Which graph describes the open sentence –1 ≤ n + 2 ≤ 6?
A. Number line showing range from negative four to four. There are two rays on the graph. The first has a right end point with a closed dot at negative two with a ray pointing left past negative four. The second has a left end point with an open circle at three with a ray pointing right past four.
B. Number line -5 to +5 in single-integer increments - assessment graphic
C. Number line showing range from negative three to three The left end point is an open circle halfway between negative one and zero. There is a closed dot at three, and a ray points past three.
D. Number line showing range from negative eight to eight. There are two rays on the graph. The first has a right end point with an open circle halfway between negative six and negative four with a ray pointing left past negative eight. The second has a left end point with an open circle at four with a ray pointing right past eight.
Answers
The value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
What will be the range of n for -1 ≤ n+2 ≤ 6 ?If we follow the above condition for the different values of n
At value of n=-3 we will get n+2=-3+2=-1
similarly at n=-2 we will get n+2=-2+2=0
and at n=-1 we will get n+2=-1+2=1
all three (-1,0,1) follow the condition -1 ≤ n+2
Similarly at n=(0,1,2,3,4) condition n+2 ≤ 6 is followed
Hence value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
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The correct graph is option C.
Sure, let's break down the steps to understand why option C is the correct graph for the open sentence [tex]\(-1 \leq n + 2 \leq 6\)[/tex]:
1. Identify the Middle Term: The middle term in the open sentence is [tex]\(n + 2\)[/tex]. This means our focus is on the expression [tex]\(n + 2\)[/tex].
2. Understand the Inequality: The inequality [tex]\( -1 \leq n + 2 \leq 6\)[/tex] can be understood as "n + 2 is greater than or equal to -1 and less than or equal to 6".
3. Subtract 2 from Each Part: To isolate [tex]\(n\)[/tex], subtract 2 from each part of the inequality:
[tex]\[ -1 - 2 \leq n + 2 - 2 \leq 6 - 2 \][/tex]
Which simplifies to:
[tex]\[ -3 \leq n \leq 4 \][/tex]
4. Draw the Number Line: Draw a number line ranging from -3 to 4, inclusive.
5. Plot the Endpoints: On the number line, mark endpoints at -3 and 4.
6. Determine the Endpoints: Since the inequality includes "equal to" signs, the endpoints should be marked with closed dots (indicating inclusion).
7. Determine the Direction of the Ray: Since the inequality does not include strict inequality signs (< or >), the rays should extend in both directions from the endpoints.
8. Indicate the Rays: Draw rays to the left of -3 and to the right of 4, indicating the range extends indefinitely in both directions.
9. Mark the Open Circle: Since the inequality involves strict inequality at -1 and 6, mark an open circle at the points halfway between -1 and -3, and 6 and 4, respectively.
10. Verify the Result: The resulting graph should have closed dots at -3 and 4, indicating the range includes those values, and open circles at -1 and 6, indicating exclusion.
Option C correctly represents these steps, making it the correct graph.
The graph is given below:
Related Questions
True or false A scalene triangle can be equilateral
Answers
Hence, The statement " A scalene triangle can be equilateral " is false .
What is scalene triangle?A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.
According to the question
A scalene triangle can be equilateral
Now according to the definition of scalene triangle :
A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.
Therefore ,
It cannot be equilateral .
Hence, The statement " A scalene triangle can be equilateral " is false .
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A class consists of 6 girls and 10 boys. if a committee of 3 is chosen at random from the class, find the probability th
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divide 60 by 3
your answer is 20 :)
Hope that made sence
What is math compass used for ?
Answers
what is 2340 divided by 53?
Answers
44.1
The (-) is there because the actual number is 44.1509433962
HELP PLEASE ASAP! BRAINLIESTTTTTT
1. Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
2. Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
4. Test the residuals of two other points to determine how well the line of best fit models the data.
5. Use the line of best fit to help you to describe the data correlation.
6. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
7. According to your line of best fit, what is the arm span of a 74-inch-tall person?
My plot:
68 inches 65 inches
68 inches 67 inches
64 inches 64 inches
36 inches 37 inches
61 inches 64 inches
69 inches 70 inches
65 inches 66 inches
70 inches 69 inches
62 inches 61 inches
71 inches 70 inches
64 inches 65 inches
70 inches 72 inches
Answers
If you are dealing with a function or model, you the convention is to use the x-axis for the independent variable, this is the input, while the y-axis is for the output or dependent varibale (which is determined by the independent variable).
A sampling distribution is constructed based on a sample size of 9. if the sampling distribution has a mean of 500 and a standard error of 15, what is the standard deviation of the original comparison population
Answers
The standard deviation of the original comparison population is 45.
Explanation:The standard deviation of the original comparison population can be calculated using the formula:
Standard deviation of the sampling distribution = standard error * sqrt(sample size)
Given that the standard error of the sampling distribution is 15 and the sample size is 9, we can substitute these values into the formula:
The standard deviation of the original comparison population can be determined by using the relationship between the standard deviation, standard error, and sample size in a sampling distribution. The formula is:
[tex]\[ \text{Standard deviation of the original comparison population} = \text{Standard error} \times \sqrt{\text{Sample size}} \][/tex]
Given a standard error of 15 and a sample size of 9, substitute these values into the formula:
\[ \text{Standard deviation of the original comparison population} =[tex]15 \times \sqrt{9} = 15 \times 3 = 45 \][/tex]
Therefore, the standard deviation of the original comparison population is 45.
Standard deviation of the original comparison population = 15 * sqrt(9) = 15 * 3 = 45
Therefore, the standard deviation of the original comparison population is 45.
Write the following statement as a conditional statement. A kite is a figure with four sides. If a figure has four sides, then it is a kites. If a figure is a kite, then it has four sides. If it is a figure, then it is a kite. If it is a figure, then it has four sides.
Answers
A kite is a figure with four sides.
A conditional statement is also called if-then statement. It is a hypothesis followed by a conclusion.
For our case the conditional statement is:
If a figure has four sides, then it is a kites
Answer:
If a figure has four sides, then it is a kites.
Step-by-step explanation:
Which plane represents the bottom of the rectangular prism above?
A) Plane DGE
B) Plane AHC
C) Plane FGH
D) Plane EDC
Answers
B
The set of all even whole numbers greater than 4 and less than 12 can be written as
Answers
Hope this helps!
Which statements must be true?
Select each correct answer.
UW=VW
UV=UK
JK=2VW
UW=12KL
UV¯¯¯¯¯∥JL¯¯¯¯¯
Answers
UV is parallel to JL that's correct
JK is 2VW that's correct
UV and UK aren't congruent
UW and UV aren't congruent
The only correct statements in relation to the given triangle are;
JK = 2VW
UV ║ JL
1) UW = VW; This is not correct because we see that UW forms a parallel line to KV but there is nothing to show about it being equal to VW. 2) UV = UK; This is not correct because there is no sign of them being congruent to each other.3) JK = 2VW; We see that UKVW forms a rhombus. This means that parallel sides are equal. Thus; UK = VW.
Since UK is equal to UJ from the triangle, then;
2UK = JK
Since UK = VW, then; 2VW = JK. Thus, the statement is true.
4) UW = 12KL; This is not correct because UW = KV = KL/2 from the diagram.5) UV ║ JL; This statement is correct because from the diagram UV is a side of the parallelogram UVLW with UV parallel to WL since opposite sides of a parallelogram are equal.Read more at; https://brainly.com/question/7447576
What set of reflections would carry triangle ABC onto itself?
'triangle ABC on the coordinate plane with point A at 0, 2, point B at 2, 4, and point C at 3, 0.
x-axis, y=x, y-axis, x-axis
x-axis, y-axis, x-axis
y=x, x-axis, x-axis
y-axis, x-axis, y-axis, x-axis
Answers
Try to test apex B to reassure that it is correct.
please help! Algebra 1 math.
Find the ordered pairs for the x- and y-intercepts of the equation 3x − 2y = 18 and select the appropriate option below.
A. The x-intercept is (0, 6); the y-intercept is (–9, 0).
B.The x-intercept is (6, 0); the y-intercept is (0, –9).
C. The x-intercept is (3, 0); the y-intercept is (0, –2).
D.The x-intercept is (0, 3); the y-intercept is (–2, 0).
Answers
When y = 0, x = 18/3 = 6
=> Answer is B
10 and two tens, and then double the amount, and 5, 3, and 2. How much now?
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Simmon made 2/3 of a pound of weighed pizza. He distributed the pizza to 6 of his friends. What was the weight of the pizza that each friend gets?
Answers
One way to find the total cost of a jacket for $55.80 with a sales tax of 2.7% is 55.80+0.027(55.80) write an equivalent expression to show another way to find the total cost
Answers
Final answer:
To find the total cost of a jacket with sales tax, you can either use the given expression or calculate the sales tax separately and add it to the original price.
Explanation:
To find the total cost of a jacket with a sales tax, you can use the expression 55.80 + 0.027(55.80) as mentioned in the question.
Another way to find the total cost is to calculate the sales tax first and then add it to the original price of the jacket. To do this, you need to multiply the original price of the jacket by the sales tax rate (2.7% or 0.027) and then add the result to the original price: 55.80 + (0.027 * 55.80).
3 times the sum of 14 and a number is 57
what the equation to represent this
Answers
3 (n + 14) = 57
If you have 256 data points, how many classes (bins) would sturges' rule suggest
Answers
Final answer:
Sturges' rule suggests using 9 classes or bins for 256 data points.
Explanation:
Sturges' rule is a method for determining the number of classes or bins required for a histogram. According to Sturges' rule, the formula to calculate the number of classes is:
K = 1 + log2(n)
Where K is the number of classes and n is the number of data points. In this case, since you have 256 data points, the number of classes suggested by Sturges' rule would be:
K = 1 + log2(256)
K = 1 + log2(28)
K = 1 + 8
K = 9
Therefore, Sturges' rule would suggest using 9 classes or bins for the histogram.
what are properties of an exponent
Answers
Hope this helps!
Your bowl contains 8 red balls, and 9 blue balls, and you draw 4 balls. in how many ways can the selection be made so that at least one of each color is drawn?
Answers
In 2156 ways the selection be made so that at least one of each color is drawn?
The question is asking for the number of ways to select balls from a bowl containing 8 red balls and 9 blue balls if 4 balls are drawn and at least one of each color is drawn.
To solve this, we must consider the different combinations of red and blue balls that meet the requirement.
Calculate the total possible outcomes: 17C4 = 2380
Calculate the outcomes where all balls of one color are drawn: 9C4 + 8C4 = 224
Subtract the outcomes where only one color is drawn from the total: 2380 - 224 = 2156 ways
A cube has a volume of 729 cubic centimeters. What can be concluded about the cube? Check all that apply. Recall the formula mr021-1.jpg. The side length, s, can be found using the equation mr021-2.jpg This is a perfect cube. The side length is 243 centimeters. The side length is 9 centimeters. Taking the cube root of the volume will determine the side length. If you multiply the volume by three, you can determine the side length.
Answers
Answer:
This is a perfect cube
The side length is [tex]9[/tex] centimeters
Taking the cube root of the volume will determine the side length
Step-by-step explanation:
we know that
The volume of a cube is equal to
[tex]V=s^{3}[/tex]
where
s is the length side of the cube
In this problem we have
[tex]V=729\ cm^{3}[/tex]
Solve for s-------> that means isolate the variable s
Find the length side of the cube s
[tex]s=\sqrt[3]{V}[/tex]
substitute the value of V
[tex]s=\sqrt[3]{729}=9\ cm[/tex] --------> a perfect cube
therefore
Statements
This is a perfect cube--------> Is true
The side length is [tex]9[/tex] centimeters -------> Is true
Taking the cube root of the volume will determine the side length ------> Is true
The side length of the cube is 9cm³ showing that the cube is a perfect cube
Volume of the cubeThe formula for calculating the volume of a cube is expressed as:
V = s³
where:
s is the side length of the cube
Given the following
V = 729cm³
Substitute the given parameters into the formula
729 = s³
s³ = 729
s = 9cm
Hence the side length of the cube is 9cm³ showing that the cube is a perfect cube
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Three students out of a group of 10 seniors will be chosen to speak in front of the school. What is the probability that Ben, Mark, and Ty will be chosen
Answers
hm, if order does not matter
then it is 3/10 that one of the 3 is chosen
assuming that one was chosen, we now have a probablity of 2/9
then the last is 1/8
so the ending probablity will be 3/10 times 2/9 times 1/8 or 6/720 or 1/120
the probablity will be 1/120
if the order does matter then it is
1/10 times 1/9 times 1/8 or 1/720 because there is 1 choice for each
Problem page ali made a shirt using 15 meters of yellow fabric and 12 meters of green fabric. how many meters of fabric did he use in all?
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Hope That Helped!
what is the greatest perfect square that,s a factor of 244 ?
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Greatest perfect square that is a factor of 244 is 4 which is the perfect square of 2 .
Given, number 244 .
Firstly the factors of 244 :
244 = 2 × 2 × 61
244 = 4 × 61
Therefore the greatest perfect square that is the factor of 244 will be 4 .
4 is the perfect square of 2.
2² = 4.
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78·112=7278·112=72 . how can you tell that her answer is wrong?
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Farmer Fred has 200 sheep on his farm.He sells 40 of them.What percentage of his sheep does he have left?
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Which answer represents a speed, not a velocity?
A. 35m/s east
B. -35 m/s down
C. 35 m/s
D. 35 m/s south
Answers
The expression that represents the speed will be 35 m/s. Then the correct option is C.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
The velocity is the rate of change of the displacement. And it is a vector quantity.
The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
In options A, B, and D, then speed depend on the direction which means they are velocity.
The expression that represents the speed will be 35 m/s. Then the correct option is C.
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A rectangle has a length one less than three times the width. If the perimeter is 46 units , find the width and length
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Let l represent the length of the rectangle.
Let w represent the width of the rectangle.
[tex] \left \{ {{2(l+w)=46} \atop {3w-1=l}} \right. [/tex]
Isolate for the l in Equation #2.
[tex]3w-1=l[/tex]
[tex]l=3w-1[/tex]
Substitute Equation #2 into Equation #1.
[tex]2(l+w)=46[/tex]
[tex]2[(3w-1)+w)]=46[/tex]
Combine Like Terms.
[tex]2(4w-1)=46[/tex]
Distribute the Parenthesis.
How? Multiply the terms inside the Parenthesis by the term outside of the Parenthesis.
[tex]2*4w-2*1=46[/tex]
[tex]8w-2=46[/tex]
Add 2 to both sides.
[tex](8w-2)+2=(46)+2[/tex]
[tex]8w=48[/tex]
Divide both sides by 8.
[tex] \frac{8w}{8}= \frac{48}{8} [/tex]
[tex]w=6[/tex]
The Answer Is:
[tex] \left[\begin{array}{ccc}w=6\end{array}\right] [/tex]
The Width is 6 units and the Length is 17 units.
Hope this helps.
-Benjamin
Which is true about rigid transformations and circles?
a.a reflection of a circle does not conserve the circle's radius.
b.a circle is only carried onto itself after each one degree rotation.
c.a translation of a circle does not conserve the circle's circumference.
d.a circle's shape is preserved regardless of any rigid transformation?
Answers
A rigid transformation is defined to be one in which the pre-image of the object and its new image after the transformation both have the exact same size and shape. So the answer in this question is:
D. a circle's shape is preserved regardless of any rigid transformation
Answer: D. a circle shape is preserved regardless of any rigid transformation.
Step-by-step explanation:
Ralphie has 23 more toys than his little brother Joey. If they were to get all of their toys out and lay them on the floor, there would be 384 toys on the floor.
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Find y'' by implicit differentiation. 4x3 + 5y3 = 2
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The value of implicit differentiation of y" of the 4x³ + 5y³ = 2 is [tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex].
To find y'', or the second derivative of y, by implicit differentiation, we'll differentiate both sides of the equation with respect to x, treating y as a function of x.
Step - 1:
Start by differentiating each term with respect to x using the chain rule:
Differentiating 4x³ with respect to x gives 12x².Differentiating 5y³ with respect to x requires the chain rule. We get 15y²(dy/dx).Since we're differentiating with respect to x, we need to multiply dy/dx by y' to indicate the derivative of y with respect to x.
Step - 2:
The right-hand side of the equation, 2, has a derivative of 0 since it is a constant.
Putting it all together, we have the equation:
[tex]12x^2 + 15y^2 \times \frac{dy}{dx} = 0.[/tex]
Now, to find y'', we differentiate this equation with respect to x, treating dy/dx as a function of x.
Differentiating 12x² with respect to x gives 24x.Differentiating 15y² × dy/dx with respect to x requires the product rule. We get [tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2}[/tex].Step - 3:
The right-hand side of the equation, 0, has a derivative of 0 since it is a constant.
Putting it all together, we have the equation:
[tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex]
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To find y'' by implicit differentiation from the equation 4x^3 + 5y^3 = 2, differentiate both sides with respect to x, apply the chain and product rules appropriately and then solve for y''.
Explanation:To find the second derivative y'' by implicit differentiation for the equation 4x^3 + 5y^3 = 2, you follow these steps:
Differentiate both sides of the equation with respect to x to find the first derivative (y').Apply the chain rule to differentiate y terms, remembering to multiply by y' (dy/dx) because you are differentiating with respect to x.The differentiation of 4x^3 yields 12x^2, and the differentiation of 5y^3 using the chain rule gives you 15y^2*y'.You then set the derivative equal to 0, because the differential of 2 with respect to x is 0.To find the second derivative (y''), differentiate your expression for y' with respect to x again, applying the chain rule and product rule as necessary.This process will provide you with the value of y''.
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