5 [11 marks] Question 4 - Exponents 1. A factory makes 1 000 000 000 yo-yos. Write the number of yo-yos in exponential form. (1) 2. Mrs. Penn has a vegetable garden. There are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. Work out the number of small squares, each 1cm by 1cm in the grid and write it in exponential form. (1) [2 marks]​

Answer:

1

Step-by-step explanation:

So, 1 dozen is 12. Two dozen is 24.

She used 24 Mud Bugs in this soup.

This soup makes 20 cups.

So, 24 Mud Bugs are in 20 cups of soup.

To find the amount of Mud Bugs in each cup of soup, you divide the amount of Mud Bugs by the number of cups.

24/20

Which equals 1.2

You asked for the nearest whole number, so there is 1 Mud Bug per sup of soup.

The amount of tax owed is $13,420

From the question, we have the following parameters that can be used in our computation:

Single with a taxable income of ​$61,000

Using the table of marginal tax, we have

Tax = 22%

So, we have

Tax = 22% * 61000

Evaluate

Tax = 13420

Hence, the amount of tax owed is $13,420

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Answer:

B) 1/2

Step-by-step explanation:

Note that pi=180.

Then we have 180/3=60 and so 5*60=300.

Thus cos 300=1/2.

Therefore, cos 5pi/3=1/2.

Answer: B

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The perimeter of a rectangle is [tex]P=2L+2W[/tex] where L is the length and W is the width.

The views shown in section 1.3, that are used to outline the mathematics consideration are:

The main difference between the three views is their stance on the nature of mathematical objects. The formalist view sees mathematical objects as abstract symbols that have no meaning outside of the formal system.

The intuitionist view sees mathematical objects as mental constructs that are derived from intuition. The Platonist view sees mathematical objects as abstract entities that exist independently of the human mind.

Another difference between the three views is their stance on the relationship between mathematics and the physical world. The formalist view sees mathematics as independent of the physical world.

The intuitionist view sees mathematics as being influenced by the physical world, but not completely determined by it. The Platonist view sees mathematics as being completely independent of the physical world.

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The statement which is not true about the circle M is ∆ABM is isosceles.

The correct answer choice is option 2.

Based on the circle M;

diameter AC,

chords AB and BC,

radius MB

Isosceles triangle: This is a type of triangle which has two equal sides and angles.

Equilateral triangle is a triangle which has three equal sides and angles.

Hence, ∆ABM is equilateral triangle.

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Answer: 140

Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.

The correct answer is b. Extrapolation since 20 is within the range.

In this scenario, finding the best predicted value for x = 20 would be an example of extrapolation. Extrapolation involves estimating values outside the given range of data based on the trend or pattern observed within the existing data.

Given the data set: 4, 10, 2, 18, 15, we can see that the values provided are not in any particular order. To perform extrapolation, it is generally helpful to first examine the trend or pattern within the data. However, without additional information or context, it is difficult to determine the underlying trend in this case.

Since the given data set does not explicitly indicate any pattern or trend, any estimation made for x = 20 would be considered extrapolation. Extrapolation involves projecting or extending the existing trend or pattern beyond the known data points. In this case, the value of 20 falls outside the range of the given data set, so estimating its corresponding value would require extending the trend beyond the known data points.

Consequently, the appropriate response is b. Extrapolation since 20 is within the range.

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The measure of the arc angle KV is 54 degrees.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore, let's find the arc angle KV in the circle as follows:

Hence,

let

arc angle KV = x

128 = 1 / 2 (202 + x)

128 = 101 + 0.5x

128 - 101 = 0.5x

27 = 0.5x

divide both sides by 0.5

x = 27 / 0.5

x = 54 degrees.

Therefore,

arc angle KV = 54 degrees.

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(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical axis represents the total attendance. The bars will correspond to the attendance numbers for each year.

(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.

(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.

(a) The bar chart of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.

(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.

The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.

(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.

The drop in attendance could indicate a potential issue that the zoo needs to address in order to attract more visitors.

Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.

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Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

A = [tex]\frac{4}{3}[/tex] π

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{120}{360}[/tex] ( r is the radius of the circle )

here r = FG = 2 with central angle = 120° , then

A = π × 2² × [tex]\frac{1}{3}[/tex]

  = [tex]\frac{4}{3}[/tex] π

Answer:

it's easy

Step-by-step explanation:

first take a deep breath and then search it

The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²

The formula for calculating the area of a circle is expressed as;

Area = πr²

Now, substitute the value, we have;

Area = 3.14 × 12²

Find the square and multiply the values, we have;

Area = 3.14(144)

Multiply the values

Area = 452. 16 cm²

Perimeter of a square take the formula;

Perimeter = 4a

Substitute the value

Perimeter = 4(12) = 48 cm

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Answer:

Step-by-step explanation:

His total expenditure is $100. After that, he sold the CD player for $125. As a result, he earned $25.

Al initially bought a CD player for $100 and then sold it for $125. After that, he bought it back for $150 and later sold it for $175. The question is whether Al made money, lost money, or broke even.

Let's examine the transactions in more detail to determine the answer.

Initially, Al bought the CD player for $100.

Now his total income is $25 and his expenditure remains at $100. Next, he purchased the same CD player again for $150. This adds to his expenditure, which is now $250.

Later, he sold the CD player for $175, which means he earned another $25, bringing his total income to $50 (i.e., $25 from the first sale and $25 from the second sale).

Since Al's total expenditure was $250 and his total income was $50, he lost money. He spent more than he earned.

He sold the CD player twice and earned a total of $50, which is less than what he spent on the CD player, which was $250. Al had a net loss of $200 ($250 - $50). Therefore, he lost money.

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Answer:

Step-by-step explanation:

I think you have to use partial fractions. Substitution won't work because the numerator is not the derivative of the denominator. I hope I am correct on this.

I have attached just the partial fractions part of the question. I did not integrate.

Answer:

11 : 1

Step-by-step explanation:

The probability of obtaining a head when a dime is flipped is 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.

The probability of rolling any particular number on a fair six-sided die is 1/6, since there are six equally likely outcomes (the numbers 1 through 6).

To find the odds against obtaining a head and rolling any number on the die, we need to multiply the probabilities of the two events. This gives us

(1/2) x (1/6) = 1/12

So the probability of obtaining a head and rolling any number on the die is 1/12.

To find the odds against this event, we need to compare the probability of the event happening to the probability of it not happening. The probability of the event not happening is 1 - 1/12 = 11/12.

Therefore, the odds against obtaining a head and rolling any number on the die are:

11 : 1

Answer:

(- 7, 4 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

P (- 7, - 4 ) → (- 7, - (- 4) ) → (- 7, 4 )

This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

To find the equation of a line in point-slope form, we need a point on the line and the slope of the line.

Given the points (0, 12) and (-6, 0), we can calculate the slope using the formula:

slope = (y2 - y1) / (x2 - x1)

Using the coordinates (0, 12) as (x1, y1) and (-6, 0) as (x2, y2):

slope = (0 - 12) / (-6 - 0)

slope = -12 / -6

slope = 2

Now that we have the slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (0, 12) as (x1, y1) and the slope (m) as 2:

y - 12 = 2(x - 0)

Simplifying the equation:

y - 12 = 2x

This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

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Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.

Answer:

Step-by-step explanation:

180 = x + x + x + 45

180 - 45 = 3x

135 = 3x

x = 135 : 3

x = 45°

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

check

180 = 45 + 45 + 45 + 45

180 = 180

same value the answer is good

Answer:

-4 is the coefficient or -4x whatever the answers are

Step-by-step explanation:

the coefficient in mathematics is basically whatever the number is infront of a variable in an expression, equation, etc.

(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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For the data point (2, 5), the residual is 5 - 6 = -1. For the data point (3, 6), the residual is 6 - 8 = -2. For the data point (4, 11), the residual is 11 - 10 = 1. For the data point (5, 14), the residual is 14 - 12 = 2. For the data point (6, 15), the residual is 15 - 14 = 1.

To plot the residuals for the given linear function, we need to calculate the difference between the actual y-values of the data points and the corresponding predicted y-values based on the linear function.

Let's start by calculating the predicted y-values using the linear function y = 2x + 2 for each x-value in the dataset:

For x = 2, the predicted y-value is 2(2) + 2 = 6.

For x = 3, the predicted y-value is 2(3) + 2 = 8.

For x = 4, the predicted y-value is 2(4) + 2 = 10.

For x = 5, the predicted y-value is 2(5) + 2 = 12.

For x = 6, the predicted y-value is 2(6) + 2 = 14.

Now we can calculate the residuals by subtracting the predicted y-values from the actual y-values.

To visualize these residuals, we can create a scatter plot with the x-values on the horizontal axis and the residuals on the vertical axis. Each data point will represent the x-value from the dataset and its corresponding residual. The residuals can be either positive or negative, so we should include both sides of the vertical axis.

By plotting the residuals, we can observe the deviations between the actual y-values and the predicted y-values based on the linear function. This plot helps us assess how well the linear function fits the data and identify any patterns or trends in the residuals.

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Answer:

first one, the one you have selected

The minor arc UB in the circle measures 46 degrees,

The external angles theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.

It is expressed as;

External angle = 1/2 × ( major arc - minor arc )

From the diagram:

External angle I = 48 degrees

Major arc ZC = 142 degrees

Minor arc UB = ?

Plug these values into the above formula and find the minor arc UB:

External angle = 1/2 × ( major arc - minor arc )

48 = 1/2 × ( 142 - minor arc )

Multiply both sides by 2:

2 × 48 = 2 × 1/2 × ( 142 - minor arc )

2 × 48 = ( 142 - minor arc )

96 = ( 142 - minor arc )

96 = 142 - Minor arc

Minor arc = 142 - 96

Minor arc = 46°

Therefore, the minor arc measures 46 degrees.

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Answer:

To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.

Cost of each amplifier: sh. 3,750

Import duty of 125% on the cost:

Import duty = 125% of sh. 3,750

= 125/100 * sh. 3,750

= sh. (125/100 * 3,750)

= sh. 4,687.50

Cost of each amplifier including import duty:

Total cost = Cost + Import duty

= sh. 3,750 + sh. 4,687.50

= sh. 8,437.50

Sales tax of 20% on the total cost:

Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50

= sh. (20/100 * 8,437.50)

= sh. 1,687.50

Total cost including sales tax:

Total cost = Total cost + Sales tax

= sh. 8,437.50 + sh. 1,687.50

= sh. 10,125

Desired profit margin of 10% on the total cost:

Profit = 10% of Total cost

= 10/100 * sh. 10,125

= sh. (10/100 * 10,125)

= sh. 1,012.50

Selling price of each amplifier:

Selling price = Total cost + Profit

= sh. 10,125 + sh. 1,012.50

= sh. 11,137.50

a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850

b) Her total earnings for the week would be: $600 + $300 = $900

c)  Her paycheck will be reduced by $100.

d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.

To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:

$15 x 40 = $600

In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:

$2,500 x 0.10 = $250

b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:

$3,000 x 0.10 = $300

On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)

c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.

d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.

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The speed of the boat in water without a current is 15 miles per hour

From the question, we have the following parameters that can be used in our computation:

Current of river = 4 miles per hour

Distance travelled = 209 miles

Time = 30 hours.

Represent the speed with x

So, we have

Next, we have

Time = Speed/Distance

So, we have

209/(x - 4) + 209/(x + 4) = 30

When evaluated, we have

x = 15

Hence, the speed is 15 miles per hour

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