Jane Curtain owns Jane's Window Fashions, a small window treatment business. In 2021 she reported to you the following: Sales $ 200,000 Cost of sales 100,000 Jane only buys merchandise upon sales Administrative costs: Rent 20,000 Phone and internet 2.000 Utilities 2,700 Insurance 1,200 Health insurance Car expenses (other than depreciation) 12,000 6,000 In 2021 Jane purchased a new Land Rover for $100,000. She used it 75% for business. She would like to take Bonus Depreciation. In 2021 Jane purchased some installation equipment (5 year life) for 5,000 In 2021 Jane had the following stock sales. Name Purch date Purch Amount Sale Date Sale amount Dapple Inc 1/15/1980 7.000 5/15/2021 10,000 WestEast 7/15/2015 6,000 6/15/20219,000 Green Acre 6/30/2021 12,000 9/30/2021 10.000 Jane received a dividend of $500 from Dapple. The ex-dividend date was 3/20/2021. Jane received a $1,000 dividend from GreenAcre. The ex- dividend date was 7/15/2021. Jane did not receive a dividend from Greenacre 2021. Jane is single with no children. She owns no cryptocurrency. Jane made 4 equal payments of $5,000 each (total $20,000) estimated payments. In 2020 her tax was $19,000. Jane has received her $1,400 stimulus payment in 2021.

The average temperature in the given box is approximately 0.995.

The average temperature in the given box can be found by computing the triple integral of the temperature distribution function t(x, y, z) over the region D and dividing by the volume of the region D. Thus, we have:

\(\[\iiint_D t(x, y, z) \, dV\]\)

where D is the region defined by

\(\[D=\left\{(x, y, z): 0\leq x\leq \ln 2, 0\leq y\leq \ln 4, 0\leq z\leq \ln 8\right\}\]\)

The temperature distribution function of the region is given by:

\(\[t(x, y, z) = 100e^{-x-y-z}\]\)

Hence, we get:

\(\[\iiint_D t(x, y, z) \, dV = \int_{0}^{\ln 2} \int_{0}^{\ln 4} \int_{0}^{\ln 8} 100e^{-x-y-z} \, dz \, dy \, dx\]\)

Let's start solving it step by step. Integrating with respect to z, we get:

\(\[\int_{0}^{\ln 8} 100e^{-x-y-z} \, dz = -100e^{-x-y-z} \bigg|_{0}^{\ln 8} = 100(e^{-x-y}-e^{-x-y-\ln 8}) = 100e^{-x-y}(1-e^{-\ln 8}) = 100e^{-x-y}\left(1-\frac{1}{8}\right) = \frac{87.5}{e^{x+y}}\]\)

Now we can compute the double integral of\($\frac{87.5}{e^{x+y}}$\) with respect to x and y as follows:

\(\[\int_{0}^{\ln 4} \int_{0}^{\ln 2} \frac{87.5}{e^{x+y}} \\),

\(dx \, dy = \int_{0}^{\ln 4} \frac{87.5}{e^y} \int_{0}^{\ln 2} e^{-x} \,\) d\(x \, dy = \int_{0}^{\ln 4} \frac{87.5}{e^y} (-e^{-x}) \bigg|_{0}^{\ln 2} \, dy = \int_{0}^{\ln 4} \frac{87.5}{e^y}\left(1-\frac{1}{e^{\ln 2}}\right) \, dy = \int_{0}^{\ln 4} \frac{87.5}{e^y}\left(1-\frac{1}{2}\right) \, dy = \frac{87.5}{2}\int_{0}^{\ln 4} \frac{1}{e^y} \, dy = \frac{87.5}{2}\left(1-\frac{1}{e^{\ln 4}}\right) = \frac{87.5}{2}\left(1-\frac{1}{4}\right) = \frac{131.25}{4}\]\)

Therefore, the triple integral over the given region D is \($\frac{131.25}{4}$\). We need to divide it by the volume of the region D, which is the product of the lengths of the sides of the box:

\(\[V = \ln 2 \cdot \ln 4 \cdot \ln 8 = 3\ln 2 \cdot 2\ln 2 \cdot \ln 2^3 = 24\ln 2^3\]\)

Thus, the average temperature is given by:

\(\[\bar{t} = \frac{\iiint_D t(x, y, z) \, dV}{V} = \frac{131.25/4}{24\ln 2^3} \approx \boxed{0.995}\]\)

Therefore, the average temperature in the given box is approximately 0.995.

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a. Fe and S4 are not independent.

b. Fe and Σo are independent.

c. S4 and Σo are independent.

d. Fe, S4, and Σo are not mutually independent.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To determine if the given events are independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities.

(a) Fe and S4:

The event Fe: The first die is even.

The event S4: The second die is 4.

These events are independent if P(Fe ∩ S4) = P(Fe) * P(S4).

P(Fe) = 1/2 (since there are three even numbers out of six possible outcomes for the first die)

P(S4) = 1/6 (since there is only one 4 out of six possible outcomes for the second die)

P(Fe ∩ S4) = 1/12 (since there is only one outcome where the first die is even and the second die is 4)

P(Fe ∩ S4) = 1/12 ≠ (1/2) * (1/6) = 1/12

Therefore, Fe and S4 are not independent.

(b) Fe and Σo:

The event Σo: The sum of the two dice is odd.

These events are independent if P(Fe ∩ Σo) = P(Fe) * P(Σo).

P(Fe) = 1/2 (as mentioned above)

P(Σo) = 1/2 (since there are three odd sums out of six possible outcomes for the two dice)

P(Fe ∩ Σo) = 1/4 (since there are three outcomes where the first die is even and the sum is odd: (2, 1), (2, 3), (2, 5))

P(Fe ∩ Σo) = 1/4 = (1/2) * (1/2) = P(Fe) * P(Σo)

Therefore, Fe and Σo are independent.

(c) S4 and Σo:

The event S4: The second die is 4.

These events are independent if P(S4 ∩ Σo) = P(S4) * P(Σo).

P(S4) = 1/6 (as mentioned above)

P(Σo) = 1/2 (as mentioned above)

P(S4 ∩ Σo) = 1/6 (since there is only one outcome where the second die is 4 and the sum is odd: (1, 4))

P(S4 ∩ Σo) = 1/6 = (1/6) * (1/2) = P(S4) * P(Σo)

Therefore, S4 and Σo are independent.

(d) Fe, S4, and Σo:

To determine if these three events are mutually independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities.

P(Fe ∩ S4 ∩ Σo) = P(Fe) * P(S4) * P(Σo)

P(Fe ∩ S4 ∩ Σo) = P(Fe) * P(S4) * P(Σo) = (1/2) * (1/6) * (1/2) = 1/24

However, there are no outcomes where all three events occur simultaneously. Therefore, P(Fe ∩ S4 ∩ Σo) = 0 ≠ 1/24.

Therefore, Fe, S4, and Σo are not mutually independent.

In summary, the events Fe and Σo are independent, while the events Fe and S4, as well as S4 and Σo, are not independent. Fe, S4, and Σo are not mutually independent.

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Answer:

Step-by-step explanation:

The algebraic identity to be used here :

We know that :

Therefore,

The zeros are :

Answer:

\(x=-\dfrac{9}{10} \quad x=\dfrac{9}{10}\)

Step-by-step explanation:

\(\begin{aligned}100x^2-81 & =(10^2)x^2-9^2\\ & = (10x)^2-9^2\end{aligned}\)

\(\textsf{Difference of Two Squares Formula}: \quad a^2-b^2=\left(a+b\right)\left(a-b\right)\)

\(\implies a=10x \: \textsf{ and } \: b=9\)

\(\implies 100x^2-81=(10x+9)(10x-9)\)

\(\begin{aligned}\textsf{To find the zeros}: \quad 100x^2-81 & = 0\\\\\implies (10x+9)(10x-9) & =0\\\implies 10x+9 & =0 \implies x=-\dfrac{9}{10}\\\implies 10x-9 & =0 \implies x=\dfrac{9}{10}\end{aligned}\)

The critical t- value used for calculating a 90 confidence interval with 29 degrees of freedom is 1.701

Given, two tagged test data.

A" cut- off point" on the t distribution is a critical- T value. When the sample size is small and the population friction is unknown, population parameters are calculated using a t- distribution, a probability distribution.

To determine whether to accept or reject a null thesis, T values are employed.

Sample size, n = 29

The confidence position = 0.90

Position of significance, α = 1-0.90

= 0.10

Degree of freedom = n- 1

= 29- 1

= 28.

For a t- test, n- 1 degrees of freedom.

Thus, the Degree of freedom = 28

degrees of freedom and 0.10 is the significance position( two- tagged)

detect the row in the t distribution table where the degrees of freedom are 28, elect the position of significance0.10( two- tagged), and move down until you reach that row.

As a result, 1.70 is the t pivotal value.

With 28 degrees of freedom, the critical t- value needed to calculate a 90 confidence interval is thus1.701.

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Answer:

it's I'd b yes so ya hope you do great

Step-by-step explanation:

A circle has central angle 144° and arc length of 4 units. The area of the corresponding sector is 7.96 square units.

A sector of a circle is an area enclosed by two radii and an arc. The formula for the area of a sector is given by:

Area of sector = (central angle/360°) x πr²

Hence, we must find the radius of the circle first using the arc length information.

Arc length = (central angle/360°) x 2πr

4 =  (144°/360°) x 2πr

r = 4 x 360°/(144° x 2π)

 = 1.59 units

The area of the circle is given by:

A = πr²

   = = π(1.59²) = 7.96 square units

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The probability that a student who has an A is a male is 60%.

To find the probability that a student who has an A is a male, we need to calculate the ratio of the number of male students with an A to the total number of students with an A.

Given that there are 19 students in total, and 6 of them are female, we can determine that there are 19 - 6 = 13 male students. Out of these male students, 7 do not have an A. Therefore, the number of male students with an A is 13 - 7 = 6.

Now, we know that there are 10 students in total who have an A. Therefore, the probability that a student with an A is a male can be calculated as the ratio of the number of male students with an A to the total number of students with an A:

Probability = Number of male students with an A / Total number of students with an A

Probability = 6 / 10

Probability = 0.6 or 60%

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The Equation of circle is (x+3)² + (y-5)² = (√20)².

We have,

Center = (-3, 5)

Point = (1, 7)

We know the standard form of Equation of circle

(x-h)² + (y-k)² = r²

where (x, y) is any point on the circle, (h, k) is the center

So, (x+3)² + (y-5)² = r²

Put the point (1, 7) in above equation we get

(1+3)² + (7-5)² = r²

(4)² + (2)² = r²

16 + 4= r²

r= √20

Thus, the Equation of circle is

(x+3)² + (y-5)² = (√20)²

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Answer:

A.point W

Step-by-step explanation:

The point that describes the intersection of line m and line n is point W. The correct option is A.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

As it is given that Line m intersects line n at point W. Therefore, The point that describes the intersection of line m and line n is point W. Thus, the correct option is A.

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The answer is

\( {x}^{2} {y}^{3} \)

I hope this helps, have a great day!

Answer:

53,47

Step-by-step explanation:

If 1 van and 6 buses with 372 students, then each bus and van had 372/7 = <<372/7=53>>53 students.

If each bus and van had the same number of students, then 4 vans and 12 buses had 453 = <<453=212>>212 students.

If 4 vans and 12 buses with 780 students, then each bus had 780-212 = <<780-212=568>>568/12 = <<568/12=47>>47 students.

Therefore, 1 van can hold 53 students and 1 bus can hold 47 students. Answer:{53,47}.

53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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The age of the artifact is 3523.77 years.

What is radioactive decay?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Here,

The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)

 All radioactive decay processes follow the first-order reaction.

The equation for the half-life for first-order reaction follows:

t(1/2) = 0.693/k....(1)

where,

k = rate constant of a first-order reaction

Given value:

t(1/2) = 5715 years

Put the value of t in equation (1), and we get

k = 0.693/5715

k = 1.21×10⁻⁴yr

The integrated rate law expression for first-order reaction follows:

t = 2.303/k×㏒(a/(a-x))

where,

t = time period

a = initial concentration of the reactant = 58.2 counts per minute

(a-x) = Concentration of reactant left after time t = 38.0 counts per minute

k = rate constant of a first-order reaction

Put the values in the equation and we get

t = 2.303/1.21×10⁻⁴㏒58.2/38

t = 3523.77 years.

Hence, the age of the artifact is 3523.77 years.

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when a = b and c = d which of the following equations must be true?​

Verify each option

option F

a+b=c+d

a = b and c = d

so

a+a=c+c

2a=2c ------> is not true

option G

a+d=b+c

a = b and c = d

a+c=a+c -----> is true

option H

a+c=a+b

c=b -----> is not true

option J

a-c=d-b

a = b and c = d

a-c=c-a -----> is not true

option k

ad=cd

a = b and c = d

ac=c^2 -----> is not true

therefore

the answer is

option G

Answer:

Initial velocity = 25 m/s

Final velocity = 0 m/s

Step-by-step explanation:

    Initial velocity is the speed in the beginning and final velocity is the speed in the end.

    The problem says the car was traveling at 25 m/s, so that is the initial velocity. The end of the problem states the car came to a complete stop after 3 seconds. Therefore, the final velocity is 0 m/s.

Answer:

The area of the base, B, equals  

✔ 21

cm2.

The volume of the prism is  

✔ 157 1/2

cm3.

Step-by-step explanation:

i took the test

The volume of prism for the given condition is 147 cm³.

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Here, Prism(Rectangle)

          Length(L) = 3.5 cm.

          Width(W) = 6 cm

         Height (H) = 7 cm

Volume = Area of Rectangle x Height

Volume of Prism: V = L x W x H

                             V = 3.5 X 6 X 7

                             V = 147 cm³

Thus, The volume of prism for the given condition is 147 cm³.

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The answer is -4 3/8

Fraction is the parts of a whole or collection of objects represented by a numerator and a denominator.

How to determine this

-1 1/2 - (3 1/2) -(-5/8)

i.e -1 1/2 -3 1/2 + 5/8

3/2 - 7/2 + 5/8

By finding the LCM

= 4(-3) - 4(7) + 1(5)/8

= -12 - 28 + 5/8

= -35/8

= -4 3/8

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Step-by-step explanation:

since there is no graph it's a bit hard to answer this question, but I'll try. I can help solve the equation that represents the ratio of the two numbers:

(x + 1/2)/y = 1/3

This can be simplified to:

x + 1/2 = y/3

To graph this equation, you would need to plot points that satisfy the equation. One way to do this is to choose a value for y and solve for x. For example, if y = 6, then:

x + 1/2 = 6/3

x + 1/2 = 2

x = 2 - 1/2

x = 3/2

So one point on the graph would be (3/2, 6). You can choose different values for y and solve for x to get more points to plot on the graph. Once you have several points, you can connect them with a line to show the relationship between x and y.

(Like I said, it was a bit hard to answer this question, so I'm not 100℅ sure this is the correct answer, but if it is then I hoped it helped.)

True, a proportion is a type of ratio in which the numerator is part of the denominator and can be expressed as a percentage.

A proportion is a mathematical relationship between two numbers, showing that one number is a part of the other or that they share a certain ratio. It compares two ratios and checks if they are equal. For example, if we have two ratios 1:2 and 2:4, these ratios are in proportion because they have the same relationship (1 is half of 2, and 2 is half of 4).
To express a proportion as a percentage, follow these steps:
Convert the ratio to a fraction: In our example, the ratio 1:2 can be converted to the fraction 1/2.
Divide the numerator by the denominator: In this case, we will divide 1 by 2, which equals 0.5.
Multiply the result by 100: Finally, multiply 0.5 by 100 to get the percentage, which is 50%.
So, the statement is true that a proportion is a type of ratio in which the numerator is part of the denominator and can be expressed as a percentage. This concept is essential in various mathematical and real-life applications, such as calculating discounts, tax rates, and percentages of various quantities.

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Answer:

STEP BYy-step explanation:

I need help with this to! When i get the answer ill let ya know

We have given that skateboard was originally priced at $53.00.

It is on sale for 15% off.

We have to determine the sale price of the skateboard.

The discount is 15%.

So we have to find 15% of $53.

Divide the percentage by 100 so we will get the the desimal form of percentage.

convert 15% into desimal

\(\frac{15}{100}=0.15\)

Multiply 0.15 by original price,

\(0.15\times 53=7.95\)

The original price discounted by this amount

Therfore he save $7.95

Sale price=53$-7.95=45.05

Therefore we get the salling price is $45.05.

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C = 20000 + (20000/n)

Thus, we have expressed C in terms of n.

Let the constant part of the average cost be represented by k. Since the average cost varies inversely with the number of machines produced, we can express this relationship as k/n. Therefore, we have:

C = k + (k/n)

Given that the average cost is $25000 when 20 machines are produced, we can substitute these values into the equation:

25000 = k + (k/20)

Simplifying this equation, we get:

20k = 500000

k = 25000

Now, we can substitute the value of k into the equation to find C in terms of n:

C = 25000 + (25000/n)

Similarly, when 40 machines are produced and the average cost is $20000, we can substitute these values into the equation to find k:

20000 = k + (k/40)

40k = 800000

k = 20000

Substituting the value of k into the equation, we have:

C = 20000 + (20000/n)

Thus, we have expressed C in terms of n.

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Answer:

18

Step-by-step explanation:

You can add each one slowly if that helps! So...

1+1 is 2.

2+7 is 9.

9+4 is 13.

13+5 is 18.

18 is your answer!! I hope this helps you out...have an amazing day!!!! :3

Answer:

Lemme answer my own question.

Step-by-step explanation:

It is 18

Answer:

1 to 75

2 to 120

3 to 165

4 to 210

5 to 255

Step-by-step explanation:

Answer:

Congruent angles have the same angle and side measure. Thus angle Q is 47 degrees and PR is 9 cm.

Step-by-step explanation:

To find the quadratic function f(x) = ax² + bx + c that goes through (4, 0) and has a local maximum at (0, 1), we can follow these steps:

Step 1: Find the vertex form of the quadratic function Since the vertex of the quadratic function is at (0, 1), we can use the vertex form of the quadratic function:

f(x) = a(x - h)² + k, where (h, k) is the vertex. Substituting the given vertex (0, 1), we get:

f(x) = a(x - 0)² + 1f(x) = ax² + 1Step 2: Find the value of aTo find the value of a, we can substitute the point (4, 0) in the equation:

f(x) = ax² + 1Substituting (4, 0), we get:0 = a(4)² + 1Simplifying, we get:

16a = -1a = -1/16

Step 3:

Find the value of b and cUsing the values of a and the vertex (0, 1), we can write the quadratic function as:f(x) = (-1/16)x² + 1To find the values of b and c, we can use the point (4, 0):

0 = (-1/16)(4)² + b(4) + c0 = -1 + 4b + c

Solving for c, we get:c = 1 - 4bSubstituting this value of c in the above equation, we get:0 = -1 + 4b + (1 - 4b)0 = 0Since the above equation is true for all values of b, we can choose any value of b. For simplicity, we can choose b = 1/4. Then:c = 1 - 4b = 1 - 4(1/4) = 0

Therefore, the quadratic function that goes through (4, 0) and has a local maximum at (0, 1) is:f(x) = (-1/16)x² + (1/4)x + 0, orf(x) = -(1/16)x² + (1/4)x.

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Answer:

-3/5

decimal form: -0.6

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

have a good day :)

Answer:

Thus, the y-intercept of the line is 7

Step-by-step explanation:

One given line can be expressed with the slope-intercept form as follows:

\(y=mx+b\qquad\qquad [1]\)

Where m is the slope of the line and b is the y-intercept.

We are given the following equation of the line:

7x-4y=-28

Let's transform the equation to look like the slope-intercept form [1].

Subtract 7x:

-4y=-7x-28

Divide by -4:

y=7/4x+7

Comparing with the equation [1]:

m=7/4

b=7

Thus, the y-intercept of the line is 7