For any real number a, \(\sqrt{a^{2} }\)=

The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

Answer:

\( b = {a}^{2} - 6\)

Step-by-step explanation:

\(a = \sqrt{b + 6} \\ squaring \: both \: sides \\ {a}^{2} = {( \sqrt{b + 6)} }^{2} \\ {a}^{2} = b + 6 \\ {a}^{2} - 6 = b \\ \huge \purple { \boxed{ b = {a}^{2} - 6}}\)

Answer:

b= a^2-6

Step-by-step explanation:

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Hope it helps :)

The second differences for the relation is -2 which is option A.

To find the second differences, we need to calculate the difference between consecutive differences of the 'y' values in the given relation.

First, let's calculate the first differences:

-9 - (-4) = -5

-4 - (-1) = -3

-1 - 0 = -1

0 - (-1) = 1

-1 - (-4) = 3

-4 - (-9) = 5

Now, let's calculate the second differences:

-5 - (-3) = -2

-3 - (-1) = -2

-1 - 1 = -2

1 - 3 = -2

3 - 5 = -2

The second differences for the given relation are all -2.

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Answer:

\(\frac{-2}{3}\)

Step-by-step explanation:

to find the slope of linear line, you need two points.  It does not matter which pints you use.  I am going to use (0,5) and (3,3)  The slope is the change in y over the change is x.  Our y values are 3 and 5.  Our x values are 3 and 0

\(\frac{3-5}{3-0}\) = \(\frac{-2}{3}\)

Answer:

b = 10

Step-by-step explanation:

"7b - 2" is supplementary to "3b + 2"

7b - 2 + 3b + 2 = 180

7b + 3b - 2 + 2 = 180

10b + 0 = 180

10b/10 - 180/10

b = 18

Answer:

The answer is

Step-by-step explanation:

Usng the formula

\(A(n) = 3(2) ^{n - 1} \)

Where n is the number of terms

For the first term

\(A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3\)

For the fourth term

\(A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24\)

For the eighth term

\(A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384\)

Hope this helps you

Answer: –3; –24; –384

Step-by-step explanation:

Answer:

The estimated number of bacteria after 20 hours is 40.

Step-by-step explanation:

This is a case where a geometrical progression is reported, which is a particular case of exponential growth and is defined by the following formula:

\(n(t) = n_{o}\cdot \left(1+\frac{r}{100} \right)^{t}\) (1)

Where:

\(n_{o}\) - Initial number of bacteria, dimensionless.

\(r\) - Increase growth of the experiment, expressed in percentage.

\(t\) - Time, measured in hours.

\(n(t)\) - Current number of bacteria, dimensionless.

If we know that \(n_{o} = 30\), \(r = 1.4\) and \(t = 20\,h\), then the number of bacteria after 20 hours is:

\(n(t) = 30\cdot \left(1+\frac{1.4}{100} \right)^{20}\)

\(n(t) \approx 39.616\)

\(n(t) = 40\)

The estimated number of bacteria after 20 hours is 40.

Answer: 8/3 and -9/4

Step-by-step explanation:

1. \(\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}\)

2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.

\(-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}\)

Answer:

28 tablespoons of olive oil

16 tablespoons of balsamic vinegar

Step-by-step explanation:

Olive oil : Balsamic vinegar

        7/3 : 8/6

Add them together:   7/3 + 8/6 = 11/3

Divide the total (44 tablespoons) by sum of ratios:  44 ÷ 11/3 = 12

Therefore, the scale factor = 12

Now multiply the ratios by the scale factors:

12 x 7/3 = 28 tablespoons of olive oil

12 x 8/6 = 16 tablespoons of balsamic vinegar

Using the distributive property, 3(50.15) can be simplified to 150.45 by multiplying 3 with each term inside the parentheses.

The distributive property is a fundamental concept in mathematics, explains how multiplication distributes over addition or subtraction. It says that you can distribute or apply the multiplication to each term inside the parentheses separately when you multiply a number by a sum or difference enclosed in parentheses.

expression: 3(50.15)

apply the distributive property, which states that a number outside parentheses can be multiplied by each term inside the parentheses.

Multiply 3 by 50.15.

3 × 50.15 = 150.45

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The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

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Answer:

dat easy

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

This can be rearranged as 4^3 * 1/(4^6)

or (4^3)/(4^6)

This can be changed to:

(4^3)/((4^3)*(4^3)

Which is equal to 1/(4^3)

or

4^(-3)

The value of c in the triangle is (b) 5 units

From the question, we have the following parameters that can be used in our computation:

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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Answer:

3 and 9

Step-by-step explanation:

x+y=12

y-x=6

y-x=6

 +x.  +x

y=6+x

x+(6+x)=12

6+2x=12

-6.    -6

2x=6

/2. /2

x=3

3+y=12

-3.  -3

y=9

Hopes this helps please mark brainliest

Answer:

\(\displaystyle (x-3)^2 + (y+2)^2 = 36\)

Step-by-step explanation:

We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.

Recall that the equation of a circle is given by:

\(\displaystyle (x-h)^2 + (y-k)^2 = r^2\)

Where (h, k) is the center and r is the radius.

Since our center is at (3, -2), h = 3 and k = -2. r = 6. Substitute:

\(\displaystyle (x-(3))^2 +(y-(-2))^2 = (6)^2\)

Simplify:

\(\displaystyle (x-3)^2 + (y+2)^2 = 36\)

In conclusion, the equation of the circle will be:

\(\displaystyle (x-3)^2 + (y+2)^2 = 36\)

Answer:

0.3125

Step-by-step explanation:

5/16 as a fraction

2r+r+s+2s =2×r + r×1 + s×1 + 2×s

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

2r+r+s+2s

=2×r + r×1 + s×1 + 2×s

Hence,

each sum as the product of two factors 2r+r+s+2s =2×r + r×1 + s×1 + 2×s

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer: An = 114 + (n - 1)-6

Step-by-step explanation:

Per 5 weeks there is  reduction of 30 patients. Divide by the common factor (5) and you see that per 1 week, there is a reduction of 6 patients. Going back in time to see what the first term was, you can create a explicit formula for this  function.

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Answer:

f(x) = −6x + 120

Step-by-step explanation:

I JUST TOOK THE TEST

Answer:

-22.3% or 22.3% less than the previous year

Step-by-step explanation:

350 - 272 = 78

78/350 = 22.3 to 3 significant figures

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

3 rd options is correct