Activity 2 1. Rudy is a business man from Soweto. Every month he makes many business calls on his cell phone. His contract on his phone has now expired and he needs to get a new cell phone. He has to choose between two options, either buying a business contract or using the pay-as-you- go option. With the business contract, he would pay a monthly subscription fee of R180 and R1,60 for each peak-call minute. With the pay-as-you-go option, you don't pay a monthly subscription, but you pay R2,60 for each peak-call minute. Business Contract Free minutes Monthly subscription Call rates None R180 per month R1,60 per minute (or part thereof) Pay-as-you-go None None R2,60 per minute (or part thereof) 1.1 Explain why the equation C = 180 + 1,60t represents the total monthly cost (C) in rands, for calls made using the business contract for a giving amount of time (t), in minutes. 1.2 Write down an equation in the form of C =........ to rep[resent Rudy's total monthly cost (C) in rand, for calls using the pay-as-you-go option for a given amount of time (t), in minutes. 1.3 Calculate the cost of Rudy's calls on the pay-as-you-go option if they add up to 82 minutes and 15 seconds.​

The set of values that shows outputs of a relation that is NOT a function is {3, 6, 8, 3, 6, 3, 8, 9, 9}.

To determine whether a relation is a function or not, we need to check whether each input has a unique output. If an input has more than one output, then the relation is not a function.

From the given inputs, we can calculate the outputs of the four relations. By examining the outputs of each relation, we can see that for the set {3, 6, 8, 3, 6, 3, 8, 9, 9}, the input 2 has an output of 3 and an output of 3, the input 5 has an output of 6 and an output of 6, and the input 6 has an output of 3 and an output of 9. Therefore, the relation that corresponds to this set of outputs is not a function.

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Represents the vector f + g.  C.

The sum of two vectors, we simply add their corresponding components.

In this case,
f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9)
So the resulting vector has components (3, 3, 9).
Now we need to find the graph that represents this vector.

Graphing a vector in three dimensions can be challenging, but we can use the following method:
Start at the origin (0, 0, 0) of the 3D coordinate system.
Move 3 units in the x-direction, 3 units in the y-direction, and 9 units in the z-direction.
Mark the endpoint of this displacement as the tip of the vector.

Option A has a similar direction, but it is longer than f + g.

Option B has the correct length, but it is pointing in the wrong direction.

Option D is pointing in the correct direction, but it is too short.

We only add the respective components of the two vectors to get their sum.

Thus, f + g = (4 - 1, 3 + 0, 7 + 2) = (3, 3, 9) in this situation.

The resultant vector has three (3), three (3), and nine (9).

We now need to identify the graph that this vector is represented by.

It might be difficult to graph a vector in three dimensions, however we can try the following approach:

Start at the 3D coordinate system's origin (0, 0, 0).

Move three units in the x, three units in the y, and nine units in the z directions.

Make a note of the vector's tip being the terminus of this displacement.

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There are 12 kids live on Robinson Street.

Since, We have to given that;

After school, all of the kids who live on Robinson Street play baseball for 3 hours.

And, Everyone gets to play catcher for 1/4 of an hour.

Let number of kids = x

Hence, We get;

x × 1/4 = 3

⇒ x = 12

Thus, There are 12 kids live on Robinson Street.

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COVARIANCE.S uses the number of data points minus one to adjust for the sample size. The functions COVARIANCE.P and COVARIANCE.S return different values when using the same data.

The reason why COVARIANCE.P and COVARIANCE.S return different values when using the same data is that they use different formulas to calculate covariance. COVARIANCE.P calculates the average of the product of deviations from the means of the two variables, while COVARIANCE.S calculates the sum of the product of deviations from the means of the two variables, divided by the number of data pairs minus one.

COVARIANCE.P assumes that the data represents the entire population, and therefore divides by the total number of data points. COVARIANCE.S, on the other hand, assumes that the data represents a sample of the population, and therefore divides by the number of data points minus one to account for the degree of freedom.

In summary, the difference between COVARIANCE.P and COVARIANCE.S lies in the way they account for the variance in the data, with COVARIANCE.P using the total number of data points, while COVARIANCE.S uses the number of data points minus one to adjust for the sample size.
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The outside of an apple seed is coated with a protective layer called the seed coat. This hard, outer layer is designed to protect the inside of the seed from damage, disease, and pests. The seed coat also helps

Regulate the moisture levels within the seed, ensuring that it doesn't dry out or become too wet. As the apple tree grows, it produces fruit that is eaten by animals. When animals eat the apple, they consume the entire fruit, including the core and seeds. The seed coat protects the seeds as they pass through the animal's digestive system, ensuring that they remain intact and ready to germinate once they are excreted.

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The question is incomplete, the complete question is:

Answer: Let's denote the masses of the four men as a, b, c, and d. Then we can use the given information to set up a system of equations:

Mean mass of 4 men is 97.5kg:

(a + b + c + d) / 4 = 97.5

a + b + c + d = 390

Modal mass is 101kg:

We know that one of the men has a mass of 101kg. Let's say that man is a. Then we have two cases:

Case 1: b, c, and d each have a mass less than 101kg.

In this case, the second largest mass must be the mode. Let's say that mass is b. Then we have:

b = a - x (where x is some positive number less than 4)

c = a - y (where y is some positive number less than 4 and not equal to x)

d = a - z (where z is some positive number less than 4 and not equal to x or y)

Note that we subtract x, y, and z from a because b, c, and d have masses less than a.

Then we have:

a + (a - x) + (a - y) + (a - z) = 390

4a - (x + y + z) = 390

Case 2: b, c, and d each have a mass greater than 101kg.

In this case, the second smallest mass must be the mode. Let's say that mass is b. Then we have:

b = a + x (where x is some positive number less than 4)

c = a + y (where y is some positive number less than 4 and not equal to x)

d = a + z (where z is some positive number less than 4 and not equal to x or y)

Note that we add x, y, and z to a because b, c, and d have masses greater than a.

Then we have:

a + (a + x) + (a + y) + (a + z) = 390

4a + (x + y + z) = 390

Range is 8kg:

The range is the difference between the largest and smallest masses. Let's say that the smallest mass is e and the largest mass is f. Then we have:

f - e = 8

Now we have three equations (either from Case 1 or Case 2) and three unknowns (a, x, and y or a, x, and z) that we can solve for to find the masses of the four men. However, the system of equations is quite complicated and solving it by hand can be tedious. One way to solve it is to use a numerical method, such as Newton's method or the bisection method. Alternatively, we can use a computer algebra system to solve it.

The value of π is best represented by multiplying 5.28 by 0.84 (option A, A)

Now, let's take a look at the information given to us. We know that the radius of the circle is 0.84 inches. The radius is the distance from the center of the circle to its edge, and it is half the length of the diameter. So, we can find the diameter by multiplying the radius by 2, which gives us a diameter of 1.68 inches.

We also know that the circumference of the circle is 5.28 inches. The circumference is the distance around the edge of the circle. We can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π is the value of pi, and r is the radius.

We can rearrange this formula to solve for π, which gives us π = C/2r. Plugging in the values we know, we get π = 5.28/2(0.84) = 3.14.

Hence the correct option is (a).

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The three points lie on the line that best represents the total cost of {y} of x pens are:  (0,0), (4, 3) and (8, 6).

We have the information from the question:

James buys 4 pens for $3.

To find the three points lie on the line that best represents the total cost of {y} of x pens.

Now, According to the question:

'x' represent the number of pens

'y' represent the total cost

When x = 0 , y = 0 and when x = 4 , y = 3

Assume, y = mx + c

∴ [tex]y = \frac{3}{4}x + c[/tex]

when x = 0 , y = 0 Plug the values of x and y in above equation.

=> [tex]0=\frac{3}{4}.0+c[/tex]

Put c = 0, we get:

[tex]y = \frac{3}{4}x[/tex]

Now, From the graph :

The three points lie on the line that best represents the total cost of {y} of x pens are:

When x = 8, [tex]y = \frac{3}{4}.8=6[/tex]

∴ It passes (0,0), (4, 3) and (8, 6).

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The equations in the box are true, as 2/5 and 4/10 are equivalent fractions.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

For the left fraction, we have that 2 out of 5 spaces are painted, hence:

2/5.

For the right fraction, we have that 4 out of 10 spaces are painted, hence:

4/10.

4/2 = 2 and 10/2 = 5, hence the simplified fraction is given as follows:

2/5.

As the fractions are equal, the statement is true.

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The least squares error for the given line is 2306.

The equation of the given line is y = 3 - 5x.

To compute the least squares error for the given line, we need to find the vertical distance between each point and the line, square them, and add them up.

Let's first find the predicted y-values for each given x-value using the equation of the line:

For x = -5, y = 3 - 5(-5) = 28

For x = 0, y = 3 - 5(0) = 3

For x = 5, y = 3 - 5(5) = -22

For x = 10, y = 3 - 5(10) = -47

Now we can find the vertical distance between each point and the line:

For the point (-5, 4), the vertical distance is 4 - 28 = -24

For the point (0, 4), the vertical distance is 4 - 3 = 1

For the point (5, 3), the vertical distance is 3 - (-22) = 25

For the point (10, 1), the vertical distance is 1 - (-47) = 48

Now we square each of these distances and add them up:

(-24)^2 + 1^2 + 25^2 + 48^2 = 2306

Therefore, the least squares error for the given line is 2306.

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Answer:

---------------------

According to the graph we can see sections with different temperatures or temperature changes:

the probability of the event is 20/216 = 5/54.To calculate , we need to find the total number of outcomes where this event occurs and divide it by the total number of possible outcomes.

The total number of possible outcomes when rolling three 6-sided dice is 6 x 6 x 6 = 216.

To count the number of outcomes where the number on the first die is strictly larger than the sum of the numbers on the other 2, we can use the following steps:

- Since the first die has to be strictly larger than the sum of the other 2, the maximum number that can appear on the other 2 dice is 5+5=10.
- Therefore, for each number from 2 to 6 that appears on the first die, we count the number of ways to get a sum less than or equal to 10 on the other 2 dice.
- Using a table or combinatorial reasoning, we can count the total number of such outcomes as 10+6+3+1+0 = 20.

Therefore, thethe probability of the event is 20/216 = 5/54.

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The statement is true for k + 1. By the principle of mathematical induction, the statement is true for all positive integers n.

To prove that the statement is true for all positive integers n, we will use mathematical induction.

Base case: When n = 1, there is only one dot in the triangle, and the total number of dots is 1, which is equal to n( n + 1)/2 = 1(1+1)/2 = 1. Therefore, the statement is true for n = 1.

Inductive step: Assume that the statement is true for some positive integer k, which means that the kth triangular number can be represented by the formula k(k+1)/2. We need to show that the statement is also true for k + 1, which means that (k+1)((k+1)+1)/2 = (k+1)(k+2)/2 dots can be represented in a triangle with k + 1 dots in its base.

To show this, we can construct a triangle with k + 1 dots in its base by adding one more row to the kth triangle. This row will have k + 1 dots, and the total number of dots in the triangle will be (k+1) + k(k+1)/2 = (k+1)(k+2)/2, which is the formula for the (k+1)th triangular number. Therefore, the statement is true for k + 1.

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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The acronym used in assessing a patient's level of consciousness is A. AVPU.

AVPU stands for Alert, Voice, Pain, and Unresponsive. This mnemonic is commonly used by healthcare professionals to quickly and easily assess a patient's level of consciousness. Here's a brief explanation of each level:

1. Alert: The patient is fully awake, responsive, and aware of their surroundings.
2. Voice: The patient responds to verbal stimuli but may not be fully alert.
3. Pain: The patient responds only to painful stimuli, such as pinching or applying pressure.
4. Unresponsive: The patient does not respond to any stimuli, indicating a potentially critical condition.

In assessing a patient's level of consciousness, the acronym AVPU is the most suitable choice among the options provided. It allows healthcare professionals to quickly evaluate a patient's responsiveness to various stimuli and determine their level of consciousness.

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The distance of point O from side AD is 5.

To find the distance of point O from side AD, we can use the fact that the area of triangle BOC is 20.

Let's denote the distance of point O from side AD as x.

We know that the area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

In triangle BOC, the base is BC with a length of 8, and the height is x (the distance of O from AD).

Therefore, we have:

(1/2) * 8 * x = 20

4x = 20

x = 5

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Answer: To differentiate this function, we need to use the product rule and the chain rule.

First, we will simplify the function:

f(y) = (1/y^2 - 3/y^4) * y(y + 9y^3)

f(y) = (y + 9y^3) / y^3 - (3y + 27y^3) / y^5

f(y) = y^-3 * (y^4 + 9y^6 - 3y^4 - 27y^6)

f(y) = 6y^4 / y^3

f(y) = 6y

Now we can differentiate:

f'(y) = 6

Therefore, the derivative of f(y) is 6.

Using product rule and power rule of differentiation, the derivative of the function f(y) = 1/y² - 3/y⁴ * (y + 9y³) is f'(y) = 12/y⁷ - 6/y⁶ - 54/y⁵.

To differentiate the given function,

We need to use product rule and the power rule of differentiation

use product rule to differentiate two terms in the function;

Let's consider the first term: 1/y²

The derivative of 1/y² with respect to y is:

d(1/y²)/dy = -2/y³

Now, let's consider the second term: -3/y⁴ * (y + 9y³)

The derivative of -3/y⁴ with respect to y is:

d(-3/y⁴)/dy = 12/y⁵

The derivative of (y + 9y³) with respect to y is:

d(y + 9y³)/dy = 1 + 27y²

Let's use product rule to differentiate the expression

Using the product rule, the derivative of the entire expression f(y) = 1/y₂- 3/y⁴ * (y + 9y³) is:

f'(y) = (1/y²) * (d(-3/y⁴ * (y + 9y³))/dy) + (-3/y⁴ * (y + 9y³)) * (d(1/y²)/dy)

Let's plug the value into the previous expression

f'(y) = (1/y²) * (12/y⁵) + (-3/y⁴* (y + 9y³)) * (-2/y³)

Simplifying further:

f'(y) = 12/y⁷ - 6(y + 9y³)/y⁷

      = 12/y⁷ - 6(y/y⁷ + 9y³/y⁷)

      = 12/y⁷ - 6/y⁶ - 54y²/y⁷

      = 12/y⁷ - 6/y⁶ - 54/y⁵

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Using trigonometric ratios, the value of sinθ,  cosθ and tanθ are 8/√113, 7/√113 and 8/ respectively.

To find the values of the trigonometric function, we have to use Pythagorean theorem first to determine the hypothenuse of the triangle.

x² = 8² + 7²

x² = 113

x = √113

x = 10.63 units

a. sin θ = opposite / hypothenuse

sinθ = 8/√113

b. cos θ = adjacent / hypothenuse

cosθ = 7/ √113

c. tan θ = opposite / adjacent

tanθ = 8/7

19.

sinθ = 0.5126

Take the sin inverse of θ

θ = sin⁻¹(0.5126)

θ = 30.84°

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Answer:

A. True

Step-by-step explanation:

[tex]\frac{6}{8}[/tex]   and   [tex]\frac{3}{4}[/tex]   are equivalent fractions.

The Solve the inequality for W,in the expression w- 9 ≥25 can  be written as  w ≥ 34.

Inequality, In mathematics, can be regarded as the statement of an order relationship which involves the use of the expression such as the greater than, greater than or equal to as well as the less than, or less than or equal to.

It should be noted that the expression helps to know the relation between two numbers or algebraic expressions which can be used to know  more about a particular expression.

Given that w- 9 ≥25

w - 9 + 9 ≥ 25 + 9

w ≥ 34

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When Aisha divides the total number of roses, which is 251, by 7, she gets 35 R 6. The correct interpretation of R 6 is that she has 6 remaining roses that are not enough to fill another vase of 7.

Aisha has a total of 251 roses (122 yellow and 129 white), and she wants to put them in vases of 7 roses each. When she divides the total number of roses by 7, she gets 35 R 6, which means that she can fill 35 vases of 7 roses each, with 6 roses left over. This remaining 6 roses are not enough to fill another vase, so they are left as leftovers. Therefore, the correct interpretation of R 6 for this situation is that Aisha has 6 remaining roses that are not enough to fill another vase of 7.

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The slope of the line that represents this relationship is 72.

Let the service fee charged by the electrician be represented by "s" and the hourly charge be represented by "h".

s + 3h = 301 (for the job that takes 3 hours)

s + 6h = 517 (for the job that takes 6 hours)

We can solve this system of equations using elimination or substitution to find the values of "s" and "h". For simplicity, we'll use the substitution method.

From the first equation, we can solve for "s" in terms of "h":

s = 301 - 3h

Substituting this into the second equation:

(301 - 3h) + 6h = 517

Simplifying:

301 + 3h = 517

3h = 216

h = 72

Substitute the provided value of h = 72 first equation:

s + 3(72) = 301

Simplifying:

s = 85

So the electrician charges a service fee of $85 and an hourly rate of $72.

The slope of the line that represents this relationship can be interpreted as the rate of change in cost per hour of work. This is simply the hourly charge, which is $72 in this case.

Therefore, the slope of the line is described as,

slope = $72/hour

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The GCF of the expression 24y and (4y² + 12y) is 4y

We have,

To find the greatest common factor (GCF) of 24y and (4y² + 12y), we can first factor out the common term of 4y from the second expression:

4y² + 12y = 4y(y + 3)

Now we can see that both expressions have a factor of 4y, so that is part of the GCF.

To find any additional factors that they have in common, we need to look at the remaining terms.

The first expression, 24y, can be factored as:

24y = 2³ x 3 x y

So the GCF of 24y and (4y² + 12y) is 4y since that is the largest factor they have in common.

Thus,

The GCF of the expression 24y and (4y² + 12y) is 4y

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We have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

To prove the inequality 2^n > n^2 using induction with a basis greater than 4, we will use n=5 as the basis.

Basis: n = 5
2^5 = 32 and 5^2 = 25. Since 32 > 25, the inequality holds true for n = 5.

Now, we need to assume that the inequality holds true for an arbitrary positive integer k > 4, and then prove that it holds true for k + 1.

Assume: 2^k > k^2 for k > 4.

Prove: 2^(k + 1) > (k + 1)^2

Step 1: Multiply both sides of the assumption by 2.
2 * (2^k) > 2 * (k^2)

Step 2: Simplify the left side of the inequality.
2^(k + 1) > 2k^2

Step 3: Show that 2k^2 is greater than (k + 1)^2 for k > 4.
2k^2 > (k + 1)^2
2k^2 > k^2 + 2k + 1

Step 4: Rearrange the inequality to show that it holds true for k > 4.
k^2 - 2k - 1 > 0

Since k > 4, it is clear that k^2 - 2k - 1 > 0, as the left side increases as k increases.

Therefore, we have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

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The aggregate demand curve shifts to the left, indicating a decrease in overall demand in the economy.

A decrease in U.S. net exports would result in a decrease in aggregate demand.

This is because net exports are a component of aggregate demand, which is the total amount of goods and services demanded in an economy.

When net exports decrease, it means that fewer goods and services are being exported from the U.S.

This, in turn, means that there is less demand for U.S. goods and services from foreign buyers.

As a result, the aggregate demand curve shifts to the left, indicating a decrease in overall demand in the economy.

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The simplified expression is (-8x + 17y).

We have,

(x+ 9y) - (9x - 8y)

Now, simplifying the given expression as

(x+ 9y) - (9x - 8y)

= x + 9y - 9x + 8y

= x - 9x + 9y + 8y

= -8x + 17y

Thus, the simplified expression is (-8x + 17y)

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Answer:

Step-by-step explanation:40 - 9 = 31+ 14= 45-21 =24.

If the submarine is 24m below the sea then a integer is -24

Answer:

56

Step-by-step explanation:

The submarine climbed 9m, so its depth is now 40m + 9m = 49m.

Then, it dove 14m, so its depth is now 49m - 14m = 35m.

Finally, it climbed 21m, so its depth is now 35m + 21m = 56m.

Therefore, the integer that represents the depth of the submarine after these changes is 56.

The height of the building is approximately 16.9 meters. The distance between the observer and the building forms the adjacent side of the triangle.

To solve this problem, we can use trigonometry and set up a right triangle with the observer's eye, the top of the building, and the ground. The distance between the observer and the building forms the adjacent side of the triangle, and the height of the building forms the opposite side. We can use the tangent function to solve for the height of the building:

tan(17 degrees) = opposite/adjacent

First, we need to convert the distance from the observer to the building from meters to centimeters, since the height of the observer's eye is given in centimeters.

47 meters = 4700 centimeters

Next, we can plug in the values we have and solve for the height of the building:

tan(17 degrees) = h/4700 + 167

h = (4700 + 167) * tan(17 degrees)

h ≈ 16.9 meters

Therefore, the height of the building is approximately 16.9 meters.

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[tex]10 - x = - 196 \\ [/tex]

let the unknown number be x

[tex]x = - 196 + 10 \\ x = - 186[/tex]

~hope it helps~

The missing number is 186.

To solve this equation, we need to isolate the variable (the unknown number) on one side of the equation. To do this, we can simplify the left side of the equation by subtracting 10 from both sides:

10 - __ = -196 -__ = -206

Then, we can isolate the variable by multiplying both sides of the equation by -1:

__ = 206

Therefore, the missing number is 186.