Kay loves to save coins. She has a piggy bank that she has been filling for a long time with only dimes and nickels. Recently, her piggy bank was filled to the brim so Kay counted her coins and she discovered that she had $10. She also noticed that she has 11 less dimes than nickels. How many coins were in Kay's bank?​

The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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Jane have 35 beads in total.

We have, ratio of the number of Mary's beads to the number of Jane's beads is 4 : 7.

The ratio of the number of Jane's beads to the number of Pauline's beads is 5 : 2.

We can Write the ratios as

Mary : Jane  :  Pauline

    4   :  7

            5       :    2

Now, Jane is common in both then

Mary : Jane  :  Pauline

20     :    35   :      14

Thus, Jane have 35 beads in total.

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Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

Hi :)

Answer:

The quotient will be decreased by 10

Step-by-step explanation:

720 ÷ 9 = 80

630 ÷ 9 = 70

Hope this helps :) !!!

Answer:

the quotient will decrease by 10 because when you divide 720 by 9 you will get 80 and when you divide 630 by 9 you will get 70. If you minus 8-0 and 70 you will get 10 hope this helps

To find the third number in the sequence given that the first number is -4 and the fifth number is 8, we need to determine the pattern or rule that governs the sequence.

One possible pattern is that the sequence is an arithmetic sequence, where each term is obtained by adding a common difference (d) to the previous term.

Let's calculate the common difference using the first and fifth numbers:

Common difference (d) = 8 - (-4)

= 8 + 4

= 12

Now, we can find the third number by adding the common difference to the first number:

Third number = First number + 2 * Common difference

= -4 + 2 * 12

= -4 + 24

= 20

Therefore, the third number in the sequence is 20.

Answer:

 [tex]\dfrac{x^2+8x+8}{2x+4}\\\\[/tex]

Step-by-step explanation:

Simplify:

        [tex]\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}[/tex]

Multiply the denominator and the numerator of the first term by 2,

                        [tex]=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}[/tex]

                       [tex]\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\[/tex]

Answer:

To calculate each person's share, we first add up the parts of the ratio, which is 1+3+6=10.

Next, we divide the total amount shared, GH4000, by the ratio sum (10):

GH4000/10= GH400

Finally, to find each person's share, we multiply the ratio part by GH400:

- Harrison's share: 1 part out of 10 parts = 1/10 * GH4000 = GH400

- Anny's share: 3 parts out of 10 parts = 3/10 * GH4000 = GH1200

- Ekua's share: 6 parts out of 10 parts = 6/10 * GH4000 = GH2400

Therefore, Harrison's share is GH400, Anny's share is GH1200, and Ekua's share is GH2400.

Step-by-step explanation:

To calculate the annuity payment for each of the given scenarios, we can use the formula for the present value of an ordinary annuity:

Annuity Payment = Future Value / [(1 - (1 + r)^(-n)) / r]

Where:

Future Value = Future value of the annuity

r = Interest rate per period (in decimal form)

n = Total number of periods

Let's calculate the annuity payment for each scenario:

Scenario 1:

Future Value = $25,850

Year = 8

Interest rate = 8% (0.08 as a decimal)

Annuity Payment = $25,850 / [(1 - (1 + 0.08)^(-8)) / 0.08]

Scenario 2:

Future Value = $1,130,000

Year = 43

Interest rate = 10% (0.10 as a decimal)

Annuity Payment = $1,130,000 / [(1 - (1 + 0.10)^(-43)) / 0.10]

Scenario 3:

Future Value = $976,000

Year = 29

Interest rate = 11% (0.11 as a decimal)

Annuity Payment = $976,000 / [(1 - (1 + 0.11)^(-29)) / 0.11]

Scenario 4:

Future Value = $149,000

Year = 16

Interest rate = 7% (0.07 as a decimal)

Annuity Payment = $149,000 / [(1 - (1 + 0.07)^(-16)) / 0.07]

After performing the calculations, you will obtain the annuity payment for each scenario.

I hope I was helpful

In this relationship, the arc length is inversely Proportional to the area. As the area increases, the arc length decreases, and vice versa.

The relationship between the arc length (s) and the area (a) of a sector, let's start by understanding the formulas for each.

The arc length of a sector can be calculated using the formula:

s = θr

where s is the arc length, θ is the central angle of the sector in radians, and r is the radius.

The area of a sector can be calculated using the formula:

a = (1/2)θr^2

where a is the area, θ is the central angle of the sector in radians, and r is the radius.

Given that the arc length is equal to one fourth of the radius, we can express this relationship as:

s = (1/4)r

Now, let's express the central angle (θ) in terms of the area (a).

From the formula for the area of a sector, we can rearrange it to solve for θ:

a = (1/2)θr^2

Multiplying both sides by 2/r^2, we get:

2a/r^2 = θ

Substituting this value of θ back into the equation for the arc length (s), we have:

s = (1/4)r = (1/4)r(2a/r^2) = (1/2a)r

Therefore, we have expressed the arc length (s) as a function of the area (a) of the sector:

s = (1/2a)r

In this relationship, the arc length is inversely proportional to the area. As the area increases, the arc length decreases, and vice versa.

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The perimeter of the pentagon ABCDE is 12.8 units

To solve for the perimeter of the pentagon, we need to find the length of each side and add them up.

The length of a line segment in a coordinate plane can be found using the distance formula which is derived from the Pythagorean theorem:

D = √(x2-x1)² + (y2-y1)²

[tex]AB: \sqrt(-6-(-4))^2 + (-3-(-2))^2 = \sqrt5 = 2.236[/tex]

[tex]BC: \sqrt(-5-(-6))^2 + (-6-(-3))^2 = \sqrt10 = 3.162[/tex]

[tex]CD: \sqrt(-2-(-5))^2 + (-5-(-6))^2 = \sqrt10 = 3.162[/tex]

[tex]DE: \sqrt(-2-(-2))^2 + (-3-(-5))^2 = \sqrt4 = 2[/tex]

[tex]EA: \sqrt(-4-(-2))^2 + (-2-(-3))^2 = \sqrt5 = 2.236[/tex]

2. 236 + 3.162 + 3.162 + 2 + 2.236 = 12.796

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The dimensions of the container in the shape of a rectangular solid are 3.41 m by 4.41 m by 7.81 m.

Let the width of the container be w.

The length of the container is w + 1.

The height of the container is 2w + 1.

The volume of the container is 84 m3.

Set up the following equation to represent the volume of the container:

w(w + 1)(2w + 1) = 84

Solve for w by expanding the left-hand side of the equation:

2w³ + 3w² + w - 84 = 0

Then use the quadratic formula to solve for w:

w = (-3 ± √(3² - 4 × 2 × (-84))) / (4 × 2)

w = (-3 ± √(9 + 672)) / 8

w = (-3 ± √681) / 8

w = (-3 ± 26.09) / 8

w = 3.41 or -5.59

Since w is the width of the container, it must be positive. Therefore, w = 3.41.

The length of the container is w + 1 = 3.41 + 1 = 4.41.

The height of the container is 2w + 1 = 2 × 3.41 + 1 = 7.81.

Therefore, the dimensions of the container are 3.41 m by 4.41 m by 7.81 m.

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Therefore, we can expect that approximately 95.45% of the 3000 metal rods produced will fall between 74.5 cm and 75.5 cm in length. To find the actual number, we multiply 0.9545 by 3000, yielding approximately 2864 rods.

To determine how many metal rods will be between 74.5 cm and 75.5 cm in length, we can use the properties of the normal distribution.

Given that the lengths of the metal rods are normally distributed with a mean of 75.0 cm and a standard deviation of 0.25 cm, we can calculate the probability of a rod falling within the specified range.

First, we find the z-scores for the lower and upper limits of the range. The z-score for 74.5 cm is

[tex]\frac{ (74.5 - 75.0) }{ 0.25} = -2,[/tex]

and the z-score for 75.5 cm is

[tex]\frac{(75.5 - 75.0)} { 0.25} = 2.[/tex]

Using a standard normal distribution table or a statistical calculator, we can determine the area under the curve between these z-scores, which represents the probability.

The area between -2 and 2 is approximately 0.9545.

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Answer:

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

Each number from 1 to 10 has same probability of 1/10.

So we have 1/10 for an '8' and 1/10 for a '9'.

The probability of either '8' or '9' is the sum of the two probabilities:

Answer:

D. Reflection across x = 2

Step-by-step explanation:

We see that it reflect across x = 2 because if you look at the graph, we see the left side rectangle is 3 points away to the left, and the rectangle on the right is 3 point to the right.

Answer:

Some points about quantum entanglement in my own words are:

Here are some additional details about quantum entanglement:

Quantum entanglement is a fascinating and mysterious phenomenon that is still not fully understood. However, it has the potential to change the world in many ways

Step-by-step explanation:

In the case of a hard money or short-term loan, the calculation for the monthly payment is slightly different. Typically, hard money loans have interest-only payments during the loan term, and the principal amount is due at the end of the term.

To calculate the monthly payment for an interest-only loan, you can use the following formula:

Monthly Payment = Loan amount * (Annual interest rate / 12)

Given:

Condo cost = $80,000

Down payment = $30,000

Loan amount = Condo cost - Down payment = $80,000 - $30,000 = $50,000

Annual interest rate = 6.00%

Loan term = 30 months

First, calculate the monthly interest rate:

Monthly interest rate = (Annual interest rate / 100) / 12 = (6.00 / 100) / 12 = 0.005

Next, substitute the values into the formula:

Monthly Payment = $50,000 * 0.005

After performing the calculations, the monthly payment for this hard money loan is $250.

I hope I was helpful

Answer:

1)

A) 0.541 or 0.54(by rounding)

B) 0.675

C)Yes, they are independent because someone doesnt have to attend prom to be a senior and vice versa

2)

a) 0.29

b) 0.04

c) Yes, they are independent because you do not have to live in Long Beach to recommend the provider and vice versa

Step-by-step explanation:

Answer:

Debbie average daily change is 8 dollars

Step-by-step explanation:

since he lost 56$ this week (7 days) you have to divide 56 by 7 and your average daily change is 8 dollars.

Answer:

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

Loss in a week is $56, so if we divide it by the number of days, we'll get daily loss amount:

The change is - $8, since we are talking about a loss.

The matching choice is A.

Answer:

1x3

2x3

                                                            2x2

                                                             3x2

Step-by-step explanation:

with the 1x3 you get 3 and with 2 x 3 you get 6 which means for the first one you get  3/6 .

for the second one 2x2 =4 and 3x2=6 which equals 4/6

The limit (x -> -2) f(x) is equal to -6.

Let's consider the function f(x) = (x² - 4) / (x + 2). We'll calculate the function values for various x-values in the table below and then determine the limit (x -> -2) f(x).

x f(x)

-3 -5

-2.5 -5.25

-2.1 -5.61

-2.01 -5.9602

-2.001 -5.996002

-2.0001 -5.99960002

Now, let's calculate the limit (x -> -2) f(x) using the function values in the table. As x approaches -2, we can observe that the function values approach a specific value:

lim (x -> -2) f(x) ≈ -6

Therefore, the limit (x -> -2) f(x) is equal to -6.

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The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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Scale factor = (10 inches / 5 inches) = 2

D. 2.

The sine of 48 Degrees is equal to one-half.

The cosine of an angle is equal to one-half when the angle is 60 degrees. Therefore, if the cosine of 42 degrees is one-half, it means that the angle of 42 degrees is complementary to the angle of 60 degrees.

Since the angles are complementary, the sine of one angle is equal to the cosine of the other angle. In this case, the sine of 48 degrees will be equal to the cosine of its complementary angle, which is 42 degrees.

Therefore, the sine of 48 degrees is equal to one-half.

The correct answer is: 1/2, because the angles are complementary.

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The probability of an atom of substance A chosen at random decaying in the next 70 years is 2.07%.

The decay rate of a radioactive substance can be calculated using the formula: N=N0e−λt, where N0 is the initial number of radioactive atoms, N is the remaining number of radioactive atoms,

t is the time in years, and λ is the decay constant expressed in inverse years.

The probability of a given radioactive atom decaying during a specific period can be found using the formula: P = 1 - e^(-λt).

In this case, the decay rate of substance A is 0.03% per year, which can be expressed as a decimal fraction of 0.0003.

Therefore, the decay constant λ = 0.0003.

The time period of interest is 70 years.

Therefore, the probability of an atom decaying during this period can be calculated as:

P = 1 - e^(-0.0003*70)P

= 1 - e^(-0.021)P

= 0.0207 or 2.07%

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Rajani's age is calculated to be 24 years old.

Let's assume the two-digit number representing Rajani's age is written as AB,

where

A represents the tens digit and

B represents the units digit.

According to the given information, Rajani's age, AB, is equal to:

Based on this information, we can form the equation:

10A + B = 4(A + B) + 6(A * B)

10A + B = 4A + 4B + 6AB

rearranging the terms:

10A - 4A = 4B + 6AB - B

6A = 3B + B(6A - 4)

6A = 3B + 2B(3A - 2)

Dividing both sides by 3A - 2:

6A / (3A - 2) = 3B / (3A - 2) + 2B

at this point, we need to check the possible values for A and B that satisfy this equation. Since the problem states that Rajani's age consists of two digits, A and B must be integers ranging from 0 to 9.

By trying different values for A and B, we find that A = 2 and B = 4 satisfy the equation:

6 * 2 / (3 * 2 - 2) = 3 * 4 / (3 * 2 - 2) + 2 * 4

12 / 4 = 12 / 4 + 8

3 = 3 + 8

The equation is true for A = 2 and B = 4.

Therefore, Rajani's age is 24 years old.

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Answer:

A

Step-by-step explanation:

To find the product of -4 and the vector [8, -1, -5, 9], you need to multiply each element of the vector by -4. Here's the calculation:

-4 * 8 = -32

-4 * -1 = 4

-4 * -5 = 20

-4 * 9 = -36

Therefore, the product of -4 and [8, -1, -5, 9] is:

[-32, 4, 20, -36]

So the correct answer is A: [-32, 4, 20, -36].

Answer:

[tex]\displaystyle \frac{cd^6}{a^4b^2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}[/tex]

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with [tex]e^{-7}[/tex]) and became positive, and vice versa with those originally in the numerator went in the denominator (like with [tex]a^{-4}b^{-2}[/tex]) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

We have successfully proven the identity cos(4A)/sin(2A) + sin(4A)/cos(2A) = cosec(2A) Thus, we have shown that the given trigonometric identity is true.

To prove the trigonometric identity: cos(4A)/sin(2A) + sin(4A)/cos(2A) = cosec(2A), we'll work on simplifying both sides of the equation separately.

Starting with the left-hand side (LHS):

LHS = cos(4A)/sin(2A) + sin(4A)/cos(2A)

To simplify this expression, we'll use trigonometric identities and algebraic manipulations.

First, let's rewrite cos(4A) and sin(4A) using double-angle formulas:

cos(4A) = cos^2(2A) - sin^2(2A)

sin(4A) = 2sin(2A)cos(2A)

Substituting these expressions into LHS, we have:

LHS = (cos^2(2A) - sin^2(2A))/sin(2A) + (2sin(2A)cos(2A))/cos(2A)

Now, let's simplify each term separately:

LHS = cos^2(2A)/sin(2A) - sin^2(2A)/sin(2A) + 2sin(2A)cos(2A)/cos(2A)

Using the identity cos^2(2A) = 1 - sin^2(2A), we can rewrite the first term:

LHS = (1 - sin^2(2A))/sin(2A) - sin^2(2A)/sin(2A) + 2sin(2A)cos(2A)/cos(2A)

Now, let's combine the fractions with a common denominator:

LHS = (1 - sin^2(2A) - sin^2(2A) + 2sin(2A)cos(2A))/sin(2A)

Simplifying further:

LHS = (1 - 2sin^2(2A) + 2sin(2A)cos(2A))/sin(2A)

Using the identity 2sin(2A)cos(2A) = sin(4A), we have:

LHS = (1 - 2sin^2(2A) + sin(4A))/sin(2A)

Now, let's simplify the right-hand side (RHS) using the reciprocal identity of sin(2A):

RHS = 1/sin(2A) = cosec(2A)

Since LHS = RHS, we have successfully proven the identity:

cos(4A)/sin(2A) + sin(4A)/cos(2A) = cosec(2A)

Thus, we have shown that the given trigonometric identity is true.

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The correct formula to find the area of the surface obtained by rotating the curve, about the x-axis is S = ∫2πy(x) √(1 + (dy/dx)²) dx.

To find the area of the surface obtained by rotating the curve, about the x-axis, we use the formula given below:

S = ∫2πy(x)ds where ds = √(1 + (dy/dx)²) dx

For the curve y = f(x),

we can use the formula given below:

S = ∫2πf(x) √(1 + (dy/dx)²) dx

The student wants to find the area of the surface obtained by rotating the curve, about the x-axis.

So, the correct formula to find the area of the surface is given below:

S = ∫2πy(x)ds = ∫2πy(x) √(1 + (dy/dx)²) dx

Where the curve is y = f(x).

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Answer:

D) 0.203π square units

Step-by-step explanation:

The area of a surface obtained by rotating the curve about the x-axis in the interval [a, b] is given by the formula:

[tex]\large\boxed{\displaystyle S=\int^{b}_{a}2\pi y\sqrt{1+\left(\dfrac{\text{d}y}{\text{d}x}\right)^2}\; \text{d}x}[/tex]

The given interval is 0 ≤ x ≤ 1. Therefore:

The equation of the curve is:

[tex]y=\dfrac{x^3}{3}=\dfrac{1}{3}x^3[/tex]

Differentiate the function using the following differentiation rule:

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

Therefore:

[tex]\dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{3}x^{3-1}=x^2[/tex]

Therefore, the integral is:

[tex]\displaystyle S=\int^{1}_{0}2\pi \left(\dfrac{1}{3}x^3\right)\sqrt{1+\left(x^2\right)^2}\; \text{d}x[/tex]

[tex]\displaystyle S=\int^{1}_{0} \left(\dfrac{2\pi}{3}x^3\right)\sqrt{1+x^4}\; \text{d}x[/tex]

[tex]\displaystyle S=\dfrac{2\pi}{3}\int^{1}_{0} x^3\sqrt{1+x^4}\; \text{d}x[/tex]

To evaluate the definite integral, use the method of substitution.

[tex]\textsf{Let}\;u=1+x^4[/tex]

Find du/dx and rewrite it so that dx is on its own:

[tex]\dfrac{\text{d}u}{\text{d}x}=4x^3 \implies \text{d}x=\dfrac{1}{4x^3}\; \text{d}u[/tex]

Find the limits in terms of u:

[tex]\textsf{When}\; x = 0 \implies u=1+0^4=1[/tex]

[tex]\textsf{When}\; x = 1 \implies u=1+1^4=2[/tex]

Rewrite the original integral in terms of u and du:

[tex]\displaystyle S=\dfrac{2\pi}{3}\int^{2}_{1} x^3\sqrt{u} \cdot \dfrac{1}{4x^3}\; \text{d}u[/tex]

[tex]\displaystyle S=\dfrac{2\pi}{3}\int^{2}_{1} \dfrac{1}{4}\sqrt{u}\; \text{d}u[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\int^{2}_{1} \sqrt{u}\; \text{d}u[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\int^{2}_{1} u^{\frac{1}{2}}\; \text{d}u[/tex]

Evaluate the integral using the integration rule:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Therefore:

[tex]\displaystyle S=\dfrac{\pi}{6}\left[\vphantom{\dfrac12}\dfrac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right]^{2}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\left[\vphantom{\dfrac12}\dfrac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]^{2}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\left[\vphantom{\dfrac12}\dfrac{2u^{\frac{3}{2}}}{3}\right]^{2}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\left(\dfrac{2(2)^{\frac{3}{2}}}{3}-\dfrac{2(1)^{\frac{3}{2}}}{3}\right)[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\left(\dfrac{4\sqrt{2}}{3}-\dfrac{2}{3}\right)[/tex]

[tex]\displaystyle S=\dfrac{\pi}{6}\left(\dfrac{-2+4\sqrt{2}}{3}\right)[/tex]

[tex]\displaystyle S=\left(\dfrac{-1+2\sqrt{2}}{9}\right)\pi[/tex]

[tex]\displaystyle S=0.203\pi[/tex]

Therefore, from the given answer options, the correct area is 0.203π square units.

So the cost of 1950 bricks is $163.80.

For the given right rectangular prism,

Dimension = 8 in x  3[tex]\frac{1}{2}[/tex] in x 3 in

Then,

Length = 8 in

Width   = 3[tex]\frac{1}{2}[/tex] in

Height  = 3 in

Now find the volume of one brick by multiplying its length, width, and height together, so,

⇒ 8 in x 7/2 in x 3 in = 84 in³

Now calculate the total volume of 1950 bricks,

⇒ 1950 x 84 in = 163800 in³

Now we can find the total cost of the bricks by multiplying the total volume by the cost per cubic inch,

⇒ 163800 in x $0.10/in = $16,380.00

Finally, round our answer to the nearest cent,

we can divide by 100 and round to two decimal places,

⇒ $16,380.00 / 100 = $163.80

So the cost of 1950 bricks, rounded to the nearest cent, is $163.80.

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