The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)
What are equations?A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.
A formula would just be 3x - 5 = 16, for instance.
When this equation is solved, we observe that the value of the variable x is 7.
So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.
If the f (x) equation contains (x, y).
Therefore, the f^-1(x) equation is as follows: (y, x).
Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).
So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x) goes through.
Therefore, the positions through which the equation of f^-1(x) travels are:
(4, 1), (6, 4)
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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?
a 26 year old policyholder with a car worth $20,000 is predicted to make 28 claims. b) holding x2 constant, a one year increase in x1 will result in a decrease of 0.5 in the predicted value of y. c) holding x1 constant, a one thousand dollar increase in x2 will result in an increase of 0.1 in the predicted value of y.
The answer statements,
a) True
b) False
c) True
IHI Insurance in the given question is implemented using the linear regression analysis because it is used in the question to calculate the value of the number of yearly claims led by policyholders for motor insurance (y) (x2).
As per the question, at random 500 policyholders were selected.
The range of ages of people are between 16 to 70 years
The price range for the cars is between $1100 to $52000
According to the linear regression equation given in the question,
⇒ I = 13 + (-0.5)x1i + (0.1)x2i
a) [tex]y^{i}[/tex] = 13 + (0.5)x1i + (0.1)x2i
Given, x1i = 26, x2i = 20
⇒ [tex]y^{i}[/tex] = 13 + (-0.5)(26) + (0.1)(20)
⇒ [tex]y^{i}[/tex] = 2
Thus, it is not equal to the claim i.e. 28, so option b is false
According to the answer derived in option b,
We can see that the coefficient of x 1i is negative and such that it will be decreased by 0.5
Thus, option a is true
Now as the coefficient of x 2i is positive it will increase by 0.1
Thus, option c is true
Therefore, option a) is true, option b) is false and option c) is true.
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IHI Insurance has conducted a multiple linear regression analysis to predict the value of the number of annual claims incurred by a motor insurance policyholder (y)based on the age of the policyholder in years (x1) and the value of the car insured in thousands of dollars (x2). The analysis was based on a random sample of 500 policyholders. The ages in the sample ranged from 16 to 70 and the values of the cars in the sample ranged from $1,100 to $52,000. The multiple linear regression equation corresponding to IHI's analysis is y^i = 13 + (-0.5)x1i + (0.1)x2i.
Select whether the following statements regarding the multiple linear regression equation are true or false:
a 26-year-old policyholder with a car worth $20,000 is predicted to make 28 claims.
b) holding x2 constant, a one-year increase in x1 will result in a decrease of 0.5 in the predicted value of y.
c) holding x1 constant, a one thousand dollar increase in x2 will result in an increase of 0.1 in the predicted value of y.
Complete the equation so that it has infinitely many solutions.
Enter the correct answer in the box in the equation.
Answer:
(2x-286)
Step-by-step explanation:
Answer:
(2x-286
Step-by-step explanation:
step by step
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Consider n circles in a plane. Into how many regions will they divide the plane?
Suppose that n circles divide the plane into rn regions. Now you add another circle, C, that non-trivially intersects each of the first n circles. Start at any point on C and travel around C; you will cross one of the other n circles 2n times.
If p0 and p1 are two consecutive crossings, the arc of C from p0 to p1 divides one of the original rnregions into two smaller regions. You do this 2n times,that gives you a recurrence,
rn+1=rn+some simple function of n,
and you can fairly easily turn it into an expression for rn that is just a summation. If you do it right, it’s a summation that you can evaluate pretty easily in closed form to get a formula for rn.
The plane divide the circle into rn regions.
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main body:
Suppose that n circles divide the plane into rn regions. Now you add another circle, C, that non-trivially intersects each of the first n circles. Start at any point on C and travel around C; you will cross one of the other n circles 2n times.
If p0 and p1 are two consecutive crossings, the arc of C from p0 to p1 divides one of the original rn regions into two smaller regions. You do this 2n times,that gives you a recurrence,
rn+1=rn+some simple function of n,
and you can fairly easily turn it into an expression for rn that is just a summation. If you do it right, it’s a summation that you can evaluate pretty easily in closed form to get a formula for rn.
Hence , the plane divide the region into rn regions.
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three couples have reserved seats in a row for a concert. in how many different ways can they be seated when
a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.
b) If each couple sits together, there are 48 different arrangements for three couples to be seated.
What is Fundamental counting principle?
If an event can happen in m different ways and another event can happen in n different ways, then the sum of the occurrences of the two events is m x n.
Given:
Three couples have reserved seats in a row for a concert.
(a) There are 3 couples, so 6 people must be seated in seats in row.
It is permutation of 6 elements, therefore, there are
6!=720 ways three couples can be seated when there is no seating restriction.
(b) We want that each couple sits together.
First we will find the number of permutations of 3 couples:
There are 3!=6 permutations of couple. (they can be ordered in 6 different ways).
Now we will find the number of permutations of each couple:
There are 2!=2 permutations of 2 people that makes a couple.
Therefore, by Fundamental Counting Principle, there are
3! ⋅ 2! ⋅ 2! ⋅ 2! = 6 ⋅ 2 ⋅ 2 ⋅ 2 = 48
ways three couples can be seated when each couple sits together.
Hence,
a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.
b) If each couple sits together, there are 48 different arrangements for three couples to be seated.
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Complete question:
Three couples have reserved seats in a row for a concert. In how many different ways can they be seated when (a) there are no seating restrictions? (b) each couple sits together?
Kiara has 80 lollipops and 32 snicker bars. She is feeling individual bags for Halloween in with like each bag contains the same combination of lollipops and snicker bars. How many bags can she feel if she wishes to have no candy left over? How many lollipops is snicker bars are in each bag?
Answer:
16 bags: 2 snicker bars and 5 lollipops in each
Step-by-step explanation:
The greatest common factor of 80 and 3 is 16.
80÷5=16
32÷2=16
And 5 represents the lollipops and 2 represents the snickers.
Which of the following expressions is equivalent to (y − 3)4?
A) y4 − 12y3 + 54y2 − 108y + 81
B) y4 + 12y3 + 54y2 + 108y + 81
C) y4 − 27y3 + 9y2 − 3
D) y3 − 9y2 + 27y − 27
The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.
What is the binomial theorem?The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.
An expression of two terms having a degree n can be represented as,
(a - b)ⁿ = [tex]^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n[/tex].
Given, (y - 3)⁴ = [tex]^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4[/tex].
(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.
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What is the length of side bc of the triangle? enter your answer in the box. Units.
The length of the side BC Iis equal to 28 units which we get by using congruency.
What is congruency?In other words, if the lengths of the sides and angles are the same for two shapes, they are congruent (the same in shape and size). When two triangles are congruent, it is frequently useful to know.
* In triangle ABC
∵ Angles B and C comes to be congruent
∴ m∠B = m∠C
* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length
∴ AB = AC
∵ AB = 4x - 7
∵ AC = 2x + 7
∴ 4x - 7 = 2x + 7 ⇒ collect same terms
∴ 4x - 2x = 7 + 7
∴ 2x = 14 ⇒ divide both the sides by 2
∴ x = 14 ÷ 2 = 7
* Now we can find the length of side BC
∵ The length of side BC = 4x ⇒ substituting the value of x
∴ The length of side BC = 4 × 7 = 28 units
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Correct QuestionWhat is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.
At a sale, coats were sold for $104 each. If the coats originally cost $160 each, what percentage of its original price was a coat sold for?
well, if we take 160 to be the 100%, what is 104 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 160 & 100\\ 104& x \end{array} \implies \cfrac{160}{104}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 20 }{ 13 } ~~=~~ \cfrac{100}{x}\implies 20x=1300\implies x=\cfrac{1300}{20}\implies x=\stackrel{\%}{65}[/tex]
Coats sold for 65% of its original price at a sale.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, at a sale, coats were sold for $104 each and the coats originally cost $160 each.
Let x% of $160 be $104.
Now, x% of 160=104
x/100 ×160=104
x=104/160 ×100
x=0.65×100
x=65%
Therefore, 65% of coats original price was a coat sold for.
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a test of which hypothesis is most important when deciding whether to use a simple linear regression model to predict y from x?
The most important measure used in regression diagnostics is the simple residual.
What is linear rigression?
In statistics, a scalar response and one or more explanatory factors are modeled using a linear approach called linear regression. Simple linear regression is used when there is only one explanatory variable; multiple linear regression is used when there are numerous explanatory variables.
Hypothesis testing is used to confirm if our beta coefficients are significant in a linear regression model. Every time we run the linear regression model, we test if the line is significant or not by checking if the coefficient is significant.
If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero.
The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.
The most important measure used in regression diagnostics is the simple residual (e). This is the difference between each observed and predicted value of Y.
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special industrial battery must have a life of at least 400 hours. a hypothesis test is to be conducted with a 0.02 level of significance. if the batteries from a particular production run have an actual mean use life of 391 hours, the production manager wants a sampling procedure that only 10% of the time would show erroneously that the batch is acceptable. what sample size is recommended for the hypothesis test? use 45 hours as an estimate of the population standard deviation. (round your answer up to the nearest integer.)
488601 is the sample size recommended for the hypothesis test.
Given,
The life of the battery = 400 hours
Significance level = 0.02
Mean = 391 hours
The production manager needs a sampling technique that would incorrectly indicate that the batch is acceptable only 10% of the time.
We have to find the sample size recommended for the hypothesis test;
Here,
Margin of error E = Z(α/2) × (σ/n²)
From this equation we get n as
n = (z × σ /E)^2
α = 0.02
From the standard normal table value we get
z(α/2) = 2.33
σ = 30
E= 0.1
Therefore,
n =(2.33*30/0.1)^2
n =488601
That is,
The sample size recommended for the hypothesis test is 488601.
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a college prep school advertises that their students are more prepared to succeed in college than other schools. to verify this, they categorize gpa's into 4 groups and look up the proportion of students at a state college in each category. they find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in gpa. they then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. can they conclude that the grades of their graduates are distributed differently than the general population at the school? test at the 0.05 level of significance.
Answer:
Yes, they can conclude that the grades of their graduates are distributed differently than the general population at the school. This is because the test statistic, chi-squared, is greater than the critical value, which is 7.81. This means that the difference between the observed and expected frequencies is statistically significant.
Step-by-step explanation:
There is a difference between the general population and college prep students in GPA.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Numbers Observed Proportion Expected (O - E) (O - E)² (O - E)²/E
0 - 0.99 19 0.07 14 5 25 1.79
1 - 1.99 28 0.21 42 -14 196 4.67
2 - 2.99 82 0.37 74 8 64 0.865
3 - 3.99 71 0.35 70 1 1 0.0142
Now, X² = the sum of (O - E)²/E
= 8.33
The P-Value is .039662. The result is significant at p < .05.
Hence,
H₀: There is no difference between the general population and the college prep students in GPA.
H1: There is a difference between the general population and the college prep students in GPA.
Test statistic = 8.33
p - Value = 0.039662
Therefore, the alternate hypothesis is true.
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HELP PLEASE!!!! URGENT!!
573x2883 long divison
Answer:
The answer is 165,1959 if you don't need to show work.
What two numbers multiplies to negative 480 and adds to negative 28?
Answer:
-40 ,12
Step-by-step explanation:
you will have to look for the factors of 480 that satisfy this condition and for this case , they're -40 and 12
a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
With an off-course speed of 11 miles per hour, the ship will go 33 miles in 3 hours.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of same size.
Here,
speed of ship= 11 miles/hour
time given= 3 hours
distance= speed * time
=11*3
=33 miles
The ship will cover 33 miles in 3 hours while moving at the speed of 11 miles/ hour off course.
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a newborn weighing 5 lb (2250 g) needs to eat 3 oz (90 ml) of formula every 3 hours. to meet this goal, how many ounces of formula per day will the parent need to feed the newborn? record your answer using a whole number.
it would be 72.94 ounces of formula per day will the parent need to feed the newborn
In this problem, the infant is fed for every 3 hours.
Then, the frequency of feeding for a day would be: (24hours/day) / 3(hours/times)= 6 times/ day.
The volume of feeding for a day that the infant need would be: = 473.68ml/day
The number of milk for every fed would be: (473.68ml/day)/ (6 times/day)= 72.94 ml/times
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Which of the following is TRUE about the slope of a line? *
A. The slope of a vertical line is zero.
B. The slope of a vertical line is undefined.
C. The slope of a line is always positive. D. The slope of a horizontal line is negative.
Answer:
Step-by-step explanation:
The answer is B.
The slope of a verticle line is "undefined" by nature. As it is infinite
Which of the following would you round and estimate to a sum of 11?
3.65 + 7.992
3.41 + 8.051
4.25 + 8.103
4.89 + 7.431
your parents gave you $50 to take your brother and sister to the movies. your ticket cost $8.25 and your siblings cost $4.25. if you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
The money left is $13.25.
Given data,
Your parents handed you $50 to spend on movie tickets for your sister and brother. You paid $8.25 for your ticket, while your siblings paid $4.25.
To know how much money you bring home after spending an extra $20 on soda and popcorn,
Your entry cost is $8.25
$4.25 for the brother's ticket
Sister's entry fee is $4.25.
$20 for soda and popcorn.
Total = 8.25 + 4.25 + 4.25 + 20.00 = $36.75
You received $50 from your parents.
You have spent $36.75.
Balance: 50.00 - 36.75 = $13.25
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(-7, 8) and (-7, 5)
Find the slope
Answer:
Slope is undefined
Step-by-step explanation:
slope = [tex]\frac{\Delta y}{\Delta x}[/tex]
[tex]\frac{5-8}{-7-(-7)}=\frac{-3}{0}[/tex]
Anything divided by zero is undefined
This should make sense visually as the points describe a vertical line at [tex]x=-7[/tex]
according to the book of odds, the probability that a randomly selected u.s. adult usually eats breakfast is 0.61.1a) explain what probability 0.61 means in this setting.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
a) This means that if you were to take a large sample of US adults and inquire them about having breakfast, about 61%(i.e. 0.61) will say that they usually have breakfast.
b) It is, for sure, expected that if we take a sample of 100, around 61% of these americans will say that they usually eat breakfast. But if the number will be 61 exactly is not a certainty and it will vary from sample to sample.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
Explanation has been provided in the answers above due to their descriptive nature.
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solve (4,19) and (9,24) in y=mx+b form
Answer:
Equation of the line:
y = x + 15
slope: 1
chegg how many cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected?
26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
We have given that standard deck of 52 cards.
And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.
So four hearts + four diamonds + five clubs = 13 cards
The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.
So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26
Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
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Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number
The lateral surface area is 667.92 m² and surface area is 1081.92 m².
What is lateral surface area?The lateral surface area of a three-dimensional object is the surface area of the object minus the area of its bases.
Given is a triangular prism,
Lateral surface area = (side1 + side2 + side3)xh = (8+9+12.04)x23 = 667.92 m²
Surface area = (side1 + side2 + side3)xh + 2base area = 667.92 + 9x23x2 = 1081.92 m².
Hence, The lateral surface area is 667.92 m² and surface area is 1081.92 m².
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what is the ratio of 500 students and 10 classrooms
Answer:
FOR EVERY 1 CLASSROOMS THERE ARE 50 STUDENTS, SO 50 STUDENTS IN EACH CLASSROOM the ration would be 50:1
Step-by-step explanation:
Answer:
I think its 50:1
Step-by-step explanation:
Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1). Is this trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement. Trapezoid abcd choose. An isosceles trapezoid.
The given trapezoid ABCD is an isosceles trapezoid and has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1).
What is trapezoid?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides. This article provides formulas for the area of the trapezium as well as its types, properties, and other trapezoids.
Here,
Segments AB and CD are parallel and 3 units apart.
Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.
The given Trapezoid ABCD that has given vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) is a isosceles trapezoid.
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i want one halve of a cupcake for myself 4 halves for my friend and 3 halves for my other friend
Answer: Split it into 8 pieces.
Step-by-step explanation: If there is 4 halves for your friend, and 3 halves for your other friend, that will be 7. If you add another one, it will be 8. Therefore, you should split the cupcake into 8 pieces.
why in models such as logistic regression we need to estimate the marginal effects of each independent variable in order to understand how a change in one independent variable affects our dependent variable.
Marginal effects can be used to express how the predicted probability of a binary outcome changes with a change in a risk factor. For example, how does 1-year mortality risk change with a 1-year increase in age or for a patient with diabetes compared with a patient without diabetes
Logistic regression, also known as logit regression, logit model, or just logit, is one of the most regression analyses taught at universities and used in data analysis. It is a non-linear model which predicts the outcome of a categorical dependent variable with respect to a vector of independent variables. When performing a logit regression with a statistical package, such as Stata, R or Python, the coefficients are usually provided by log-odds scale. In short, this means that point estimates are complicated to interpret, however the sign and the confidence interval of estimates can be interpreted. For that reason, it is interesting to interpret the logit model in the probability scale, i.e. as probabilities.
Marginal effect:Marginal effects measure the impact that an instantaneous change in one variable has on the outcome variable while all other variables are held constant. In the simple OLS model with linear effects, estimated coefficients are always equal to marginal effects.
Independent Variable:An Independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. Other factors (such as what they eat, how much they go to school, how much television they watch) aren't going to change a person's age. In fact, when you are looking for some kind of relationship between variables you are trying to see if the independent variable causes some kind of change in the other variables, or dependent variables.
Dependent Variable:Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does.
Many people have trouble remembering which is the independent variable and which is the dependent variable. An easy way to remember is to insert the names of the two variables you are using in this sentence in they way that makes the most sense. Then you can figure out which is the independent variable and which is the dependent variable:
(Independent variable) causes a change in (Dependent Variable) and it isn't possible that (Dependent Variable) could cause a change in (Independent Variable).
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Given: -6x < 36. Choose the solution set. {x | x < -6} {x | x > 6} {x | x > -6} {x | x < 6}.
The correct answer is this inequality {x | x > -6}
What does a math inequality look like?
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
Given that:
-6x < 36
we multiply -1 on both the sides
6x > -36
divide 6 on both the side
x > -6
Hence the correct answer is this inequality {x | x > -6}.
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Darren bought 53.11 pounds of fruit for a class party. The class ate 0.6 pounds of the fruit. How much fruit is left?