25 POINTS
On a piece of paper, use a protractor and a ruler to construct △ABC with AB=6 cm, m∠A=80°, and m∠B=50°.

What is AC?

Counting numbers are another name for natural numbers. These are 1, 2, 3, and so forth.

Natural numbers plus zero are whole numbers.

Natural numbers, whole numbers, and the opposites of whole numbers are all considered integers. These numbers range from -3 through -2, -1, 0, 1, 2, 3, etc.

Integers, whole numbers, rational numbers, and numbers that may be expressed as fractions are all considered rational numbers. In this case, fraction [tex]\frac{a}{b}[/tex], where; a and b must both be integers.

All non-rational numbers are categorized as being irrational. These figures cannot be expressed as fractions. This includes decimals like [tex]\pi[/tex], [tex]\sqrt{2}[/tex], and 3.2576352417942 that doesn't end or repeat.

The collection of all rational and irrational numbers, as well as their subsets, is known as the Real Number System.

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The probability to get tails is 0.50.

What is rounding 2decimal place?

The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

The probability of an event is the ratio of the number of outcomes of the required event to the number of total outcome.

In a coin, there are two parts in coins that are tails and heads.

The total number of possible outcomes is 2.

The number of tails of a coin is 1.

The probability to get tails is = 1/2

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Answer:

Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: 3.14 means pi

A linear equation, with five variables, has an infinite number of solutions.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let linear equation:

5 =  x + a + b + c + y

In this equation,

there are five variables, x, a, b, c and y.

And the number of equation is one.

That means,

the number of unknowns > the number of equation

5>1.

Substitute the value of 4 variables to find the value of one variable.

Let, we have to find solutions as subject to y.

We so obtain varied values of y when preserving distinct values of x, a, b, c.

Therefore, infinitely many solutions are possible.

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To find your target heart rate, multiply the percentage of how hard you want to work by your Maximum heart rate and then add your Resting heart rate

To find your target heart rate, you will need to calculate your maximum heart rate and resting heart rate. Maximum heart rate is calculated by subtracting your age from 220. Resting heart rate is your heart rate when you are completely at rest. Once those two values are calculated, you can use the following formula to find your target heart rate:

Target Heart Rate = [(Percentage of How Hard You Want to Work X Maximum Heart Rate) - (Maximum Heart Rate - Resting Heart Rate)] + Resting Heart Rate

For example, if you are 35 years old, your maximum heart rate is 220 - 35 = 185. If your resting heart rate is 60, you can use the following formula to find your target heart rate if you want to work at 70% of your maximum heart rate:

Target Heart Rate = [(0.7 X 185) - (185 - 60)] + 60

Target Heart Rate = 153 bpm

In summary, to find your target heart rate, you will need to calculate your maximum heart rate and resting heart rate and then use the above formula to determine your target heart rate. Knowing your target heart rate will help you monitor your exercise intensity and ensure that you are working out at the appropriate level for your fitness goals.

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The value of 4 to the 3rd power =64

According to the power rule of exponents,

am = m times a x a x a

Thus, 43 can be written as 4 × 4 × 4 = 64.

Thus, the value of 4 to the 3rd power i.e., 4^3 is 64

Exponent is the process of representing huge numbers as powers, according to the definition. Exponent, then, is the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

Answer:

x=4

y= 5

Step-by-step explanation:

6x+y=29

3x-y=7

Let's add them together

9x = 36

x= 4

Then put 4 back in the equation for x

6(4) + y =29

24 + y = 29

y= 5

The complete question should be: What is the per capita personal income for a given state in 2004, represented by the value [?] on the vertical axis of the state table?

The missing value on the vertical axis represented by [?] must be $21,200.

In order to determine the missing value on the vertical axis represented by [?], we need to consider the per capita personal income for each of the states listed in the table. The states are listed in order from highest income to lowest income. The highest-earning state is listed first with a per capita personal income of $52,000. The next-highest-earning state has a per capita personal income of $21,200. Therefore, the missing value on the vertical axis represented by [?] must be $21,200.

To enter this answer, first identify the numerical keypad on the calculator. Then, enter the numerical value of $21,200 (21200) using the keypad. Finally, press the “enter” or “equals” key to submit the answer. This will cause the missing value on the vertical axis to be displayed on the calculator screen.

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Answer:

6138

Step-by-step explanation:

First, we have to find the population of the city in 2015

6% = 0.06

193,000 times 0.06 = 11580 people increase

We know it is increasing, so we have to add them

193,000 + 11580 = 204580 people in 2015

Now let's find the 3% decrease

3% = 0.03

204580 times 0.03 = 6137.4

So, about 6138 people decrease from 2015 to 2020

Answer:

Step-by-step explanation:

The number of events is 5 (since there are 5 red marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%.

(well i'll give it my best shot)

14:17

 ⬇️

let's add 14 and 17 together.

***************

14 + 17 = 31

14 = 14/31 (*fraction*)

17 = 17/31 (*fraction*)

I hope this helps in any way possible.

Merry Christmas (Eve), Happy New Year, and Happy Holidays!

Answer:

C

Step-by-step explanation:

3 [tex]\frac{1}{8}[/tex] ÷ 1 [tex]\frac{5}{8}[/tex] ( change mixed numbers to improper fractions )

= [tex]\frac{25}{8}[/tex] ÷ [tex]\frac{13}{8}[/tex]

to perform the division

leave first, change ÷ to × , turn second fraction ' upside down '

= [tex]\frac{25}{8}[/tex] × [tex]\frac{8}{13}[/tex] ( cancel 8 on numerator/ denominator )

= 25 × [tex]\frac{1}{13}[/tex]

= [tex]\frac{25}{13}[/tex]

= 1 [tex]\frac{12}{13}[/tex]

The discriminant of the equation 3x² - 6x + 5 = 0 is -24

Given,

The equation; 3x² - 6x + 5 = 0

We have to find the discriminant of the equation;

Discriminant of equation;

Any equation with the formula ax2 + bx + c = 0 and an alpha value of 0 is a quadratic equation. The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not.

Here,

a = 3

b = -6

c = 5

Then,

Discriminant, D = b² - 4ac

D = -6² - 4 × 3 × 5

D = 36 - 60

D = -24

That is,

The discriminant of the equation is -24

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The cartesian equation for x = t² and y = 2 + 3t is x = (1/9)y² - (4/9)y + (4/9).

Where the value of A, B, and C are 1/9, - 4/9, and 4/9.

The parameter t that we have

The cartesian equation x = (1/9)y² - (4/9)y + (4/9)

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Answer:

2x² - 3x - 6 = 0

Step-by-step explanation:

the standard form of a quadratic equation is

ax² + bx + c = 0 ( a ≠ 0 )

here a = 2 , b = - 3 and c = - 6 , then

2x² - 3x - 6 = 0 ← in standard form

The value of x in the equation x² = 16 is  ± 4

        Here, x² = 16

        Taking square root on both sides,

        [tex]\sqrt{x^{2} } =\sqrt{16}\\[/tex]

        Simplifying the radicals,

         x = ± 4

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For two variable inequalities which has equal to inequal sign is shown in the graph as a solid line.

An algebraic expression of two variables having equal to inequal sign or inequal sign with it.  such as ≥ and ≤ are equal to inequal sign and < and > are inequal sign.

The way we solve linear equation is similar to solve the inequalities. The inequalities which have equal to inequal sign ≤ or ≥ is plotted on the graph and identify the boundary with solid line.

hence, we indicate an equal to inequality on a graph for variables by solid line.

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The solution of the given system of equations 6x + 2y = 4 , 9x -3 y = 12 is equal to x =1 and y = -1.

As given in the question,

Given system of equations are :

6x + 2y = 4     ____(1)

 9x -3 y = 12   _____(2)

Multiply (1) by 3 and (2) by 2 and add equation (1) and  (2) to eliminate y variable and get the value of variable x ,

18x + 6y = 12

18x - 6y = 24

36x      = 36

⇒x = 36 / 36

⇒ x = 1

Substitute value of x = 1 in the given equation (1) to get the value of variable y,

6(1) + 2y = 4

⇒ 6 + 2y = 4

⇒ 2y = 4 - 6

⇒ y = -1

Therefore, given system of equations 6x + 2y = 4 , 9x -3 y = 12 solution is equal to x = 1 and y = - 1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 6x + 2y = 4 , 9x -3 y = 12?

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Answer:

C. Subtraction Property of Equality

Step-by-step explanation:

The equation is

m<1 + m<2 = m<2 + m<4

m<1 = m<4

We see that is subtraction property, so the answer is C

The Median for the following data 3 445 712 767 will be 578.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sorting of the sample data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Here n = 4, So [4/2 + (4/2)+1}/2, So the median will be 578.5.

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The Median is calculated because it helps us determine where a dataset's "center" is, the median is a crucial measure to compute. It also helps us determine what a dataset's "typical" value is.

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change. The median is the mean of any two numbers that fall in the middle of a dataset.

What are Mean, Median, and Mode?

Different measures of the center in a set of numerical data include mean median and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.

Mean = The result of summing all the data points and dividing by the total number of data points is the "average" value.

Median = Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

Mode = The number that appears the most frequently, or the one that does so most frequently.

So, we can say that the Median is generally calculated to find the center of the given dataset.

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The range of the function f(x) = x² - 6x with domain of (-7, -2, 1) is calculated to be (91, 16, -5)

The domain is controlled by the input values. considering the points (-7, -2, 1)

The range is solved using the given function

f(x) = x^2 - 6x

substituting for x in the function

for x = 7

= 7² - 6 * -7 = 91

for x = -2

= -2² - 6 * -2 = 16

for x = 1

= 1² - 6 * 1 = -5

The range is (91, 16, -5)

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Answer:

  (A)  $26

Step-by-step explanation:

You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.

Let x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.

The given relations tell us ...

  a = 1 + 1/3(x -1)

  b = 6 + 1/3(x -a -6)

  c = x -a -b = 40

Substituting for b gives us ...

  40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4

  44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3

  66 = x -a . . . . . . . . . multiply by 3/2

Substituting for a gives us ...

  66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)

  99 = x -1 . . . . . . . multiply by 3/2

  100 = x . . . . . . add 1

Then ...

  a = 1 + 1/3(100 -1) = 1 + 99/3 = 34

  b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26

Byron received $26.

__

Additional comment

Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.

  Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.

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We are aware that a discrete function is one that satisfies the criteria for a function and has a countable domain (represented as a collection of disconnected points) (each input has at most one output). Many inputs in discrete functions won't have any outputs.

According to the inquiry,

All three of the functions have a y-intercept and, given the facts in the question, f(x) is the highest maximum.

The largest maximum of the three functions—g(x), f(x), and f(y)—has an x-intercept.

Three distinct discrete functions are displayed in the table.

f(x)minimum: 1 g(x)minimum; -4 12 h(x)minimum-5; as a result, f(x)maximum: 10 g(x)maximum; 3 12 h(x)maximum; 12 f(x)domain; (0, 2) g(x)domain; (-2, 2) h(x)domain; (0, 1) g(x)y-inter (0, -5)

Using the procedures above, we may conclude that f(x) has no x.

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The two important first steps in data analysis are data cleaning and exploring it, so, option A is correct.

A measure of the relationship between two variables is a correlation. Variables can be related in a number of ways, including linearly, non-linearly, and in other ways. Variables can also have varying degrees of association with one another. The most popular linear coefficient used to determine how closely two variables correlate is called Pearson's correlation coefficient, or PCC.

The steps of data analysis are shown below,

First, define the question. Identifying your purpose is the first stage in any data analysis procedure.

Gathering the data is the second step.

Third step: data cleaning.

The fourth step is data analysis.

Five: Present your findings.

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If you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Consequently, if you have three side lengths, you should discover the lowest angle by finding the angle that is opposite the smallest side, the medium-sized angle by finding the angle that is opposite the medium-sized side, and the greatest angle by finding the angle that is opposite the largest side.

Therefore, if you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

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