The sum of the alternating subtraction and addition sequence 300-297+294-291+...+6-3 can be calculated by pairing the numbers and determining the partial sums, which consistently equal 3. With 49 complete sets of these operations within the range given, the total sum is 147.
Explanation:The sequence provided is a series of alternating subtractions and additions of integers in a specific pattern. To determine the sum of such a sequence, we can pair the numbers in such a way that each subtractive pair (e.g., 300-297) is combined with its subsequent additive pair (e.g., 294). This will result in a series of partial sums which are consistently 3 (e.g., 300-297+294 equals 297). As the pattern continues, each group of four numbers adds up to 3.
Since all groups add up to 3, and we know that each set of two operations (a subtraction followed by an addition) gives us 3, we need to find out how many such sets there are. Given that our numbering starts with 300 and ends with 3 (decreasing by 3 every time), we can see there are 99 numbers in the sequence (since (300 - 3) / 3 + 1 = 99). And because every four numbers make up one set, there would be 99 / 2 = 49.5 sets. We only consider the entire sets, which would be 49 in total, ignoring the last number (3) that does not form a complete set.
Therefore, multiplying 49 sets by 3 gives us the total sum of the pattern, which would be 147. It is important to double-check calculations to ensure accuracy when dealing with sequences and series.
A construction company was contracted to build a cylindrical storage tank with a diameter of 48 feet and height of 25 feet. Just before construction was to begin, it was learned that a new law allows tanks to be a maximum of 9 feet in height. If the tank is redesigned to meet the law, but has the same volume, what is its new diameter?
Simplify six to the -3rd power over six to the fifth power
Connor is asked to find the probability of rolling a prime number on a die. He states that this is a simple event. True or false? A. True B. False
Dorothy types 120 words per minute .How many words does Dorothy type in 1.75 minutes ?
517.21 km what is the nearest 10km?
What type of stock receives an equal part of the profits on each share to be distributed after all other obligations of a company have been satisfied?
I WILL GIVE BRAINLIEST
Julian compared numbers with similar digits. Using mathematical language, explain how each set of numbers is different
SET A: 13.542 and 35.42
SET B: 781 and 78.1
SET C: 1.2 and 01.20
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
7 < h < 9
7 > h > 9
h < 7 or h > 9
h > 7 or h < 9
Answer:
Option C is correct.
The inequalities can be written as one statement as : h<7 or h>9
Step-by-step explanation:
Let h be the working hours
Antonio can drive home after working less than 7 hours.
Less than symbol represented by ('<')
then, we have h<7
Antonio after working more than 9 hours.
More than symbol represented by ('>').
then, we have h>9
Since, we use inequalities when there is a range of possible answers for a given situation
Now, as per the given statement,
the inequalities can be written as one statement as; h<7 or h>9
Point D represents a negative number. Which point represents the opposite of that number?
The negative number - 7 and its opposite number 7 are represented on the number line.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
Point D represents a negative number which is -7.
We know that if the number is 'a', then the opposite number of the number 'a' will be '-a'.
Then the point representing the opposite of that number will be given as,
⇒ -(-7)
⇒ 7
The negative number - 7 and its opposite number 7 are represented on the number line.
The diagram is given below.
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The complete question is given below.
Point D represents a negative number which is - 7. Which point represents the opposite of that number?
A dance competition on television had five elimination rounds. After each elimination, only one-fourth of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 512 128 32 8 2 Compute the average rate of change of f(x) from x = 2 to x = 4 and describe what it represents.
−60 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−120 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−60 contestants per round, and it represents the number of contestants who will reach the final round
−120 contestants per round, and it represents the number of contestants who will reach the final round
Answer:
A
Step-by-step explanation:
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)
Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)
how do you slove this problem
Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He has 72 pencils and 24 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
Answer:
3 pencils
Step-by-step explanation:
We are given Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.
Number of pencils=72
Number of calculators=24
If Zayed creates the greatest number of identical packages
Then , we find GCF of 72 and 24
[tex]72=2\times 2\times 2\times 3\times 3[/tex]
[tex]24=2\times 2\times 2\times 3[/tex]
GCF=[tex]2\times 2\times 2\times 3[/tex]
Hence, Zayed creates 24 packages.
Number of pencils in each package=[tex]\frac{72}{24}=3[/tex]
Hence, 3 pencils and one calculator will be in each package .
Answer:
3 pencils
Step-by-step explanation:
Solve 2a 2 - 3a - 2 = 0
{-1/2, 2}
{1/2, -2}
{}
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
A=1 ≥ 2x
B=6x ≥ 3 + 8x – 4
and on a graph
.5 shaded to the left
- .5 shaded to the right
.5 shaded to the right
checking all that apply the correct answers would be A B and C
The correct answers are:
A) 1 ≥ 2x ; B) 6x ≥ 3 + 8x – 4 ; and .5 shaded to the left
Explanation:
Our inequality given is 6x ≥ 3 + 4(2x - 1). First we use the distributive property:
6x ≥ 3 + 4(2x) + 4(-1)
6x ≥ 3 + 8x - 4
This means A is correct.
Next we can subtract 8x from each side:
6x-8x ≥ 3+8x-4-8x
-2x ≥ 3-4
-2x ≥ -1
Divide both sides by -1 (remember to flip the inequality symbol):
-2x/-1 ≥ -1/-1
2x ≤ 1
This can also be written as 1 ≥ 2x, so B is correct.
To finish solving this, divide both sides by 2:
2x/2 ≤ 1/2
x ≤ 0.5
To graph this, we circle 0.5 and fill it in (since it is less than or equal to), and shade to the left (since it is less than).
A triangle can have sides whose lengths are 9cm, 16cm, and
True or false, the product of two rational numbers is never equal to 1.
The product of two rational numbers can indeed be equal to 1. For example, 2/3 (two-thirds) and 3/2 (three-halves) are both rational numbers, and their product is 1.
Explanation:The product of two rational numbers can indeed equal to 1. This is a False statement. For example, if we take 2/3 (two-thirds) and 3/2 (three-halves), both are rational numbers because they can be expressed as fractions, i.e., ratios of two integers. In this case, if we multiply these two numbers together, i.e., (2/3)*(3/2), we get 6/6, which equals 1. Therefore, it's possible that the product of two rational numbers can equal 1, hence proving the provided statement to be false.
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Write 2 expressions that represent the areas of 4 triangles
Sarah received $55 for her birthday. She used some of that money to buy 3 shirts priced at m dollars each.
How much money does Sarah have left?
Write your answer as an expression.
How do you convert from a radical expression to a rational exponent?
Im just a little confused so if someone could explain this to me, thatd be great!
To convert a radical expression to a rational exponent, identify the root index of the radical as this will be the denominator of the rational exponent. The base remains unchanged. The rational exponent is 1 over the root index.
Explanation:To convert a radical expression to a rational exponent, you need to understand the connection between them. In mathematics, the 'nth root of a' can be written as a radical expression or as a to the power of 1/n, which is the rational exponent form.
For example, if we have √a (square root of a), which is a radical expression, it can be written as a^(1/2) in rational exponent form. Similarly, the cube root of a (3√a) translates to a^(1/3).
Here are the steps for conversion:
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Pls solve 7x-4(6-x)+12 and show steps pls.
A plant is already 11.50 meters tall, and it will grow 9 centimeters every month. The plant's height, H (in meters), after x months is given by the following function.
H (x) = 0.09x + 11.50
What is the plant's height after 15 months?
The plants height after 15 months is:
What are linear equations?"A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution."
Given the function is
[tex]H(x)= 0.09x + 11.50[/tex]
Also given,
Number of months are 15
[tex]\(H(x)= 0.09*15 + 11.50 \\H(x)= 1.35 + 11.50 = 12.85[/tex]
Hence, the plant's height after 15 months is 12.85 meters.
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Please help!! I attached an image, will give most brainliest
Which of the following approaches can be used to construct a parallelogram? Select one: a. Measure equal segments on parallel lines, then join the endpoints of these segments. b. Construct two congruent angles, then bisect them. c. Construct the perpendicular bisector of a segment, then bisect two of the right angles. d. Construct two perpendiculars to a parallel line.
Final answer:
The correct approach to constructing a parallelogram is to measure equal segments on parallel lines and then join the endpoints of these segments, which ensures opposite sides are equal and parallel.
Explanation:
The student has asked which of the following approaches can be used to construct a parallelogram. The correct approach is Measure equal segments on parallel lines, then join the endpoints of these segments, which corresponds to option a. This method utilizes the properties of parallelograms, where opposite sides are equal in length and parallel to each other. The Euclidean Geometry postulates that relate to this method include E1 Two points determine a line, E2 Line segments can be extended, and the Parallel postulate: Given a line and a point not on the line, no more than one line can be drawn through the point and parallel to the given line.
To construct a parallelogram, you can follow these simplified steps:
Select any two parallel lines.
Measure and mark equal length segments on each of the lines.
Join the corresponding endpoints of these segments to form the parallelogram.
A boy moves 4 miles south. Then he turns 90 degrees to the left. He moves forward 6 miles. H turns 90 degrees to the left. He moves forward 4 miles. How far is he now than from his starting point?
please help! I have a deadline tonight!!!!
solve the inequality 2(p – 7) > 8
The solution to the given inequality 2(p – 7) > 8 is p > 11.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question following as:
2(p – 7) > 8
We have to determine the solution to the given inequality.
As per the question, we have
2(p – 7) > 8
Open the parentheses and apply the distributive property of multiplication,
2p - 14 > 8
Add 14 both sides of the above in inequality,
2p - 14 + 14 > 8 + 14
2p > 22
Divided by 2 into both sides of the above in inequality,
p > 11
Therefore, the solution to the given inequality is p > 11.
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A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone is what shape?
Answer:
The answer is a triangle.
Step-by-step explanation:
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
For better visualization, you can also see the attached image.
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
The answer is a triangle.
A cross-section of a cone taken perpendicular to the base and intersecting the apex of the cone is a triangle.
When you cut a cone perpendicular to its base and through its apex, the resulting cross-section will be a triangle. The shape of the cross-section depends on the angle at which you make the cut. If the cut is parallel to one of the sides of the cone, the cross-section will be a right-angled triangle.
If the cut is made at an angle to the sides of the cone, the cross-section will be an isosceles or scalene triangle.
In any case, the cross-section will always be a triangular shape with its vertices at the apex of the cone and the points where the cut intersects the base of the cone.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
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Ravi and Tikiera are making Halloween Pencil Toppers to raise money for the Math Club. Ravi can make one pencil topper in 10 minutes and Tikiera can make one pencil topper in 9 minutes. If they work together, how quickly can they make one pencil topper? Round your answer to the nearest tenth of a minute.
A high school student volunteers to present a report to the administration about the types of lunches students prefer. He surveys members of his class and records their choices. What type of sampling did the student use? systematic random sampling
Answer:
the answer is convenience sampling
Step-by-step explanation: