When a sphere is moved about its center it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position. Prove using something related to orthogonal properties.

The amount of feed the container can hold is 232 11/16 cubic inches. The correct option is the third option - two hundred thirty-two and eleven-sixteenths in3

From the question, we are to calculate how much feed the container can hold.

From the given information, the container is a rectangular prism

To calculate how much fed the container can hold, we will determine the volume of the rectangular prism

Volume of a rectangular prism is given by the formula

Volume = Length × Width × Height

Thus,

Volume of the container = 4 1/4 × 18 1/4 × 3

Volume of the container = 232 11/16 cubic inches

Hence,

The quantity of feed it can hold is 232 11/16 cubic inches

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Nachelle needs to score 110 on Exam B in order to do equivalently well as she did on Exam A.

Given data: Nachelle earned a score of 725 on Exam A that had a mean of 700 and a standard deviation of 50.

She is about to take Exam B that has a mean of 100 and a standard deviation of 20.Let x be the score on Exam B that Nachelle needs to do equivalently well as she did on Exam A.

According to the Z-score formula, Z = (x - μ) / σ where Z is the standard score, x is the value of the element, μ is the population mean, and σ is the standard deviation.

Let's calculate the Z-scores for Nachelle's scores on Exams A and B.

Z-score for Nachelle's score on Exam AZ1 = (725 - 700) / 50 = 0.5

Z-score for Nachelle's score on Exam BZ2 = (x - 100) / 20 = (x - 100) / 20

Now, if Nachelle has to do equivalently well on Exam B as she did on Exam A, then the Z-scores for both exams should be equal.

Hence,0.5 = (x - 100) / 20Solving for x,x - 100 = 0.5 × 20 = 10x = 100 + 10 = 110.

Therefore, Nachelle needs to score 110 on Exam B in order to do equivalently well as she did on Exam A.

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In this case, since the curve is not a cylindrical helix, there is no well-defined axis.

A cylindrical helix is a curve in 3D space that follows the path of a cylinder as it is unwrapped along a line. The curve is parameterized by a vector function α(t) = (x(t), y(t), z(t)), where x(t) = r cos(t), y(t) = r sin(t), and z(t) = ht, with r and h being the radius and height of the cylinder, respectively.

In this case, the parameterization of the curve is given by α(t) = (at, bt^2, t^3). To determine if it is a cylindrical helix, we need to check if it follows the path of a cylinder as it is unwrapped along a line.

First, let's look at the z-coordinate, which corresponds to the height of the curve. We see that it is a cubic function of t, which means that the curve is not a horizontal line and it does not lie in a plane. This suggests that the curve may be a helix.

Next, let's look at the x and y-coordinates. The x-coordinate is a linear function of t, which means that it varies uniformly along the curve. The y-coordinate, on the other hand, is a quadratic function of t, which means that it changes faster than the x-coordinate.

This indicates that the curve may be a spiral, which is a type of helix that has an additional circular motion in the x-y plane as it moves along the z-axis. To confirm that the curve is a spiral, we need to check that the radius of the circle traced out by the curve in the x-y plane is constant.

To find the radius, we can take the derivative of the x and y-coordinates with respect to t:

dx/dt = a

dy/dt = 2bt

The radius of the circle is given by:

r = sqrt(x^2 + y^2) = sqrt(a^2 + 4b^2t^2)

We can take the derivative of r with respect to t to see if it is constant:

dr/dt = 4bt/sqrt(a^2 + 4b^2t^2)

We see that dr/dt is not constant, which means that the radius of the circle traced out by the curve is changing as it moves along the z-axis. Therefore, the curve is not a spiral.

In summary, the necessary and sufficient conditions for the curve to be a cylindrical helix are:

The z-coordinate of the curve is a linear function of t, i.e., z(t) = ht.

The radius of the circle traced out by the curve in the x-y plane is constant.

In this case, the curve does not satisfy condition 2, which means that it is not a cylindrical helix.

The axis of the curve is the line along which the cylinder is unwrapped. In this case, since the curve is not a cylindrical helix, there is no well-defined axis.

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We do not have enough evidence to conclude that the true mean melting point differs from 95 at a significance level of 0.01.

To determine if the true mean melting point differs from 95, we can use a one-sample t-test with a significance level of 0.01.

The null hypothesis is that the true mean melting point is equal to 95, and the alternative hypothesis is that the true mean melting point is different from 95.

We can calculate the t-statistic using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

where sample size is 16, sample mean is 94.32, hypothesized mean is 95, and sample standard deviation is the same as the population standard deviation of 1.20.

Plugging in these values, we get:

[tex]t = (94.32 - 95) / (1.20 / \sqrt{(16)} ) = -2.6667[/tex]

Using a t-distribution table with 15 degrees of freedom (n-1=16-1), and a two-tailed test at a significance level of 0.01, the critical t-value is ±2.947.

Since our calculated t-value of -2.6667 falls within the acceptance region (-2.947 < -2.6667 < 2.947), we fail to reject the null hypothesis.

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The probability that we draw a total of 4 cards is approximately 0.074.

The probability that we draw a total of n cards is a function of n.

the expected number of times we draw a card until we get a heart or a face card is: E(X) = 1/p = 3.25.

To solve this problem, we can use the geometric distribution, which models the number of trials needed to get the first success in a sequence of independent trials.

Since we are drawing a heart or a face card, there are 16 cards (4 face cards and 12 hearts) out of 52 that are successful. Therefore, the probability of success is:

p = 16/52 = 4/13

What is the probability that we draw a total of 4 cards

We want to find the probability that we get the first success on the fourth trial, i.e., we draw three non-successes followed by a success. The probability of this event is:

P(X = 4) = [tex](1 - p)^3 * p = (9/13)^3 * (4/13) = 0.074[/tex]

We want to find the probability that we get the first success on the nth trial, i.e., we draw n-1 non-successes followed by a success. The probability of this event is:

[tex]P(X = n) = (1 - p)^(^n^-^1^) * p[/tex]

The expected value of a geometric distribution is 1/p. Therefore, the expected number of times we draw a card until we get a heart or a face card is:

E(X) = 1/p = 13/4

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Answer:

Step-by-step by steo

Total number of students = n(P∪M)=100

                   Number of students who passed in physics= n(P)=55

                   Number of students who passed in maths= n(M)=67

                   Number of students who passed both physics and maths=n(P∩M)

                   ⇒n(P∪M)=n(P)+n(M)−n(P∩M)

                   ⇒100=55+67−n(P∩M)

                   ⇒n(P∩M)=122−100

                   ⇒n(P∩M)=22

Step - 2 : Find number of students who passed only in physics

                   Number of students passed in physics = 55

                   Number of students passed in physics and maths both = 22

                   ∴Number of students passed only in physics = 55−22=33

The values of x and y in the system of equations, x - y = 5 and 3x - 2y = 12, are: x = 2  y = -3

Given the system of equations:

x - y = 5 --> eqn. 1

3x - 2y = 12 --> eqn. 2

Rewrite equation 1:

x = 5 + y --> eqn. 3

Substitute x for 5 + y into equation 2:

3(5 + y) - 2y = 12

15 + 3y - 2y = 12

15 + y = 12

y = 12 - 15 [subtraction property]

y = -3

Substitute y = -3 into equation 3:

x = 5 + (-3)

x = 2

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angle 1 and angle 8 are alternate exterior angles.

option D.

Alternate exterior angles are pairs of angles that are located on opposite sides of a transversal line intersecting two parallel lines, and their values are equal.

These angles are positioned in such a way that they are outside of the two parallel lines, but on opposite sides of the transversal.

For the given diagram, the alternate exterior angles are determined as;

angle 1 and angle 8 are alternate exterior angles.

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The margin of error for a 80% confidence interval for the population mean is  57.82 square feet.

The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. To find the margin of error for a 80% confidence interval, we need to use the formula:

Margin of error = z*(σ/√n)

where z is the z-score corresponding to the level of confidence (80% corresponds to z=1.282), σ is the population standard deviation (given as 137), and n is the sample size (given as 19).

Plugging in the values, we get:

Margin of error = 1.282*(137/√19) = 57.82

Therefore, the margin of error for a 80% confidence interval is 57.82 square feet.

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The graph of the polynomial function​ that passes through the points P(−2,2) and Q(1,0) is added as an attachment

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

The graph passes through the points P(−2,2) and Q(1,0)

Assuming the graph is a linear function

So, we have

y = mx + c

Where

c = y when x = 0 and m = slope

This gives

-2m + c = 2

m + c = 0

Subtract the equations

So, we have

-3m = 2

m = -2/3

Solving for c, we have

-2/3 + c = 0

Evaluate

c = 2/3

So, the equation is f(x) = -2/3x + 2/3

See attachment for the graph

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Complete question

Draw the graph of polynomial function f(x) containing the points P(−2,2) and Q(1,0)

Answer:

Step-by-step explanation:

First, organize the numbers; 1,1,1,2,2,3,4,5,5,6. The median is the middle number, in this case, 2 and 3 are in the middle. You'd add 2+3 which equals 5, then divide by 2 to get 2.5. The median is 2.5, to find the mode you need to see how many times one number appears. The mode is 1, the range is the largest number minus the smallest number. The range is 5, to find the mean you add all numbers up, then divide by how many numbers there are. All the numbers added up are 30, now divide that by 10 to get 3. The mean is 3. The standard deviation is 1.7 x 6.5 = 20.8

I'm only an algebra student so I may not be entirely correct.

The maximum number of strings that can be cut before the volleyball net falls apart into two pieces, considering a mesh with m squares on the horizontal dimension and n squares on the vertical dimension, is min(m+1, n+1).

To determine the maximum number of strings that can be cut before the volleyball net falls apart into two pieces, considering the mesh has m squares on the horizontal dimension and n squares on the vertical dimension, we can solve this as a network problem. Here's a step-by-step explanation:

1. Visualize the volleyball net as a graph with nodes representing the intersections of the strings and edges representing the strings themselves.

2. Observe that there are (m+1) nodes horizontally and (n+1) nodes vertically. This is because each square has a node at each corner, so there is an additional node on each side.

3. To separate the net into two pieces, you need to cut all the strings along a specific row or column of the mesh.

4. The maximum number of strings you can cut will be the minimum number of strings needed to cut through the entire mesh either horizontally or vertically.

5. If you choose to cut the strings horizontally, there will be (m+1) strings to cut for each row. Similarly, if you choose to cut the strings vertically, there will be (n+1) strings to cut for each column.

6. Compare the number of strings to cut in both directions, and choose the direction with the minimum number of strings to cut.

7. The maximum number of strings that can be cut before the net falls apart into two pieces is the minimum between (m+1) and (n+1).

So, the maximum number of strings that can be cut before the volleyball net falls apart into two pieces, considering a mesh with m squares on the horizontal dimension and n squares on the vertical dimension, is min(m+1, n+1).

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a)  The perimeter of the figure [tex]p = 12x + 19[/tex]

b) The perimeter of the figure when [tex]x = 4[/tex] is 67 units.

c)  The perimeter of the figure when[tex]x = 2[/tex] is 43 units

d)  The perimeter of the figure is [tex]3x^2 + 5x + 8[/tex] units.

a) The perimeter P of the figure is the sum of the lengths of its sides:

[tex]P = a + b + c + d[/tex]

Substituting the given expressions for a, b, c, and d in terms of x, we get:

[tex]P = (x + 7) + (2x + 2) + (8x) + (x + 10)[/tex]

[tex]= 12x + 19[/tex]

b) Substituting x = 4, we get:

[tex]P = 12x + 19[/tex]

[tex]= 12(4) + 19[/tex]

[tex]= 67[/tex]

Therefore, the perimeter of the figure when [tex]x = 4[/tex] is 67 units.

c) Substituting [tex]x = 2,[/tex] we get:

[tex]P = 12x + 19[/tex]

[tex]= 12(2) + 19[/tex]

[tex]= 43[/tex]

Therefore, the perimeter of the figure when[tex]x = 2[/tex] is 43 units.

d) Substituting the given expressions for a, b, c, and d in terms of x, we get:

[tex]P = x^2 + (4x + 8) + 2x^2 + x[/tex]

[tex]= 3x^2 + 5x + 8[/tex]

Therefore, the perimeter of the figure when[tex]a = x^2, b = 4x + 8, c = 2x^2,[/tex] and [tex]d = x[/tex] is [tex]3x^2 + 5x + 8[/tex] units.

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Answer:

78° + 95° + (2x + 115)° + 72° = 360°

(2x + 360)° = 360°, so x = 0.

The angle of elevation from Row A to the bottom of the screen 13.3.

The angle of depression from Row P to the bottom of the screen 4.4

let angle of elevation of Row A to the bottom of the Screen be Ae

So, tan Ae = 2.5 - 5.8tan 11  /5.8

tan Ae = 0.23665

Ae = 13.3

Now, let the angle of depression of Row P to the bottom of the screen be P

tan P  =  2.3 tan 11- 2.5/ 2.5

tan P = 0.077

P = 4.4

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The total percent composition for all the elements in the compound CgH10N402 is 61.73%.

To calculate the molecular mass of CgH10N402, we need to add up the atomic masses of all the atoms in the compound. The atomic masses can be found on the periodic table.

The molecular formula indicates that the compound contains:

1 carbon atom (C) with atomic mass of 12.01 g/mol

10 hydrogen atoms (H) with atomic mass of 1.01 g/mol

1 nitrogen atom (N) with atomic mass of 14.01 g/mol

4 oxygen atoms (O) with atomic mass of 16.00 g/mol

Molecular mass (M) = (1 x 12.01) + (10 x 1.01) + (1 x 14.01) + (4 x 16.00) = 162.14 g/mol

Therefore, the molecular mass for the compound CgH10N402 is 162.14 g/mol.

To determine the percent composition of each element in the compound, we need to divide the mass contribution of each element by the total molecular mass and multiply by 100%.

Percent composition of C:

Mass contribution of C = 1 x 12.01 g/mol = 12.01 g/mol

% C = (12.01 g/mol / 162.14 g/mol) x 100% = 7.41%

Percent composition of H:

Mass contribution of H = 10 x 1.01 g/mol = 10.10 g/mol

% H = (10.10 g/mol / 162.14 g/mol) x 100% = 6.23%

Percent composition of N:

Mass contribution of N = 1 x 14.01 g/mol = 14.01 g/mol

% N = (14.01 g/mol / 162.14 g/mol) x 100% = 8.63%

Percent composition of O:

Mass contribution of O = 4 x 16.00 g/mol = 64.00 g/mol

% O = (64.00 g/mol / 162.14 g/mol) x 100% = 39.46%

Therefore, the percent composition for the element C, H, N, O in the compound CgH10N402 are:

%C = 7.41%

%H = 6.23%

%N = 8.63%

%O = 39.46%

The total percent composition for all the elements in the compound must add up to 100%.

Total percent composition = %C + %H + %N + %O = 7.41% + 6.23% + 8.63% + 39.46% = 61.73%

Therefore, the total percent composition for all the elements in the compound CgH10N402 is 61.73%.

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The missing length of the triangle is given as follows:

x = 35 units.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the missing length is obtained as follows:

x² + 12² = 37²

x = sqrt(37² - 12²)

x = 35 units.

The image is blurry, hence the mistake in Jeff's part cannot be explained.

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To find the temperature of the sun, we'll use the ideal gas law equation, which is PV = nRT. We're given pressure (P), density (ρ), average molecular weight (M), and the gas constant (R). First, we'll find the number of moles (n) and then solve for temperature (T). After the calulation the answer is found out to be option b which is approximately 2.4 x 10^7 K.

1. Calculate the number of moles (n) using the formula n = ρ/M.
  n = 1.4 g/cc / 2 g/mol = 0.7 mol/cc
2. Rearrange the ideal gas law equation to solve for temperature (T): T = PV / nR
3. Plug in the values:
  P = 1.4 x 10^10 atm
  V = 1 cc (since we are considering 1 cc of the gas)
  n = 0.7 mol
  R = 8.4 x 10^7 erg/mol/K
  T = (1.4 x 10^10 atm) x (1 cc) / (0.7 mol) x (8.4 x 10^7 erg/mol/K)
4. Perform the calculation:
  T = 1.4 x 10^10 / (0.7 x 8.4 x 10^7) = 2.38 x 10^7 K
The temperature of the sun is approximately 2.4 x 10^7 K (option b).

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The inequality is x > 9.5 and the numbers greater than 9.5

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

55 < 6x - 2

Adding 2 on both sides , we get

6x > 57

Divide by 6 on both sides , we get

x > 9.5

So , x satisfies all numbers greater than 9.5

Hence , the inequality is x > 9.5

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The scale factor of the dilation of the circles is 5

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

The circles

From the circles, we have the following parameters

Diameter of big circle Q = 20

Diameter of the small circle R = 4

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

Scale factor of the dilation = Radius of big circle/Radius o the small circle

So, we have

Scale factor of the dilation = 20/4

Evaluate

Scale factor of the dilation = 5

Hence, the scale factor of the dilation is 5

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(a)The logistic differential equation for these data.

dP/dt = 0.0017P(1 - P/5900)

(b) After 50 years, we would need to repeat this process 50 times to get an estimate of the population.

(c) P(t) = 6900/(1 + 5.882[tex]e^(-0.0017t))[/tex]

(d) The population after 50 years is 5869.4.

(a) The calculated differential condition for populace development is:

dP/dt = kP(1 - P/K)

where P is the populace, t is time, k is the development rate, and K is the carrying capacity.

Substituting the given values, we get:

dP/dt = 0.0017P(1 - P/5900)

(b) Utilizing Euler's strategy with step measure h = 1, we have:

P(0) = 1000

P(1) = P(0) + hdP/dt(P(0))

P(1) = 1000 + 10.00171000(1 - 1000/5900)

P(1) ≈ 1008

After 50 years, we would rehash this prepare 50 times to induce a gauge for the population.

(c) To discover an equation for the populace after a long time, able to utilize the calculated condition with starting condition P(0) = 1000. Joining both sides, we get:

∫(1/P) dP = ∫k(1 - P/K) dt

ln|P| = kt - ln|K - P|

Utilizing the starting condition, we get:

ln|1000| = k0 - ln|K - 1000|

ln|K - 1000| = ln|K| + ln|1000|

ln|K - 1000| = ln|K1000|

K - 1000 = K1000/e^(k0)

K - 1000 = K*1000/1

K = 6900

In this manner, the equation for the populace after a long time is:

P(t) = 6900/(1 + 5.882e^(-0.0017t))

(d) To discover the populace after 50 a long time, able to utilize the equation:

P(50) = 6900/(1 + 5.882e^(-0.001750))

P(50) ≈ 5869.4

The populace after 50 a long times is around 5869.4. 

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The equation of the following line include the following: E. y = -2x .

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 0)/(-4 - 0)

Slope (m) = 8/-4

Slope (m) = -2.

At data point (-4, 8) and a slope of -2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 8 = -2(x + 4)  

y - 8 = -2x - 8

y = -2x

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The maximum total power of the electronic components that can safely be mounted on this circuit board is 4.2 W.

The maximum total power of the electronic components that can safely be mounted on the circuit board is determined by the amount of heat that can be removed from the channel by the air flow without exceeding the maximum allowable temperature of 50°C on the channel surface.

To calculate the maximum total power of the electronic components, we need to determine the heat transfer rate from the channel to the air flow

where Q is the heat transfer rate, h is the convective heat transfer coefficient, A is the surface area of the channel, and ΔT is the temperature difference between the channel surface and the air.

The convective heat transfer coefficient can be calculated using the Nusselt number correlation for flow inside a rectangular channel:

Nu =  8.24

h =  8.240.02551 /0.2 = 1.048 W/m

where L is the channel's hydraulic diameter, equal to [tex]2*(0.2*14)/(0.2+14)[/tex]  = 0.278 cm = 0.00278 m.

The surface area of the channel is A = 20.220 + 20.214 + 14[tex]*20[/tex] = 120.8 cm[tex]^2[/tex] = 0.01208 [tex]m^2.[/tex]

The temperature difference between the channel surface and the air is ΔT = 50°C - 15°C = 35°C.

Therefore, the maximum heat transfer rate from the channel to the air flow is:

Q = hAΔT = 1.0480.0120835 = 0.0042 kW

This means that the maximum total power of the electronic components that can be safely mounted on the circuit board is:

P = Q = 0.0042 kW = 4.2 W

Therefore, the maximum total power of the electronic components that can safely be mounted on this circuit board is 4.2 W.

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Answer:

3.29 cm.

Step-by-step explanation:

The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

376.8 = (1/3)π(6^2)h

Simplifying:

376.8 = 36πh

h = 376.8 / (36π)

h ≈ 3.29 cm

Therefore, the height of the orange cone is approximately 3.29 cm.

The diameter of the circle is determined as 20.12 units.

The radius of the circle is calculated by applying the following formula as shown below;

The let the distance between 9 and center of the circle O = x

The radius of the circle, r = 9 + x --- (1)

Draw a line from circumference from point 10 to center O, this line is the radius = r

Apply Pythagoras theorem;

r² = 10² + x² ------ (2)

From the first equation, recall, r = 9 + x

(9 + x)² = 10² + x²

81 + 18x + x² = 100 + x²

81 + 18x = 100

18x = 100 - 81

18x = 19

x = 19/18

x = 1.06

The radius of the circle = 9 + x

r = 9 + 1.06

r = 10.06

The diameter of the circle = 2r

= 2 x 10.06

= 20.12 units

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Answer:

Area of the circle = 55.39 in²

Circumference of the circle = 26.38 in

Step-by-step explanation:

Given, the diameter of the circle = 8.4

so the radius is given by the formula

∴ d = 2r

→ 8.4 = 2×r

→r=4.2 in      [i]

Area of the circle = π×r²     [ii]

substituting the value of r in equation [ii]

we get,

area of circle = 3.14×(4.2)²

                      =55.39 in²

circumference of the circle =2πr     [iii]

substituting the value of r in equation [iii]

we get,

circumference of the circle = 2×3.14×4.2

                                             = 26.38 in

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Answer: The range of the incorrectly recorded data is:

96 - 50 = 46

The actual range of the data is:

96 - 50 = 46

The range is not affected by the correction of the 4th hour data because the range only depends on the difference between the highest and lowest values, which remains the same.

Step-by-step explanation:

The participant's RER at that point in time was approximately 0.0009 (rounded to 4 decimal places).

To calculate the participant's Respiratory Exchange Ratio (RER) at that point in time, you will use the formula:

RER = VCO2 / VO2

Given the participant's VO2 was 1004 L/min and VCO2 was 0.932 L/min, plug these values into the formula:

RER = 0.932 / 1004

Now, divide 0.932 by 1004:

RER ≈ 0.0009

So, the participant's RER at that point in time was approximately 0.0009 (rounded to 4 decimal places).

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The value of the expression is 4y.

Given is an expression, [tex]12x^{2} y/ 3x^2[/tex], we need to simplify it,

[tex]12x^{2} y/ 3x^2[/tex]

= 12 × x² × y / 3 × x²

= 4 × x² × y / x²

= 4y

Hence, the value of the expression is 4y.

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