I need help with this question

If Scarlet Company received an invoice for $53,000.00 that had payment terms of 3/5 n/30 and made a partial payment of $16,800.00 during the discount period, the balance of the invoice is $34,610.

To calculate the balance of the invoice, follow these steps:

Therefore, the balance of the invoice is $34,610.

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Solution

Given the function below

Where

Also recall that the contangent formula is

Thus;

From the above deduction,

sinθ is the denominator,

Hence, the domain of validity is defined for the set of real numbers except for sinθ = 0

The height of the building is estimated to be approximately 172.49 meters. Since sound travels at a speed of 340 m/s, the additional time for the sound wave to reach back to the observer should be taken into account to get an accurate estimation of the building's height.

Based on the given information that it took 5.9 seconds for the water to fall from the building to the pond, we can calculate the height of the building. Using the equation for free-fall motion, h = 0.5 * g *\(t^2\), where h is the height, g is the acceleration due to gravity, and t is the time, we can substitute the values and solve for h. The height of the building is estimated to be approximately 172.49 meters.

Regarding the second question, if the time for the sound to travel back to the observer is not considered, the height of the building would be underestimated. This is because the sound would take some time to travel back up, and not accounting for this additional time would result in a lower estimate of the building's height.

To find the height of the building, we can use the equation for free fall motion:

h = 0.5 * g * \(t^2\)

where h is the height of the building, g is the acceleration due to gravity (approximately 9.8 m/\(s^2\)), and t is the time it took for the water to fall (5.9 seconds).

Plugging in the values, we have:

h = 0.5 * 9.8 * \((5.9)^2\)

h ≈ 172.49 meters

Therefore, the height of the building is estimated to be approximately 172.49 meters.

For the second question, if the time for the sound to travel back to the observer is not considered, it would lead to underestimating the height of the building. This is because the sound wave needs time to travel from the observer to the top of the building and then back down to the observer.

By not accounting for the time taken for the sound wave to return, the estimated height would only be based on the time it took for the water to fall. Since sound travels at a speed of approximately 340 m/s, the additional time for the sound wave to reach back to the observer should be taken into account to get an accurate estimation of the building's height.

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Answer:

y = -1/5 + 7

Step-by-step explanation:

Substitute the point (1,2) for the x and the y in the equation, set the 4 to b since we are solving for b.

2 = -5(1) + b  now solve for b

2 = -5 + b

+5   +5

7 = b

we know that the slope must be the reciprocal for it to be perpendicular

y = -1/5 + 7 add b (7) to the equation and change the reciprocal

$16,200

1) Coletando los datos

Valor presente: 5,000

rate: 9%

Tiempo: 36 meses

2) Escribindo la formula y despues aplicando los datos, tienemos:

Mira que subtraemos de lo Valor Futuro, el Principal. A -P = i

3) Entonces el interés simple és $16,200

Answer:

\(x \le -4\)

Step-by-step explanation:

Given

\(\qquad16x - 7 \leq -71\)

Required

Solve

Start by adding 7 to both sides

\(\qquad16x - 7 + 7 \leq -71 + 7\)

\(\qquad16x - 7 + 7 \leq -64\)

\(\qquad16x \leq -64\)

Divide both sides by 16

\(\frac{16x}{16} \leq \frac{-64}{16}\)

\(\frac{16x}{16} \leq -\frac{64}{16}\)

\(x \leq -\frac{64}{16}\)

\(x \le -4\) --- The solution

Answer:

x < -4

I did this on khan academy

The area of the shaded region in the rectangle is given as follows:

42 units squared.

The area of a rectangle of base b and height h is given by the multiplication of these dimensions, as follows:

Area = base x height.

For the shaded region in this problem, given by the image shown at the end of the answer, the area can be obtained as the subtraction of the area of the entire rectangle by the area of the non-shaded region.

The entire rectangle has base 11 and height 12, hence it's area is given as follows:

Ar = 11 x 12 = 132 units².

The non-shaded region has base of 9 units and height of 10 units, hence it's area is given as follows:

An = 9 x 10 = 90 units².

Then the area of the shaded region on the rectangle is calculated as follows:

As = Ar - An = 132 - 90 = 42 units².

The rectangle is given by the image shown at the end of the answer.

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The surface area of the  gas tank capsule represented to 1 dp is about 9079.2 cm²

The surface area of a solid object is the area of all the faces of the object.

Part of the dimension of the gas tank obtained from a similar question on the website is; Total length of the gas tank = 85 cm

Therefore;

Radial length of the tank = (85 cm - 51 cm)/2 = 17 cm

The surface area of the tank can be found as the surface area of a composite figure. The extreme right and left part of the tank together form a sphere, while the middle portion is a cylinder. Therefore, we get;

Surface area = 4 × π × 17² + 2 × π × 17 × 51 = (1734 + 1156) × π = 2890·π

Surface area of the figure = 2890·π cm² ≈ 9079.2 cm²

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Answer: yes but... i might be wrong so i think no cause i had a question like this and it was no

Step-by-step explanation:

The weight of the astronaut with gear on the moon is 80 pounds.

The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.

The pull of gravity on Earth = 10 m/s²

Thus, Given:

Weight of object on Earth: 25 pounds

Weight is described as the product of mass and the acceleration due to gravity

Thus, 25 = 10 * mass

mass = 2.5 unit

Weight of the object on the Moon: 4 pounds

4 = 2.5 * acceleration due to gravity on the moon

Acceleration due to gravity on the moon = 1.6 m/s²

Weight of astronaut with gear on earth = 500 pounds

500 = mass * 10

mass = 50 units

Weight of astronaut with gear on earth = 50 * 1.6

= 80 pounds

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The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Thus, the measure of angle A using the law of sine is found as:  ∠A = 39.37°.

The square of just about any one side of such a triangle is the difference between the sum of the squares of the other two sides along with the double product of the other sides and cosine angle contained between them, according to the law of cosine.

Given:

In ΔABC, a= 9, c=5 and ∠B = 120°.

Then, by law of cosine;

b² = a² + c² - 2ac* cosB

Put the values:

b² = 9² + 5² - 2*9*5*cos(120°)

b² = 151

b = √151

For finding the angle A, use the law of sine.

a/sin A = b/sin B

a sin B = b sin A

sin A = asinB / b

sin A = 9(√3 /2) / √151

Sin A = 9√453 / 302

Sin A = 0.63

A = 39.37°.

Thus, the measure of angle A using the  law of sine is found as:  ∠A = 39.37°.

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Answer:

40x + 90y <2400

18x + 30y < 500

Step-by-step explanation:

Lee washes houses. It takes him 40 minutes to wash a one-story home, and he uses 18 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses 30 gallons of water. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his income washing one- and two-story houses. Let x represent the number of one-story houses and y represent the number of two-story houses. What are the constraints for the problem

Let

x=one story houses

y=two story houses

The constraints are the following:

1. Lee works no more than 40 hours each week.

40 hours=40 × 60 minutes

=2400 minutes

2. Lee's truck holds 500 gallons of water.

it takes Lee 40 minutes and 18 gallons of water to wash a one-story house.

it takes Lee 90 minutes and 30 gallons of water to wash a two-story house.

First constraint:

40*x + 90*y < 2400

40x + 90y <2400

Second constraint:

18*x + 30*y < 500

18x + 30y < 500

Answer:

It’s D

Step-by-step explanation:

To ensure the answer is reasonable when converting a larger unit to a smaller unit, multiply by the conversion factor, check the resulting value, and perform the reverse conversion.

To know if the answer is reasonable when converting a larger unit to a smaller unit, follow these steps:
1. Multiply the given value by the conversion factor from the larger unit to the smaller unit.
2. Check if the resulting value is a reasonable amount for the smaller unit. For example, if converting kilograms to grams, the answer should be in the range of hundreds or thousands.
3. Verify your answer by performing the conversion in reverse, from the smaller unit back to the larger unit, to see if you obtain the original value.

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Answer:

11

Step-by-step explanation:

Supplementary means that the sum of the two angles equal to 180, so add the two measures and make them equal to 180. Add the two x's, subtract the two constants.

To show that the series (−1)n − 1bn, where bn = 1 n if n is odd and bn = 1 n2 if n is even, is divergent, we can use the alternating series test.

First, we can note that when n is odd, bn = 1 n, which is a decreasing sequence that approaches 0 as n increases. Therefore, the alternating series (−1)n − 1bn converges by the alternating series test.

However, when n is even, bn = 1 n2, which is also a decreasing sequence that approaches 0 as n increases. But the absolute value of the terms in the series, |(−1)n − 1bn| = |(−1)n − 1(1/n2)|, does not approach 0 as n increases.

To see why, note that when n is even, the term (−1)n is always 1, while the term 1/n2 is always positive. Therefore, the terms in the series alternate in sign and do not decrease in absolute value.

As a result, the series (−1)n − 1bn is not absolutely convergent, and therefore, it is divergent by the alternating series test.

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Answer: approx 13.54 (full decimal : 13.416666667)

Step-by-step explanation:

Area = Base Area x Height   OR    Length x Width x Height

5/3 x 13/4 x 5/2

5 x 13 x 5 = 325

3 x 4 x 2 = 24

325/24 = approx 13.54

Answer:

b) y

Step-by-step explanation:

joannes speed = 250/2.5 =100km/h

francois speed = 100-10 = 90km/h

after 5h, francois would have travelled 450

The ways the students can be seated is 239500800

From the question, we have

Total number of chairs, n = 12

Total number of students, r = 10

The number of ways the students can be seated is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 12 and r = 10

Substitute the known values in the above equation

Total = 12C10

Apply the  formula

ⁿPᵣ = n!/(n - r)!

So, we have

Total = 12!/2!

Evaluate

Total = 239500800

Hence, the number of ways is 239500800

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Answer:

$125

Step-by-step explanation:

a rent collector is entitled to 2½% of all rents collected if he collected rents totaling $5,000.00 calculate his commission:

2 1/2% = 0.025

$5,000 * 0.025  = $125

Answer:

y = 5 - 3x

Step-by-step explanation:

3x + y = 5 ( subtract 3x from both sides )

y = 5 - 3x

Answer:

y = 5 - 3x

making y the subject:

changing sides, changes positive (+) sign to negative (-)

changing sides, changes negative (-) sign to positive (+)

The equation solved for L is L = 24(R - r)/T.

To solve the equation T = 24(R - r)/L for L, we can start by isolating L on one side of the equation:

T = 24(R - r)/L

First, we can multiply both sides of the equation by L to eliminate the denominator:

TL = 24(R - r)

Next, we can divide both sides of the equation by T to isolate L:

L = 24(R - r)/T

Thus, the equation solved for L is L = 24(R - r)/T. This equation allows us to calculate the length of the tapered cylinder (L) given the taper per foot (T), the initial radius (R), and the final radius (r) of the rod. It's important to note that the lengths R, r, and L are measured in inches.

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Each hippo receives 0.6 pumpkins, according to an expression.

Mathematical operators such as addition, subtraction, multiplication, and division are used to form an expression using numbers or variables. For instance, "4 added to 2" in mathematics will be expressed as 2+4.

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

3/5 = 0.6.

Each hippo receives 0.6 pumpkins, according to an expression.

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Answer:

x = 10, y = 7.5

Step-by-step explanation:

Given the triangles are similar then the ratios of corresponding sides are equal, that is

\(\frac{AE}{AC}\) = \(\frac{DE}{BC}\), substitute values

\(\frac{x}{4}\) = \(\frac{12.5}{5}\) ( cross- multiply )

5x = 50 ( divide both sides by 5 )

x = 10

and

\(\frac{AD}{AB}\) = \(\frac{DE}{BC}\) , that is

\(\frac{y}{3}\) = \(\frac{12.5}{5}\) ( cross- multiply )

5y = 37.5 ( divide both sides by 5 )

y = 7.5

Answer:

D. Subtract 1.1j from both sides.

Step-by-step explanation:

hope this helps :P

The true statement about isolating the variable j is (d) Subtract 1.1j from both sides.

Equations are expressions that have equal values, when compared with the "=" sign

The equation is given as:

5.6j – 0.12 = 4 + 1.1j

The variable in the equation is j, and it can be isolated by subtracting 1.1j from both sides of the equation.

So, we have:

4.5j - 0.12 = 4

Hence, the true statement is (d) Subtract 1.1j from both sides.

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The logarithmic equation for (4/5)x = y is x = log5/4y, therefore, the correct option is (B) 4/5=logyx

Given (4/5)x = y

To write in logarithmic equation, we have to rearrange the given equation into exponential form. To

Exponential form of (4/5)x = y is given as x = log5/4y

To write a logarithmic equation we can use the formula x = logby which is the logarithmic form of exponential expression byx = b^x

Thus The logarithmic equation for (4/5)x = y is x = log5/4y, therefore, the correct option is (B) 4/5=logyx.

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During the year, Poch Co. incurred cost of goods sold of $59,823 million on net sales of $76,643 million. To find Poch's return on sales ratio, we need to divide the cost of goods sold by the net sales and multiply by 100.

The calculation would be:
Return on Sales Ratio = (Cost of Goods Sold / Net Sales) * 100
Plugging in the given values:
Return on Sales Ratio = ($59,823 million / $76,643 million) * 100
Now, let's solve the calculation:
Return on Sales Ratio = (0.7807) * 100
Return on Sales Ratio ≈ 78.07%
Since none of the provided answer options match with the calculated ratio, we cannot determine the exact return on sales ratio.

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Answer:

hi play truth and dare to with me in g met

tan 49 = x/55

x = 55 * tan 49 = 63.27