Petrol Brand Preference Suppose the table below shows the frequency distribution for the petrol brand most preferred by a sample of 50 motorist in Windhoek: Petrol brand Number of motorists NAMCOR 12 ENGEN 8 PUMA 6 SHELL 24 Required: a) What is the likelihood that a randomly selected motorist prefers PUMA? b) What is the chance that a randomly selected motorist does not prefer NAMCOR? c) What is the probability that a motorist in the selected sample prefers either NAMCOR, ENGEN, PUMA or SHELL? 2022 VACATION SCHOOL

Answer:

To the nearest tenth, the length is 6.4 meters, and the width is 3.4 meters.

Step-by-step explanation:

Let w be the width of the rectangle. Then l = w + 3, and we have:

\( w(w + 3) = 22\)

\( {w}^{2} + 3w = 22\)

\( {w}^{2} + 3w - 22 = 0\)

Calculating the discriminant:

\( \sqrt{ {3}^{2} - 4(1)( - 22)} = \sqrt{9 + 88} = \sqrt{97} \)

So by the quadratic formula, and discarding the negative solution, we then obtain:

\(w = \frac{ - 3 + \sqrt{97} }{2} = 3.4\)

\(l = w + 3 = 3.4 + 3 = 6.4\)

From this expression, we can see that the approximation D(h) converges to the true value f'(x) with an error term of O(h^2). Therefore, the order of convergence for the given formula as h approaches 0 is 2.

To find the order of convergence as h approaches 0 for the given formula, we need to examine how the error term behaves as h gets smaller.

Let's denote the approximation of f'(x) using the given formula as D(h). The true value of f'(x) is denoted as f'(x).

Using Taylor's expansion, we can write:

\(f(x + h) = f(x) + hf'(x) + h^2/2 f''(x) + h^3/6 f'''(x) + ...\\f(x - h) = f(x) - hf'(x) + h^2/2 f''(x) - h^3/6 f'''(x) + ...\\f(x + 2h) = f(x) + 2hf'(x) + 4h^2/2 f''(x) + 8h^3/6 f'''(x) + ...\\f(x - 2h) = f(x) - 2hf'(x) + 4h^2/2 f''(x) - 8h^3/6 f'''(x) + ...\)

Substituting these expressions into the given formula, we have:

\(D(h) = [-f(x + 2h) + 8f(x + h) - 8f(x - h) + f(x - 2h)] / (12h)\\= [-f(x) - 2hf'(x) - 4h^2/2 f''(x) - 8h^3/6 f'''(x) + 8f(x) + 8hf'(x) - 8hf'(x) + 8h^2/2 f''(x) - 4h^2/2 f''(x) + 4hf'(x) + f(x) + 2hf'(x) + 4h^2/2 f''(x) + 8h^3/6 f'''(x)] / (12h)\)

Simplifying the expression, we have:

D(h) = f'(x) + O\((h^2\))

where O(\(h^2\)) represents the error term that is proportional to \(h^2.\)

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Answer:

BD=5.5

Step-by-step explanation:

11 divided by 2 gives you the answer

The measure of BD in the triangle ABC is 5.5 units.

Given that, BC = 14, AB = 11, and the perimeter of triangle ABC is 39.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Now, the perimeter of triangle ABC = AB+BC+AC

⇒ 11+14+AC=39

⇒ 25+AC=39

⇒ AC=39-25

⇒ AC=14 units

Since, BC=AC=14 units, so ΔABC is isosceles triangle

Thus, DC is perpendicular bisector to AB, then AB/2 = BD

= 11/2 = 5.5 units

Therefore, the measure of BD in the triangle ABC is 5.5 units.

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Answer:

β = (-0.19 dB).

Step-by-step explanation:

The formula which is used to calculate the decibel level of a sound is given by :

\(\beta=10\log (\dfrac{I}{I_o})\)

I is intensity of the sound of a ticking clock

\(I_o=10^{-12}\\) watts per square meter

Since, \(1\ \text{inch}^2=\dfrac{1}{1550}\ \text{m}^2\)

The intensity of a monster truck is converted into per square meter as follows:  

\(10^{-9}\ {W/in^2}= \dfrac{10^{-9}}{1550}\ W/m^2\\\\10^{-9}\ {W/in^2}=6.45\times 10^{-13}\ W/m^2\)

So, Decibal level is :

\(\beta=10\log (\dfrac{6.45\times 10^{-13}}{10^{-12}})\\\\\beta =-0.19\ dB\)

So, the decibel level of the sound of a ticking clock is (-0.19 dB).

Answer:

30dB

Step-by-step explanation:

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

The probability mass function of the hypergeometric distribution can be written as:

P(X = x) = (M choose x) * (N-M choose n-x) / (N choose n)

n = total number of oranges in the group from which the 50 pieces are selected
m = total number of successes (i.e. oranges) in the group from which the 50 pieces are selected
n [ choose ] m = number of ways to choose m oranges out of n oranges in the group
success [ choose ] = the desired outcome of selecting an orange in each trial (i.e. success)
the key components of a hypergeometric distribution. In this case, we are randomly selecting 50 pieces, and the random variable X represents the number of oranges selected. Here are the components:

1. Population size (N): The total number of pieces in the population.
2. Number of successes in the population (M): The total number of oranges in the population.
3. Sample size (n): The number of pieces you are selecting, which is 50 in this case.
4. Number of successes in the sample (x): The number of oranges selected in the sample, represented by the random variable X.

The probability mass function of the hypergeometric distribution can be written as:

P(X = x) = (M choose x) * (N-M choose n-x) / (N choose n)

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Answer:

50.82

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

it as a interior angle of a regular polygon is 23

Answer:

x=7

Step-by-step explanation:

Step #1- Set the two lines equal to each other

10+12=x+15

Step #2- Solve for the line you have all values for

10+12=22

Step#3- Plug 22 back into the equation where the two lines are set equal to each other

22=x+15

Step #4- Solve for X algebraically

22=x+15

22-15=x

7=x

On solving the provided question we can say that

1. circle centered at the origin with a radius of 10 is:

\(x^{2} +y^{2} =100\)

2. circle with center R(-1, 8) and a radius of 5 is:

\((x + 1)^2 + (y - 8)^2 = 25\)

3. center P(8, -5) and a radius of 24.5 is:

\((x -8)^2 + (y +5)^2 = 24.5\)

4. the origin and passing through the point (9, -2) is:

\(x^{2} +y^{2} -18x+4y+85=0\)

5. center B(0, -2) and passing through the point (-6, 0) is:

\((x )^2 + (y +2)^2 = 40\)

6. center F(11, 4) and passing through the point (-2, 5) is:

\((x -11)^2 + (y - 4)^2 = 1708\)

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

circle centered at the origin with a radius of 10 is:

\(x^{2} +y^{2} =100\)

circle with center R(-1, 8) and a radius of 5 is:

\((x + 1)^2 + (y - 8)^2 = 25\)

center P(8, -5) and a radius of 24.5 is:

\((x -8)^2 + (y +5)^2 = 24.5\)

the origin and passing through the point (9, -2) is:

\(x^{2} +y^{2} -18x+4y+85=0\)

center B(0, -2) and passing through the point (-6, 0) is:

\((x )^2 + (y +2)^2 = 40\)

center F(11, 4) and passing through the point (-2, 5) is:

\((x -11)^2 + (y - 4)^2 = 1708\)

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To find the curvature of the curve defined by the vector function r(t) = < t^2, ln(t), t ln(t) > at a given point, we need to calculate the curvature using the formula:

κ = |dT/ds| / ||dT/ds||,

where dT/ds is the unit tangent vector and ||dT/ds|| is its magnitude.

Let's proceed with the calculations:

Step 1: Find the first derivative of r(t) to get the tangent vector T(t):

r'(t) = < 2t, 1/t, ln(t) + t/t > = < 2t, 1/t, ln(t) + 1 >.

Step 2: Calculate the magnitude of the tangent vector:

||r'(t)|| = sqrt((2t)^2 + (1/t)^2 + (ln(t) + 1)^2)

         = sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1).

Step 3: Differentiate r'(t) to find the second derivative:

r''(t) = < 2, -1/t^2, 1/t + 2/t > = < 2, -1/t^2, (t + 2)/t >.

Step 4: Calculate the magnitude of the second derivative:

||r''(t)|| = sqrt(2^2 + (-1/t^2)^2 + ((t + 2)/t)^2)

          = sqrt(4 + 1/t^4 + (t^2 + 4t + 4)/t^2)

          = sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2).

Step 5: Calculate the curvature:

κ = |dT/ds| / ||dT/ds||

  = (||r'(t)|| / ||r''(t)||^3)

  = ((sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1)) / (sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2))^3).

To find the curvature at a specific point, substitute the value of t into the expression for κ.

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Answer:

To determine which region represents the solution to a system of linear inequalities, you need to graph each inequality on the same coordinate plane and then find the intersection of the regions that satisfy each inequality. This intersection is the solution to the system of linear inequalities, as every point in this region satisfies all of the inequalities in the system.

To graph the solution, you can use a number line for each variable and plot the inequalities as points or lines on the coordinate plane. For example, if the system of linear inequalities is given by the equations y > 2x + 3 and y < -x + 5, you can plot the lines y = 2x + 3 and y = -x + 5 on the coordinate plane and find the intersection of the two lines. This intersection represents the solution to the system of linear inequalities, as every point in this region satisfies both inequalities.

Another way to find the solution to a system of linear inequalities is by using algebra to solve the system. This involves writing the equations in standard form, eliminating variables, and solving for the remaining variable. The solution can then be written as a set of ordered pairs that represent the points on the coordinate plane that satisfy the system of linear inequalities.

In either case, the solution to a system of linear inequalities is the region of the coordinate plane that satisfies all of the inequalities in the system.

Step-by-step explanation:

Rearranging the equation so q is the independent variable is; q = -1.6r

We are given the expression;

-7q + 12r = 3q - 4r

Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;

-7q - 3q = -4r - 12r

-10q = -16r

q = 16r/10

q = -1.6r

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Using Percentage formula , The change in the price of a jar of peanut butter is 15.02%.

Percentage : It is defined as a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.

First of we need to calculate difference between initial price and final price to

get the change in price.

Initial Price of jar of peanut butter = $ 5.99

Final price of jar of peanut butter = $ 6.89

Change in price of a jar of peanut butter = final price of jar of peanuts butter - initial price of jar of peanuts butter

= $ 6.89 - $ 5.99 = $ 0.9.

Percent change in price = ((Change in Price)/(initial price))× 100

percent change = (0.9/5.99)× 100 = 15.02

Hence, 15.02% is the change in price of a jar of peanuts butter.

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We can represent 0.614 using only 5 tenths as \(\mathbf{\dfrac{6.14}{10}}\)

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The accepted method for representing both integer and non-integer numbers is the decimal number system.

From the given information, we are to represent 0.614 by using only 5 tenths.

Representing 0.614 in the same form, we have:

\(\mathbf{=\dfrac{0.614\times 1000}{1\times 1000}}\)

\(\mathbf{=\dfrac{614}{1000}}\)

\(\mathbf{=\dfrac{6.14}{10}}\)

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Answer: 6.14/10

Step-by-step explanation:

There are approximately 2.471 acres in a hectare in Australia.

An acre and a hectare are both units of area measurement used in different parts of the world. In Australia, the metric system is used, which includes the use of hectares as a standard unit of measurement for land area.

One hectare is equal to 10,000 square meters or approximately 2.471 acres. This conversion factor may vary slightly in different regions of the world, depending on the specific definition of an acre and the rounding conventions used.

It is important to note that the use of hectares is becoming increasingly common in other parts of the world as well, especially in countries that have adopted the metric system.

However, in some countries, including the United States and the United Kingdom, the acre remains a commonly used unit of land area measurement.

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We are tasked with defining an expression fibs that generates the infinite sequence of Fibonacci numbers using the given procedure. Additionally, using fibs, we need to define a function fib that returns the nth Fibonacci number, and an expression that calculates the first Fibonacci number greater than one thousand.

Part a) To define the fibs expression, we can use a list comprehension in Haskell. We start with the initial Fibonacci numbers, [0, 1], and generate the subsequent numbers by taking the sum of the previous two numbers. We can achieve this by zipping the list with its tail and mapping over the resulting pairs to calculate the next Fibonacci number. The expression fibs = 0 : 1 : [a + b | (a, b) <- zip fibs (tail fibs)] will generate the infinite sequence of Fibonacci numbers.

Part b) Using fibs, we can define the fib function that returns the nth Fibonacci number. Since the Fibonacci sequence is 0-indexed, we can simply access the nth element from fibs using !! indexing. For example, fib n = fibs !! n will return the nth Fibonacci number.

To calculate the first Fibonacci number greater than one thousand, we can use the takeWhile function along with a lambda expression to specify the condition > 1000. By applying takeWhile (> 1000) fibs, we can obtain a list of Fibonacci numbers greater than one thousand, and then take the first element using head to get the desired result.

The fibs expression generates the infinite sequence of Fibonacci numbers, the fib function returns the nth Fibonacci number, and the expression head (takeWhile (> 1000) fibs) calculates the first Fibonacci number greater than one thousand.

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Answer:

2,4

Step-by-step explanation:

Answer:

Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1

Step-by-step explanation:

The answer is A because the axis of symmetry is in between 0 and 1, the vertex lies on 0.5 and -0.75, and the parabola opens down so the coefficient of a is -1, and the y-int or the value of c is -1

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

Further Explanation:

Given:

Calculation:

The standard form of the parabola is shown below.

Here, the parabola has vertex at  and has the symmetry parallel to x-axis and it opens left.

The general form of the parabola can be expressed as follows,

The graph is a downward parabola.

From the graph it has been observed that the vertex of the parabola is

Symmetry of the graph is  

The -intercepts of the graph is  Therefore, the value of is  

The value of  is -1 as the graph is a downward parabola.

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic sections

Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola.

Answer:

12

Step-by-step explanation:

Finding the 'value' means we need to calculate a number answer.

1/8 (x^3 - 4) (t^2 + 8)

Fill in 2 for x and 4 for t.

=1/8(2^3 - 4)(4^2 + 8)

inside of parenthesis we'll work on exponents first.

= 1/8 (8 - 4) (16 + 8)

Still inside of parenthesis, do the subtracting or adding next.

= 1/8 (4) (24)

This is all multiplying.

= 12

Answer:

508.94 in²

Step-by-step explanation:

Answer: sum, multiple

Step-by-step explanation:

A number is divisible by 9 if the sum of digits is a multiple of 9.

Answer:

Step-by-step explanation:

A number is divisible by 9 if the sum of digits is a divisible of 9.

A scenario for y = 4x + 2 could be the cost of buying movie tickets. Let's say the cost of one movie ticket is $4 and there is a $2 service charge.

Using the equation y = 4x + 2, where x is the number of tickets bought, we can calculate the total cost.

For example, if someone were to buy two tickets, x would be equal to 2. Plugging this into the equation, we get y = 4(2) + 2 = $10. This means that the total cost of buying two movie tickets is $10.

Another scenario could be the time it takes to complete a task. Let's say that a person can complete a task in 2 hours if they work at a rate of 4 units per hour, with an additional 2 units of work required to complete the task. Using the equation y = 4x + 2, where x is the number of hours worked, we can calculate the total time it would take to complete the task.

For example, if someone were to work for 3 hours, x would be equal to 3. Plugging this into the equation, we get y = 4(3) + 2 = 14. This means that the total time it would take to complete the task is 14 hours.
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Answer:

The slope is 4 and y-intercept is actually 3... (I hope)

Remember rise over run, here you can see that it goes up 4 and over 1.

I am so sorry, I'm not good at explaining

Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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The surface area of square pyramid is 207.04 square inches.

Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.

The formula to find the surface area of square pyramid is A=a²+2a√(a²/4+h²)

Here, a=8 inches and h=8 inches

Now, A= a²+2a√(a²/4+h²)

A= a²+2a√(a²/4+h²)

A= 8²+2×8√(8²/4+8²)

A= 64+16√(16+64)

A= 64+16√80

A= 64+16×8.94

A= 207.04 square inches

Therefore, the surface area of square pyramid is 207.04 square inches.

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Answer:

14 3/8 pounds

Step-by-step explanation:

6 pounds plus 8 pounds= 14 pounds. 1/4 + 1/8= 3/8. 1/4 can be turned into 2/8, and 2/8 plus 1/8 equals 3/8. Hope this helps :)

Answer:

the first one

Step-by-step explanation:

Answer: A. y = 32 x minus one-half

a) The probability of finding oil is 0.7, or 70%.

b) The probability of finding medium-quality oil, given the soil test, is 0.4706.

(a) To calculate the probability of finding oil, we need to add the probabilities of finding high-quality oil and medium-quality oil since these are the two possible outcomes where oil is present. So, the probability of finding oil is:

P(oil) = P(high-quality oil) + P(medium-quality oil)

P(oil) = 0.5 + 0.2

P(oil) = 0.7

(b) In this case, event A is finding oil, and event B is the particular type of soil identified by the test.

We are given the following probabilities:

P(soil | high-quality oil) = 0.20

P(soil | medium-quality oil) = 0.80

P(soil | no oil) = 0.20

P(high-quality oil) = 0.5

P(medium-quality oil) = 0.2

P(no oil) = 0.3

To calculate the probability of finding high-quality oil, given the soil test, we use Bayes' theorem:

P(high-quality oil | soil) = P(soil | high-quality oil) x P(high-quality oil) / P(soil)

P(high-quality oil | soil) = 0.20 x 0.5 / P(soil)

To calculate P(soil), we use the law of total probability:

P(soil) = P(soil | high-quality oil) x P(high-quality oil) + P(soil | medium-quality oil) x P(medium-quality oil) + P(soil | no oil) x P(no oil)

P(soil) = 0.20 x 0.5 + 0.80 x 0.2 + 0.20 x 0.3

P(soil) = 0.34

Therefore, we can calculate P(high-quality oil | soil) as:

P(high-quality oil | soil) = 0.20 x 0.5 / 0.34

P(high-quality oil | soil) = 0.2941

We can use the same formula to calculate the probability of finding medium-quality oil:

P(medium-quality oil | soil) = P(soil | medium-quality oil) x P(medium-quality oil) / P(soil)

P(medium-quality oil | soil) = 0.80 x 0.2 / 0.34

P(medium-quality oil | soil) = 0.4706

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