To include the personal assets and transactions of a business's owner in the records and reports of the business would be in conflict with the

To find the mean salary of 20 workers, 12 men and 8 women, you need to follow these steps:

Assuming you have the salaries of all 20 workers, the steps above will give you the mean salary. If you only have the salaries of the men and women separately, you can find the mean salary for each group and then take a weighted average based on the proportion of men and women in the sample. For example:

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The mean salary of all 20 workers is $46,000.

To find the mean salary of 20 workers, 12 men and 8 women, you need to sum up the total salaries of all the workers and divide by the total number of workers (20).

Assuming you have the salaries of all 20 workers, you can add up the salaries of all the workers and divide by 20 to get the mean salary.

If you don't have the salaries of each worker but have the average salary of men and women separately, you can use the weighted average formula to find the overall mean salary.

If the average salary of men is $50,000 and the average salary of women is $40,000, you can calculate the overall mean salary as follows:

(mean salary of men * number of men + mean salary of women * number of women) / total number of workers

= (50,000 * 12 + 40,000 * 8) / 20

= 46,000

Therefore, the mean salary of all 20 workers is $46,000.

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Your complete question is:

How to find the mean salary of 20 workers 12 men 8 women, If the average salary of men is $50,000 and the average salary of women is $40,000?

The coordinates of the points where the graph of y = \(x^3\) - \(6x^2\) - 58x + 1 has a slope of 5 are (-3, -47) and (7, -153).

To find the coordinates of the points where the graph has a slope of 5, we need to determine the values of x for which the derivative of the function y = \(x^3 - 6x^2\) - 58x + 1 is equal to 5.

1. Find the derivative of the function:

The derivative of y = \(x^3 - 6x^2\) - 58x + 1 can be found by taking the derivative of each term separately:

dy/dx = \(3x^2\)- 12x - 58.

2. Set the derivative equal to 5:

Setting the derivative equal to 5 gives us the equation: \(3x^2\) - 12x - 58 = 5.

3. Rearrange the equation:

Rearranging the equation gives us: \(3x^2\) - 12x - 63 = 0.

4. Solve the quadratic equation:

We can solve the quadratic equation by factoring or using the quadratic formula. Factoring \(3x^2\) - 12x - 63 = 0 gives us (x - 7)(3x + 9) = 0.

Setting each factor equal to zero, we have two possible values for x:

x - 7 = 0 --> x = 7,

3x + 9 = 0 --> x = -3.

5. Find the corresponding y-values:

Substituting the x-values into the original function, we can find the corresponding y-values:

For x = -3, y = (-\(3)^3 - 6(-3)^2\) - 58(-3) + 1 = -47.

For x = 7, y = \(7^3 - 6(7)^2\) - 58(7) + 1 = -153.

Therefore, the coordinates of the points where the graph has a slope of 5 are (-3, -47) and (7, -153), in increasing order of x-value.

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If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS =  36°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of ∠1 = 2x + 4

The measure of ∠2 = 3x - 3

The measure of ∠TRS is -

∠TRS = ∠1 + ∠2

Since, PR is a bisector then ∠1 = ∠2.

The equation is -

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

-x = -7

x = 7

Substitute the value of x in the angles -

∠1 = 2(7) + 4

∠1 = 14 + 4

∠1 = 18°

∠2 = 3(7) - 3

∠2 = 21 - 3

∠2 = 18°

So, the value of ∠TRS is -

∠1 + ∠2

18° + 18°

36°

Therefore, the measure of ∠TRS is 36°.

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Answer:

AAA

Step-by-step explanation:

There's no angle angle angle (AAA) because all triangle's angles add up to 180

it seems that is wrong.sorry for that.

The polynomial that satisfies the conditions is: p(t) = (1/4)(t - 1)² (t - 2)³

This polynomial has a root of multiplicity 2 at t = 1 and a root of multiplicity 3 at t = 2, and also satisfies p(0) = 2 and p'(0) = 1.

The other root of p(t) can be found by factoring the polynomial further, but since the degree of the polynomial is 6, it will have 3 additional roots, which can be found using various mathematical methods such as the Rational Root Theorem or numerical methods.

Polynomials are mathematical expressions that involve variables raised to a power and are combined using addition and subtraction operations. The degree of a polynomial is the highest power of the variable in the expression.

A zero of a polynomial is a value of the variable for which the polynomial evaluates to zero. The multiplicity of a zero is the number of times the factor (t - zero) appears in the polynomial's factorization.

Given the conditions that the polynomial p(t) has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, we can write p(t) as the product of factors (t - 1)² and (t - 2)³:

p(t) = a(t - 1)² (t - 2)³

where a is some constant. To find the value of a, we use the fact that p(0) = 2 and p'(0) = 1. We evaluate p(0) and p'(0) using the polynomial expression above, then solve for a.

First, we find p(0):

p(0) = a(0 - 1)² (0 - 2)³ = a(-1)² (-2)³ = a * 8

Next, we find p'(0):

p'(t) = 2a(t - 1)(t - 2)³ + a(t - 1)² * 3(t - 2)²

p'(0) = 2a(-1)(-2)³ + a(-1)² * 3(-2)² = 16a + 12a = 28a

Now that we have expressions for p(0) and p'(0), we can solve for a:

p(0) = a * 8 = 2 => a = 1/4

p'(0) = 28a = 1 => 28 * 1/4 = 1

So the polynomial that satisfies the conditions is:

p(t) = (1/4)(t - 1)² (t - 2)³

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Given: The function given are

Required: To find the function-

Explanation: The function can be determined as follows-

Putting the values of the function f(x) and g(x)-

Final Answer: Option A is correct.

4times, 2inches occur on the interval 0 < x < 20

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To determine the smallest number of students to sample for a 95% confidence interval with a width of no more than 6%.

We need to consider the desired level of confidence and the desired margin of error.

Determine the margin of error: The margin of error is the maximum allowable distance from the sample estimate to the true parameter value. In this case, the width of the confidence interval is given as 6%, so the margin of error is half of that, which is 3%.

Find the critical value: The critical value is determined based on the desired level of confidence. For a 95% confidence interval, the critical value is approximately 1.96.

Use the formula: The formula to calculate the minimum sample size is given by n = (Z * σ / E)^2, where n is the sample size, Z is the critical value, σ is the population standard deviation (if known), and E is the margin of error.

In this case, since the population standard deviation is not provided, we can use a conservative estimate by assuming the worst-case scenario of σ = 0.5 (assuming a binary outcome, such as success or failure).

Substitute values and solve: Plugging in the values into the formula, we have n = (1.96 * 0.5 / 0.03)^2. Calculating this expression gives us the minimum sample size required to achieve a 95% confidence interval with a width no more than 6%.

Note that the formula used assumes a finite population size. If the population is very large or infinite, a different formula may be used (such as using a 1.96 critical value for large samples).

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Step-by-step explanation:

It is given that,

The height of the sail on a boat is 7 feet less than 3 times the length of its base.

Let the length of the base is x.

ATQ,

Height = (3x-7)

Area of the sail is 68 square feet.

Formula for area is given by :

\(A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0\)

x = 8 feet and x = -3.73 feet

So, length is 8 feet

Height is 3(8)-7 = 17 feet.

So, its height and the length of the base is 17 feet and 8 feet respectively.

Answer:

2673

Step-by-step explanation:

2673

I've lost my pen so I can't write it down on paper, sowwy

Question

Farmer Jim keeps 12 hens in every cooper if farmer Jim has 20 coops

a) how many hens does she have ?

b) if every hens lays 9 eggs on Monday how many eggs will farmer Jim collect on Monday

Answer:

a) 240 hens

b) 2160 eggs

Step-by-step explanation:

a) Farmer Jim keeps 12 hens in every cooper if farmer Jim has 20 coops

Hence,

1 coop = 12 hens

20 coops = y hens

Cross Multiply

y hens = 20 coops × 12 hens/1 coop

y hens = 240 hens

Therefore Farmer Jim has 240 hens

b) We are told in question b that: if every hens lays 9 eggs on Monday how many eggs will farmer Jim collect on Monday?

From question a) we determine that the number of hens that Farmer Jim has:

240 hens

Hence,

1 hen = 9 eggs

240 hens = z eggs

z eggs = 240 hens × 9 eggs/1 hen

z eggs = 2160 eggs

Therefore, on Monday Farmer Jim will collect 2160 eggs

Yes, AAS proves congruence.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

AAS congruence can be proved in easy steps.

Suppose we have two triangles ABC and DEF, where

∠B = ∠E [Corresponding angles] ∠C = ∠F [Corresponding angles] And

AC = DF [Adjacent sides]

By the angle sum property of the triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equations 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangles ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by AAS congruency,

Δ ABC ≅ Δ DEF

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The shape that has a bigger area is the regular hexagon

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

Both of these shapes are inscribed in a circle

By comparison, the number of sides are

Pentagon = 5 sides

Hexagon = 6 sides

This means that the regular hexagon has a larger area

The large area is as a result of the larger number of sides and longer side length compared to the regular pentagon.

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Answer:

commutative property of multiplication

Step-by-step explanation:

Answer:

2.15500

Step-by-step explanation:

hope it's help

#MASTER GROUP

# FIRST MASTER

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Answer:

initial value = 5

Step-by-step explanation:

the initial value is the value of y when x = 0.

this is the same as the y- intercept.

from the graph at (0, 5 )

that is when x = 0 the initial value is 5

Answer:

8 units

Step-by-step explanation:

2(3x-3)=4x-1

6x-6=4x-1

2x=5

x=2.5

3x-3

3(2.5)-3

4.5

Answer:

Let's assume the height of the cylinder to be 'h' and its radius to be 'r'. We can use the given information to form two equations.

First, we know that the volume of the cylinder is 1540 cm³:

V = πr²h = 1540

Second, we know that the difference between the height and the radius is 3 cm:

h - r = 3

Using the second equation, we can solve for 'h' in terms of 'r':

h = r + 3

Substituting this into the first equation, we get:

πr²(r + 3) = 1540

Expanding the left side of the equation and simplifying, we get:

πr³ + 3πr² - 1540 = 0

We can solve for 'r' using the cubic formula, but it's easier to notice that 'r' must be close to 10. We can try different values of 'r' until we get an answer close to 1540. If we try 'r' = 10, we get:

π(10)²(10+3) = 3300π

So, the radius is approximately 10 cm and the height is approximately 13 cm.

To find the total surface area of the cylinder, we need to find the area of the top and bottom circles and the area of the curved surface. The area of each circle is πr², so the total area of the circles is:

2πr² = 200π cm²

The area of the curved surface is the circumference of the circle times the height of the cylinder, or 2πrh. Substituting the values of 'r' and 'h' that we found earlier, we get:

2π(10)(13) = 260π cm²

Therefore, the total surface area of the cylinder is:

200π + 260π = 460π ≈ 1442.4 cm²

So, the total surface area of the cylinder is approximately 1442.4 cm².

So, the percentage of data values represented on a box plot that falls between the lower quartile and the upper quartile is 50%.

In a box plot, the lower quartile (Q1) represents the 25th percentile, and the upper quartile (Q3) represents the 75th percentile. The interquartile range (IQR) is the range between the lower quartile and the upper quartile. To determine the percentage of data values that fall between the lower quartile and the upper quartile, we need to consider the IQR.

The IQR represents the middle 50% of the data. Therefore, the percentage of data values between the lower quartile and the upper quartile is 50%. In other words, half of the data values are within the IQR range, while the remaining 50% are outside this range, including the lower 25% below the lower quartile and the upper 25% above the upper quartile.

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64 out of 73 were opposed.

Set up a ratio as number opposed over number surveyed :

64/73 = x/657

Cross multiply:

73x = 42048

Divide both sides by 73:

X = 576

576 are opposed, now subtract this from total people surveyed:

657 - 575 = 81

81 are not opposed.

Answer:

2

Step-by-step explanation:

-6 divided by a positive number would make it a positive number welcome

Answer:

the answer is on line and it have the correct work

The combined saving of Lucas and Owen is equal to $210.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the ratio of Owen's and Lucas's savings is 4:3. The ratio becomes 8:5 when 120 is added to Owen's and 60 is added to Lucas's amount.

The combined income will be calculated as,

O / L = 4 / 3

3O = 4L

6O = 8L

The new equation is,

( O + 120 ) / ( L + 60) = 8 / 5

8L - 5O = 120

Now solve the equation to get the values of O and L.

8L - 5O = 120

6O - 5O = 120

O = 120

The value of L will be,

L = ( 6O ) / 8

L = ( 6 x 120 ) / 8

L = 6 x 15

L = 90

Combine income = L + O

Combine income = 90 + 120 = $210

Therefore, the combined saving of Lucas and Owen is equal to $210.

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By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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In order to determine the practical significance requires considering both the effect size measures and the context of the study

One way to determine practical significance is by using effect size measures. Effect size is a standardized measurement of the magnitude of a treatment or intervention.

A common equation used to calculate effect size is Cohen's d, which is the difference between the means of two groups divided by the standard deviation.

Another equation used is the odds ratio, which is the ratio of the odds of an event occurring in one group compared to another.

Additionally, it is important to consider the context of the study when evaluating practical significance.

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Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

Answer:

N - 3

Step-by-step explanation:

It is a series of -3 so:

7 -3 = 4

4 - 3 = 1

1 - 3 = -2

So:

N-3

where N is the present value in the sequence.

Answer:

2 1/4

Step-by-step explanation:

The amount of paper needed to wrap the considered box which has dimension of 10 by 10 by 6 inches is 440 sq. inches

Let the three dimensions(height, length, width) be x, y,z units respectively.

The surface area of the cuboid is given by

\(S = 2(a\times b + b\times c + c\times a)\)

A box is usually in shape of a cuboid.

For this case, its dimensions are 10 inches, 10 inches, and 6 inches.

The amount of wrapper we need is approx same as the area of its surface (assuming we're going to measure the paper needed in terms of its area).

Thus, we get:

Amount of the paper we need to wrap the considered box = surface area of that box = surface area of cuboid of dimension 10 inch by 10 inch by 6 inches = S (say), then:

\(S = 2(10\times 10+ 10\times 6 + 6\times 10)\\S = 440\)(in sq. inches)

Thus, the amount of paper needed to wrap the considered box which has dimension of 10 by 10 by 6 inches is 440 sq. inches

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