JohanVanDeVaseYesterdayMathematicsHigh SchoolTARIFF SYSTEMSQUESTION 1 [13 marks]A shopping mall in Bloemfontein has several parking garages, each with its own tariff system. The table below shows the tariffs on garage A and garage B.(Please show calculation)Parking TariffsNumber of hours (h)0 < h < 11 < h < 22 < h < 44 < h < 66 < h < 7h > 7Garage AFreeR5,50R15,50R30,50R50,50R75,50Garage BR5,00R7,00R11,00R26,00R41,00R61,00Question 1.1 [4 marks]Sellwane works at the shopping mall. She arrives at 7:30 and leaves at 17:00 each day. Which parking garage is cheaper for her to use?Question 1.2 [3 marks]Isaac was having coffee with his friends at a restaurant at the shopping mall. They arrived at the mall at 8:23 and left at 10:53, how much would he pay if he used garage B?Question 1.3 [2 marks]On Monday morning Karabo parked her car in one of the parking garages and paid R26,00. In which garage did she park and for how long?

The distance s as a function of time is  s = 50√(162t² -126t +25)

Take miles and hours to be the problem's units.

The distance of the first plane from point p is provided by

x = 150 -450t

The distance of the second plane from point p is given by

y = 200 -450t

The Pythagorean theorem can be used to calculate the distance between them because their flight trajectories are at right angles (s).

s² = x² + y²

s² = (150 -450t) (150 -450t)

² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²

... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)

... s = 50√(162t² -126t +25)

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The probability of drawing a blue socks and white socks is 1/12.

Given that, a drawer contains 10 red socks, 6 white socks and 8 blue socks.

Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.

As we know the probability of an event = Number of favorable outcomes/Total number of outcomes

Total number of outcomes = 10+6+8=24

Probability of getting blue socks = 8/24 = 1/3

Probability of getting white socks = 6/24 =1/4

Now, probability of an event = 1/3 × 1/4 = 1/12

Therefore, the probability of drawing a blue socks and white socks is 1/12.

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Answer:

c

Step-by-step explanation:

The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.

Given:

Let's solve for the following:

• (a). Find C'(x).

Here, we are to find the derivative of C(x).

Apply the sum rule:

• (b). The critical numbers of C(x).

The critical numbers will be the points where the graph changes direction.

Using the derivative, let's solve for x.

Factor the left side using the rational root test:

Now factor using the AC method:

Equate each factor to zero and solve for x:

Therefore, the critical numbers of C(x) are:

x = -6, 5

• (C). Increasing interval.

Use the critical points to find the increasing and decreasing intervals.

Using interval notation, the increasing interval is:

• D. Decreasing interval:

Using interval notation, the decreasing interval is:

ANSWER:

(a). C'(x) = x³ - 4x² - 35x + 150

(b). x = -6, 5

(c). Increasing: (-6, 5) U (5,∞)

Decreasing: (-∞, -6)

The fill in the blanks (that uses division) can be filled as -1.2([tex](\frac{2}{5} )[/tex] ÷ -2, -0.48÷-2 and 0.24.

According to the question,

We have the following information:

-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2

Now, we have to solve this problem and fill the blanks at the same time.

Now, the first step would be to write the question.

So, for the first blank we have:

-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2

Now, the required number is (2/5).

Now, the next step is to multiply -1.2 with 2/5:

-2.4/5

-0.48

So, the second blank can be filled by -0.48.

Now, the third step would be to divide -0.48 by -2:

-0.48÷-2

0.24

So, the next blank can be filled by 0.24.

Hence, the numbers in the blanks are [tex]\frac{2}{5}[/tex], -0.48 and 0.24 respectively.

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Christian, this is the solution to the problem:

p = 2l + 2w

Solving for l, we have:

2l = p - 2w

Dividng by 2 at both sides:

2l/2 = (p - 2w)/2

l = (p - 2w)/2

The correct answer is D.

Victor earns 19% commission

He sold a microscope that cost $368.84.

so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796

Rounding to the nearest cent

So,

the commission = $70.08

Given the parent function:

If y is shifted right by 7 units, we obtain:

If y is compressed horizontally by a factor of 7, we have:

If y is stretched vertically by the factor 7, we obtain:

A shift downwards by 7 units gives:

the answer is 8

add 3+2, that gives u 5, add 7+5 which is 12, do 12-4 its equal to 8

Answer:

Yes

Step-by-step explanation:

-36/6 = -6

Integers are the whole numbers (0.1.2.3.4.5....) and their opposites ...-4,-3,-2,-1

Answer:

I eat birds tasty

Answer:

See below

Step-by-step explanation:

2 + 7  = 9       2 and 7 are prime     the answer is odd but not prime

Arc STU and arc SRU can form the complete circle. Therefore

Dividing both sides by 2, we have

Also, substitute 2 m

pick yes in options 2 and 3

pick no in options 1 and 4

200 is the 17th term of the progression

What is arithmetic progression?

Arithmetic progression or arithmetic sequence (AP) is a numerical series in which the difference between subsequent terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2. A finite arithmetic progression, or simply an arithmetic progression, is a finite section of an arithmetic progression. An arithmetic series is the sum of a finite arithmetic progression. An arithmetic series is the sum of the elements of a finite arithmetic progression. A closed expression determines the product of the members of a finite arithmetic progression with a beginning element a1, common differences d, and n elements in total.

This can be solved using arithmetic progression

Aₙ = a + (n - 1)d

where, Aₙ = 24, d = 35 - 24 = 11

so, n = (Aₙ - a)/d + 1 = (200-24)/11 + 1 = 17

Hence, 200 is the 17th term of the progression

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SOLUTION

If a coordinate is refleted over the x-axis, the formula to apply is

So for B(-5, -5), this becomes

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following formula for the statement

They ask us to rewrite this formula solving for the total price of the computer, it would be like this:

If it is given  f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².

To solve this problem we have to know more about mathematical functions.

What is a mathematical function?

A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.

Example:  f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.

Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.

g(x) = 2- x².

f(x) = 3x - 6.

Therefore,

f(g(x)) = 3( 2- x² ) - 6.                 [where g(x) = 2- x²]

So,  f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²

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The complete question:

Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))

To put

In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means

And now we solve it, therefore

Remember that

Then

Now we can simplify it

And we have it in the standard form

The volume of a rectangular prism is given by

Where L is the length, W is the width, and H is the height of the rectangular prism.

For the given case, we have

Length = 17 in

Width = 8 in

Height = 19 in

Let us substitute these values into the above formula

Therefore, the volume of the given rectangular prism is 2584 cubic inches.

Answer:

1 and 7 and 0

Step-by-step explanation:

Solution:

Given:

The greatest common factor (GCF) is factored out of the expression.

The GCF is 12.

Hence,

Therefore, the factorization of the given polynomial 36a - 12b - 60c is;

Step 1:

Write the equation

Step 2:

Use trial and error to find one the the factor

x - 3 is a factor

Because when you substitute x = 3, the result is zero

Hence, 3 is zero of the polynomial

Step 3

Use the long division

3:4 ratio

height: 52 in

width: height * 4/3 = 52*4/3 = 208/3 in

Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches

9:16 ratio

height: 52 in

width: height * 16/9 = 52*16/9 = 832/9 in

Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches

Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches

Note that Cosine law can be used if three sides of the triangle are given in order to get the angles.

For example, in getting the measurement of angle C

Then take the arccos to get the angle C.

From the problem, we have :

We need to find the measurement of angle F using the same formula above.

Taking the arc cosine :

The answer rounded to the nearest 10th is

We need to find the value for x using the inverse operation:

Then:

Let us solve for x:

The x is subtracting, so it will add up to the other side:

Now, the 84 is positive, so it will be negative on the other side:

Hence, the solution for x is -77.

Given:

a. H0: µ = 0

b. H0: µ ≥ 0

c. H0: µ ≤ 0

d. H0: µ

Required:

To choose the hypotheses that is not valid.

Explanation:

The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

Here the option d is not valid.

Final Answer:

The option d is not valid.

H0: µ < 0

Answer:

Step-by-step explanation:

The quadratic equation in standard form is represented by:

For the following equation;

Compute all the terms on the left side, equalizing 0:

Answer:  [tex](x,y) \to (x+8, y+4)[/tex]

==================================================

Explanation:

The x coordinate of A and A' are -3 and 5 respectively.

This is an increase of +8 since -3+8 = 5

Therefore, we shift the preimage 8 units to the right to get the image point.

That explains how x turns into x+8.

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

The y coordinates of A and A' are 1 and 5 respectively.

This is an increase of +4, so we shift the preimage up 4 units.

This signals that y turns into y+4

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

To recap we found that,

Therefore we get to the answer [tex](x,y) \to (x+8, y+4)[/tex]

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

To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.

[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\[/tex]

This confirms the answer is correct.