what is the distance along the unit circle between any two successive 8th roots of 1?

a. π/8
b. π/6
c. π/4
d. π/2

The instrument used to measure the air taken in by and expelled from the lungs is called a spirometer. It measures lung volumes and capacities.

Which are important indicators of lung function and respiratory health. Spirometry is a common test used to diagnose and monitor respiratory diseases such as asthma, chronic obstructive pulmonary disease (COPD), and pulmonary fibrosis.

air that a person inhales and exhales. It measures several lung volumes and capacities, including:

Tidal Volume (TV): This is the amount of air that is inhaled or exhaled during normal breathing.

Inspiratory Reserve Volume (IRV): This is the additional amount of air that can be inhaled after a normal inhalation.

Expiratory Reserve Volume (ERV): This is the additional amount of air that can be exhaled after a normal exhalation.

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Michael is 33 years old and Brandon is 21 years old.

To find the current age of Michael and Brandon, we can use the information given in the problem to set up and solve a system of equations.

Let x be Brandon's current age, and y be Michael's current age.

From the problem, we know the following:

Michael is 12 years older than Brandon: y = x + 12

Seventeen years ago, Michael was 4 times as old as Brandon: y - 17 = 4(x - 17)

We can substitute the first equation into the second equation to eliminate y:

y - 17 = 4(x - 17)

x + 12 - 17 = 4(x - 17)

x - 5 = 4x - 68

3x = 63

x = 21

So, Brandon's current age is 21 years old.

We can use this information to find Michael's current age:

y = x + 12

y = 21 + 12

y = 33

So, Michael's current age is 33 years old.

Simultaneous equations are a set of two or more equations that contain the same variables. These equations must be solved together, or "simultaneously," in order to find the values of the variables. Solving simultaneous equations involves finding values for the variables that will make all the equations true at the same time.

The goal of solving a system of simultaneous equations is to find the values of the variables that satisfy all the equations in the system. The solution of the system of equations is the set of values that satisfy all the equations in the system.

In short, simultaneous equations are a set of two or more equations that contain the same variables. Solving simultaneous equations is to find the values of the variables that satisfy all the equations in the system. There are different methods to solve simultaneous equations such as substitution, elimination, and graphing.

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Answer:

a

Step-by-step explanation:

your a could be the same.

The change in one variable related to the change in more than one other variable is measured using multiple regression analysis.

A statistical method known as multiple regression is used on datasets intended to show a link between a single response or dependent variable and a number of independent factors.

Even though linear regression is frequently employed, it can only be utilized with one independent variable and one dependent variable. Non-linear regression is not predicted by linear regression, which is also limited to the training dataset.

We employ multiple regression to account for the same restrictions. It focuses on removing one particular limitation, which is allowing for the analysis of multiple independent variables.

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Answer:

8. -8

9. 19

10. 32

Step-by-step explanation:

I will not do your entire homework sheet in one answer, but I will do a couple for you.

8. (24÷6)-(2×6)

4 - 12

-8

9. 48 ÷ 6 × 3 - 5

8 × 3 - 5

24 - 5

19

10. (35 ÷ 5) × 2 + 3 × 6

7 × 2 + 3 × 6

14 + 18

32

Answer:

1) 10   2) 27  3) 66  4)73  5) 2  6) 54  7) 71/2 or 35.5 or 35 1/2

8) -8   9) 19  10) 32

Step-by-step explanation:

PEMDAS

1) 8+8÷4    2) 4x6+3   3) 10x7-4   4) 59-45÷5x3+41  5) 6x3÷(17-8)    

8+2                24+3         70-4          59-27+41                18÷9

=10                =27             =66              =73                     =2

6) 10x4+(49÷7)x2                7) 4+ 27/2 +18     8) (24 ÷ 6)-(2x6)                  

40+7x2  →  40+14                    22+ 27/2                   4  -  12                                      

=54                                              =71/2 or 35.5            = -8                                          

9) 48÷6 x 3 -5              10) (35÷5) x2 +3x6

   24-5                                     7x2+18  

=19                                           14+18

                                                =32

Answer:

The amount is 4/5 of 5/6 is in 2/3.

Step-by-step explanation:

There 4/5 is 5/6 in the fraction 2/3 which is determined by the division operation.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

For example 4/2 = 2

We have to determine how many 5/6 are in the fraction 2/3.

The numbers are given in the question below

2/3 and 5/6

According to the given question, the required solution would be as:

⇒ 2/3 ÷ 5/6

⇒ (2/3) / (5/6)

Reciprocal the terms of the numerator in the above expression

⇒ (2/3) × (6/5)

Apply the multiplication operation,

⇒ 12 / 15

Reduce the fraction in the simplest form,

⇒ 4/5

Therefore, there 4/5 is 5/6 in the fraction 2/3.

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Answer:

yes it is.....................

Step-by-step explanation:

9.5 = 19/2

So it is a rational number (and so is not irrational)

1 newton-meter = 0.73756 pound-feet

To convert a value in newton-meters to pound-feet, you simply need to multiply the value in newton-meters by the conversion factor.

For example, let's say we have a torque of 100 newton-meters, and we want to convert this to pound-feet. Using the conversion factor above, we have:

100 newton-meters * 0.73756 pound-feet/newton-meter = 73.756 pound-feet

Answer:

approximately 452.16

Step-by-step explanation:

4 squared = 16*9 = 144

144*3.14 = 452.16

The z-score of 3 would be 60.94 years old.

a) Z-score of the minimum age is -0.909 and the z-score of the maximum age is 1.003.

The formula for finding z-score is given by,

z= x - μ / σ

Here, x = 31.84 (mean), μ = 31 (minimum age), and σ = 9.534 (standard deviation).

So, z-score of the minimum age = (-0.16) / 9.534

= -0.909z-score of the maximum age

= (x - μ) / σ

= (x - 31) / 9.534

Here, x = maximum age

So, 1.003 = (x - 31) / 9.534x - 31

= 9.534 * 1.003x - 31

= 9.57x = 9.57 + 31

= 40.57

So, the z-score for the minimum age is -0.909 and the z-score for the maximum age is 1.003.b)

The maximum age has the more extreme z-score because it has a higher value of z-score (1.003) than the minimum age (-0.909).c) Someone with a z-score of 3 would be 60.94 years old.

The formula for finding x (age) is given by,

x = μ + zσHere,

μ = 31.84 (mean),

z = 3 (given), and σ = 9.534 (standard deviation).

So, x = 31.84 + 3 * 9.534x

= 31.84 + 28.602

= 60.94

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The equation represents a line which is parallel to the line 7y−x=−28 is y=1/7 x.

The given equation is 7y-x=-28.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, equation can be rewritten as x-7y-28=0

So, slope of line = 1

As we know, slope of parallel lines are equal. If the slopes of two parallel lines are represented as m1, m2 then we have m1 = m2.

Now, m1 = m2 = 1

Find the slope of the original line and use the point-slope formula y−y1=m(x−x1) to find the line parallel to 7y−x=−28.

y=1/7 x

Therefore, the equation represents a line which is parallel to the line 7y−x=−28 is y=1/7 x.

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Answer:

-4a² + 7a + 4

Step-by-step explanation:

Subtract -4 + 3a² from 7a - a².

(7a - a²) - (-4 + 3a²) =

= 7a - a² + 4 - 3a²

= -4a² + 7a + 4

Answer:

106

Step-by-step explanation:

the average of the 3 numbers is calculated as

average = \(\frac{86+113+119}{3}\) = \(\frac{318}{3}\) = 106

The average of 86, 113, and 119 is 106

The average can be calculated as follows:

Given the formula:
\(A=\frac{x+y+z}{3}\)

Substitute x=86, y=113, and z=119 into the given formula

\(A=\frac{86+113+119}{3}\)

Add the numerator.

\(A=\frac{318}{3}\)

Divide the number.

\(A=106\)

Therefore the average of 86, 113, and 119 is 106.

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Answer&Step-by-step explanation:

Graphically, the point is the solution because it is the point that is on both lines.

Algebraically, that point, (5,-4), which means x=5 and y=-4, makes both of the equations true. That point "works" in both equations.

Answer: No association

Step-by-step explanation:

There is absolutely no pattern going on. This means that the miles ran per week are not really affecting the standing heartbeat. Therefore, I'd say there is no association.

To find a possible equation of the inverse log function, we can use the properties of exponential functions and logarithms.

We know that the given exponential function has a base of 3, an asymptote at y = -6, and passes through the point (2, 3).

The general form of an exponential function with base 3 is:

y = a * \(3^x\)

Since the exponential function has an asymptote at y = -6, we can set the limit as x approaches negative infinity to determine the value of "a":

lim(x->-∞) \(a * 3^x = -6\)

As x approaches negative infinity, the value of\(3^x\) becomes very close to 0, and the equation simplifies to:

a * 0 = -6

Since any value multiplied by 0 is 0, we can conclude that "a" must be 0 in this case.

Thus, the equation of the exponential function with base 3 becomes:

y = 0 * \(3^x\) = 0

The inverse function of y = 0 is x = 0.

Therefore, a possible equation for the inverse logarithmic function is:

x = log₃(y)

This equation represents the inverse relationship between the original exponential function and the logarithmic function.

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The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.

Quadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.

From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.

For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.

The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown

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The Simplification of each of the expressions has been given below. The solution to the simultaneous equation using substitution method is x = -8, y = -16

(5³)(5^7)

= (75)(78,125)

= 5,859,375

(x^5)(x^-10)

= x^(5-10)

= x^-5

-8x³y^6 / 4x^5y^4

= -8x³y^6 - 4x^5y^4

= -12x^(3-5)y^(6-4)

= -12x²y²

2x - 9 + 4x + 1

= 6x - 8

(5v² - 9v) + (4v + 8)

= 5v² - 9v + 4v + 8

= 5v² - 5v + 8

8(-6y + 9)

= -48y + 72

(4r - 3) (4r + 3)

= 16r² + 12r - 12r - 9

= 16r² - 9

6x -7 = x + 8

6x - x = 8 + 7

5x = 15

x = 15/5

x = 3

2(3x - 4) - 2x = 2(x - 7)

6x - 8 - 2x = 2x - 14

4x - 8 = 2x - 14

4x - 2x = -14 + 8

2x = -6

x = -6/2

x = -3

y = x - 8

y = 2x

y = x - 8

2x = x - 8

2x - x = -8

x = -8

y = 2x

y = 2(-8)

y = -16

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Answer:

1/3 and 6/18 their relationship is 6

Step-by-step explanation:

I think this might be the answer but I was confused as to what it meant as well. Sry if it’s wrong :(

Answer:

3.2

Step-by-step explanation:

3.2/1

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer

Your saviour has come!

The answer is A

Step-by-step explanation:

Answer:

7pm

Step-by-step explanation:

A train arrives every 2 hours and a bus every 3 so in 6 hours time a bus and a train will arrive together

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

Here are some additional explanations:

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The value of n that makes all of the numbers in the set {32 + n, n/8, and √(n + 23)} natural numbers is n = 63.

To find the smallest value of n so that all of the numbers in the set {32 + n, n/8, and √(n + 23)} are natural numbers, we need to determine the factors of the given numbers. We know that a natural number has no fractional part and is greater than or equal to 1.

We can find the smallest value of n by taking the Least Common Multiple (LCM) of the denominators of the fractions in the given set. So, let's begin:1. 32 + n = natural number

If n = 0, then 32 + n = 32, which is not a natural number. If n = 1, then 32 + n = 33, which is a natural number. Therefore, the value of n that makes 32 + n a natural number is n = 1.2. n/8 = natural number

If n is a multiple of 8, then n/8 is a natural number. Therefore, the value of n that makes n/8 a natural number is any positive multiple of 8.3. √(n + 23) = natural number

If n + 23 is a perfect square, then √(n + 23) is a natural number. Therefore, the value of n that makes √(n + 23) a natural number is any number that is 1 less than a perfect square.

We need to find the smallest value of n that satisfies all three conditions above. The LCM of 8 and 1 is 8. The smallest multiple of 8 that is 1 less than a perfect square is 63. Thus, the smallest value of n is 63.

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