Suppose The Diameter Of A Circle Is 6 Units What Is Its Circumference? Use 3.14 For Pi And Enter Your (2024)

Based on the given information, the volume of the rectangular prism is 90 cubic units.

What is the volume of the rectangular prism?

The volume of a rectangular prism is given by the formula:

V = l x w x h

where V is the volume, l is the length of the prism, w is the width of the prism, and h is the height of the prism.To find the volume of a rectangular prism, you simply multiply the length, width, and height of the prism together. The result will be in cubic units, since volume is a measure of three-dimensional space.

The formula for the volume of a rectangular prism is V = l x b x h, where l, b, and h are the length, width, and height of the prism, respectively.

Substituting the given values, we get:

V = 6 x 5 x 3

V = 90

Therefore, the volume of the rectangular prism is 90 cubic units

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Answer:5 8

Step-by-step explanation:left 2 up 3

The angles of ΔABC are ∠A = 40.86° , ∠B = 69.57°, and ∠C = 69.57° (rounded to two decimal places)

What are the angles of triangle?

To find the angles of ΔABC, we can use the Law of Cosines and the Law of Sines. The Law of Cosines relates the sides and angles of a triangle, and states that for any triangle ABC with sides a, b, and c and angles A, B, and C opposite the respective sides:

c² = a² + b²- 2ab cos(C)

b² = a² + c² - 2ac cos(B)

a²= b² + c² - 2bc cos(A)

The Law of Sines relates the sides and angles of a triangle and states that:

sin(A)/a = sin(B)/b = sin(C)/c

Using the given values, we can solve for the angles:

a = 24 ft, b = 21 ft, c = 21 ft

c² = a² + b² - 2ab cos(C)

(21)² = (24)² + (21)² - 2(24)(21) cos(C)

441 = 1053 - 1008 cos(C)

cos(C) = (1053 - 441) / (2 * 24 * 21)

cos(C) = 0.3541667

C = [tex]cos^{-1(0.3541667)}[/tex]

C = 69.57° (rounded to two decimal places)

b² = a² + c² - 2ac cos(B)

(21)² = (24)² + (21)² - 2(24)(21) cos(B)

441 = 1053 - 1008 cos(B)

cos(B) = (1053 - 441) / (2 * 24 * 21)

cos(B) = 0.3541667

B = [tex]cos^{-1(0.3541667)}[/tex]

B = 69.57° (rounded to two decimal places)

A = 180 - B - C

A = 180 - 69.57 - 69.57

A = 40.86° (rounded to two decimal places)

Therefore, the angles of ΔABC are ∠A = 40.86°, ∠B = 69.57°, and ∠C = 69.57° (rounded to two decimal places).

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Answer:

∠ A = ∠ X = 54°

Step-by-step explanation:

given Δ ABC ≅ Δ XYZ , then corresponding angles are congruent , that is

∠ A ≅ ∠ X

5n + 34 = - 2 + 14n ( subtract 14n from both sides )

- 9n + 34 = - 2 ( subtract 34 from both sides )

- 9n = - 36 ( divide both sides by - 9 )

n = 4

then

∠ A = 5n + 34 = 5(4) + 34 = 20 + 34 = 54°

∠ X = - 2 + 14n = - 2 + 14(4) = - 2 + 56 = 54°

The correct options are B. C. E, For events A and B to be independent, the occurrence of event B should not affect the probability of event A. In other words, P(A|B) = P(A) and P(A|BC) = P(A), where BC is the complement of B.

Therefore, the following equalities would indicate that events A and B are independent:

P(A) = P(B) (This equality is not always true, so it does not indicate independence.)

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|B) = P(B) (This equality is not always true, so it does not indicate independence.)

P(A|BC) = P(A)

So, the equalities that indicate that events A and B are independent are:

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|BC) = P(A)

Therefore, the correct options are:

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|BC) = P(A)

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A company also tries to encourage sales by periodically offering 10% off coupon codes. Suppose that we select a day at random. Let A = a coupon code is offered and let B = the customer makes a purchase. Which of the following equalities would indicate that events A and B are independent? Check all that apply.

A. P(A) = P(B)

B. P(A|B) = P(A|BC)

C. P(A|B) = P(A)

D. P(A|B) = P(B)

E. P(A|BC) = P(A)

We can see that the vertex of the parabola is (-2, 4), and since the coefficient of the squared term is negative, the parabola opens.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The given function f(x) = - ( x+ 2) * (x+2) + 4 is written in standard form of a quadratic function, which is:

f(x) = a(x - h)(x-h) + k

where a, h, and k are constants.

In this case, we can rewrite the function in the standard form by completing the square:

f(x) = - ( x+ 2) * (x+2) + 4

= - (x*x + 4x + 4) + 4 (expand and simplify)

= - (x*x + 4x + 4) + 4(1) (factor out -1 from the first two terms)

= - (x*x + 4x + 4 - 4) + 4 (add and subtract 4 inside the parenthesis)

= - (x + 2)*(x+2) + 4 (factor the perfect square trinomial)

So, the quadratic function is written in standard form as f(x) = - (x + 2)*(x+2) + 4.

Therefore, we can see that the vertex of the parabola is (-2, 4), and since the coefficient of the squared term is negative, the parabola opens

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Answer:

[tex]{2}^{5} , \: {6}^{2} , \: {3}^{4} , \: {5}^{3} \: \: (ans)[/tex]

Step-by-step explanation:

Given Numbers:

In their exponential form -

[tex] {6}^{2} [/tex]

[tex] {3}^{4} [/tex]

[tex] {2}^{5} [/tex]

[tex] {5}^{3} [/tex]

On getting simplified -

[tex] {6}^{2} = 36[/tex]

[tex] {3}^{4} = 81[/tex]

[tex] {2}^{5} = 32[/tex]

[tex] {5}^{3} = 125[/tex]

As stated in question:To order the given numbers from starting with the smaller to the bigger that is, in ascending order.

In ascending order -

32, 36, 81, 125

Or,

[tex] {2}^{5} , \: {6}^{2} , \: {3}^{4} , \: {5}^{3} [/tex]Extras:If needed, ordering of the required numbers from bigger to smaller that is in descending order.

In descending order -

125, 81, 36, 32

Or,

[tex] {5}^{3} , \: {3}^{4} , \: {6}^{2} , \: {2}^{5} [/tex]Hence, required answer:

From small to big that is in ascending order-

[tex]{2}^{5} , \: {6}^{2} , \: {3}^{4} , \: {5}^{3} \: \: (ans)[/tex]

The critical value for this interval is 2.093. The margin of error is:105.364 < μ < 122.636

What is random sample ?

A random sample is a subset of a larger population that is chosen in such a way that every member of the population has an equal chance of being selected. In other words, a random sample is a sample that is chosen at random from the population, without any bias or preference for certain members of the population.

[tex]ME = 2.093 * (10/\sqrt{20}) = 9.145[/tex]

The confidence interval is:

114 - 9.145 < μ < 114 + 9.145

105.855 < μ < 122.145

(b) For a 95% confidence interval with a sample size of 26, we can also use the t-distribution with n-1 degrees of freedom. The critical value for this interval is 2.064. The margin of error is:

[tex]ME = 2.064 * (10/\sqrt{26}) = 8.636[/tex]

The confidence interval is:

114 - 8.636 < μ < 114 + 8.636

105.364 < μ < 122.636

(c) For a 98% confidence interval with a sample size of 20, we can use the t-distribution with n-1 degrees of freedom. The critical value for this interval is 2.861. The margin of error is:

[tex]ME = 2.861 * (10/\sqrt{20}) = 12.462[/tex]

The confidence interval is:

114 - 12.462 < μ < 114 + 12.462

101.538 < μ < 126.462

The GCF given term of[tex]10x^4y^3 and 4x^3y^2 is 2x³y².[/tex]

What is Greatest Common Factor ?

Greatest Common Factor (GCF) is the largest factor that two or more numbers have in common. In other words, it is the greatest number that divides evenly into two or more given numbers without leaving a remainder.

To find the Greatest Common Factor (GCF) of 10x^4y^3 and 4x^3y^2, we need to find the largest factor that both terms have in common.

We can break down each term into its prime factors as follows:

[tex]10x^4y^3[/tex] = 2 * 5 * x * x * x * x * y * y * y

[tex]4x^3y^2[/tex]= 2 * 2 * x * x * x * y * y

The factors that both terms have in common are 2, x^3, and y^2. Therefore, the GCF is:

[tex]2 * x^3 * y^2[/tex]

Which simplifies to:

2x³y²

Therefore, the GCF of [tex]10x^4y^3 and 4x^3y^2 is 2x³y².[/tex]

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Answer:

X and C are the variables

A variable is a symbol which represents a mathematical object, in this case they will be x and c.

The solution to the system of equations 2x + 3y = -1 and 5x - 2y = -12 is x = -2 and y = 1.

What is the solution to the system of equation?

Given the system of equation in the question;

2x + 3y = -1

5x - 2y = - 12

To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation.

Let's solve the first equation, 2x + 3y = -1, for x:

2x + 3y = -1

2x = -3y - 1

x = (-3/2)y - 1/2

Now we can substitute this expression for x into the second equation,

5x - 2y = -12:

Plug in x = (-3/2)y - 1/2

5((-3/2)y - 1/2) - 2y = -12

Distributing the 5 and simplifying, we get:

(-15/2)y - 5/2 - 2y = -12

(-15/2)y - 2y = -12 + 5/2

(-19/2)y = -19/2

y = 1

Now we can substitute y = 1 into either equation to find x.

Let's use the first equation:

2x + 3y = -1

Plug in y = 1

2x + 3(1) = -1

2x + 3 = -1

2x = -4

x = -2

Therefore, the solution of equations is x = -2 and y = 1.

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ANSWER C.(0.97)

Have a nice day

Answer: c. 0.97

Step-by-step explanation:

We are being asked to find P(X≤2). In other words, what is the probability of 2 or less broken crayons. To do this, we will add up all of the P(X) values that are 2 or less.

P(0) + P(1) + P(2)

0.52 + 0.35 + 0.1

0.97

Answer:

[-5;5].

Step-by-step explanation:

1. the min and max of y=sin[x] is '-1' and '+1'. Then

2. the required minimum of f[x]=5sin[x] is '-5'

maximum of f[x]=5sin[x] is '+5'.

8a. 4 m, 6 m, 9 m set of Iengths can form a triangIe. (YES)

What is a triangIe?

Three edges and three vertices define a triangIe as a poIygon. It is one of the fundamentaI geometric shapes. TriangIe ABC is the designation for a triangIe with vertices A, B, and C. When three points are non-coIIinear in EucIidean geometry, they each produce a distinct triangIe and pIane.

The sum of any two sides of is greater than the third side, then the sides form a triangIe.

8a.

The sides of a triangIe are 4 m, 6 m, 9 m.

4 + 6 = 10 > 9

6 + 9 = 15 > 4

4 + 9 = 13 > 6

The sides form a triangIe.

8b.

The sides of a triangIe are 5 cm, 10 cm, 15 cm.

5 + 10 = 15

5 + 15 = 20 > 10

10 + 15 = 25 > 5

The sum of the first two sides is equaI to the third side. Thus it does not form a triangIe.

8c.

The sides of a triangIe are 17 in, 22 in, 43 in.

17 + 22 = 39 < 43

17 + 43 = 60 > 22

22 + 43 = 65 > 17

The sum of the first two sides is Iess than the third side. Thus it does not form a triangIe.

8d.

The sides of a triangIe are 20 ft, 21 ft, 35 ft.

20 + 21 = 41 > 35

20 + 35= 55 > 21

21 + 35 = 56 > 20

The sides form a triangIe.

8b. 5 cm, 10 cm, 15 cm of Iengths can not form a triangIe. (NO)

8c. 17 in, 22 in, 43 in set of Iengths can not form a triangIe. (NO)

8d. 20 ft,

21 ft, 35 ft set of Iengths can form a triangIe. (YES)

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Jackson plays for 14 minutes and Cooper plays for 34 minutes, with Cooper playing 20 minutes more than Jackson.

The ratio of Jackson's time to Cooper's time is 3:7. Cooper spends 20 minutes more on his games than Jackson does. This can be expressed as Jackson spending x minutes, and Cooper spending (x+20) minutes.

The ratio of 3:7 can be expressed as 3/7=x/(x+20).

Solving the equation, x=14 and x+20=34.

Therefore, Jackson plays for 14 minutes and Cooper plays for 34 minutes.

This can be checked by multiplying the ratio: 3/7*34=14.

In conclusion, Jackson plays for 14 minutes and Cooper plays for 34 minutes, with Cooper playing 20 minutes more than Jackson.

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The graph representation of the function f(x) is below.

Define the term Graph?

A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system.

Given function; [tex]f(x) = x^3 - 3x^2 - 4x[/tex]

We can find the,

Factors of f(x) are, [tex]x(x+1)(x-4)[/tex]

Roots of f(x) are x=0, x= -1, and x= 4

On the x-axis, the graph rises through -1 before falling and crossing through 0. Through 4, it turns up once more before heading toward positive infinity to complete.

The plotted graph of the function f(x) is represented below.

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The Roots of f(x) are x=0, x= -1, and x= 4 and the graph representation of the function f(x) is below.

Define the term Graph?

A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system.

Given function; [tex]f(x) = x^3 - 3x^2 - 4x[/tex]

We can find the,

Factors of f(x) are, x (x+1) (x-4)

Roots of f(x) are x=0, x= -1, and x= 4

On the x-axis, the graph rises through -1 before falling and crossing through 0. Through 4, it turns up once more before heading toward positive infinity to complete.

The plotted graph of the function f(x) is represented below.

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The magnitude of the resultant force is 84.85 pounds and the direction angle is S61.2°E.

To calculate the magnitude of the resultant force, we will use the Pythagorean Theorem. The formula is a2 + b2 = c2, where a and b are the magnitudes of the two forces, and c is the magnitude of the resultant force. We are given the magnitudes of the two forces, so we plug in the values to get 702 + 502 = c2. We solve for c by taking the square root of both sides, which gives us the magnitude of the resultant force, 84.85 pounds.Next, we need to calculate the direction angle of the resultant force. We will use the Law of Cosines. The formula is c2 = a2 + b2 - 2abcosC, where C is the angle between the two forces. We plug in our values to get 842 = 702 + 502 - 2(70)(50)cosC, and solve for cosC. We then take the inverse cosine of both sides to get the angle C, which is S61.2°E. The direction angle of the resultant force is S61.2°E.

To calculate the magnitude of the resultant force:

a = 70 pounds

b = 50 pounds

[tex]a2 + b2 = c2[/tex]

702 + 502 = c2

4900 + 2500 = c2

7400 = c2

c = √7400

c ≈ 84.85 pounds

So the magnitude of the resultant force is approximately 84.85 pounds.

To calculate the direction angle of the resultant force:

c2 = a2 + b2 - 2abcosC

842 = 702 + 502 - 2(70)(50)cosC

7400 - 4900 - 2500 = - 140000cosC

cosC = -2400/-140000

cosC ≈ 0.017143

C = [tex]cos^-1(0.017143)[/tex]

C ≈ 88.8°

The angle between the two forces is 88.8°. However, we need to find the direction angle of the resultant force, which is the angle between the resultant force and the positive x-axis. To do this, we subtract the angle between the two forces from 180°:

180° - 88.8° = 91.2°

So the direction angle of the resultant force is S91.2°E (south 91.2 degrees east).

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Answer:

Mathematics score ≥ 52

Step-by-step explanation:

Inequalities:

Let the score in French = x

Score in Mathematics = 20 more than French

= 20 + x

Score in social studies = half of mathematics score

[tex]= \dfrac{1}{2}*(20 +x)[/tex]

[tex]= \dfrac{1}{2}*20 + \dfrac{1}{2}*x \ \ \ {\text{\bf [Distributive property]}}\\\\= 10 + \dfrac{1}{2}x[/tex]

Total score > 110

[tex]x + x + 20 + 10 + \dfrac{1}{2}x > 110\\\\\ \ \ \ \ \ \ \ \ 30 + 2x + \dfrac{1}{2}x > 110\\\\[/tex]

[tex]30 + \dfrac{4x+x}{2} > 110[/tex]

[tex]30 + \dfrac{5x}{2} > 110[/tex]

Subtract 30 from both sides,

[tex]\dfrac{5x}{2} > 110 - 30\\\\ \dfrac{5x}{2} > 80[/tex]

Multiply the entire equation by 2,

5x > 80*2

5x > 160

Divide both sides by 5,

x> 160 ÷5

x > 32

Mathematics is 20 more than x.

Mathematics marks will be greater than or equal to 52.

Mathematics score ≥ 52

14 + (-5) = 9 represents the correct expression of the distance between the friends.

To find the distance between the friends, we need to add up the total distance they have walked in opposite directions. We can represent the distance Joy walked forward as 14, and the distance Shaunte walked backwards as -5 (since she walked in the opposite direction). Therefore, the expression that correctly represents the distance between the friends is:

14 + (-5) = 9

So the distance between the friends is 9 steps.

The method used to find the distance between the friends was to calculate the total distance that each person walked, and then add or subtract these distances depending on the direction they walked. This is an example of using vector addition and subtraction to find the net displacement between two objects. In this case, the net displacement is simply the distance between the friends.

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Step-by-step explanation:

Negative slope means the line tilts downward from the left to the right....

Answer:

Step-by-step explanation: a

Answer: -1

Step-by-step explanation:

To find the slope of the line that contains the points (-8, -1) and (-5, -4), we can use the following formula:

slope = (change in y) / (change in x)

So, if we plug in the coordinates of the two points, we get:

slope = (-4 - (-1)) / (-5 - (-8))

slope = (-4 + 1) / (-5 + 8)

slope = -3 / 3

slope = -1

Therefore, the slope of the line that contains the points (-8, -1) and (-5, -4) is -1.

Thus, the account balance after 13 years when compounded monthly is found as: A = $9446.0.

Define about the term compounded monthly?

The amount that is added to a loan as interest favors the lender with accepting the loan and lowers their risk of default. Simple interest refers to an interest rate that is a fixed percentage of the loan's principle.

We need to know the principal, the interest rate, and the time period in order to calculate the monthly compound interest.

The formula for compounded monthly:

A = P [tex](1 + r/n)^{n*t}[/tex]

In which,

P = principal $4,353

A = amount after compounding

r = annual interest rate 6%

t = time in years 13 years

n = number of times compounded 12.

Put the values.

A = 4353 [tex](1 + 0.06/12)^{12*13}[/tex]

A = 4353 * 2.17

A = $9446.0

Thus, the account balance after 13 years when compounded monthly is found as: A = $9446.0.

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The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4) raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4) raise to the power -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

Answer:

f(x) = 1.12 * f(x-1) (number of customers in the x-th month)

Step-by-step explanation:

The number of customers is increasing by 12% each month, which means that the number of customers in the next month will be 100% + 12% = 112% = 1.12 times the number of customers in the current month.

If we let f(x) be the number of customers in the x-th month, and assuming that the company has 68 customers when it opens, we can write:

f(1) = 68 (number of customers in the first month)

f(2) = 1.12 * f(1) (number of customers in the second month)

f(3) = 1.12 * f(2) (number of customers in the third month)

f(4) = 1.12 * f(3) (number of customers in the fourth month)

...

f(x) = 1.12 * f(x-1) (number of customers in the x-th month)

This recursive formula shows that the number of customers in each month is 1.12 times the number of customers in the previous month.

The surface area of the composite shape is 328 cm².

What is the surface area of the composite shape?

The surface area of the composite shape is calculated as follows:

The surface area of composite shape = surface area of the large cuboid - surface area of the small cuboid + (6 * 8) cm² + (10 * 8) cm²

The surface area of the large cuboid:

The top and bottom faces each have an area of length x width = 14 cm x 8 cm = 112 cm².

The front and back faces each have an area of height x width = 8 cm x 8 cm = 64 cm².

The left and right faces each have an area of length x height = 14 cm x 8 cm = 112 cm².

Therefore, the total surface area of the cuboid is:

= 2(112 cm²) + 2(64 cm²) + 2(112 cm²)

= 224 cm² + 128 cm² + 224 cm²

= 576 cm²

The surface area of the large cuboid:

The top and bottom faces each have an area of length x width = 10 cm x 6 cm = 60 cm².

The front and back faces each have an area of height x width = 8 cm x 6 cm = 48 cm².

The left and right faces each have an area of length x height = 10 cm x 8 cm = 80 cm².

Therefore, the total surface area of the cuboid is:

= 2(60 cm²) + 2(48 cm²) + 2(80 cm²)

= 120 cm² + 96 cm² + 160 cm²

= 376 cm²

So, the surface area of the composite shape = 576 cm² - 376 cm² + 48 cm² + 80 cm²

The surface area of the composite shape = 328 cm²

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Thus, the final amount in the account of the women after reaching teh age of 65 is $22,3101.5.

Explain about the compounded quarterly?

A quarterly compounded rate means that the principal amount gets compounded four times over the course of a full year. According to the compound interest procedure, if the duration of compounding is longer inside a year, the investors would receive higher future values for their investment.

For the question:

From starting age 50 to 60:

Initial amount R = $1700

rate of interest i = 0.07/4 = 0.0175

number of time compounded n = 4*10 = 40 (compounded quarterly)

Now,

Future Value (ordinary annuity) S:

S = R[tex][\frac{(1 + i)^{n} - 1 }{i}][/tex]

S = 1700*[tex][\frac{(1 + 0.0175)^{40} - 1 }{0.0175}][/tex]

S = 1700*57.23

S = $97298.0

Now,

The $97,298.0 earns as compounded interest.

New ordinary annuity started over a period of 5 years till 65 age.

$97,298.0 compounded monthly for 5 years:

Future value A:

A = P[tex](1 + i)^{n}[/tex]

n = 12*5 = 60 years

i = 7% = 0.07

A = $97,298.0[tex](1 + 0.07/12)^{60}[/tex]

A = 137,190.0

Future value for mutual fund:

S = R [tex][\frac{(1 + i)^{n} - 1 }{i}][/tex]

S = 400[tex][\frac{(1 + 0.07/12)^{60} - 1 }{0.07/12}][/tex]

S = 400* 71.6

S = 85,911.5

Total amount = 137,190.0 + 85,911.5

Total amount = $22,3101.5

Thus, the final amount in the account of the women after reaching teh age of 65 is $22,3101.5.

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Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Thus, the cardinal number of the set E is found to be: N(E) = 6.

Explain about the cardinal number?

A cardinal number describes or expresses how many of anything are present.

So all natural numbers are often refereed to as cardinal numbers. Cardinal numerals have been used for counting. When an ordinal number is an integer that represents the location or place of an object.

The description of a cardinal number is really a number that is used to express quantity in whole numbers. Decimals and fractions are not regarded as cardinal numbers. Natural numbers and numbering numbers constitute cardinal numbers. Each of them is a positive integer.

Given data:

N(CxE) = 18

C = {4, 5, 6)

In which N is the cardinal number, that is the total elements present in the set.

So,

N(C) = 3

Given that: N(CxE) = 18

The formula for the Cartesian product is:

N(CxE) = N(C) * N(E)

18 = 3* N(E)

N(E) = 18 /3

N(E) = 6

Thus, the cardinal number of the set E is found to be: N(E) = 6.

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Complete questions:

Find N(E), Given That N(CxE) = 18 And C = {4, 5, 6).

Α. 6

B. 9

C. 3

D. 5