What does e equal in e/2 < 3? Please help. I need a quick answer.

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.

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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Each student will receive approximately 0.1667 parts of a whole cantaloupe when Mr. Chu evenly divides 4 cantaloupes among 24 students.

The subject of this problem is how to divide a quantity fairly between multiple recipients, also known as division. If Mr. Chu is slicing 4 cantaloupes and wants to divide them equally among 24 students, we need to find how much each student would receive.

This is solved by simply dividing the total quantity of cantaloupes by the number of students. So, 4 (whole cantaloupes) divided by 24 (students) equals 0.1667.

Therefore, each student will get approximately 0.1667 of a whole cantaloupe.

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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°.

Answer:.1

Step-by-step explanation:

A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log 100 = 2

because

102 = 100

This is an example of a base-ten logarithm. We call it a base ten logarithm because ten is the number that is raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. If you wanted, you could use two as a base unit. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight: 

log2 8 = 3

because

23 = 8

In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written 

log

and a base ten logarithmic equation is usually written in the form:

log a = r 

A natural logarithm is written

ln

and a natural logarithmic equation is usually written in the form:

ln a = r

So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.

Final answer:

Logarithms are used in Mathematics to solve exponential equations by converting them into linear equations. They involve finding the exponent to which a base must be raised to equal a given number. Properties of logarithms, such as the product and quotient rules, help manipulate and solve logarithmic equations.

Explanation:

Logarithms are mathematical tools used to solve exponential equations and simplify complex calculations. They are the inverse function of exponential functions and help us solve for the unknown exponent in an equation.

Logarithms work by converting exponential equations into linear equations. When we take the logarithm of a number, we are finding the exponent to which a base must be raised to equal that number. For example, the logarithm (base 10) of 100 is 2, because 10 raised to the power of 2 equals 100.

The properties of logarithms allow us to manipulate them to solve equations. Some key properties include:

The expression 2x-3 represent's: The number of songs downloaded by Nicholas.

The variable x represents: The number of songs downloaded by Sabrina.