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The simplified form of the given radicals is -23

From the question, we are to combine the given radicals

The given radicals are

\(-3\sqrt{81} +\sqrt{16}\)

NOTE: \(\sqrt{81 }= 9\) and \(\sqrt{16} = 4\)

∴ \(-3\sqrt{81} +\sqrt{16}\) becomes

-3(9) + 4

= -27 + 4

= -23

Hence, the simplified form of the given radicals is -23

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The student researcher can determine if the standard deviations are significantly different and if the new analytical method can be considered a replacement for the conventional method with the specified confidence level.

To determine if the standard deviations are significantly different, we calculate the F value using the formula F = (s1^2 / s2^2), where s1 and s2 are the standard deviations of Method 1 and Method 2, respectively. In this case, s1 = 0.160 ppm and s2 = 0.110 ppm.

We then compare the calculated F value to the critical F value from the F distribution table at the 95% confidence level. If the calculated F value is greater than the critical F value, it indicates that the standard deviations are significantly different.

To compare the data sets from Method 1 and Method 2, we calculate the t calc value using the formula t calc = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2)), where X1 and X2 are the means of Method 1 and Method 2, respectively, and n1 and n2 are the number of replicate measurements. In this case, X1 = 4.210 ppm, X2 = 4.360 ppm, n1 = n2 = 6.

The calculated t calc value is then compared to the critical t value from the Student's t distribution table at the desired confidence level (99% in this case). If the calculated t calc value is greater than the critical t value, the student researcher can assert with confidence that the new analytical method can be considered a replacement for the conventional method.

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Answer:

The correct equation will be "\(\frac{x^2}{(1466)^2} +\frac{y^2}{(1953)^2} =1\)".

Step-by-step explanation:

In the above question, the figure is missing. Please find below the attachment of the figure.

According to the question,

Radius of a moon,

r = 1000 km

The max. distance from moon's surface to the satellite,

a = 953 km

The min. distance from moon's surface to the satellite,

b = 466 km

Now,

As per the question or the diagram,

⇒ \(a_1=a+r\)

        \(=953+1000\)

        \(=1953 \ km\)

⇒ \(b_1=b+r\)

        \(=466+1000\)

        \(=1466 \ km\)

hence,

The equation of ellipse will be:

⇒ \(\frac{x^2}{b_1^2} +\frac{y^2}{a_1^2} =1\)

On substituting all the values, we get

⇒ \(\frac{x^2}{(1466)^2} +\frac{y^2}{(1953)^2} =1\)          

Let's try to understand how we can solve this equation

Given equation,4f+2=6f-12

Now we will take the terms on one side and constants on the other.

=> 2+12=6f-4f

=> 14=2f

=>7=f

So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.

a) Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b) Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c) Both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities

a. Angular velocity is defined as the rate of change of angular displacement. It is given by the formula:

ω = v / r

where ω is the angular velocity, v is the tangential velocity, and r is the radius of the curve.

For Elaine: ω = 4.2 m/s / 17.3 m = 0.242 rad/s

For Tori: ω = 4.6 m/s / 34.6 m = 0.133 rad/s

Since Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b. Centripetal acceleration is the acceleration directed towards the center of the circular path. It is given by the formula:

a = ω^2 * r

where a is the centripetal acceleration, ω is the angular velocity, and r is the radius of the curve.

For Elaine: a = (0.242 rad/s)^2 * 17.3 m = 0.099 m/s^2

For Tori: a = (0.133 rad/s)^2 * 34.6 m = 0.622 m/s^2

Since Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c. The centripetal acceleration remains the same regardless of the angular velocity. It only depends on the radius of the curve. Therefore, both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Energy consumption is the amount of power used over time, measured in watt-hours (Wh) or kilowatt-hours (kWh). It is calculated by multiplying the power (measured in watts) by the time for which it is used.

To calculate energy consumption, you will need to know the amount of power being used and the time over which it is being used. Power is typically measured in watts (W), and energy is the product of power and time, so energy consumption is the number of watts used multiplied by the number of hours for which they are used.

For example, let's say you want to calculate the energy consumption of a light bulb that uses 60 W of power and is left on for 4 hours. The energy consumption would be:

Energy consumption = 60 W * 4 hours = 240 Wh (watt-hours)

This is the amount of energy that the light bulb used over the 4-hour period.

You can also convert watt-hours to other units of energy, such as kilowatt-hours (kWh). To do this, you would divide the watt-hours by 1,000. In the example above, the energy consumption would be 0.240 kWh.

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The design that resulted in the shortest line is the one that minimized the distance between the start and end points.

This can be achieved by using a straight line design, as it is the shortest distance between two points. In other words, the shortest line design is the one that does not have any curves or detours, and instead goes directly from the start point to the end point. This is because the shortest distance between two points is always a straight line, and any other design would result in a longer line. Therefore, the design that resulted in the shortest line is the one that used a straight line.

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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According to the given data we have the following equation:

2b-9=5b+6

To solve the variable b of the equation we would make the following:

2b-9=5b+6

First move the variable 5b to the left side, and -9 to the right side.

So:

2b-5b=6+9

Next, add all the elements

-3b=15

Finally calculate b by dividing 15/-3

b=15/-3

b=-5

Therefore, if the variable b=-5, hence check:

2b-9=5b+6

2(-5)-9=5(-5)+6

-10-9=-25+6

-19=-19

The correct statement regarding the sentence square root of 49 = 7 is given as follows:

C. 7 is the length of the side of a square whose area is 49.

Considering a square of side length s, we have that the area and the perimeter of the square are given as follows:

In the context of this problem, the expression is given as follows:

square root of 49 = 7.

For a square with area of 49 units squared, the side length is obtained as follows:

s² = 49

s = square root of 49

s = 7.

Which means that option C is the correct option.

The problem is given by the image shown at the end of the answer.

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Answer:

y = -x

Step-by-step explanation:

Answers 1 and 4 have an offset (+2 and -1) that interferes.  x = 2 is not a proportion.  It is simply a statement that x = 2.  It is not allowed in the high stakes room.

The Function Header includes the name of the function .

it tells us  what type of data it expects to receive and the type of data it will return to the calling function or program.

The body of the function contains the instructions to be executed.

Three parts of function header,

1- return type

2- function name

3- argument list

The function's name is included in the header, which also provides information about the parameters and the type of data the function will return to the caller function or application. The instructions that must be followed are contained in the function's body.

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The complete question is :-

what is the function header and its parts?

Answer:

Step-by-step explanation:

Given system:

Solve by graphing (see attached).

The solution is the point of intersection of the two lines:

Answer:

\(n=-9\)

Step-by-step explanation:

Subtract 10 on both sides giving you: -7n = 63

The divide -7 to both sides giving you -9

Tip: A negative divided by a positive is a negative.

The sum of all the internal angle is \($180^{\circ}$\).

The sum of all the internal angle is \($180^{\circ}$\).

\($$\angle A+\angle B+\angle C=180^{\circ}$$\)

1. 34 and 88

\(34+88+\angle C=180 \\\)

\(122+\angle C=180 \\\)

\(\angle C=180-122 \\\)

\(\angle C=58^{\circ}\)

2. 45 and 90

\(45+90+\angle C=180 \\\)

\(135+\angle C=180 \\\)

\(\angle C=180-135 \\\)

\(\angle C=45^{\circ}\)

3. 10 and 102

\(10+102+\angle C=180 \\\)

\(112+\angle C=180\)

\(\angle C=180-112 \\\)

\(\angle C=68^{\circ}\)

4. \($\boldsymbol{x}$\)and 50

\(x+50+\angle C=180 \\\)

\(\angle C=180-50-x \\\)

\(\angle C=(130-x)^{\circ}\)

The complete question is,

Find the measure of the third angle of a triangle given the measures of two angles.

1. 34 and 88

2. 45 and 90

3. 10 and 102

4. x and 50

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The line of symmetry is a line which divides the shape in two equal similar parts. It is line along which if shape is folded then two shapes overlap each other and both are exactly equal to each other.

For example, the shape of square. If the square is cut or fold along it diagonal then two similar traingles are obtained that are exactly simillar. So diagonal of a square is a line of symmetry for the square. There is possible that a figure has more than one line of symmetry.

If any line does not divides the shape in two equal half, then such line is not a line of symmetry for that shape.

The required experimental probability that the next batter will get a hit is 2/11.

A number that indicates how likely an event is to occur is called its probability. It is communicated as a number in the reach from 0 and 1, or, utilizing rate documentation, in the reach from 0% to 100 percent. The higher the probability, the more likely the event is to occur.

The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials or events.

In this case, we are given that 4 out of 22 batters have gotten a hit so far. Therefore, the experimental probability that the next batter will get a hit is:

P(hit) = Number of hits / Total number of batters

P(hit) = 4/22

Simplifying:

P(hit) = 2/11

Therefore, the experimental probability that the next batter will get a hit is 2/11.

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Answer:

14400

Step-by-step explanation:

(105-15)²

We will solve it with Identity:

(a-b)² = a²+2ab-b²

So,

Answer:

The answer is -4

Step-by-step explanation:

Hope this helps! :)

A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Multiplying Polynomials Find each product. 1) \(6v(2v + 3) 2) 7(-5v - 8)3) 2x(-2x -3)6v(2v + 3)\)

To distribute the 6v over the binomial 2v + 3, we multiply 6v by each term inside the parenthesis:

\(6v(2v) + 6v(3)\)

\(= 12v^2 + 18v7(-5v - 8)\)

To distribute the 7 over the binomial -5v - 8, we multiply 7 by each term inside the parenthesis:

\(7(-5v) + 7(-8)= -35v - 562x(-2x - 3)\)

To distribute the 2x over the binomial -2x - 3, we multiply 2x by each term inside the parenthesis:

\(2x(-2x) + 2x(-3)= -4x^2 - 6x\)

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Answer:

Step-by-step explanation:

Since the lengths of the shelves are given in cm and the answer is to be expressed in cm, then let's convert the length of the whole board from 2.5 m to cm. Since there are 100 cm in a m, then multiply 2.5 by 100 to get 250 cm. Now let's start with the expressions for the shelves. The lengths of all the shelves are based on the length of the first shelf. You can usually tell which object is the main one because it is mentioned the most number of times. The first shelf is mentioned 3 times so that is the main shelf that the measurements of all the other shelves are based upon. Let's call the first shelf x. The second shelf is 18 cm longer than twice the length of the first so the second shelf is 2x + 18.

The third shelf is 12 cm shorter than the first so the third shelf is x - 12.

The last shelf is 4 cm longer than the first shelf so the last shelf is x + 4. Since he needs to use all 250 cm of the board, we add all the shelves together and set them equal to 250 cm:

x + 2x + 18 + x - 12 + x + 4 = 250 and

5x + 10 = 250 and

5x = 240 so

x = 48. The first shelf is 48 cm long. But we need the length of the second shelf. The expression for the second shelf is 2x + 18, so 2(48) + 18 = 114 cm.

Answer: -240 = -4π / 3, 60 = π / 3, 270 = 3π / 2, 945 = 21π / 4, -30 = -π / 60, 195 = 13π / 12

Step-by-step explanation:

The formula for converting Degrees into Radians is Degrees * (π / 180) = Radians.

For -240, we have -240 * (π / 180) = -240π / 180 and simplifying gives us -4π / 3

60:  60 * (π / 180) = 60π / 180 = π/3

270:  270 * (π / 180) = 270π / 180 = 3π / 2

945:  945 * (π / 180) = 945π / 180 = 21π / 4

-30:  -30 * (π / 180) = -30π / 180 = π / 60

195:  195 * (π / 180) = 195π / 180 = 13π / 12

Answer:

The function rule is f(x)=2x+3. It cut the three out.

Step-by-step explanation: cut the three out

Answer:

16 berries

Step-by-step explanation:

Answer:

x= 22

Step-by-step explanation:

11x - 4 = 238

11x = 242

x= 22