The coordinates of the endpoints of rs are r(1,11) and s(6,1). point t is on rs and divides it such that rt:st is 4:1.
the coordinates of the point t are (5, 3)
We may utilise the notion of section formula to get the coordinates of point T, which states that if we have two points A(x1, y1) and B(x2, y2) and a point P splitting the line segment AB in the ratio m:n, then the coordinates of point P can be calculated using the following formula:
P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
In this situation, we have the coordinates of points R and S, as well as the ratio of T divided by RS. So, let's enter the following values into the formula to determine T's coordinates:
Let the coordinates of point T be (x, y), and the ratio of T to RS be 4:1, implying that RT:ST = 4:1. This means that RT = 4/5 (RS length) and ST = 1/5. (length of RS).
RS length =[tex]sqrt((6-1)^2 + (1-11)^2)[/tex] = [tex]sqrt (146)[/tex]
RT=[tex](4/5) * sqrt(146)[/tex] = [tex](4/5) * 12.083[/tex] = 9.666
ST =[tex]1/5* sqrt(146)[/tex] = [tex]1/5* 12.083[/tex] = 2.4166
We get the following using the section formula:
x = (4×6 + 1×1)/(4+1) = 5
y = (4×1 + 1×11)/(4+1) = 3
T = (5, 3)
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At 7:00 A.M. Joe starts jogging at
6 mi/h. At 7:10 A.M. Ken starts off
after him. How fast must Ken run in
order to overtake him at 7:30 A.M.?
Provide steps please
The speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.
What is meant by the speed of an object?
The size of a change in an object's position over time is measured by its speed. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. It is a scalar value.
Given,
Time at which Joe starts jogging = 7 am
Time at which Ken starts jogging = 7.10 am
Speed of Joe = 6mi/h
Let Speed of Ken required to overtake Joe = x mi/h
Since Ken has to overtake Joe by 7.30, both will have travelled the same distance by 7.30.
Time taken by Ken to cover the distance = 7.30 - 7.10 20 minutes = 20/60=1/3 h
Time taken by Joe to cover the distance = 7.30 - 7 = 30 minutes = 1/2 h
Distance = speed * time
Both cover the same distance.
6 * 1/2 = x * 1/3
x = 9 mi/h
Therefore the speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.
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xwhat is the correct relationship of the three principles: weak mathematical induction, strong mathematical induction, and the well ordering principle for the integers? [only one answer is correct.] group of answer choices they are none of them equivalent to each other. any one of the three is equivalent to each of the other two of the three. the well-ordering principle for the integers is not equivalent to either mathematical induction, which are equivalent to each other. the well-ordering principle for the integers is equivalent to strong mathematical induction and neither is equivalent to weak mathematical induction.
The correct relationship of the three principles is: The well-ordering principle for the integers is equivalent to strong mathematical induction, and neither is equivalent to weak mathematical induction.
The well-ordering principle for the integers states that every non-empty set of non-negative integers has a least element. Strong mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for all cases up to a certain value, and then proving that it must also be true for the next case.
This requires assuming the truth of all cases up to a certain value, which is where the well-ordering principle comes in. Weak mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for a particular case, and then proving that it must also be true for the next case.
Weak mathematical induction does not require assuming the truth of all cases up to a certain value, and is therefore weaker than strong mathematical induction.
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Use the substitution method to solve the system of linear equations.
y = x - 4
4x + y = 26
Answer:
y = 2 and x = 6
Step-by-step explanation:
Let y = x - 4 be equation a
Let 4x + y = 26 be equation b
Substitute a into b:
4x + (x-4) = 26
5x - 4 = 26
5x = 30
x = 6
Substitute the value of x into a:
y = x - 4
y = 6 - 4
y = 2
CHECK:
4x + y = 26
4*6 + 2 = 26
24 + 2 = 26
26 = 26
LHS = RHS
Therefore, y = 2 and x = 6
Mrs. Ellis is shopping for school
supplies with her children. Hansen
selected 3 one-inch binders and 2 two-
inch binders, which cost a total of $20.
Pam selected 3 one-inch binders and 5
two-inch binders, which cost a total of
$32. How much does each size of
binder cost?
Answer:
Each one-inch binder costs $2.67 and each two-inch binder costs $6.
Step-by-step explanation:
Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".
From Hansen's purchase, we know that 3x + 2y = $20.
From Pam's purchase, we know that 3x + 5y = $32.
We can use these two equations to solve for the cost of each size of binder. If we subtract the first equation from the second, we get:
2y = $32 - $20 = $12
So, y = $6, which is the cost of a two-inch binder.
Next, we can plug this value back into either of the original equations to find the cost of a one-inch binder:
3x + 2($6) = $20
Expanding the right side, we get:
3x + $12 = $20
Subtracting $12 from both sides, we get:
3x = $8
Finally, dividing both sides by 3, we find that:
x = $2.67
So, each one-inch binder costs $2.67 and each two-inch binder costs $6.
the scores on a standardized test are normally distributed with a mean of 100 and standard deviation of 5. what test score is 1.4 standard deviations
A test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.
To find the test score that is 1.4 standard deviations above the mean, we need to use the formula:
z = (x - μ) / σ
where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.
In this case, we know that z = 1.4, μ = 100, and σ = 5. So we can rearrange the formula to solve for x:
x = z * σ + μ
Substituting the values we know, we get:
x = 1.4 * 5 + 100 = 107
Therefore, a test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.
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Discount % is always calculated on the:
a) CP ( cost price).
b) SP ( selling price).
c) MP ( marked price).
d) None of these.
(8,12) and (x,9) where m = -1/2
Answer:
Step-by-step explanation:
The slope of a line between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, we are given that m = -1/2, so substituting in the two points we have:
-1/2 = (9 - 12) / (x - 8)
Expanding and simplifying the equation:
-1/2 = -3 / (x - 8)
Multiplying both sides by -2:
1 = 3 / (x - 8)
Multiplying both sides by (x - 8):
x - 8 = 3
Adding 8 to both sides:
x = 11
So the x-coordinate of the second point is x = 11.
Suppose C(x)= x^2−13x+74 for 0 ≤ x ≤25 represents the marginal cost in hundreds of dollars to produce an additional x thousand pens. Find how many additional thousand pens can be produced with marginal cost of no more than $5,200. Write the largest interval containing all possible answers
Answer: 78.39 thousand, (78,390)
Step-by-step explanation:
Using the quadratic formula with this gives us two answers, 78.39 and -65.39. Since a negative answer doesnt make sense in this context, we will go with 78.39 thousand pens, (78,390 pens). The limit on x however doesn't seem to make sense as it says x </= 25 and x>/= 0. The only two answers are both above and below this limit.
Solve for x. Round to the nearest tenth .
Thank you!
The solution of x in the triangle is 11.5
How to determine the solution of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the Pythagoras theorem, we have the following equation
x^2 = 13^2 - 6^2
Evaluate the expression
x^2 = 133
Take the square roots of both sides
x = 11.5
Hence, the solution is 11.5
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I have been stuck on this question for a little while now
Answer:
could write 21 + 38 + 75 = 134
Step-by-step explanation:
Transcribed image text: T8.7 A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the pro- portion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the propor- tion of all customers who are satisfied. The market- ing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error? (a) The margin of error will be about 4 times larger. (b) The margin of error will be about 2 times larger. (c) The margin of error will be about the same size. (d) The margin of error will be about half as large. (e) The margin of error will be about one-fourth as large. T8.8 Thirty-five people from a random sample of 125 work- ers from Company A admitted to using sick leave when they weren't really ill. Seventeen employees
The answer is (b) The margin of error will be about 2 times larger.
The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.
That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).
In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:
sqrt(1000/250) times the original margin of error.
Simplifying this expression, we get:
sqrt(4) times the original margin of error.
So the margin of error for the smaller sample will be about 2 times the original margin of error.
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A significance test about a proportion is conducted using a significance level of 0.025. The test statistic equals 1.33. The​P-value is 0.10. a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed? b. If this test resulted in a decision​ error, what type of error was​ it?a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed?b. If this test resulted in a decision​ error, what type of error was​ it? Type II Type Upper I
a. If H0 is true then the test is designed for probability of type I error of 0.025 .b. Here the p Value is 0.10 . So this indicates that the H0 is true in this test . But there is a decision error if we Reject the Null hypothesis H0.
A hypothesis is an educated guess or statement that attempts to explain a particular phenomenon or answer a specific research question. It is an essential element of the scientific method, which involves testing a proposed explanation through experimentation or observation. The purpose of a hypothesis is to guide researchers in designing an experiment that can be used to either support or refute the proposed explanation.
A hypothesis is typically based on prior knowledge, observations, or theories related to the research question. It is important for a hypothesis to be testable, measurable, and specific to allow researchers to evaluate the results objectively. A hypothesis can be developed in various fields of study, including natural sciences, social sciences, and humanities.
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Complete Question: -
A significance test about a proportion is conducted using a significance level of 0.025. The test statistic equals 1.33. TheP-value is 0.10. a. If Upper H 0 were true, for what probability of a Type I error was the test designed? b. If this test resulted in a decision error, what type of error was it?
a. If Upper H 0 were true, for what probability of a Type I error was the test designed?
b. If this test resulted in a decision error, what type of error was it? Type II Type Upper I
Sam wants to make five banana pancakes. He has a recipe for 20 pancakes,
and the recipe requires two-thirds of a cup of milk. How much milk is needed
for 5 pancakes?
The recipe requires two-thirds of a cup of milk, and Sam needs 1/3 cup of milk to make 5 banana pancakes.
What is the proportion?
A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.
The recipe for 20 banana pancakes requires 2/3 cup of milk.
To find out how much milk is needed for 5 pancakes, we can use proportion. We can set up a proportion that relates the amount of milk needed to the number of pancakes:
(milk needed) / 2/3 cup = 5 pancakes / 20 pancakes
Simplifying the right side of the equation, we get:
(milk needed) / 2/3 cup = 1/4
To solve for the milk needed, we can cross-multiply:
milk needed = (2/3 cup) * (1/4) = 1/3 cup
Therefore, Sam needs 1/3 cup of milk to make 5 banana pancakes.
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Explain why the comparison is either reasonable are unreasonable
Answer:
Reasonable
Step-by-step explanation:
The comparison 3.84 > 3.8 is reasonable.
In this comparison, 3.84 is a larger number than 3.8, so it makes sense to say that 3.84 is greater than 3.8. When comparing decimal numbers, we can simply compare the values to the right of the decimal point. In this case, both 3.84 and 3.8 have two digits to the right of the decimal point, so we can compare those digits directly. Since 4 is greater than 8, it follows that 3.84 is greater than 3.8.
The comparison is reasonable because it is based on a correct understanding of the relative sizes of the numbers involved.
4x^-3 y^-2 for x = 2 and y = 1? Pls Show work
Answer:
To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:
4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5
So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.
Step-by-step explanation:
what is the mode of the number of girl in the three classes?
There is no mode of the number of girl in the three classes.
What is Mode of the Data?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.
Given:
The data for boys: 15, 12, 12
The data for Girls: 14, 12, 16
As, mode is the most repeating data.
We can see that the data repeats in boys but not for the Girls.
So, number of boys have the mode but the number of girls do not have the mode.
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There is a total of
wholes in 72
.
The remaining fractional part is .
2
The whole number whose sum is 72 cannot be in the ratio C. 3/4.
How to explain the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them
The whole number must be divided by sum of two ratio particularly
A.5 + 7=12
72 can be divided by 12
B.3+5=8
72 can be divided by 8
C.4+3=7
72 can not be divided by 7
D.4+5=9
72 can be divided by 9
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The whole number whose sum is 72 cannot be in the ratio
A. 5/7
B. 3/5
C. 3/4
D. 4/5
Help Please im stuck
The exponential equation after solving gives -26.
What are Exponential Equations?Exponential equations are equations where the independent variable, x is in the exponent.
The given equation is,
[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]
We know that 125 = 5³
[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]
The base in the both sides of the equation is 5.
So,
7x + 5 = 3(2x - 7)
7x + 5 = 6x - 21
7x - 6x = -21 - 5
x = -26
Hence the value of x is -26.
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What is 100 x 2 - 100 ?
Answer:
100
Step-by-step explanation:
100x2=200
200-100=100!
Answer:
100
Step-by-step explanation:
First do 100 multiplied by 2 you will then get 200
Next step is to do 200 subtracted by 100 which will give you 100.
HELPPPPPPPPPPPPPPPPPPPPP
Answer: look at the image for the answer and solution
Step-by-step explanation:
A___is a numerical measure of the outcome of a probability experiment
An objective tally of the results of a probability experiment is called a random variable. It gives a number to each potential result of the experiment, and its values are decided by chance.
What exactly is probability?How something is to Happen is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics defines series of events subject to probability.
The probability equation is what?Always between 0 and 1 are the possible outcomes. Probability = Number of favourable outcomes / Total number of outcomes is how the general probability formula is written. Alternatively, P(A) = f / N.
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Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
The simplified form of the expression √x × ⁴√x in rational exponent form is x^3/4.
What is the simplified form of the expression?Given that, square root of x times the fourth root of x.
√x × ⁴√x
To simplify the expression, rewrite using the least common index of 4.
Since ⁿ√xᵃ = x^(x/n)
√x = x^(1/2)
and
⁴√x = x^(1/4)
Hence, we have;
x^(1/2) × x^(1/4)
Using exponent rule
x^( 1/2 + 2/4 )
Add 1/2 and 1/4
x^( 1/2 + 1/4 )
x^3/4
Therefore, the simplified form is x^3/4.
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which expression can be used to calculate the rate per second at which the machine launches the balls? (5 points) a fraction 12 over 2 b fraction 2 over 12 c fraction 48 over 2 d fraction 2 over 48
The expression that can be used to calculate the rate per second at which the machine launches the balls is a) Fraction 12 over 2.
To calculate the rate per second at which the machine launches the balls is:
First, we need to know the meaning of rate is: it is the amount of something per unit of time. In this case, we want to find the rate at which the machine launches the balls per second.
The fraction 12 over 2 represents the number of balls launched by the machine in 12 seconds. If we want to find the rate per second, we need to divide this number by the number of seconds.
12/ 2 = 6, so the machine launches 6 balls in 1 second.
Therefore, the rate per second at which the machine launches the balls is 6.
So, the expression that can be used to calculate the rate per second at which the machine launches the balls is Fraction 12 over 2, which simplifies to 6.
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In a quadrilateral field ABCD angle b is equal to 90 degree ab is equal to 80 metre BC is equal to 150 m c d is equal to 120 m and DA is equal to 250 m find the area of the field in the actor find the price of the field if it goes to 12000 rupees per hector
The area of the field is 2.384 hectares and price of the field is $28,608
The area of a quadrilateral given its sides and the diagonal:
Area = 1/4 × √[4s^2d^2 - (b^2 + d^2 - a^2 - c^2)^2]
where s = (a + b + c + d)/2 is the semi perimeter,
a, b, c, d are the lengths of the sides
d is the length of the diagonal.
Substituting the given values,
s = (80 + 150 + 120 + 250)/2
= 300
a = 80, b = 150, c = 120,
d = √(250^2 + 80^2)
= 259.8076
Area = 1/4 × √[4(80+150+120+250)^2*(259.8076)^2 - (80^2 + 259.8076^2 - 150^2 - 120^2)^2]
≈ 23844.17 square meters
To convert square meters to hectares, we divide by 10,000:
Area = 23844.17 / 10,000 hectares
≈ 2.384 hectares
Therefore, the area of the field is approximately 2.384 hectares.
The price of the field = 12,000/hectare,
Total price = 2.384 hectares × $12,000/hectare
= $28,608
Therefore, the price of the field is $28,608.
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which of the following is most likely to be possible? group of answer choices making a grouped frequency table from an ordinary frequency table making a normal curve from a bimodal distribution making an ordinary frequency table from a grouped frequency table making a bimodal distribution from a normal curve
The most likely option (b) to be possible is making a grouped frequency table from an ordinary frequency table.
A frequency table is a way of organizing data into classes or categories based on the number of times a particular observation or value occurs.
Now, let's examine the options provided. Making a grouped frequency table from an ordinary frequency table is possible, as we can simply group the values into intervals and calculate the frequencies for each interval. This allows us to better visualize and understand the distribution of the data.
Making a normal curve from a bimodal distribution is not possible, as a bimodal distribution has two distinct peaks or modes, while a normal distribution has only one. A normal curve is symmetrical and bell-shaped, and represents a continuous distribution of values.
Making an ordinary frequency table from a grouped frequency table is also possible, as we can simply list the intervals or classes and their corresponding frequencies, without the need to group them into intervals.
Finally, making a bimodal distribution from a normal curve is possible, as we can add two normal distributions with different means and standard deviations to create a bimodal distribution. However, it is important to note that a bimodal distribution may not always be appropriate for the given data.
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The t-value changes depending on the number of data points collected.
a. True
b. False
Answer:
true
the t-value does change depending on the number of data points collected.
It is true that the t-value can change depending on the number of data points collected.
What is t-value ?The t-value is a statistic used in hypothesis testing to determine whether a sample mean is significantly different from a population mean.
The formula for calculating the t-value includes the sample size (n) in the denominator, which means that as the sample size increases, the t-value decreases (assuming all other factors remain constant).
In other words, a larger sample size will generally result in a smaller t-value, which in turn may affect the interpretation of the results of a hypothesis test. Therefore, the t-value can change depending on the number of data points collected.
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which three values are smaller than 1/2:
A. 1/4
B. 0.26
C. 3/5
D. 67%
E. 0.74
F. 40%
Answer: A, B, F
Step-by-step explanation:
For convenience sake, let's establish early on that 1/2 is equal to 0.5 or 50% in their decimal and percentage forms respectively.
- A as a decimal is 0.25, which is not only smaller than 1/2, but it is exactly half of the value, so A works.
- B is also smaller than the decimal of 0.5, therefore it counts.
- 3/5 as a decimal is 0.5, which is greater, so doesn't count.
- 67% is bigger than 50%, so doesn't count.
- 0.74 is bigger than 0.5, so doesn't count.
- 40% is smaller than 50%, so it counts.
Answer:
A, B, and F
Step-by-step explanation:
A. 1/4 = 25%
B. .26 = 26%
F. 40%
paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?
Paul records data that the number of hot chocolates sold increases as temperature outside decreases. The depiction of the finding is "There is a correlation between two variables". So, the correct option is A.
Specifically, the data suggest that there is a relationship between two variables - the number of hot chocolates sold and the temperature outside.
When the temperature outside decreases, more hot chocolates are sold, and when the temperature increases, fewer hot chocolates are sold. This indicates that there is a correlation between the two variables, as they appear to be related.
However, we cannot determine from this information alone whether the correlation is strong or weak, or whether it is positive or negative.
The strength of the correlation would depend on how much the sales of hot chocolate increase or decrease as the temperature changes, while the direction of the correlation (positive or negative) would depend on whether the increase or decrease in hot chocolate sales is associated with an increase or decrease in temperature, respectively.
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Complete question is:
Paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?
a) There is a correlation between two variables
b) There is a strong , positive correlation between two variables
c) There is a weak , positive correlation between two variables
d) There is a negative correlation between two variables
PLEASE HELP!!!
Write a linear equation given slop is -1/3 and the point (-9,-1)
The equation of a line is y = -1/3x - 4
How to determine the equation of the lineThe general formula for the equation of a line is expressed as;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the linex is a point on the x-axis of the linec is the intercept of the line on the y -axisFrom the information given, we have that;
Slope, m = -1/3
Substitute the values
-1 = -1/3(-9) + c
expand the bracket
-1 = 3 + c
collect like terms
= -4
Hence, the equation is y = -1/3x - 4
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Solve the inequality for x and identify the graph of its solution.
2|x+3|< 4
Choose the answer that gives both the correct solution and the correct graph.
