1. A finance company charges $55 simple interest on a sum of money which is
borrowed for five months. Given that the rate
of interest is 12% per annum, find the sum of
the money.

Options:
1) $1200
2) $1100

Answer:

To find out actual distance on earth, we need to measure scale. The scale is 1cm to 15 km. Thus, 10 cm on map is equal to ( 10*15) = 150 km on earth. Thus, actual distance on earth is 150 km.

Factors that make it more likely that buying an extended warranty is a good idea are II. The product has a high probability of needing repair in the next few years and III. The product is a major purchase that you are unlikely to soon replace.

Among the given factors, options II and III are the ones that make it more likely that buying an extended warranty is a good idea.

Option II states that the product has a high probability of needing repair in the next few years. If the product is known to be prone to malfunctions or has a history of requiring frequent repairs, purchasing an extended warranty can provide financial protection and peace of mind.

Option III suggests that the product is a major purchase that you are unlikely to soon replace. In such cases, an extended warranty can be beneficial, as it extends the coverage period beyond the manufacturer's warranty, offering protection against potential future repairs or defects that may arise after the manufacturer's warranty has expired.

Therefore, the answer is c. II and III, as these factors increase the likelihood that buying an extended warranty is a good idea.

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Answer:

\(1) \: {2}^{3} \\ 2) \: {3}^{6} \\ 3) \: {4}^{4} = 4 \times 4 \times 4 \times 4 = 256\)

Answer:

\(n^{3} + 15n^{2} + 56n\)

Step-by-step explanation:

First FOIL  (n + 7)(n + 8) and then distribute n

(n + 7)(n + 8) = \(n^{2} +15n + 56\)

 n (\(n^{2} +15n + 56\))

= \(n^{3} + 15n^{2} + 56n\)

To determine whether the given sequence converges or diverges, we will examine each of the provided sequences and find their respective limits as n approaches infinity.

1. an = (-1)^n

The sequence alternates between -1 and 1 as n increases. Since it does not approach a specific value, the sequence diverges. Your answer for this sequence is NONE.

2. an = n^2 * e^(-n)

To find the limit as n approaches infinity, we can apply L'Hopital's Rule:

lim (n^2) / (e^n) as n approaches infinity.

Applying L'Hopital's Rule twice, we get:

lim (2n) / (e^n) and then lim (2) / (e^n).

As n approaches infinity, the denominator (e^n) increases without bound, so the limit becomes 0. The sequence converges to 0.

3. an = (3n - 1)! / (3n + 1)!

To find the limit as n approaches infinity, let's rewrite the sequence as:

an = 1 / [(3n)(3n + 1)]

As n approaches infinity, the denominator (3n)(3n + 1) increases without bound, and the sequence converges to 0.

In summary:
1. The sequence (-1)^n diverges (NONE).
2. The sequence n^2 * e^(-n) converges to 0.
3. The sequence (3n - 1)! / (3n + 1)! converges to 0.

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Answer:

The area of the sector is 9.43 ft^2

Step-by-step explanation:

Here, we want to find the area of the sector with a central angle of 30 degrees

To do this, we use the formula below;

Area of sector = theta/360 * pi * r^2

theta = central angle = 30 degrees

r = radius = 6 ft

Thus, we have it that;

Area of sector = 30/360 * pi * 6^2

= 30/10 * pi = 3 * 3.142 = 9.43 ft^2

Based on the information provided in the question, it is not possible to determine the fraction of water in the gas at 100°C that will separate by condensation on the ground.

The fraction of water in the gas at 100°C that is separated by condensation on the ground can be calculated using the concept of relative humidity. However, the information provided in the question is insufficient to directly determine the fraction. Additional data, such as the initial moisture content in the soil or the specific humidity of the air, is needed for an accurate calculation.

To calculate the fraction of water separated by condensation, we need to compare the amount of water vapor in the air at 100°C to the maximum amount of water vapor the air can hold at that temperature, which is determined by the dew point.

However, the question does not provide the initial moisture content of the soil or the specific humidity of the air, which are necessary for calculating the relative humidity. Without this information, we cannot determine the fraction of water that will condense on the ground.

The relative humidity can be calculated using the following formula:

Relative Humidity = (Actual Water Vapor Pressure / Saturation Water Vapor Pressure) * 100

But without the specific values for actual water vapor pressure and saturation water vapor pressure, we cannot proceed with the calculation.

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For evaluating the line integral by the two following methods,

a. directly the value of the line integral is 62.5.

b. using Green's Theorem the value is also 62.5.

(a) Direct evaluation:

Parametrize the four sides of the rectangle C as follows:

The bottom side from (0,0) to (5,0): r(t) = <t, 0>, 0 ≤ t ≤ 5

The right side from (5,0) to (5,4): r(t) = <5, t>, 0 ≤ t ≤ 4

The top side from (5,4) to (0,4): r(t) = <t, 4>, 5 ≥ t ≥ 0

The left side from (0,4) to (0,0): r(t) = <0, t>, 4 ≥ t ≥ 0

Then we can evaluate the line integral as follows:

∫C xy dx + x² dy

= ∫[0,5] xy dt + ∫[0,4] 25 dt + ∫[5,0] 4x dt + ∫[4,0] 0 dt (by direct computation)

= 62.5

Therefore, the value of the line integral is 62.5.

(b) Evaluation using Green's Theorem:

Green's Theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. Specifically, for a smooth vector field F = <P, Q> and a simple closed curve C that encloses a region D, Green's Theorem states that:

∫C P dx + Q dy = ∬D (∂Q/∂x - ∂P/∂y) dA

In this case, we have F = <y, x²>, and the region D is the rectangle enclosed by C.

We can apply Green's Theorem as follows:

∬D (∂Q/∂x - ∂P/∂y) dA

= ∬D (2x) dA

= 2 ∫[0,4] ∫[0,5] x dy dx

= 2 ∫[0,5] x [y]4_0 dx

= 62.5

Therefore, the value of the line integral using Green's Theorem is also 62.5, which matches the direct evaluation in part (a).

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There are total 80 ways to form a committee out of 7 women and 8 men which contains at least one 1 man and woman.

There are 7 women and 8 men in the faculty of mathematics department of the school.

Now, a committee has to be formed of five members such that at least one woman and at least one man must be on the committee.

Now, two positions are fixed so now the combinations that we have to make are,

= 1 + 1 + ¹³C₂

= 1 + 1 + 78

= 80

So, the total number of possible combinations are 80.

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In binary representation, each bit can be either 0 or 1. Using five binary bits, we can obtain 32 different numbers. Therefore, the correct answer is (B).

With five binary bits, we have five positions, and each position can have two possibilities (0 or 1). To calculate the total number of different numbers we can obtain, we need to raise 2 to the power of the number of bits. In this case, we have \(2^5,\) which equals 32. Therefore, we can obtain 32 different numbers using five binary bits. To understand this concept, we can think of each binary bit as a switch that can be either on (1) or off (0). With five switches, we have a total of 32 different combinations or numbers that can be represented. These numbers range from 0 (all switches off) to 31 (all switches on). Therefore, the correct answer is (B), which states that we can obtain 32 different numbers using five binary bits.

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rate = 3l/minute÷60 = 0.05l/s

t = 450s

capacity = ?

rate = c/t

c = rate*t

c = 0.05*450

c = 22.5litres.

c = 22500ml

Answer:

c

Step-by-step explanation:

The minimum number of comparisons needed to sort small array of 6 elements is 8 and the lower bound of 6 comparisons (median) is 5.

To find the minimum number of comparisons, follow these steps:

To find the lower bound of 6 comparisons (median), follow these steps:

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Answer:

Step-by-step explanation:

4 and 6

The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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Answer:

2x + 3y = -6

Step-by-step explanation:

The equation of the new line will be identical to that of the given line except that the constant term will differ.

Start with the given 2x + 3y = 3 and replace x with 3 and y with -4.  We get:

2(3) + 3(-4) = C, and C = 6 - 12 = -6

The equation of the new line is therefore 2x + 3y = -6

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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Answer:

343

Step-by-step explanation:

There are quarters(25¢), loonies ($1), and toonies ($2)

And total number of coins is 9

If loonies ($1), and toonies ($2) are one, then quarters(25¢) is 7

If quarters(25¢), and toonies ($2) are one, then loonies ($1)is 7

If loonies ($1), and quarters(25¢) are one, then toonies ($2) is 7

So possible number number of combination for an item that cost between $10 and $12 is

= 1^3 * 1^3 * 7^3

= 343

hope this helps, stay safe :)

The number of different combinations of coins could Teo use to pay for an item that costs between $10 and $12 is 17.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

Given that,

Teo has a combination of quarters, loonies, and toonies in his pocket.

Total number of coins = 9

1 quarter = $0.75

1 loonie = $1

1 toonie = $2

If he uses fewer toonies than loonies,

Total number of combinations of 9 coins = 1³ × 1³ × 7³ = 343

We need the number of combinations in between $10 and $12.

We can form the following combinations.

(2 × $1) + $2 gives $4. Remaining can be 8, 9 and 10 quarter coins.

(3 × $1) + (2 × $2) gives $7. Remaining can be 4, 5 and 6 quarter coins.

(3 × $1) + (1 × $2) gives $5. Remaining can be 7, 8 and 9 quarter coins.

(4 × $1) + (3 × $2) gives $10. Remaining can be 1 or 2 quarter coins.

(4 × $1) + (2 × $2) gives $8. Remaining can be 3, 4 and 5 quarter coins.

(4 × $1) + (1 × $2) gives $6. Remaining can be 6, 7 and 8 quarter coins.

Total number of combinations = 3 + 3 + 3 + 2 + 3 + 3 = 17

Hence the total number of combinations are 17.

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Approximately 16% of the design is black.

Since the radius of each circle increases by 2 inches, the diameter of each circle increases by 4 inches. Thus, the diameter of the largest circle is 2 + 4(5) = 22 inches.

The area of each circle is proportional to the square of its radius, so the area of the smallest circle is π(\(2^2\)) = 4π square inches. The area of the second circle is π(\(4^2 - 2^2\)) = 12π square inches, the area of the third circle is π(\(6^2 - 4^2\)) = 20π square inches, and so on.

The total area of the design is the sum of the areas of all the circles, which is:

4π + 12π + 20π + 28π + 36π = 100π

The black area in the design consists of four quarter circles, each with a radius of 4 inches. The area of a one-quarter circle is:

(1/4)π(\(4^2\)) = 4π

So the total black area is 4 times this, or 16π.

The percent of the design that is black is:

(16π / 100π) x 100% ≈ 16%

Therefore, approximately 16% of the design is black.

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Answer:

b

Step-by-step explanation:

Answer:

r < 1

-

1. Move the constant to the right

9- 4r > 5

2. Calculate

-4r > 5 - 9

3. Divide both sides

-4r > -4

4. Solution

r < 1

The equation of the graph is  (b) f(x) = |x - 7| - 3

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

The graph

The graph is an absolute value graph

An absolute value graph is represented as

f(x) = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have

Vertex = (h, k) = (7, -3)

So, we have

f(x) = a|x - 7| - 3

Solving for a, we have

a|4 - 7| - 3 = 0

This gives

a = 1

So, we have

f(x) = |x - 7| - 3

Hence, the equation of the graph is f(x) = |x - 7| - 3

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The student used an incοrrect sign fοr the secοnd term. The cοrrect equivalent expressiοn using the distributive prοperty is 7y - 35.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

The mistake made by the student is d. An incοrrect sign was used fοr the secοnd term.

Tο distribute the 7 tο the terms inside the parentheses using the distributive prοperty, we need tο multiply 7 by each term inside the parentheses. Sο, we have:

7(y - 5) = 7y - 35

The secοnd term is negative, nοt pοsitive as shοwn in the student's attempted expressiοn.

Therefοre, the student used an incοrrect sign fοr the secοnd term. Thecοrrect equivalent expressiοn using the distributive prοperty is 7y - 35.

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Answer:

y - 2 = - 5(x - 7)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (7, 2) , thus

y - 2 = - 5(x - 7) ← equation in point- slope form

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The relation accepts reflexive, symmetry, and transitive.

Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.

If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.

And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.

Given r is a relation on the set of all nonnegative integers R(a,b)

Reflexive - YES. A given number a will always have the same remainder when divided by 5.

Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.

Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.

Therefore the relation accepts reflexive, symmetry, and transitive.

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Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

N÷4×K

Step-by-step explanation:

It would be easy to explain if the unknown numbers had values

35:50 and 21:30

multiply or divide both sides by the same number

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The equivalent ratios are :

and

they can be further simplified into 7 : 10

The Extreme Value Theorem does not apply on the open interval (0, 1].

What is the Extreme Value Theorem?

The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.

(a) If f is not continuous, the Extreme Value Theorem does not hold. Here is a sketch to illustrate this:

In the graph above, the function f(x) has a vertical asymptote at x = 0 and a hole at x = 1. The function is not continuous on the interval [0, 2], so the Extreme Value Theorem does not apply.

There is no global minimum or maximum on the interval, as the function keeps increasing as x approaches 0 and keeps decreasing as x approaches 2.

(b) If [a, b] is replaced with (a, b], the Extreme Value Theorem does not hold. Here is a sketch to illustrate this:

In the graph above, the function f(x) is defined on the open interval (0, 1]. The function has a horizontal asymptote at y = 0 and a local maximum at x = 1/2.

However, there is no global maximum on the interval (0, 1], since the function keeps increasing without bound as x approaches 0.

Therefore, the Extreme Value Theorem does not apply on the open interval (0, 1].

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Note that the solution to y in the above-given matrix is 29/4 or 7.25

The matrix equation can be written in the form:

| 2  7 |   | x |   | 8 |

| 2  6 | * | y | = | 6 |

We can solve for y by first isolating the matrix with y on one side of the equation, and then applying matrix inverse to both sides. Here are the steps:

Step 1: Transpose the matrix on the left side

| x |   | 2  2 |^-1   | 8 |

| y | = | 7  6 |    * | 6 |

Step 2: Find the inverse of the matrix on the left side. The inverse of a 2x2 matrix [a, b; c, d] is given by 1/(ad - bc) * [d, -b; -c, a]. Applying this formula, we get:

| x |   | -3/4  1/4 |   | 8 |

| y | = |  7/4 -1/4 | * | 6 |

Step 3: Multiply the two matrices on the right side. We get:

| x |   | -3/4  1/4 |   | 8 |   |  1 |

| y | = |  7/4 -1/4 | * | 6 | = |  1 |

| x |   | -3/4*8 + 1/4*6 |   |  1 |

| y | = |  7/4*8 - 1/4*6 | = | 29/4 |

Therefore, the solution is y = 29/4.

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