If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?​

The lengths of the two segments below then tell whether they are congruent

YZ = 4

XW = 12

not congruent

This is further explained below.

Generally, A number line is a depiction of a graded straight line that serves as an abstraction for real numbers, which are symbolized by the

Number lines are used in introductory mathematics. It is generally accepted that a real number may be assigned to each point on a number line and that each point can be assigned to a real number.

YZ = Z - Y = 1 -(-3) = 4

XW = W -X = 5 -(-7) = 12

Because the segments are not the same length, they cannot be considered congruent.

In conclusion, It is self-evident that segment YZ will not have the same length as segment XW since it is just a portion of the latter.

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Answer:

19

Step-by-step explanation:

Answer:

100 ft.

Step-by-step explanation:

Let x = height of tree

height/height = shadow length/shadow length

5/x = 2/40

2x = 200

x = 100 ft.

Answer:

B. (3, 14).

Step-by-step explanation:

Substitution means that you first solve for one variable, and then use that solution to find the other.

For example, if x = y, and x + 5 = 7, you can say that y + 5 = 7.

Now, moving on to the actual problem.

The first equation says that y = 6x - 4, and the second equation says y = 7x - 7.

That means for the first equation, instead of y, it is valid to say that 7x - 7 = 6x - 4.

7x - 7 = 6x - 4

7x - 6x = -4 + 7

x = 3.

You could put the x=3 into the y = 7x - 7 equation to find what the y-coordinate is.

y = 7 * 3 - 7

y = 21 - 7

y = 14.

And there you have your coordinates! (3, 14).

Hope this helps!

Answer:

Step-by-step explanation:

The chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic if the expected frequency in each cell is at least 5.

The chi-square statistic is a measure of how different an observed frequency is from the expected frequency. It is calculated by taking the difference between the observed and expected frequency in each cell, squaring it, and then summing the results. This measure can then be compared to a chi-square distribution with degrees of freedom equal to the number of cells minus one. If the calculated statistic is larger than the expected value from the chi-square distribution, then it can be concluded that the observed frequency differs significantly from the expected frequency.
In order to use the chi-square approximation, it is important that the expected frequency in each cell is at least 5. This is because the chi-square approximation only works well when there are large expected frequencies. When expected frequencies are smaller than 5, the chi-square statistic is not an accurate measure of the difference between the observed and expected frequencies.

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Answer:

It is growth and the percentage rate of increase is 7.5%

Step-by-step explanation:

The exponential equation is as follows;

y = 550(1.075)^x

Now, I can identify that the exponential equation is that of growth.

This is because what is in the bracket i.e can be represented as 1+ 0.075

The 0.075 represents the margin of increase as we move on from one value to another

The percentage rate can be gotten by expressing 0.075 as a percentage

That would be expressing is as a fraction

This is just 7.5/100 which means what we have is 7.5%

The proof starts by assuming n is a composite integer and proceeds to show that there must exist a prime divisor of n that is less than or equal to √n by contradiction.

To produce a proof that if n is a composite integer, then n has a prime divisor less than or equal to √n, the steps should be arranged in the following order:

Assume n is a composite integer.

Express n as a product of its prime factors.

Suppose all prime factors of n are greater than √n.

Take the product of all prime factors of n.

The product obtained in step 4 is greater than n.

This contradicts the fact that n is a composite integer.

Therefore, the assumption made in step 3 is false.

There must exist at least one prime factor of n that is less than or equal to √n.

Hence, if n is a composite integer, then n has a prime divisor less than or equal to √n.


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Answer:

\((513 + 391) \div (2013 - 339) \\ \\ 904 \div 1674 \\ \\ = 0.5400\)

This statement is False as the probability of intersection of two events is always less than the probability of union.

This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.

The chance of two events A and B occurring together can be calculated using the following formula to see why:

According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.

When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:

Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.

P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:

This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.

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Answer:

\(2.28*10^7\)

Step-by-step explanation:

\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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He have 48 different possible outfits to wear at work with three one-piece jump suits, five pairs of work pants, and eight work shirts.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that.

Here,

5 pants with each of 8 shirts,

=5 x 8

=40 combinations of shirts and pants.

40 shirt/pants outfits + 8 jumpsuits = 48 total outfits.

With three one-piece jumpsuits, five pairs of work pants, and eight work shirts, he has 48 different work-appropriate outfit options.

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a) Using the Avrami equation with n = 1.2 and 90% completion in 180 seconds, the parameter k is found to be approximately 0.00397. b) The rate of transformation, r, is approximately 0.0367 per second.


a) The Avrami equation is given by the equation t = k * (1 – exp(-r^n)), where t is the transformation time, k is a parameter, r is the rate of transformation, and n is a constant (in this case, n = 1.2). Given t = 180 seconds and the transformation is 90% complete, we can rearrange the equation to solve for k: k = t / (1 – exp(-r^n)). By substituting the values, we find k ≈ 0.00397.
b) To determine the rate of transformation, we can rearrange the Avrami equation and solve for r: r = (-ln(1 – (t / k)))^(1/n). Plugging in the values t = 180 seconds and k ≈ 0.00397, and n = 1.2, we can calculate r ≈ 0.0367 per second. This represents the rate at which the transformation progresses per unit time.

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Answer: angle BCD is 77°

Step-by-step explanation:

       BDC+CDA=119°

-5x+52°-2x+32°=119°

            -7x+84°=119°

                   -7x=35°

                      x=-5°

Then substitute x in the equation for BDC

-5(-5)+52°=BDC

   25+52°=BDC

       BDC=77°

Answer:

3

Step-by-step explanation:

is the input (which is the 'x' coordinate) is 3 then the output (or 'y' coordinate is 3

Answer:

\(x=-4,\:x=-5\)

Step-by-step explanation:

\(x^2+9x+20=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}x^2+9x+20:\quad \left(x+4\right)\left(x+5\right)\\\\\left(x+4\right)\left(x+5\right)=0\\\\Using\:the\:Zero\:Factor\:Principle:\\\quad\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\\\mathrm{Solve\:}\:x+4=0:\quad x=-4\\\\\mathrm{Solve\:}\:x+5=0:\quad x=-5\\\\x=-4,\:x=-5\)

Answer:

Factored form: (x+4)(x+5) = 0

x = -5 or -4

Step-by-step explanation:

To factor x^2 + 9x + 20, we need to find 2 numbers that multiply to 20 and add up to 9.

The reason for that is because when you multiply (x+a)(x+b) using FOIL, you will get x^2 + ax + bx + ab.

Anyway, 4 and 5 would satisfy this, because 4+5 = 9 and 4*5 = 20. We can then factor the equation to (x+4)(x+5).

To solve (x+4)(x+5) = 0, we need to make either x+4 = 0 or x+5 = 0. That means x can be either -5 or -4.

Answer:

$65

Step-by-step explanation:

50 x 0.30

= 15

50 + 15

= 65

Herman Hollerith proposed the use of punched cards for counting the census.

The punched card system for counting the census was proposed by Herman Hollerith. Hollerith was an American inventor and statistician who developed the punched card tabulating machine. He presented his idea in the late 19th century as a solution to the challenge of processing and analyzing large amounts of data efficiently.

Hollerith's system involved encoding information on individual cards using punched holes to represent different data points. These cards were then processed by machines that could read and interpret the holes, enabling the automatic counting and sorting of data. The punched card system revolutionized data processing, making it faster and more accurate than manual methods.

Hollerith's invention laid the foundation for modern computer data processing techniques and was widely adopted, particularly by government agencies for tasks like the census. His company eventually became part of IBM, which continued to develop and refine punched card technology.

In summary, Herman Hollerith proposed the use of punched cards for counting the census. His invention revolutionized data processing and laid the groundwork for modern computer systems.

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To determine the resulting scale of the photomap and the area it will cover in hectares, we need to consider the given information.

Enlargement of Aerial Photo: The aerial photo is being enlarged from a 23 cm square format to an 80 cm square format. This means the dimensions of the photo are being increased by a scale factor of (80/23). To calculate the resulting scale of the photomap, we can use the concept of similar triangles. The ratio of corresponding sides of similar triangles is equal to the ratio of their corresponding dimensions.  Scale factor = (Focal length of camera) / (Altitude of Lear Jet) Scale factor = 152 mm / 12,200,000 mm (12.2 km = 12,200,000 mm) Scale factor = 1/80,263 This means that one unit on the photomap represents 80,263 units in the actual area. Area in hectares = 6400 cm^2 / 10,000 = 0.64 hectares

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The maximum value of the periodic function is 11.

The amplitude of a periodic function represents the maximum distance from the average value or the midline. In this case, the given function has an amplitude of 14, which means it oscillates between a maximum value and a minimum value, each differing by 14 units.

The minimum value of the function is -3. Since the amplitude is 14, we can determine the maximum value by adding the amplitude to the minimum value. Thus, the maximum value is obtained by adding 14 to -3:

Maximum value = -3 + 14 = 11

Therefore, the maximum value of the periodic function is 11.

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The probability that both people own a dog is approximately 0.4096, or 40.96%.

To solve this problem, we can use the formula for calculating the probability of the intersection of two independent events: P(A and B) = P(A) x P(B).

Let's define A as the event that the first person owns a dog, and B as the event that the second person owns a dog. Since the two people are chosen at random, we can assume that these events are independent.

According to the problem, P(A) = P(B) = 0.64, since 64% of people own dogs. Therefore, the probability of both events occurring is:

P(A and B) = P(A) x P(B) = 0.64 x 0.64 = 0.4096

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Answer:

False

Step-by-step explanation:

Lines that intersect at right angles are called parallel. False

They are called intersecting lines.

Answer:

False

Step-by-step explanation:

This is false, lines that are always the same distance apart and never intersect are paralle. Line that intersect at a right angle are called perpendicular. See the image.

Answer:

Step-by-step explanation:

First, we have to find 14% of 56

14% of 56 is = 56 x 14/100

                  = 7.84

Now we have to increase the number 56 by 14%, which means we have to add 14% of 56 (7.84) to the given number (56)  

56 + (14% of 56)

= 56 + 7.84

= £63.84

Answer:

j = 35 - k

35 = j + k

k = 35 - j

(the 2nd, 3rd, and 4th one)

In addition to premises, warrants, and conclusions, two additional elements of rhetorical argument are evidence and counterarguments.

The two additional elements of rhetorical argument are evidence and counterarguments.

Evidence refers to the supporting material or proof that is presented to back up the premises and warrants in an argument. This can include statistics, facts, expert testimony, or personal experiences.

Counterarguments are the opposing viewpoints or objections that may arise in response to the argument. By addressing and refuting potential counterarguments, the speaker or writer strengthens their own argument and shows that they have considered multiple perspectives on the issue at hand.

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The difference between the number of heads and the number of tails in 100 coin tosses follows the distribution of a box (i, ii, iii, iv, v). The expected value for the difference can be calculated, as well as the standard error.

(a) The difference "number of heads − number of tails" in 100 coin tosses follows the distribution of Box (ii). The box represents the sum of 100 draws, which corresponds to the number of times the coin lands on heads or tails. Each box represents a different distribution, and in this case, Box (ii) accurately models the difference.

(b) To find the expected value for the difference, we need to consider that the coin has an equal probability of landing on heads or tails. In 100 tosses, the expected value is half of the total tosses, which is 50. So, the expected value for the difference between the number of heads and the number of tails is 50.

(c) The standard error for the difference can be calculated as the square root of the variance. In this case, since the coin tosses are independent and have the same probability, the variance is equal to the number of tosses divided by 4. Therefore, the standard error is the square root of 100 divided by 4, which is 5.

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Answer:

y=-1/4x-9/4

Step-by-step explanation:

Answer:

 g(x) = f(5x)

Step-by-step explanation:

We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).

Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...

 g(x) = f(x/(1/5))

 g(x) = f(5x)