A loss is not expected when production volume exceeds the breakeven point.
Therefore , If production volume is greater than the breakeven point, the company is expected to make a profit.
The given question is incomplete , the complete question is
When production volume exceeds the breakeven point, we can expected
(a) profit
(b) fixed cost to decrease
(c) marginal revenue to decrease
(d) a loss
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At the beach, Ayana and her sister both built sandcastles and then measured their heights. Ayana's sandcastle was 1/2 of a foot tall and her sister's was 3/8 of a foot tall. How much taller was Ayana's sandcastle than her sister's?
Write your answer as a fraction or as a whole or mixed number.
Ayana's sandcastle is 1/8 foot taller than her sister's.
What is fraction?Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, specific value, or a thing.
Given,
Ayana's sandcastle was 1/2 of a foot tall
Her sister's was 3/8 of a foot tall.
Difference between the height of the both sandcastle
= 1/2 - 3/8
= (4 - 3)/8
= 1/8
Hence, Ayana's sandcastle is taller than her sister's by 1/8 foot.
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Can someone help me with this aleks question
Solve -3x + 7 = 2x -3. Write the solution as an integer or decimal.
x = __
Answer:
x = 2
Step-by-step explanation:
- 3x + 7 = 2x - 3 ( subtract 2x from both sides )
- 5x + 7 = - 3 ( subtract 7 from both sides )
- 5x = - 10 ( divide both sides by - 5 )
x = 2
Can somebody PLEASE give me the right answer? I have been given 2 different answers 48 and 5.76 ALSO PLEASE SHOW THE WORK
Step-by-step explanation:
Not much work to show really. It's 36% of 16, which is 5.76
what is the unsigned octal equivalent of the following unsigned hexadecimal value?
The process of converting a hexadecimal value to octal involves two steps: first converting the hexadecimal value to binary, and then converting the binary value to octal.
Hexadecimal is a number system that uses 16 digits, from 0 to 9 and A to F, to represent values. It is commonly used in computer science, as it provides a concise representation of binary data.
To convert a hexadecimal value to an octal value, the hexadecimal number must first be converted to binary, and then the binary number must be converted to octal.
The octal number system uses 8 digits, 0 to 7, to represent values. To convert a binary number to octal, the binary number is split into groups of 3 bits each, starting from the rightmost bit.
The value of each group is then found by adding up the values of the bits that are turned on.
In this case, the unsigned hexadecimal value is given, and we need to find its unsigned octal equivalent.
To do this, we first convert the hexadecimal value to binary. We then group the binary digits into groups of 3 bits each and find the octal equivalent of each group.
The final answer is the concatenation of the octal values of each group, from left to right.
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g what is the expression for the probability density function of this weibull distribution?
The expression for the probability density function of the Weibull distribution will be: f(x) = k * x^(k-1) * e^(-x^k)
The expression for the probability density function (pdf) of a Weibull distribution is given by:
f(x) = k * x^(k-1) * e^(-x^k)
where:
x is the random variable
k is the shape parameter, which determines the shape of the distribution
e is the base of the natural logarithm
The shape parameter can take on any positive value, and the distribution is typically characterized by a shape that is either increasing or decreasing, depending on the value of k.
If the value of the k is less than 1, the distribution has a decreasing hazard rate, indicating that the failure rate decreases over time.
If the value of the k is greater than 1, the distribution has an increasing hazard rate, indicating that the failure rate increases over time.
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An 8-ounce serving of apples contains 8% of your daily vitamin C. How many ounces of apples would you need to get 100% of our daily vitamin C?
Answer:
Step-by-step explanation:
You would need 100 ounces of apples to get 100% of your daily vitamin C.
We know that 8 ounces of apples contains 8% of your daily vitamin C.
To find out how many ounces of apples are needed to get 100% of your daily vitamin C, we can use the following proportion:
(8 ounces / 8%) = (x ounces / 100%)
where x represents the number of ounces needed for 100% of the daily vitamin C.
To solve for x, we can cross-multiply and divide:
8 ounces * 100% = 8% * x ounces
8 ounces * 100 = 8 * x ounces
800 = 8x
x = 100
Therefore, you would need 100 ounces of apples to get 100% of your daily vitamin C.
Member of a club bought on book for $3. 50 and each member need a pair of knitting needle for $3. 20 and yarn for $5. 40. They pent $63. 70 in total how amny memebr are there?
The price per book is $3.50, the knitting needle is $3.20, the yarn is $3.20 and the total spent is $63.70. Then, the number of members present there are 7 members.
An equation is a formula that connects two expressions with an equal sign and expresses their equivalence.
Given the price of the book is $3.50. The price of a knitting needle is $3.20. And, the price of the yarn is $5.40. The total amount spent by the member is $63.70.
Let us consider the number of members as x. The given situation is written in an equation as,
[tex]\begin{aligned} 3.50 + 3.20x + 5.40x &= 63.70\\8.60x& = 63.70 - 3.50\\8.60x& = 60.20\\x &= \frac{60.20}{8.60}\\x &= 7\end{aligned}[/tex]
The required answer is 7.
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if the sample coefficient of determination (r2) is 0.80, this means that:select one:20 percent of the variation in the dependent variable is explained by the regression20 percent of the variation in the independent variable is explained by the regression.80 percent of the variation in the dependent variable is explained by the regression.80 percent of the variation in the independent variable is explained by the regression.
The interpretation is that 18% of the variation in the dependent variable can be explained by the variation in the independent variable.
Coefficient of determination R²
The percentage of variance in the dependent variable that is explained by the independent variable is shown by the coefficient of determination. R² value is always in the range between 0 and 1. As opposed to 1, which shows that the independent variable fully explains the variation in the dependent variable, 0 means that the independent variable is utterly ineffective at predicting the variance in the dependent variable. It is stated as a percentage.
Interpretation of
R²=0.18
Since
R² is expressed in percentage terms,
R²=0.18
=18/100
=18%
Accordingly, the variation in the independent variable can account for 18% of the variation in the dependent variable. 82% of the variance is unaccounted for and cannot be attributed to the independent variable.
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The full question would be
How do you interpret a coefficient of determination, r 2, equal to 0.18 A? The interpretation is
Evaluate the following expreion when x = 4 and y = 5 Fraction with x quared plu y cubed in the numerator and 2 plu x in the denominator
When x = 4 and y = 5, the expression evaluates to 23.5.
Evaluate x and y expressionThe expression is (x² + y³)/(2 + x). Plugging in x = 4 and y = 5, we get:
(4² + 5³)/(2 + 4) = 16 + 125/(2 + 4) = 141/(6) = 23.5.
So when x = 4 and y = 5, the expression evaluates to 23.5.
The method of substituting values for variables in an expression to find its numerical value is a fundamental concept in algebra and mathematics. When evaluating an expression, we simply replace the variables with the given values and perform the arithmetic operations according to the rules of arithmetic. This process allows us to find the numerical result of the expression for a specific set of inputs.
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Use the integers that are closest to the number in the middle.< 48
Integers include zero, a positive natural number, and a negative integer represented by a minus sign, and the missing integers in the given situation are 5 < √48 < 7.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.
The inverse additives of the equivalent positive numbers are the negative numbers.
The boldface Z is a common mathematical symbol for the set of integers.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.
Integer examples include -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
So, we have:
__ < √48 < __
We know that:
√48 = 6.92
Then,
5 < √48 < 7
Therefore, integers include zero, a positive natural number, and a negative integer represented by a minus sign, and the missing integers in the given situation are 5 < √48 < 7.
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Complete question:
Use the integers that are closest to the number in the middle.
__ < √48 < __.
Start with y divide by 7 then add 2
The condition "y divide by 7 then add 2" can be represented as expression, [tex]\frac{y}{7} +2[/tex]
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
A condition,
y divide by 7 then add 2
Here, we have to apply two operation to complete this expression,
1. Division
2. Addition
First, doing division operation,
y divide by 7
⇒ y/7
Now, second operation which is addition of 2
⇒ [tex]\frac{y}{7} + 2[/tex]
Hence, the expression is [tex]\frac{y}{7} + 2[/tex]
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[tex]3x-1\ \textgreater \ 2\\[/tex]
The solution to the inequality is x > 1
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
3x - 1 > 2
Subtract -1 from both sides of the expression
So, we have
3x > 3
Divide both sides by 3
This gives
x > 1
Hence, the solution is x > 1
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