a.Donkey Kong is an arcade game where an animated figure, Mario, jumps over barrels. In the original game, it was virtually impossible to get through to Level 22 before Mario was ‘killed’ by the game. This was an unintended consequence of how the number of bonus points was calculated and stored.

The number of bonus points a player starts with when they move onto a new level depends on the number of the level that they are moving onto. Behind the scenes, Donkey Kong takes the level that is about to be entered, multiplies it by 10 and adds 40, thus yielding the first two digits of the player’s starting bonus.

So, for example, if a player is about to start Level 2, the bonus number is calculated like this:

2 × 10 + 40 = 60.

This bonus number is stored in a single byte as an unsigned integer. The bonus number will never be 0.

i.Write down and evaluate an expression for the number of different unsigned integers that can be represented in a single byte. Then write down the largest unsigned integer that can be represented if no representation for 0 is required.
ii.Find the bonus number associated with Level 22. Explain why storing this bonus number will cause a problem.
iii.For Level 22, the bonus number actually stored is 4. Give one likely explanation for this.
iv.The bonus number is multiplied by 100 before it is displayed on the screen, so for Level 22 the number displayed on the screen is 400. The displayed number decreases by 100 every 1.75 seconds. When the displayed number reaches 0, Mario is automatically killed. How many seconds does the player have to finish Level 22?

The value of the inverse function \(f^{-1}(7)\) is 2.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Let the given function is  \(f:X\rightarrow Y\)

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

\(f^{-1}: Y \rightarrow X\)

such that:

\(\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X\)

This means, inverse of 'f' is undo operator, that takes back the effect of 'f'

We are given that f(x) = 3x+1 and \(f^{-1} = x-\frac{1}{3}\)

Then We can find it by plugging 7 in for x in the \(f^{-1}(x)\).

So, \(f^{-1}(7)\) =  7-1/3

\(f^{-1}(7)\) = 6/3

\(f^{-1}(7)\) = 2

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Answer:

Step-by-step explanation:

Yes, the lines are parallel.

so its d. trust me :)

Using the linear function given in this problem, the formula underestimates the median weekly earnings in 2013 by $3, as 657 < 660.

The function that estimates the median weekly earnings n years after 1980 is:

W = 13n + 231.

2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by W when n = 33, that is:

W = 13 x 33 + 231 = 660.

657 < 660, hence the formula underestimates the median weekly earnings in 2013 by $3.

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Answer:

162, 163, and 164.

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 489

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 489

3X + 3 = 489

3X + 3 - 3 = 489 - 3

3X = 486

3X/3 = 486/3

X = 162

Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.

162 + 163 + 164 = 489

We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.

Answer:

161, 163, 165

Step-by-step explanation:

x + x+2 + x +4 =489.

This is how we calculate three consecutive odd integers!

Combine like terms:

3x+6=489

3x=483

x=161

Three numbers are:

161, 161+2, 161+4.

161, 163, 165

Answer:  C=t+50

Step-by-step explanation: This equation means that Clare's score equals Tyler's score plus 50.

Only one choice is correct here.

Answer:

A no solution

Step-by-step explanation:

y = 2x + 10

3y - 6x = 30

3(2x+10) -6x =30

6x +30 -6x =30

6x -6x = 30-30

0=0

Answer:

The cost price of 250 grams of super mix cocoa is Kshs.650/1.3=Kshs.500.

The cost price of 1 kg of super mix cocoa is Kshs.500*4=Kshs.2000.

If x kg of cocoa A is mixed with (1-x) kg of cocoa B, then the cost price of the mixture is Kshs.1800x+Kshs.2400(1-x).

Therefore, Kshs.1800x+Kshs.2400(1-x)=Kshs.2000.

Solving for x, we get x=2/3.

Therefore, the cocoa types A and B are mixed in the proportion 2:1.

Answer:

23 players.

Step-by-step explanation:

5 x 4 + 3 = 23

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer: It doubles

Step-by-step explanation:

Inflation erodes the value of a currency thereby reducing the purchasing power that customers have as they will only be able to buy less gods and services for the same amount as before.

An increase in inflation is directly proportional to a decrease in purchasing power which means that if the inflation rate doubles, the decrease in purchasing power doubles as well.

For instance, if inflation is 10%, the value of a dollar becomes 0.9c. If Inflation doubles to 20%, the dollar goes to 0.8c. Meanwhile the purchasing power would have gone from $1 to 0.8c which would translate to a 20% decrease.

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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Answer:

The product of polynomial \((-2m^3+3m^2-m)(4m^2+m-5)\) is \(\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}\)

Step-by-step explanation:

We need to find the standard form of polynomial that represents the product of \((-2m^3+3m^2-m)(4m^2+m-5)\)

Finding the product of polynomial

\((-2m^3+3m^2-m)(4m^2+m-5)\\=-2m^3(4m^2+m-5)+3m^2(4m^2+m-5)-m(4m^2+m-5)\\=-8m^5-2m^4+10m^3+12m^4+3m^3-15m^2-4m^3-m^2+5m\\Combining\:like\:terms\\=-8m^5-2m^4+12m^4+10m^3+3m^3-4m^3-15m^2-m^2+5m\\=-8m^5+10m^4+9m^3-16m^2+5m\\\)

So, the product of polynomial \((-2m^3+3m^2-m)(4m^2+m-5)\) is \(\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}\)

Answer:

130

Step-by-step explanation:

Answer:

stratified sample

Step-by-step explanation:

The kind of sample that is being described is known as a stratified sample. This would be the type of sample because the researchers are dividing the entire student population that exists into various different categories or groups. The groups that have been created are home-schooled students, private school students, and public school students. All of the students are still part of the student population and therefore represent their groups.

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

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Answer:618.014

Step-by-step explanation: It may look like hundredths which is where must people mess up but it is instead thousandths.

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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Answer:

Step-by-step explanation:

You want to know the intervals on which f(x) = sin(x)/(2+cos(x)²) is increasing and decreasing, and the relative extremes.

The quotient rule can be used to find the derivative of f(x). Where the derivative is positive, the function is increasing.

  f'(x) = ((2+cos(x)²)cos(x) +sin(x)(2cos(x)sin(x)))/(2+cos(x)²)²

  f'(x) = (cos(x)(2 +cos(x)² +2sin(x)²)/(2+cos(x)²)²

  f'(x) = cos(x)(3+sin(x)²)/(2+cos(x)²)²

We observe that the factors (3+sin(x)²) and (2+cos(x)²) are both positive for all x. This means the sign of the derivative will match the sign of cos(x).

The function is increasing where cos(x) > 0, on the intervals ...

  (0, π/2) ∪ (3π/2, 2π)

The function is decreasing where cos(x) < 0, on the interval ...

  (π/2, 3π/2)

The first derivative test tells us the function will have a relative maximum where the function goes from increasing to decreasing, at x = π/2. The function value at that point is ...

  f(π/2) = sin(π/2)/(2 +cos(π/2)²) = 1/2

The relative maximum is at (π/2, 1/2).

The first derivative test tells us the function will have a relative minimum where the function goes from decreasing to increasing, at x = 3π/2. The function value at that point is ...

  f(3π/2) = sin(3π/2)/(2 +cos(3π/2)²) = -1/2

The relative minimum is at (3π/2, -1/2).

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:1/1

Step-by-step explanation:

Answer:

Step-by-step explanation:  0.03

Answer:

Hope the pictures will help you........

The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Answer:

105

Step-by-step explanation:

the angle of aec is just a little more that 90°

We can determine the interquartile range of each block by using the mean: (D) Block 1 IQR: 20; Block 2 IQR: 5

The mean, often known as the arithmetic mean, is a statistic that expresses the central tendency of a collection of numerical data.

It is calculated by summing up all of the dataset's values and dividing the result by the total number of values.

Since it gives a single value that summarises the entire dataset, the mean is frequently employed as a typical value for a dataset.

Outliers in the dataset, however, have the potential to have an impact.

We must first establish the quartiles in order to determine the interquartile range (IQR) for each block.

This can be accomplished by first determining the median (Q2) of each block, followed by the medians of the lower (Q1) and upper (Q3) halves of the data.

Block 1's:

Q1: median of {25, 60, 70, 75, 80} = 70

Q2: median of {85, 85, 90, 95, 100} = 90

Q3: median of {70, 75, 80, 85, 90} = 80

IQR = Q3 - Q1 = 80 - 70 = 10

Block 2's:

Q1: median of {70, 70, 75, 75, 75} = 75

Q2: median of {75, 75, 80, 80, 85} = 80

Q3: median of {80, 85, 100, 75, 75} = 82.5

Therefore, we can determine the interquartile range of each block by using the mean: (D) Block 1 IQR: 20; Block 2 IQR: 5

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Correct question:

Mr. Sofi drew a random sample of 10 grades from each of his Block 1 and Block 2 Algebra Unit 2 Test. The following scores were the ones he drew:

Block 1: 25, 60, 70, 75, 80, 85, 85, 90, 95, 100.

Block 2: 70, 70, 75, 75, 75, 75, 80, 80, 85, 100.

What is the interquartile range of each block?

1. Suppose you are pouring two solutions and they react to each other and form another product that is undesirable or the reaction of these two are exothermic (liberation of heat) and results in an explosion. Hence not pour at the same time.

2. Number of grams present = (% strength × total volume ) ÷ 100

3. % strength depend on amount of solute and total amount of solution.

Since here the amount of solute silver nitrate is 20ml and total volume of solution is 80+20=100 ml.

Hence % strength will not change.

4. % strength of the solution is important because it tells about relative amount of solute present in solution, hence it play a great role to define the definite composition.

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