Prime Number is a number whose only factors are itself and one. For example 1,3,5,7,11,13,17,19,23… Now consider the following arguments : Every even number greater than 2 can be expressed as sum of two primes. Now consider the following premises:
Premise 1 : 4 = 2 + 2
Premise 2 : 10 = 5 + 5
Premise 3 : 12 = 5 + 7
Premise 4 : 16 = 5 + 11
Premise 5 : 18 = 5 + 13
Premise 6 : 22 = 11 + 11
Premise 7 : 30 = 7 + 23
Premise 8 : 32 = 3 + 29
Premise 9 : 40 = 3 + 37
Premise 10 : 52 = 5 + 47
Premise 11 : 100 = 3 + 97
Conclusion : every whole number is sum of two prime numbers.
All 11 cases are different, yet the rule applies to all. This outcome offers a strong inductive argument in favor of the conclusion or rule specified. It can be strengthened by additional cases that confirm the rule. Conjecture specified will be true because each number can be specified as sum of two primes. As each whole number will have difference os 1, 2, 3, 5, or 7 between the number and the nearest prime number. Consider the following example :
34 = 31 + 3
36 = 33 + 3
Hence the conjecture “Every number greater than two can ve expressed as the sum of two primes” is true.
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25 POINTS!!!!!
In the figure below, lines m and n are parallel:
Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.
In the diagram shown, ∠7 measures 92 degrees. What is the measure of ∠8?
8 degrees
88 degrees
92 degrees
180 degrees
7 and 8 have to equal 180 degrees
180- 92 = 88
so angle 8 is 88 degrees
Answer:
The correct option is B) 88°.
Step-by-step explanation:
Consider the provided information.
Consider the figure 1,
m∠7=92°, then by using the property of liner pair angles, we have
m∠7 + m∠8 = 180° (Liner pair angles)
⇒m∠8 + 92° = 180°
⇒m∠8 = 180 - 92
⇒m∠8 = 88°
Therefore, the measure of m∠8 is 88°.
Hence, the correct option is B) 88°.
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line 2x + 5y = 10 is:
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10
Hence the slope of the line 2x + 5y = 10 is -2/5
Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:
[tex]y-y_1=m(x-x_1)\\\\y-(-4)=-\frac{2}{5} (x-5)\\\\y+4=-\frac{2}{5} x+2\\\\y=-\frac{2}{5} x-2[/tex]
The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
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Q equal 1/2 p plus 15 solve for p
Suppose that 21 girls and 21 boys enter a mathemat- ics competition. furthermore, suppose that each entrant solves at most six questions, and for every boy-girl pair, there is at least one question that they both solved. show that there is a question that was solved by at least three girls and at least three boys.
Individuals shall draw a table consisting of 21 boys in each column and 21 girls in each row as shown on the image below.
The table will have 21x21 = 441 boxes. Mark each box with a letter showing the problem solved by both that boy and girl. Since at least one problem was solved by a girl and a boy, therefore each box will have a letter. Each entrant solved at most six questions, so there can be at most six letters in any row or column. This means six different letters can be there in a row only if at least 11 of the boxes contain letters appearing three or more times in the row. Individuals go through each row and color all the boxes, say blue. Therefore, 11 boxes in each row must be colored blue.
The number of the boxes that must be colored blue = 21 x 11 = 231. Individuals can apply the same process to the columns and color at least 231 boxes, say green. But the total boxes are 441 only. Therefore, by Pigeonhole principle, there will be some boxes which will be both blue and green. The problem of doubly colored boxes represents a problem solved by at least three boys and three girls.
The Pigeonhole Principle is used to show that there must be a question solved by at least three girls and three boys in a math competition with 21 girls and 21 boys.
To show that there is a question solved by at least three girls and three boys, we will use the Pigeonhole Principle.
We have 21 girls and 21 boys, each solving at most six questions.Let's assume no question is solved by at least three girls and three boys.The total number of questions solved would be at most 21 x 6 = 126, which is fewer than 21 x 2 + 21 x 2 = 84, a contradiction.Therefore, there must be a question solved by at least three girls and three boys.Find the critical points of the function. (enter your answers as a comma-separated list.) g(x) = 4 − x2
Sara bought two pounds of strawberries for $5.12. What is price in dollars per ounce of strawberries 1 pound =16 ounces
In an eye color study, 25 out of 50 people in the sample had brown eyes. in this situation, what does the number .50 represent?
The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.
Explanation:In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).
Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.
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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)
452.16 cm3
840.54 cm3
1,055.04 cm3
1,456.96 cm3
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
What is the difference of (4-5y)-2(3.5y-8)?
How l can write a brief summary about measurement for 3rd grade
Mr. Thomas purchased a car for $30,000. in 4 years the value of the car decreased to $22,000. Which integer represents the average net change in value per year?
What does n equal in: -6(n+1) = 42 . Need help quickly. Thank you!
There are 9 red and 6 green marbles in a bag. A child reaches in the bag and randomly takes one marble. What is the probability pf that child getting a green marble
Answer: The required probability that the child took a green marble is 40%.
Step-by-step explanation: Given that there are 9 red and 6 green marbles in a bag and a child reaches in the bag and randomly takes one marble.
We are to find the probability that the child took a green marble.
Let S denote the sample space of choosing a marble from the bag and A be the event of choosing a green marble.
Then,
n(S) = 9 + 6 = 15 and n(A) = 6.
Therefore, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{15}=\dfrac{2}{5}\times 100\%=40\%.[/tex]
Thus, the required probability that the child took a green marble is 40%.
What is the greatest common factor of 49 and 84? 3 4 7 9
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If (7^2)x = 1, what is the value of x? Explain your answer.
If (7^0)x = 1, what are the possible values of x? Explain your answer.
(7^2)x = 1
7^2 = 49
49x = 1
x = 1/49
(7^0)x=1
7^0 = 1 (anything raised to 0 = 1)
1x = 1
x = 1
Kareem runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Hello, I am taking Quantitative methods for business, which has a lot of excel based mathematics and I was wondering if anyone could help. Here is the question:
Refer to the table that illustrates customer’s complaints about a manufacturing company.
A. What is the probability a customer complained during the guarantee period?
B. What is the probability that a customer complained about an electrical problem or a mechanical problem?
Table is included in attachment. Also Thank you!!!
Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)
The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\((-5, 6)\) and \((0, 1)\)[/tex]
Calculate the slope m:
[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]
Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
Now, simplify and compare with the given options:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
a girl is the same age if she takes 3/4 of her age +9 or 1/4 +21. what is her age?
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
At the beginning of a basketball season, the Panthers won 30 games out of 66 games. At this rate, how many games will they win in a normal 106-game season?
Evaluate the expression below when x = -2. x2 − 8 x + 6
there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
20. What percent of 392 is 98? 22. 33% of what number is 145? 24, 17 is 40% of what number?
what is an angle between a side of a polygon and the extension of its adjacent side
The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.
Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.
What is the smallest natural number that has three distinct prime factors in its factorization?
Joanne has 2a^3 number of animals. Ronnie has 3a^3 number of animals . Odessa has a^4 number of animals . How many animals do Joanne , Ronnie, and Odessa have altogether?
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The sum of two integers is greater than 12. One integer is 10 less than the other. What are the values of the integers?