Simplify the expression. cos x/cot x

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

D) g(x) = -4x²

Step-by-step explanation:

From f(x) to g(x), there is a reflection about the x-axis, followed by a vertical stretch.

So, we know that g(x) needs to have a negative leading coefficient, which eliminates the first two options.

Now C can't work because that would involve a vertical compression since the absolute value of the leading coefficient is less than 1

Therefore, D is correct!

Answer:

y=−210+5x

Step-by-step explanation: easy

Answer: x <= -70 or x >= 22.

Step-by-step explanation:

The solution to the inequality is x <= -70 or x >= 22.  To solve the inequality, we can begin by isolating the absolute value term.   |1/5x + 2| + 4 >= 6   |1/5x + 2| >= 2   Next, we can split the inequality into two cases:   1/5x + 2 >= 2 or 1/5x + 2 <= -2   Solving for the first case:   1/5x + 2 >= 2   1/5x >= 0   x >= 0   Solving for the second case:   1/5x + 2 <= -2   1/5x <= -4   x <= -20   Therefore, the solution is x <= -70 or x >= 22.

The angle  made by one of the tensions suspending particle P is 50⁰.

The angle θ made by one of the tensions is calculated by applying trig identities as follows;

the force opposite the angle = weight of the block = mg

W = 7.75 kg x 9.8 m/s²

W = 75.95 N

The angle θ made by one of the tensions is calculated as follows;

cos θ = (38 N ) / ( 59 N)

cos θ = 0.6441

θ = arc cos (0.6441)

θ = 50⁰

Thus, the angle θ made by one of the tensions is determined as 50 degrees.

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The missing part of the question is in the image attached.

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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The reconciled difference between the bank balance and the ledger balance is Br. 479.69.

To reconcile the bank balance with the company's ledger balance, we need to consider the various transactions and adjustments provided in the information.

Starting with the company's ledger balance on July 31:

Ledger balance: Br. 4,173.83

Deposit made after banking hours:

Add: Br. 410.90

Updated ledger balance: Br. 4,584.73

Erroneously charged check:

Add: Br. 79

Updated ledger balance: Br. 4,663.73

Outstanding checks:

Deduct the amounts of the outstanding checks:

Deduct: Br. 100.00 (Check 801)

Deduct: Br. 10.25 (Check 888)

Deduct: Br. 294.50 (Check 890)

Deduct: Br. 205.00 (Check 891)

Updated ledger balance: Br. 4,054.98

Incorrectly charged check:

Add: Br. 90 (Br. 210 - Br. 120)

Updated ledger balance: Br. 4,144.98

Proceeds from collection of interest-bearing note:

Add: Br. 500

Updated ledger balance: Br. 4,644.98

Interest earned on average account balance:

Add: Br. 24.75

Updated ledger balance: Br. 4,669.73

Incorrectly recorded check:

Deduct: Br. 90 (Br. 100 - Br. 10)

Updated ledger balance: Br. 4,579.73

Bank fee for handling note receivable:

Deduct: Br. 5.00

Updated ledger balance: Br. 4,574.73

NSF check from customer:

Deduct: Br. 50.25

Updated ledger balance: Br. 4,524.48

Service charge by the bank:

Deduct: Br. 12.70

Updated ledger balance: Br. 4,511.78

Erroneously recorded check:

Deduct: Br. 27 (Br. 85 - Br. 58)

Final ledger balance: Br. 4,484.78

To reconcile the bank balance, we compare the bank statement balance of Br. 4,964.47 with the final ledger balance of Br. 4,484.78.

Bank statement balance: Br. 4,964.47

Ledger balance: Br. 4,484.78

To calculate the difference:

Bank balance - Ledger balance:

Br. 4,964.47 - Br. 4,484.78 = Br. 479.69

Therefore, the difference between the bank balance and the ledger balance is Br. 479.69.

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Answer:

29 2-point baskets were made

13 3-point baskets were made

Step-by-step explanation:

Given:

x=number of 2-point baskets scored

y=number of 3-point baskets scored

First set of equations:

[tex]2x+3y=97[/tex]

Second set of equations:

[tex]x+y=42[/tex]

Solve for x or y in the second equation:

[tex]x+y=42\\y=42-x[/tex]

plug in y into the first equation:

[tex]2x+3(42-x)=97[/tex]

[tex]2x+126-3x=97\\[/tex]

combine like terms

[tex]x+126=97[/tex]

[tex]x=126-97\\x=29[/tex]

So, 29 2-point baskets were made.

Now plug in 29 for x in the second equation:

[tex]29+y=42[/tex]

subtract 29 from both sides

y=13

So, 13 3-point baskets were made.

Hope this helps! :)

Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Answer: Therefore, the commission rate is 18%.

Step-by-step explanation: To find the commission rate, we divide the commission earned by the total sales and then express it as a percentage.

Commission Rate = (Commission Earned / Total Sales) * 100

In this case, the commission earned is $540 and the total sales are $3000. Plugging these values into the formula, we have:

Commission Rate = (540 / 3000) * 100

Calculating this expression, we get:

Commission Rate = 0.18 * 100

To simplify the expression, we can use the rule of exponents to add the exponents of 2:`2^-6*2^6 = 2^0 = 1`.Therefore, our final answer is:`1(5)(5^2) = 1(5)(25) = 125`

In order to solve this problem, we will use the rule of exponents which states that if we have the same base, then we can multiply their exponents and add them.

If we have the same base, then we can divide their exponents and subtract them. And if we have a power of a power, then we can multiply their exponents.

Given that `(2^-6)(5)(2^3*5)^2`We can first simplify the expression inside the parentheses:`(2^3*5)^2 = 2^6*5^2`

Now we can substitute this back into the original expression:`(2^-6)(5)(2^6*5^2)`

To simplify the expression, we can use the rule of exponents to add the exponents of 2:`2^-6*2^6 = 2^0 = 1`

Therefore, our final answer is:`1(5)(5^2) = 1(5)(25) = 125`

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Answer:

[tex]f(x) = {(x + 3)}^{2} = {x}^{2} + 6x + 9[/tex]

Step-by-step explanation:

move 3 units to the left

[tex] {x}^{2} [/tex]

hence

[tex] {(x + 3)}^{2} [/tex]

The area of the garden in this problem is given as follows:

201.07 ft².

For the rectangular part of the garden, the area is given by the multiplication of the dimensions as follows:

22 x 31 = 682 ft².

For the semi-circle, the radius is given as follows:

r = 0.5 x 22

r = 11 ft.

Hence the area is given as follows:

A = 0.5 x π x 11²

A = 190.07 ft.

Hence the total area is given as follows:

190.07 + 11 = 201.07 ft².

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The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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Answer:

-3, 3, 0.54545455, 8, 3.14159265..., 0, 2.44948974, 6

these are the real numbers

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

29

Step-by-step explanation:

7 + 4 = 11 --> 4 = 2²

11 - 9 = 2 --> 9 = 3²

2 + 16 = 18 --> 16 = 4²

18 - 25 = -7 --> 25 = 5²

Notice that the pattern is adding and then subtracting the next square number up. Therefore, the next number in the sequence would be -7 + 36 = 29 since 6²=36.

Answer:

5

Step-by-step explanation:

-2（3x+2)> -8x+6

-6x-4> -8x+6

-6x+8x> 6+4

2x> 10

x> 10/2

x> 5

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

[tex]label("$52^\circ$", N + 0.3*dir(52), NE);[/tex]

[tex]label("$134^\circ$", S + 0.3*dir(134), SE);[/tex]

draw(O--A--B--cycle,dashed);

[tex]label("$x$", (N+A)/2, W);[/tex]

[tex]label("$y$", (S+B)/2, E);[/tex]

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

[tex]$$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$[/tex]

From the south observation point, we have:

[tex]$$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$[/tex]

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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Answer:

Step-by-step explanation:

2/3 of n = 24

2n/3 = 24

2n = 72

n = 36

Half of 36 is 18

Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

The simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.

To simplify the expression (2^-6)(5)(2^3*5)^2, let's break it down step by step:

First, we can simplify 2^-6. A negative exponent indicates taking the reciprocal of the base raised to the positive exponent. In this case, 2^-6 can be written as 1/(2^6).

Next, we can evaluate (2^35)^2. Inside the parentheses, we have 2^35. This can be simplified to 8*5, which equals 40. Then, we raise 40 to the power of 2, resulting in 40^2.

Now, let's put everything together:

(2^-6)(5)(2^3*5)^2 = (1/(2^6))(5)(40^2)

To simplify further, we can simplify the powers of 2 and 40:

2^6 = 64

40^2 = 1600

Substituting these values back into the expression:

(1/64)(5)(1600) = (5/64)(1600)

We can further simplify by multiplying 5 and 1600:

(5/64)(1600) = 800/64

Finally, we can simplify 800/64 by dividing both numerator and denominator by 8:

800/64 = 100/8 = 25/2

Therefore, the simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.

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Answer:

Therefore, the vertices of the image L'M'N' after rotating the triangle 180° counterclockwise about the origin are:

L'(1, -4), M'(1, 0), N'(3, -4)

Step-by-step explanation:

To determine the vertices of the image L'M'N' after rotating the triangle LMN 180° counterclockwise about the origin, we can apply the rotation transformation to each vertex.

The rotation of a point (x, y) by 180° counterclockwise about the origin can be obtained by switching the signs of both coordinates. So, if the original vertex is (x, y), the rotated vertex will be (-x, -y).

Applying this to each vertex:

L'(-x, -y) = L'(-(-1), -(4)) = L'(1, -4)

M'(-x, -y) = M'(-(-1), -(0)) = M'(1, 0)

N'(-x, -y) = N'(-(-3), -(4)) = N'(3, -4)

Therefore, the vertices of the image L'M'N' after rotating the triangle 180° counterclockwise about the origin are:

L'(1, -4), M'(1, 0), N'(3, -4)

l = 8.1 ft to the nearest tenth

In mathematics, an arc of a circle is defined as a portion of the boundary of a circle.

It is a fraction of the total circumference of a circle.

Let point O be the center of the circle and let angle POQ be denoted by x, since the sum of angles at a point is 360°, then,

x = 360 - 150 - 65 - 73

x = 72°

The formula for the length of an arc is given by

l = (θ/360) × 2πr............. Equation 1

Where,

r = radius of the circle

θ = angle subtended by the arc at centre of circle

π = 3.14

Substitute r = 6.48 and θ = 72 into eqn. 1

l = (θ/360) × 2πr

l = (72/360) × 2 × 3.14 × 6.48

l = 0.2 × 2 × 3.14 × 6.48

l = 8.13888 ft

l = 8.1 ft to the nearest tenth

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Using a two-column proof, we can show that segment AM is congruent to segment СМ as explained below in the given table.

The image attached below shows parallelogram ABCD having two diagonals, AC and BD. To proved that segment AM is congruent to segment CM, we would apply the two-column proof as shown below:

Statement                                        Reason                                      

1. Parallelogram ABCD                  1. Given

2. AD║BC                                        2. Properties of parallelogram

3. <MAD ≅ <MCB;                           3. Alternate interior angles theorem.

<ADM ≅ <CBM                            

4. AD ≅ CB                                      4. Properties of parallelogram

5. ΔADM ≅ ΔCBM                           5. ASA congruence theorem

6. AM ≅ CM                                     6. CPCTC

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Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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Answer:

D. 60.3

Step-by-step explanation:

Finding the mean,

M = (sum of values of data)/(number of data)

now, number of data = 9,

calculating the mean,

M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9

M = 543/9

M = 60.333

M = 60.3

The surface areas of the figures are 336, 82 and 836

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

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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Answer:

Since the polynomial is of degree 5 and has three known roots, it has two unknown roots. If the coefficients of the polynomial are real, then the two unknown roots must be either real or a conjugate pair of complex numbers. If the coefficients of the polynomial are complex, then the two unknown roots can be any complex numbers. Therefore, the statement that describes the number and nature of all roots for this function depends on whether the coefficients of the polynomial are real or complex.