A broker gets 45% of the commission and an agent gets 55%. How much does an agent earn when a house is sold for $73,400.00 and the rate of commission is 5 1/2 %

Answer:To calculate the remaining amount of U234 after a given time period, we can use the formula for radioactive decay:

N = N0 * (1/2)^(t / T)

Where:

N is the remaining amount of the substance after time t

N0 is the initial amount of the substance

T is the half-life of the substance

In this case, the initial amount N0 is 100 grams, the time t is 10,000 years, and the half-life T is 2.52 * 10^5 years. Plugging these values into the formula, we can calculate the remaining amount:

N = 100 * (1/2)^(10,000 / 2.52 * 10^5)

N = 100 * (1/2)^(0.0397)

N ≈ 100 * 0.963

N ≈ 96.3 grams

Therefore, after 10,000 years, approximately 96.3 grams of the 100 gram sample of U234 would remain.

Step-by-step explanation:

The approximately 97.05 g of the 100 g sample of U234 will remain after 10,000 years.

The half-life of U234 is 2.52 x 10^5 years. Half-life is the time taken for half of the radioactive atoms to decay. After one half-life, half of the original radioactive sample will have decayed;

after two half-lives, only one-quarter of the original sample remains; and so on. To calculate the amount of U234 remaining after 10,000 years, we can use the following formula:

Amount remaining = original amount × (1/2)^(number of half-lives)

The number of half-lives can be calculated by dividing the time elapsed by the half-life of U234.

Therefore,Number of half-lives = time elapsed ÷ half-life of U234= 10,000 ÷ 2.52 x 10^5= 0.0397 (rounded to four significant figures)Substituting the values into the formula,

Amount remaining = 100 × (1/2)^0.0397= 100 × 0.9705= 97.05 g (rounded to three significant figures)

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The amount of state tax Selina owes is $77.42.

To calculate the amount of state tax Selina owes, we need to follow the given information.

Selina's gross pay for two weeks is $840. We need to determine her federal tax contribution based on the provided tax table.

Looking at the federal tax table, we find that for a gross pay of $840, the federal tax withheld for 0 withholding allowances is $98.

Next, we calculate the state tax deduction, which is 21% of the federal tax contribution:

State tax deduction = 21% of $98

State tax deduction = 0.21 * $98

State tax deduction = $20.58

Finally, we subtract the state tax deduction from the federal tax contribution to find the amount of state tax Selina owes:

State tax owed = Federal tax contribution - State tax deduction

State tax owed = $98 - $20.58

State tax owed = $77.42

Therefore, the amount of state tax Selina owes is $77.42.

None of the provided options (a, b, c, d) match the calculated amount.

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Answer:

B. $16.56

Step-by-step explanation:

Got it right on edge 2023

Answer:

A

Step-by-step explanation:

Notice that the image of the point A(1,5) is A'(8,5).

Since the image and the original points have the same y-coordinates, so there is no vertical translation.

However, we do notice that the x-coordinate increases from x=1 to x=8.

So, there is a horizontal translation to the right by 8-1=7 units.

Answer: The 128 oz box is the better buy.

Answer:

First subtract (4) and (3x) from each side of the equation to isolate the x ... 5x-4=3x-8 One solution was found : x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

To solve for x, we will first simplify the left side of the inequality by finding a common denominator for the fractions:

5/6x - 1/3 > 4/3

Multiplying both sides by 6 to eliminate the fractions, we get:

5x - 2 > 8

Adding 2 to both sides, we have:

5x > 10

Dividing both sides by 5, the final answer is:

x > 2

Hope this helps!

Answer:

Steve would have paid off the loan in 12 months, or 1 year.

The last payment would be $150.

Step-by-step explanation:

Let's say Steve took out a loan of $1500 on Jan. 1, 2022 and was to make monthly payments of $150.

The interest rate is 20% per annum.

Since the interest is compounded annually, the balance at the end of the first year would be $1500 * (1 + 0.2) = $1800`.

After making 12 monthly payments of $150, the balance at the end of the first year would be $1800 - 12 * $150 = $0.

So Steve would have paid off the loan in 12 months, or 1 year.

The last payment would be $150.

a.) The null hypothesis states that the number of hours worked by the software developers is not related to the mean number of hours.

The alternate hypothesis states that the number of hours worked by the software developers is related to the mean number of hours.

b.) The source of error we may be making when null hypothesis is rejected is that the mean hours will remain 44 hours.

Alternate hypothesis is the type of hypothesis that is used to statistically test a result of a research and it is used to disprove the null hypothesis.

The null hypothesis is used to show that there is not relationship between two variables that are used in a research problem.

When a null hypothesis is rejected, it means that there is a relationship between the two variables of the research question.

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Answer:  16

Step-by-step explanation:

Given:

Enclosure is 4 m x 18 m x 7 m

Find:

How many 30 m³ spaces can you make in  the enclosure.  This will tell you how many otters can live

Solution:

Cuboid is same as cube

Volume for cube = Length x width x height

Volume for cube = 4 x 18 x 7

Volume for cube = 504 m³

Divide 504 by 30 to find the number of spaces the enclosure can hold

Can hold = 540/30

Can hold = 16.8

You cannot hold 16.8 otters because you cannot have a portion of an otter so you round down to 16.

16 is your answer

Answer:

f = 65

s = 144

t = 144

u = 77

Step-by-step explanation:

the sum of a triangles angles will always be 180

so we can subtract 37 and 78 from 180 to find f which is 65

in regards to s and t, the sum of those 4 angles will be 360, and we can assume the opposite sides of the angles are the same.

so the other side of the 36 angle will also be 36, so we subtract 36 and 36 from from 380 which gives us 288

then we divide it by 2 because we have 2 unknown angles that are the same size, then we get 144 for s and 144 for t

the sum of the angles of a polygon will always be 360

so we can subtract 86 and 53 and t (which we now know is 144) from 360 to find u

so u = 77

Answer:

I am not sure sorry about this I'll try to figure it out

Expression in factored form

a² - 36 = (a + 6)(a - 6)

49 - 25b² = (7 - 5b)(7 + 5b)

c² + 9 = Not possible (sum of squares)

10081 - 16d² = (101 - 4d)(101 + 4d)

64 + 121b² = Not possible (sum of squares)

Let's factorize each expression:

a² - 36:

This expression is a difference of squares, as it can be written as (a + 6)(a - 6). Therefore, the factored form is (a + 6)(a - 6).

49 - 25b²:

This expression is also a difference of squares. It can be factored as (7 - 5b)(7 + 5b).

c² + 9:

This expression is not factorable because it is a sum of squares. The factored form is not possible.

10081 - 16d²:

This expression is a difference of squares. It can be factored as (101 - 4d)(101 + 4d).

64 + 121b²:

This expression is not factorable because it is a sum of squares. The factored form is not possible.

To summarize:

a² - 36 = (a + 6)(a - 6)

49 - 25b² = (7 - 5b)(7 + 5b)

c² + 9 = Not possible (sum of squares)

10081 - 16d² = (101 - 4d)(101 + 4d)

64 + 121b² = Not possible (sum of squares)

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The present value of the investment in the fund is $2,455.32.

In order to calculate the present value of the investment in a fund, which is expected to generate $3,000 per year for the next 5 years with an interest rate of 4% per year compounded continuously,

we can use the formula for the present value of an annuity:

PV = A / r,

where PV is the present value, A is the annuity payment, and r is the interest rate.

However, since the interest rate is compounded continuously, we need to use the formula PV = A / e^(rt),

where e is the constant 2.71828, t is the time period in years, and r is the interest rate.

In this case, A = $3,000, r = 4%, and t = 5 years.

Therefore, the present value of the investment is:

PV = $3,000 / e^(0.04 x 5)

= $3,000 / e^(0.2)

= $3,000 / 1.2214

= $2,455.32 (rounded to the nearest cent).

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Answer:

The answers are all in 2d.p

1)523.81cm³

2)166.67m³

3)754.29m³

Step-by-step explanation:

1)V=1/3pir²h

V=1/3×10²×5×22/7

V=523.81cm³

2)V=4/3pir³

V=4/3×5³

V=166.67m³

3)V=1/3pir²h

V=1/3×22/7×6²×20

V=754.29m³

The final amount is $2203. 2

From the information given, the formula for finding the amount is expressed as;

A=Pert

Such that the parameters are;

Substitute the values, we have;

A = 300 × [tex]2.71^(^2^*^1^)[/tex]

Multiply the exponents, we have;

A = 300 × [tex]2.71^2[/tex]

Find the square value and multiply, we get;

A = $2203. 2

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Answer:

Step-by-step explanation:

Let's calculate the total cost of the bike and the dining table first.

The cost of the bike is ₹56,725.

The cost of the dining table is ₹8,800.

To find the total cost, we add the cost of the bike and the cost of the dining table:

₹56,725 + ₹8,800 = ₹65,525

So, the total cost of the bike and the dining table is ₹65,525.

To determine which item is costlier, we compare the costs of the bike and the dining table. In this case, the bike is costlier as it costs ₹56,725, while the dining table costs ₹8,800.

Now, let's calculate the amount that Somraj deposited in his wife's account.

He initially had ₹1,78,500 in his bank account and withdrew the entire amount along with the interest of ₹20,489. Therefore, the total amount withdrawn is:

₹1,78,500 + ₹20,489 = ₹1,98,989

From this amount, he spent ₹36,725 on the laptop, ₹8,800 on the dining table, and ₹56,725 on the bike. So, the total amount spent on these items is:

₹36,725 + ₹8,800 + ₹56,725 = ₹1,02,250

To find the amount deposited in his wife's account, we subtract the total amount spent from the total amount withdrawn:

₹1,98,989 - ₹1,02,250 = ₹96,739

Therefore, Somraj deposited ₹96,739 in his wife's account.

Answer:

a. 65,525

b. bike

c. 96,739

Step-by-step explanation:

a.

total cost of the bike and the dining table,

= 56,725 + 8,800

= 65,525

b.

bike is costlier than the dining table.

c.

total amount somraj received from bank

= 1,78,500 + 20,489

= 198,989

total expenditures

= 36,725 + 8,800 + 56,725

= 102,250

amount he saved to deposit in his wife's account

= 198,989 - 102,250

= 96,739

True. In a right prism, all the lateral faces are indeed rectangles.

Given data ,

A right prism is a three-dimensional solid with congruent polygonal bases and rectangular lateral faces that connect the corresponding sides of the bases.

Bases: A right prism has two parallel polygonal bases that are congruent. The bases can be any polygon, such as a triangle, rectangle, square, pentagon, etc. The shape of the bases determines the overall shape of the prism.

Height: The height of a right prism is the perpendicular distance between the two bases. It is the length of the lateral edges connecting the corresponding vertices of the bases.

Lateral Faces: The lateral faces of a right prism are rectangular in shape. They are perpendicular to the bases and connect the corresponding edges of the bases. The lateral faces are always parallelograms, and their opposite sides are equal in length.

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The measurement of the length of 6 feet is 182.88 cm after unit conversion.

Given data ,

To convert feet to centimeters, we need to know the conversion factor between the two units.

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

1 foot is equal to 30.48 centimeters.

To convert 6 feet to centimeters, we can use the conversion factor:

A = 6 feet x 30.48 centimeters/foot

On simplifying the equation , we get

A = 182.88 centimeters.

Therefore , the value of A is A = 182.88 cm

Hence , 6 feet is equal to 182.88 centimeters.

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Answer:

[tex]\sin\theta=\frac{4}{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \cos^2\theta+\sin^2\theta=1\\\\\biggr(\frac{6}{10}\biggr)^2+\sin^2\theta=1\\\\\frac{36}{100}+\sin^2\theta=1\\\\\sin^2\theta=\frac{64}{100}\\\\\sin\theta=\frac{8}{10}=\frac{4}{5}[/tex]

The length of CO is approximately 41.89 units, rounded to two decimal places.

We have a circle O with radius 32. WC is a tangent segment to the circle at point W, and its length is 27. We are required to find the length of CO.

Since WC is tangent to the circle, it is perpendicular to the radius drawn from the center of the circle to the point of tangency (W). Let's label the center of the circle as point C.

We can use the Pythagorean theorem to find the length of CO. According to the theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, CO is the hypotenuse, and WC and OW are the other two sides of the right triangle.

Using the Pythagorean theorem, we have:

CO^2 = WC^2 + OW^2

CO^2 = 27^2 + 32^2

CO^2 = 729 + 1024

CO^2 = 1753

Taking the square root of both sides, we get:

[tex]CO ≈ √1753[/tex]

CO ≈ 41.89

Therefore, the length of CO is approximately 41.89 units, rounded to two decimal places.6

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The solution to the system of equations using Cramer's rule is x = -1 and y = 2.

To solve the system of equations using Cramer's rule, we'll need to determine the values of x and y by calculating the determinants of various matrices.

The given system of equations is:

8x + 5y = 2 (Equation 1)

2x - 4y = -10 (Equation 2)

First, let's calculate the determinant of the coefficient matrix, D:

D = |8 5|

|2 -4|

D = (8 * -4) - (5 * 2)

D = -32 - 10

D = -42

Next, we'll calculate the determinant of the matrix formed by replacing the x coefficients with the constants from the right side of the equations, Dx:

Dx = |2 5|

|-10 -4|

Dx = (2 * -4) - (5 * -10)

Dx = -8 + 50

Dx = 42

Similarly, we'll calculate the determinant of the matrix formed by replacing the y coefficients with the constants, Dy:

Dy = |8 2|

|2 -10|

Dy = (8 * -10) - (2 * 2)

Dy = -80 - 4

Dy = -84

Now, we can find the values of x and y:

x = Dx / D

x = 42 / -42

x = -1

y = Dy / D

y = -84 / -42

y = 2

Therefore, the solution to the system of equations is x = -1 and y = 2.

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The absolute value equation for x = -4 can be written as:

|x - (-2)| = 2

We have,

For x = -8, the absolute value equation can be written as:

|x - c| = d

Substituting x = -8 into the equation, we have:

|-8 - c| = d

To satisfy the given solution set, we need to determine the values of c and d that make the equation true.

Since x = -8, the absolute value of -8 minus c should be equal to d.

For x = -8, a suitable choice of c would be -12 and d would be 4.

This gives us:

|-8 - (-12)| = 4

|4| = 4

Therefore, the absolute value equation for x = -8 can be written as:

|x - (-12)| = 4

Similarly, for x = -4, the absolute value equation can be written as:

|x - c| = d

Substituting x = -4 into the equation, we have:

|-4 - c| = d

To satisfy the given solution set, we need to determine the values of c and d that make the equation true.

Since x = -4, the absolute value of -4 minus c should be equal to d.

For x = -4, a suitable choice of c would be -2 and d would be 2. This gives us:

|-4 - (-2)| = 2

|-2| = 2

Therefore,

The absolute value equation for x = -4 can be written as:

|x - (-2)| = 2

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you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:quantom physics x=y

Step-by-step explanation:

need to get oxygen

The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.

We have,

To find the angle equivalent to θ between 0 and 360 degrees, we can use the inverse cosine function [tex](cos^{-1}).[/tex]

The given value of cos θ = 4/5 represents the cosine of an angle in the first quadrant. In the first quadrant, all trigonometric functions are positive, including cosine.

Taking the inverse cosine [tex](cos^{-1})[/tex] of both sides of the equation, we get:

θ =[tex]cos^{-1}(4/5)[/tex]

The inverse cosine function returns the angle whose cosine is equal to the given value.

Evaluating [tex]cos^{-1}(4/5)[/tex] using a calculator or trigonometric tables, we find the value to be approximately 36.87 degrees.

Therefore,

The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.

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The measure of DF is 2.28.

We have,

Triangle ABC ≅ Triangle DEF

So,

The ratio of the corresponding sides is equal.

Now,

BA/ED = AC/DF

Substitute the values.

11/3.3 = 7.6/DF

DF = (7.6 x 3.3) / 11

DF = 7.6 x 0.3

DF = 2.28

Thus,

The measure of DF is 2.28.

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The missing value E, the total revenue for the period 2017/18, is approximately 186.67.

To calculate the missing value E, the total revenue for the period 2017/18, we need to determine the total revenue of the provincial sector first.

Given that the revenue of the local government sector is 20, 12% of the provincial sector, we can set up the following equation:

20 = 0.12 × Provincial sector revenue

To find the value of Provincial sector revenue, we divide both sides of the equation by 0.12:

Provincial sector revenue = 20 / 0.12

Provincial sector revenue = 166.67

Now that we know the revenue of the provincial sector is 166.67, we can find the missing value E, which represents the total revenue for the period 2017/18. Since the local government sector always receives a larger share than the provincial sector, we can assume that the total revenue is the sum of the revenues of both sectors:

E = Local government sector revenue + Provincial sector revenue

E = 20 + 166.67

E = 186.67

Therefore, the missing value E, the total revenue for the period 2017/18, is approximately 186.67.

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Answer:

628.3 cubic inches

Step-by-step explanation:

Since the base diameter of the cylinder is d=20 inches, so its radius r is:

[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]

Then, the volume V of the cylinder with radius r=10 inches and height h=2 inches is:

[tex]V=\pi r^{2} h=\pi\times 10^{2}\times 2=628.3[/tex]

Answer:

To find the volume of a cylinder, we need to use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height. Since we are given the diameter of the base, which is 20 inches, we can find the radius by dividing it by 2. So, r = 20 / 2 = 10 inches. The height is given as 2 inches. Plugging these values into the formula, we get:

V = π(10)^2(2)

V = π(100)(2)

V = 200π

To get the volume in cubic inches, we need to multiply this by the conversion factor of 1 cubic inch per cubic inch. This does not change the value, but it gives us the correct units. So,

V = 200π cubic inches

To round this to the nearest tenths place, we need to look at the hundredths digit. If it is 5 or more, we round up; if it is less than 5, we round down. Using a calculator, we can approximate π as 3.14. So,

V ≈ 200(3.14) cubic inches

V ≈ 628 cubic inches

The hundredths digit is 0, which is less than 5. So we round down and keep the tenths digit as it is. Therefore,

V ≈ 628.0 cubic inches

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The area of the surface obtained by rotating a curve around the x-axis is given by the formula A=2π∫a^b f(x) sqrt{1+[f'(x)]^2}dx. The value of A depends on the curve and its bounds of integration a and b.

To find the area of the surface obtained by rotating a curve about the x-axis, we first need to sketch the curve and determine its bounds of integration.

Next, we need to express the curve in terms of x, so that we can integrate using the formula above.

Once we have the integral, we can evaluate it to find the area of the surface. Some common curves that are rotated about the x-axis include y=sin(x), y=cos(x), y=x^2, y=1/x, and y=e^x.

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Answer:

A) 1.134π 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 equation of the curve is:

[tex]x=\sqrt[3]y \implies y=x^3[/tex]

The given interval is 0 ≤ y ≤ 1.

When y = 0, x = 0, and when y = 1, x = 1. Therefore:

Differentiate the function y = x³ using the following differentiation rule:

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

Therefore:

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

Therefore, the integral is:

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

[tex]\displaystyle S=\int^{1}_{0}2\pi \left(x^3\right)\sqrt{1+9x^4}\; \text{d}x[/tex]

[tex]\displaystyle S=2\pi\int^{1}_{0} x^3\sqrt{1+9x^4}\; \text{d}x[/tex]

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

[tex]\textsf{Let}\;u=1+9x^4[/tex]

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

[tex]\dfrac{\text{d}u}{\text{d}x}=36x^3 \implies \text{d}x=\dfrac{1}{36x^3}\; \text{d}u[/tex]

Find the limits in terms of u:

[tex]\textsf{When}\; x = 0 \implies u=1+9(0)^4=1[/tex]

[tex]\textsf{When}\; x = 1 \implies u=1+9(1)^4=10[/tex]

Rewrite the original integral in terms of u and du:

[tex]\displaystyle S=2\pi\int^{10}_{1} x^3\sqrt{u}\cdot \dfrac{1}{36x^3}\; \text{d}u[/tex]

[tex]\displaystyle S=2\pi\int^{10}_{1} \dfrac{1}{36}\sqrt{u}\; \text{d}u[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\int^{10}_{1} \sqrt{u}\; \text{d}u[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\int^{10}_{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}{18}\left[\vphantom{\dfrac12}\dfrac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right]^{10}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\left[\vphantom{\dfrac12}\dfrac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]^{10}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\left[\vphantom{\dfrac12}\dfrac{2u^{\frac{3}{2}}}{3}\right]^{10}_{1}[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\left(\dfrac{2(10)^{\frac{3}{2}}}{3}-\dfrac{2(1)^{\frac{3}{2}}}{3}\right)[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\left(\dfrac{20\sqrt{10}}{3}-\dfrac{2}{3}\right)[/tex]

[tex]\displaystyle S=\dfrac{\pi}{18}\left(\dfrac{-2+20\sqrt{10}}{3}\right)[/tex]

[tex]\displaystyle S=\left(\dfrac{-1+10\sqrt{10}}{27}\right)\pi[/tex]

[tex]\displaystyle S=1.134\pi[/tex]

Therefore, from the given answer options, the correct area is 1.134π square units.