1. Prove that at any party of 31 people, there’s always a person who knows an even number of others. (Assume that acquaintance is mutual: if Alice knows Zelda, then Zelda knows Alice.)

The binary expansion 1100101 base 2 can be converted to base 4 and base 10. In base 4, the expansion is 313 and in base 10, it is 101.

To convert the binary expansion 1100101 base 2 to base 4, we group the binary digits into pairs from right to left. Starting from the rightmost pair, we convert each pair to its equivalent base 4 digit. In this case, the pairs are 01, 01, 10, and 11, which correspond to the base 4 digits 1, 1, 3, and 3, respectively. So the base 4 expansion is 313.

To convert the binary expansion 1100101 base 2 to base 10, we can use the positional value system. Each binary digit represents a power of 2. Starting from the rightmost digit, we assign powers of 2 to each digit in increasing order from right to left. In this case, the digits are 1, 0, 1, 0, 0, 1, and 1, which correspond to the powers of 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, and 2^0, respectively. Evaluating these powers of 2, we get 64, 0, 16, 0, 0, 2, and 1. we obtain 64 + 0 + 16 + 0 + 0 + 2 + 1 = 101 in base 10.

Therefore, the binary expansion 1100101 base 2 is equivalent to 313 base 4 and 101 base 10.

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Answer:

answer is a

Step-by-step explanation:

first solve

solve for gcf

flip

divide

then you add

and you get 0.928838

Answer:

+100 nasan yung tanong ah

Answer:

[tex]\frac{5}{13}[/tex]

Step-by-step explanation:

sine of A = [tex]\frac{opposite}{hypotenuse}[/tex]

opposite = 5

adjacent = 12

hypotenuse = 13

Answer:

C.) 12/13

Explanation:

trust me

Answer:

I can't see the whole picture, but if it's half of the circle, it's the radius. if the line goes all the way through the circle, it's the diameter

Answer:

I think it’s the diameter

Step-by-step explanation:

Answer:

opposite of 55 degrees would be KL

opposite of 97 degrees would be ML

opposite of 28 degrees would be MK

Step-by-step explanation:

mark me brainliest if right!!!

Answer:

[tex]15 x = 6.60[/tex]

[tex]x = 44\ hundredths[/tex]

Step-by-step explanation:

Given

[tex]\frac{6.60}{15}[/tex]

Required

Complete the model

[ ] x = 6.60

x = _ hundredths

[tex]\frac{6.60}{15}[/tex]

Equate to x

[tex]x = \frac{6.60}{15}[/tex]

Multiply both sides by 15

[tex]15 * x = \frac{6.60}{15} * 15[/tex]

[tex]15 * x = 6.60[/tex]

[tex]15 x = 6.60[/tex]

So, we have:

[ ] x = 6.60 =====> [tex]15 x = 6.60[/tex]

Recall that:

[tex]x = \frac{6.60}{15}[/tex]

[tex]x = 0.44[/tex]

This implies that:

[tex]x = 44\ hundredths[/tex]

Hence:

x = _ hundredths =====> [tex]x = 44\ hundredths[/tex]

Answer:

1/30 ton of rock left

Step-by-step explanation:

1/3+ 1/2= 5/6

5/6 - 4/5= 1/30 ton of rock left at the construction site.

Answer:

y= -1/3x + 13/3

Step-by-step explanation:

we can find the equation of the line thanks to this formula

y-y1 = m(x-x1) where y1 and x1 indicate the coordinates of the point, while m indicates the slope

y-2 = -1/3(x-7)

y = -1/3x+7/3+2

y= -1/3x + (7+6)/3

y = -1/3x+13/3

Answer:

He should have done 8^2 + 15^2= x^2 because the hypotenuse is always the longest side and in Pythagorean theorem C represents the longest side

[tex] {x}^{2} = {(8)}^{2} + {(15)}^{2} [/tex]

[tex] {x}^{2} = 64 + 225[/tex]

[tex] {x}^{2} = 289[/tex]

[tex]x = \sqrt{289} [/tex]

[tex]x = 17[/tex]

The two alternative formulations of the OLS regressions have differences in their parameter estimates and interpretations. The first model can be represented as: inci = Be + B1edi + B2sexi + εi, where sexi equals 1 for males and 0 for females. The second model is given by: inci = a0 + a1edi + a2sexi + ei, where sexi equals 0 for males and 1 for females.

The first model, the intercept term B0 represents the average income earned by men (when sexi equals zero) who have no education. The coefficient B1 represents the increase in income for each additional year of education. B2 represents the average difference in income between men and women when education is the same. Thus, B2 is the coefficient of the dummy variable for sex.In the second model, a0 represents the average income earned by women (when sexi equals one) who have no education. a1 represents the increase in income for each additional year of education, and a2 represents the average difference in income between men and women when education is the same. Thus, a2 is the coefficient of the dummy variable for sex.The interpretation of the coefficients is different between the two models. In the first model, B2 represents the average difference in income between men and women. In the second model, a2 represents the average difference in income between women and men. Thus, the coefficients of the dummy variable for sex have opposite signs and different interpretations. Also, the intercept terms in the two models are different, which reflects the difference in the average income earned by men and women in the two models. The parameter estimates from the OLS regressions for these alternative formulations will differ as well.

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Answer:

A.   52°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc.

m∠B = 1/2 (m of arc AC)

26 = 1/2 (m of arc AC)

52 = (m of arc AC)

18 cm is correct .

Step-by-step explanation:

The sum of two smaller sides is greater that the largest side.

It is given that the two sides of a triangle measure 8 cm and 15 cm.

Case 1: Let 8 cm and 15 cm. are smaller side. So,

Third side < 8 + 15

Third side < 23

It means 3rd side must be less than 23

Case 2: Let 15 cm is the largest side.

15 < Third side + 8

15 - 8 < Third side

7 < Third side

It means 3rd side must be greater than 7.

Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Savings account:

PV= $1,000

n= 1

i= 0.045

Fixed Deposit:

PV= $1,000

n= 1

i= 0.06

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

Savings account:

FV= 1,000*1.045^1

FV= $1,045

Fixed deposit:

FV= 1,000*1.06^1

FV= $1,060

The Answer is:

−72 r + 755

Answer:

-72r + 755

Step-by-step explanation:

-8(9r – 1) – 9(-85 + 2)

-72r + 8 - 9(-83)

-72r + 8 + 747

-72r + 755

Answer:

B: 6.5 inches

Step-by-step explanation:

Given,  

Area of the rectangle = 45.5 sq. inches  

The Base of the rectangle = 7 inches  

45.5 = l * 7  

l = 45.5/7

l = 6.5 inches

Answer:

silly billy your a tree with branches and leaves hogwarts has an olw that deleivers letters

Step-by-step explanation:

Therefore, the margin of error of a 98% confidence interval estimate of the percentage of the population that favor free tuition is 4.2%.

The margin of error is the difference between the sample statistic and the population parameter. It shows how much the sample result can deviate from the actual population parameter.Here, the sample size n = 750, and the proportion of adults in the US who favor free tuition for four-year colleges is p = 330/750 = 0.44.Using the z-distribution, we can calculate the margin of error for the 98% confidence interval as follows:zα/2 = z0.01/2 = 2.33margin of error = zα/2 * √(p(1-p)/n)margin of error = 2.33 * √(0.44(1-0.44)/750)margin of error ≈ 0.042 or 4.2%Therefore, the margin of error of a 98% confidence interval estimate of the percentage of the population that favor free tuition is 4.2%.

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Answer:

(1, - 1)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The lines intersect at (1, - 1)

Then (1, - 1 ) is the solution to the system.

Answer:

it could also be [tex]\frac{20}{4}[/tex] or [tex]\frac{10}{2}[/tex]

Step-by-step explanation:

Simplify.

[tex]\frac{40}{8}[/tex] ÷ 2 = [tex]\frac{20}{4}[/tex]

[tex]\frac{20}{4}[/tex] ÷ 2 = [tex]\frac{10}{2}[/tex]

To determine the probability of selecting a card that is less than 8 or a club from a standard deck of cards, we need to consider the number of favorable outcomes and the total number of possible outcomes.

First, let's calculate the number of cards that are less than 8. There are four suits (hearts, diamonds, clubs, and spades), and each suit has cards numbered 2 through 7. So, there are 4 suits * 6 cards per suit = 24 cards that are less than 8.

Next, let's calculate the number of clubs in the deck. There are 13 cards in each suit, and one of those suits is clubs. Therefore, there are 13 clubs in the deck.

To find the probability, we add the number of favorable outcomes (cards less than 8 or clubs) and divide it by the total number of possible outcomes (52 cards in a deck).

Probability = (24 + 13) / 52 = 37 / 52 ≈ 0.7115

Therefore, the probability of selecting a card that is less than 8 or a club is approximately 0.7115 or 71.15%.

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Answer:

Yes it is

Step-by-step explanation:

It passes the vertical line test.

yes,Pi is 3.142 or 22/7

Step-by-step explanation:

22/7=3.14285714

Answer:

round 55666777 for 5th 50th is not a big game for a player who will give the 8th or 3rd season to 466

When you multiply the numerator and denominator of a fraction by the same number, you are effectively scaling up or scaling down the fraction without changing its value. The math drawing demonstrates how the number of parts and the size of the parts change, while still representing the same amount, thus showing why the two fractions are equal.

To explain why multiplying the numerator and denominator of a fraction by the same number results in an equivalent fraction, let's use the example you provided: 2/4.

First, let's understand the concept of a fraction. A fraction represents a part of a whole. The numerator represents the number of parts we have, and the denominator represents the total number of equal parts that make up the whole.

In the given example, 2/4, the numerator is 2, indicating that we have 2 parts out of a total of 4 equal parts. The denominator tells us that the whole is divided into 4 equal parts.

Now, let's say we want to multiply both the numerator and denominator by the same number, let's say 4. The new fraction becomes (2 * 4) / (4 * 4), which simplifies to 8/16.

Let's visualize this using a math drawing. Consider a rectangular shape representing the whole, divided into 16 equal parts, like a grid of squares, with 8 of those squares shaded. This represents the fraction 8/16.

Now, let's compare this to the original fraction, 2/4. If we draw a rectangle divided into 4 equal parts, and shade 2 of those parts, we can see that it represents the same amount as the fraction 8/16. By multiplying both the numerator and denominator by 4, we have essentially scaled up the size of each part and increased the number of parts.

Visually, the original fraction of 2/4 had fewer total parts (4) but larger-sized parts, while the equivalent fraction of 8/16 had more total parts (16) but smaller-sized parts. However, the total shaded area in both cases remains the same, which indicates that the fractions are equal.

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Answer:

30

Step-by-step explanation:

30

The mean, median, and mode of the given monthly salary is 1794, 1790, and 1940, respectively.

Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.

Mode: It is the most common value in a given data set.

Median: In an ordered data set, the median is the number in the middle.

Mean: It is the total number of values divided by the sum of all values.

For the given data, the mean, median and the mode of the data can be found as shown below,

Sum of the Observations

= 1940 + 1660 + 1860 + 2100 + 1720 + 1540 + 1760 + 1940 + 1820 + 1600

= 17940

Number of Observations = 10

The mean of the data is,

Mean = Sum of Observations / Number of Observations

          = 17940 / 10  
          = 1794

The median of the data can be found by arranging the data in an order first. Therefore, the data can be arranged as,

The median of the data is,

Median = (Sum of the two mid values) / 2

             = (1760 + 1820) / 2

             = 1790

The mode of the data is 1940, since this is repeated twice.

b.

If the salary of each employee is increased by 5% that means that the value of each observation in the data will increase by 5%. Therefore, The raise increases the mean, median, and mode by 5% each.

c.

As it is now required to find the mean, median, and mode of the annual salary; there is a need to multiply the monthly salary of each employee by 12. Therefore, the value of each observation will be 12 times its original value. These values are 12 times the mean median, and mode of the monthly salaries.

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The answer is arg 2 = tan^-1(3/2) where : = (a + ai)(b + b/3i) where a and b are positive real numbers.

To determine arg 2, we need to first find the value of :.

Expanding the given expression, we get:

: = (a + ai)(b + b/3i)

: = ab + ab/3i^2 + abi + ab/3i

: = ab - ab/3 + abi + ab/3i

: = (2ab/3) + (ab)i

Now, we can find the modulus of : as:

|:| = sqrt((2ab/3)^2 + (ab)^2)

|:| = sqrt(4a^2b^2/9 + a^2b^2)

|:| = sqrt(13a^2b^2/9)

And, we can find the argument of : as:

arg(:) = tan^-1((ab)/(2ab/3))

arg(:) = tan^-1(3/2)

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Answer:

61

Step-by-step explanation: