select all expressions equivalent to (3^3*3^-4)^-3

Answer:

c+ 64 ≥ 120;c  ≥ 56

Step-by-step explanation:

He needs to get at least 120 cans.  He has 64 cans already.  C is the number of cans he still needs to get.

c+ 64 ≥ 120

Subtract 64 from each side

c  ≥ 56

1.1.1 Short-term investment: An example of a short-term investment is investing in a 3-month Treasury bill. These are government-issued debt securities with a maturity of less than one year, providing a relatively low-risk investment option with a fixed interest rate.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a maturity of 5 years. Corporate bonds offer a higher yield compared to government bonds, making them suitable for investors with a moderate risk appetite seeking stable income over a longer time horizon.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. Stocks represent ownership in a company and have the potential for higher returns over an extended period, although they also involve higher risk.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. These bonds pay a fixed interest rate over the bond's duration, providing a predictable stream of income for the investor.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. The mortgage payment remains constant throughout the loan term, typically spanning several years, and includes both the principal repayment and the interest charged by the lender.

1.1.1 Short-term investment: A short-term investment option is the 3-month Treasury bill. Treasury bills are considered low-risk investments issued by the government, and they offer a fixed interest rate that is determined through an auction process. Investors can purchase Treasury bills directly from the government or through a broker.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a 5-year maturity. Corporate bonds are issued by companies to raise funds, and they pay a fixed interest rate to bondholders over the bond's duration. The bond's yield and risk profile depend on the creditworthiness of the issuing company.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. A diversified portfolio consists of a mix of stocks from different sectors and regions, spreading the risk across multiple companies. The goal is to achieve long-term capital appreciation and potentially earn dividends from the stocks held in the portfolio.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. Government bonds are issued by national governments to finance their operations. The bond's interest rate is fixed at the time of issuance, and the investor receives periodic interest payments until the bond reaches maturity, at which point the principal amount is returned.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. When purchasing a property with a mortgage loan, the borrower agrees to make fixed monthly payments that include both the principal repayment and the interest charged by the lender. The monthly payment amount remains constant throughout the mortgage term, typically ranging from 15 to 30 years.

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The points for the vertical tangent are (9, 0).

To find the points where the given parametric curve has horizontal and vertical tangents, we need to determine the values of t that satisfy these conditions.

First, let's find the derivative of y with respect to x using the chain rule:

dy/dx = (dy/dt) / (dx/dt)

Given x = 9 - t² and y = t³ - 12t, we can compute the derivatives:

dx/dt = -2t

dy/dt = 3t² - 12

Now, let's express dy/dx in terms of t:

dy/dx = (dy/dt) / (dx/dt)

= (3t² - 12) / (-2t)

= (3(t² - 4)) / (-2t)

= -3(t² - 4) / (2t)

= -3(t + 2)(t - 2) / (2t)

For a horizontal tangent, dy/dx = 0. Therefore, we have:

-3(t + 2)(t - 2) / (2t) = 0

This equation is satisfied when t = -2 and t = 2.

Substituting these values of t back into the parametric equations, we can find the corresponding (x, y) coordinates:

For t = -2:

x = 9 - (-2)² = 9 - 4 = 5

y = (-2)³ - 12(-2) = -8 + 24 = 16

So, the point for the horizontal tangent with the smaller y-value is (5, 16).

For t = 2:

x = 9 - 2² = 9 - 4 = 5

y = 2³ - 12(2) = 8 - 24 = -16

So, the point for the horizontal tangent with the larger y-value is (5, -16).

To find the vertical tangent, we need to find the values of t for which dx/dt = 0. From dx/dt = -2t, we have:

-2t = 0

This equation is satisfied when t = 0.

Substituting t = 0 into the parametric equations, we find:

x = 9 - 0² = 9

y = 0³ - 12(0) = 0

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Answer:

slope= 2 I case you need that :)

Answer:

Below.

Step-by-step explanation:

One way is to plot some points:

When x = 0, y = 2(0) - 4 = 4  So plot (0,-4).

In a similar way you can plot  when x = 1, y = 2(1) - 4 = -2 that is (1, -2).

Also 2(3) - 4 giving the point (3, 2).

Now draw a line passing through these 3 points.

If you cant draw a line through these points then Ive made a mistake in the calculations

Using trigonometric identities and algebraic manipulations, we derive an expression for sin x and cos x in terms of cos y. The value of (sin x + cos x)(sin y + cos y) is 2.49.


1. Start with the given equations sin(x+y) = 0.9 and sin(x-y) = 0.6.
2. Rewrite the equations using trigonometric identities. For sin(x+y) = 0.9, we have sin x cos y + cos x sin y = 0.9. For sin(x-y) = 0.6, we have sin x cos y - cos x sin y = 0.6.
3. Add the two equations together to eliminate the sin x cos y term: 2 sin x cos y = 1.5.
4. Divide both sides by 2 to solve for sin x cos y: sin x cos y = 0.75.
5. Square both sides of the equation to get (sin x cos y)^2 = 0.75^2. This gives us sin^2 x cos^2 y = 0.5625.
6. Use the trigonometric identity sin^2 x + cos^2 x = 1 to rewrite sin^2 x as 1 - cos^2 x: (1 - cos^2 x) cos^2 y = 0.5625.
7. Expand and rearrange the equation: cos^2 x cos^2 y - cos^4 x = 0.5625.
8. Use the identity cos^2 x = 1 - sin^2 x to substitute for cos^2 x: (1 - sin^2 x) cos^2 y - (1 - sin^2 x)^2 = 0.5625.
9. Expand and simplify: cos^2 y - sin^2 x cos^2 y - (1 - 2sin^2 x + sin^4 x) = 0.5625.
10. Combine like terms: cos^2 y - sin^2 x cos^2 y - 1 + 2sin^2 x - sin^4 x = 0.5625.
11. Rearrange the equation to isolate sin^2 x terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 1 + 0.5625 = 0.
12. Combine like terms: sin^4 x - sin^2 x (cos^2 y + 2) + cos^2 y - 0.4375 = 0.
13. Solve the quadratic equation for sin^2 x: sin^2 x = [(cos^2 y + 2) ± √((cos^2 y + 2)^2 - 4(cos^2 y - 0.4375))] / 2.
14. Simplify the expression: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 4cos^2 y + 4 - 4cos^2 y + 1.75)] / 2.
15. Further simplify: sin^2 x = [(cos^2 y + 2) ± √(cos^4 y + 5.75)] / 2.
16. Since 0 ≤ y ≤ x ≤ π/2, the value of cos y is positive. Therefore, cos^2 y + 2 is positive.
17. Thus, the equation simplifies to sin^2 x = (cos^2 y + 2 + √(cos^4 y + 5.75)) / 2.
18. Take the square root of both sides: sin x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2].
19. Since 0 ≤ y ≤ x ≤ π/2, the value of sin x is positive.
20. Therefore, sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - sin^2 x).
21. Substituting the values of sin x and cos x, we have sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √(1 - [(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2]).
22. Simplify the expression: sin x + cos x = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] + √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
23. Multiply the two terms: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75)) / 2] * √[(2 - cos^2 y - √(cos^4 y + 5.75)) / 2].
24. Simplify: (sin x + cos x)(sin y + cos y) = √[(cos^2 y + 2 + √(cos^4 y + 5.75))(2 - cos^2 y - √(cos^4 y + 5.75))] / 2.
25. Multiply the terms inside the square root: (sin x + cos x)(sin y + cos y) = √[4 - 2cos^2 y - 2√(cos^4 y + 5.75) + 4√(cos^2 y + 2) - 2cos^2 y + cos^4 y + 5.75] / 2.
26. Combine like terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) + 2cos^2 y - 2cos^2 y - 2√(cos^4 y + 5.75)] / 2.
27. Cancel out the common terms: (sin x + cos x)(sin y + cos y) = √[5 + 2√(cos^2 y + 2) - 2√(cos^4 y + 5.75)] / 2.
28. Simplify the expression: (sin x + cos x)(sin y + cos y) = √[5 - 2√(cos^4 y + 5.75) + 2√(cos^2 y + 2)] / 2.
29. The value of (sin x + cos x)(sin y + cos y) is 2.49.

Therefore, the value of (sin x + cos x)(sin y + cos y) is 2.49.

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In this problem, we use the product-to-sum trigonometric identities and the given information that sin(x+y) = 0.9 and sin(x-y) = 0.6 to find that the value of (sin x + cos x)(sin y + cos y) equals 1.5.

In this problem, you're asked to find the value of (sin x + cos x)(sin y + cos y). Before we solve it directly, let's take advantage of the given information: sin(x+y) = 0.9 and sin(x-y) = 0.6.

To solve this, we can use the product-to-sum trigonometric identities: sin(A)+cos(A)sin(B)+cos(B) = sin(A+B)+sin(A-B). According to the problem, sin(x+y) = 0.9 and sin(x-y)=0.6. Therefore, we have 0.9 + 0.6 which results in 1.5. Thus, the value of (sin x + cos x)(sin y + cos y) equals 1.5.

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Therefore, Robin Hartman earns $738.

To calculate Robin Hartman's earnings, we need to determine the additional amount earned based on the sales over $6,500.

Step 1: Calculate the amount of sales over $6,500:

Sales over $6,500 = Total sales - $6,500

Sales over $6,500 = $11,100 - $6,500

Sales over $6,500 = $4,600

Step 2: Calculate the additional earnings based on sales over $6,500:

Additional earnings = 2% of sales over $6,500

Additional earnings = 0.02 * (Sales over $6,500)

Additional earnings = 0.02 * $4,600

Additional earnings = $92

Step 3: Calculate the total earnings:

Total earnings = Base earnings + Additional earnings

Total earnings = $646 + $92

Total earnings = $738

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Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

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Answer:

$4.25 ?

Step-by-step explanation:

8.5/2=4.25

Step-by-step explanation:

To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.

Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.

The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.

The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.

The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.

The value of "numTrans" immediately before the second clear statement would be 2.

Here, we have,

To declare the variable "numTrans" as a variable that remains in memory after UpdateBalance() returns, we need to use the keyword "persistent" before the variable declaration.

So the statement would be:

persistent numTrans;

To increment the variable "numTrans" by one for each call to UpdateBalance() after the first call,

we can use the following statement inside the UpdateBalance() function:

numTrans = numTrans + 1;

This statement will increment the value of "numTrans" by one each time UpdateBalance() is called after the first call.

Considering the following script:

clear all;

UpdateBalance(1000.00);

UpdateBalance(-23.78);

clear all;

UpdateBalance(900.00);

The value of "numTrans" immediately before the second clear statement would be 2. This is because "numTrans" was incremented by 1 in the second call to UpdateBalance(), so it would have a value of 2.

The final value of "acctBalance" after the script executes would depend on the initial value of "acctBalance" before the script is run. Without that information, we cannot determine the final value of "acctBalance" accurately.

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complete question:

Consider the following function definition that modifies the account balance function above to also keep track of the number of transactions that are executed using the variable numTrans. 1) Write a statement to declare the variable num Trans as a variable that remains in memory after UpdateBalance() returns. Incorrect Which keyword is used to maintain a variable's value between function calls? function [ curBalance ] = UpdateBalance( updateAmt) % UpdateBalance Updates bank account balance stored as % persistent variable % Inputs: updateAmt - amount to be added to balance; % debits use negative values % Outputs: curBalance - current account balance persistent acctBalance; و Check Show answer 2) Write a statement that increments variable num Trans by one for each call to UpdateBalance() after the first call. Incorrect Use the assignment operator and an arithmetic expression to update the variable. % The first time the function is called acctBalance will be [], so % updateAmt should be assigned as an initial balance. Also, the % number of transactions should be initialized. if isempty(acctBalance) acctBalance = updateAmt; numTrans = 1; else acctBalance = acctBalance + update Amt; end fprintf('Executing Transaction No. %d\n', numTrans); curBalance = acctBalance; end Check Show answer 3) Consider the following script that calls the modified function UpdateBalance() above: clear all; UpdateBalance (1000.00) UpdateBalance (-23.78) clear all; UpdateBalance (900.00) What is the value of numTrans immediately before the second clear statement? Check Show answer 4) What is the final value of acctBalance after the script above executes? Write your answer to two decimal places. Check Show answer

Answer:

Step-by-step explanation:

(let's assume that people are either classified as man or woman)

m=man

b=buy

a

a.) we are looking for b

we are given

m'=.4

b|m'=.37

b|m=.21

b=b∩m+b∩m'

b∩m= (1-.4)(.21)

b∩m'=.4*.37

b= .274

b.) we are looking for m'|b

m'|b= m'∩b/b

m'∩b=.4*.37

b= .274

m'|b=.540145985

c.)

m|b'= m∩b'/b'

m=m∩b'+m∩b (law of total probability)

.6=m∩b'+.6*.21

m∩b'=.474

.474/(1-.274)= .652892561985

Answer:

If it is the dance committee question the answer is 400<72+4t. Hope this helps!

Answer:

In standard notation, the number is \(2.6 * 10^4\) light years

Step-by-step explanation:

We have to write the number 26,000 in standard notation,

in standard notation, there is 1 number before the decimal and all others come after the decimal and some power of 10 is multiplied depending upon the number,

in our case,

26000 = 2.6 * 10^4

(since the number is 26 thousand 2.6 ten thousand and ten thousand = 10^4)

A hexagonal bipyramid has twelve symmetries. The two symmetries of a hexagonal bipyramid using both words and permutation notation are as follows: The rotation symmetry of order 6 through the central axis, along with six rotation axes, each of order 2 perpendicular to it are two of the twelve symmetries of a hexagonal bipyramid.

The permutation notation is (123456), (12), (34), (56), (35)(46), and (36)(45).

Reflection symmetry is the second symmetry of a hexagonal bipyramid. It has a reflection symmetry through the plane containing any two opposite vertices.

The permutation notation is (1 6)(2 5)(3 4), (12)(65), (34)(56), (36)(54), (35)(46), and (16)(25)(34)(56).Where (1 6)(2 5)(3 4) indicates a three-fold rotation and three mirrors.

(12)(65) represents a two-fold rotation and two mirrors. (34)(56) shows the two-fold rotation and two mirrors while (36)(54) represents two mirrors and a two-fold rotation.

(35)(46) represents a two-fold rotation and two mirrors, and (16)(25)(34)(56) represents four mirrors.

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The 7th term of the sequence to the nearest thousandth is 223.949

These are sequence that increases in an exponential form.

The formula for calculating the nth term of a geometric sequence is expressed as:

Tn = ar^n-1

Given the following parameters

a = 75

r = 1.2

n = 7

Substitute the given parameter into the formula

T7 = 75(1.2)^6
T7 = 223.949

Hence the 7th term of the sequence to the nearest thousandth is 223.949

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Answer:

504

Step-by-step explanation:

Their boss should promote and facilitate open communication and understanding between Yan and Tracy to foster a more inclusive and collaborative work environment.

In a diverse workplace, it is crucial for the boss to encourage inclusivity and bridge the gap between individuals with different world views. By promoting open communication and understanding, the boss can create opportunities for Yan and Tracy to learn from each other and gain a broader perspective.

This can be achieved through team-building exercises, diversity training, or creating a supportive space for discussions on cultural differences. The goal is to foster a work environment where individuals feel comfortable expressing their views, learning from others, and working together towards common goals. By addressing the perceived distance between Yan and Tracy, the boss can help create a more inclusive and harmonious work atmosphere.

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Answer:

23

Step-by-step explanation:

3z + 2(z-1)

Let z=5

3*5 +2( 5-1)

15 +2(4)

15+8

23

The domain on which the graph described as in the image is increasing is to be determined; (-4, ∞).

It follows from the task content that the domain for which the function described by the graph is increasing is to be determined.

Since the graph is a quadratic function which opens upward and whose minimum point is at; x = -4.

Also, since a graph of a function, f(x) is increasing when f'(x) > 0.

Therefore, by observation the graph is increasing on the domain defined by; (-4, ∞).

Put simply, the function is increasing in the Domain; x > -4.

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After 10 days, the colony would be as large as 989, based on the exponential growth of 67% every 2 days.

An exponential growth refers to a constant rate or percentage of growth in the number or value of some variables.

Exponential growth can be modeled using the exponential growth function and used to determine the future quantity or amount of the variables.

Initial number of the bacteria microorganisms = 55

Growth rate = 67% every 2 days

Daily growth rate = 33.5% (67% ÷ 2)

The number of days involved, t = 10 days

The ending number of the bacteria microorganisms = Future Amount = 55(1 + 33.5%)^t

= 55(1.335)^10

= 989

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Answer:

55 0.67 ^5

Step-by-step explanation:

The future amount = ? micro organisms

5 ori 5 fac 25 și cu 25 egal 14 și cu 14 egal 100 și cu 100 egal 12

Step-by-step explanation:

sper ca team ajutat

Answer:

∠ 6 = 45°

Step-by-step explanation:

∠ 6 and 45° are vertically opposite angles and are congruent , so

∠ 6 = 45°

This question is incomplete because it was not written correctly.

Complete Question:

K(-5, -1), L(-2, 4), M(3, 1), N(-2, 4)

Determine the most precise name for KLMN (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope.

Answer:

The precise name for KLMN is either a square or a rhombus

Step-by-step explanation:

To find the length of the sides, when you have vertices (x₁, x₂)and (y₁, y₂) we use the formula

√(x₂-x₁)²-(y₂-y₁)²

K(-5, -1), L(-2, 4), M(3, 1), N(-2, 4)

Side/ Length KL = K(-5, -1), L(-2, 4)

= √(x₂-x₁)²-(y₂-y₁)²

= √(-2 -(- 5))² + (4 - (-1))²

= √3² + 5²

= √9 + 25

= √34

Side/ Length LM = L(-2, 4), M(3, 1),

= √(x₂-x₁)²-(y₂-y₁)²

= √(3 - (-2))² + ( 1 - 4)²

= √5² + -3²

= √25 + 9

= √34

Side/ Length MN = M(3, 1), N(-2, 4)

√(x₂-x₁)²-(y₂-y₁)²

= √(-2 - 3)² + (4 - 1)²

= √-5² + 3²

= √25 + 9

= √34

Side/ Length KN = K(-5, -1), N(-2, 4)

√(x₂-x₁)²-(y₂-y₁)²

= √(- 2 -(- 5)² + (4 - (-1))²

= √3² + 5²

= √9 + 25

= √34

From the above calculation, we can see that

KL = √34

LM = √34

MN = √34

KN = √34

This means Length KL = LM = MN = KN

This shape is a Square and a Rhombus. This reason is a square and a rhombus are Quadrilateral shapes whose sides are equal to each other.

Answer:

Okay so im gonna put the pictures here, it might look like spam but i promise you its not

Step-by-step explanation:

The numbers are in order from x > 7 to x < 2

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Based on the values in the table represent a linear function, the common difference of the associated arithmetic sequence is 15.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ = a₁ + (n - 1)d

Where:

Based on the information provided in the given table, we can calculate the common difference by subtracting the first term from the second term as follows;

Common difference, d = a₂ - a₁ = a₃ - a₂

Common difference, d = 23 - 8 = 38 - 23

Common difference, d = 15.

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The standard deviation of the sample  = 28.

An indicator of how much a set of values vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, while when it is high, the values tend to deviate from that mean more.

The standard deviation is a tool for calculating market volatility or the variation in asset prices from their mean. A high standard deviation indicates that prices are moving erratically and that an investment will indeed be risky. Low standard deviation indicates stable prices and low risk for investments.

A specimen of 196 observations has a variance of 784. determine the sample's standard deviation.

variance = 784

we have to find the stranded deviation:

stranded deviation  = √variance

                                  = √784

                                  =  28

The standard deviation of the sample  = 28.

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the term 35x^3y^4 could appear in the binomial expansion of (5x^2y^3 + 7/5)^2.

The term 35x^3y^4 involves x raised to the power 3 and y raised to the power 4. Therefore, this term could appear in the expansion of (5x^2y^3)^2, which is equal to 25x^4y^6. The term 35x^3y^4 is not part of this expression, but we can obtain it by multiplying 25x^4y^6 by (7/5) to get:

(7/5) × 25x^4y^6 = 35x^3y^4

what is binomial expansion?

Binomial expansion refers to the algebraic expansion of an expression that has two terms connected by addition or subtraction. It involves raising a binomial expression to a certain power using Pascal's triangle or the binomial theorem. The expansion results in a polynomial expression with several terms, each consisting of a coefficient and a variable raised to a power. Binomial expansion has various applications in mathematics, including probability theory, combinatorics, and calculus.

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Answer:

22x2 -  9x) -  9

Trying to factor by splitting the middle term

   Factoring  4x2-9x-9  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -9 .

     -36    +   1  =  -35  

     -18    +   2  =  -16  

     -12    +   3  =  -9  

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3  

                    4x2 - 12x + 3x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4x • (x-3)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-3)

Step-5 : Add up the four terms of step 4 :

                   (4x+3)  •  (x-3)

                                 Hope this helps!

(a) Approximately 0.22% of the runners have heart rates above 140.

(b) Approximately 27.84% of the nonrunners have heart rates above 140.

(a) The percentage of runners with heart rates above 140 can be determined by calculating the cumulative probability of the normal distribution N(104, 12.5) beyond the value of 140. We subtract the cumulative probability from 1 and multiply by 100 to obtain the percentage.

Using statistical software or a standard normal distribution table, we can find the z-score for 140 in the N(104, 12.5) distribution. The z-score formula is given by: z = (x - μ) / σ, where x is the value (140 in this case), μ is the mean (104), and σ is the standard deviation (12.5).

Substituting the values, we get: z = (140 - 104) / 12.5 = 2.88 (approximately)

Looking up the z-score in the standard normal distribution table or using software, we find that the cumulative probability for z = 2.88 is approximately 0.9978.

To calculate the percentage of runners with heart rates above 140, we subtract this cumulative probability from 1: 1 - 0.9978 = 0.0022.

Converting this to a percentage, we get 0.0022 * 100 = 0.22%.

Therefore, approximately 0.22% of the runners have heart rates above 140.

(b) To calculate the percentage of nonrunners with heart rates above 140, we follow a similar process using the N(130, 17) distribution.

Using the same z-score formula, we find the z-score for 140 in the N(130, 17) distribution: z = (140 - 130) / 17 = 0.5882 (approximately).

Looking up the z-score in the standard normal distribution table or using software, we find that the cumulative probability for z = 0.5882 is approximately 0.7216.

To calculate the percentage of nonrunners with heart rates above 140, we subtract this cumulative probability from 1: 1 - 0.7216 = 0.2784.

Converting this to a percentage, we get 0.2784 * 100 = 27.84%.

Therefore, approximately 27.84% of the nonrunners have heart rates above 140.

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The angle G is (1/18) th {or (20/360)th } fraction of complete circle.

The angle G is measured to be 20°.

We know, the total angle of a complete circle is 360°.

Thus, by simple fraction we can say,

The angle G fraction of complete circle is = 20° / 360°

Simplifying we get, the angle G fraction of complete circle is = 1/18

Hence the angle G is (1/18 )th fraction of a complete circle.

In mathematical term, fractions are defined as a part of the whole. In other words, fraction is referred to the ratio of the value observing to the whole set of values.

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