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The gross wages of Xavier Brown when worked 43.5 hours in the week will be Gross pay=$730.625

The total amount earned by any worker with his basic pay like incentives allowances etc.

It is given that Xavier Brown works on a 40-hour week basis and-a-half paid for overtime work.

Last week she worked 43.5

The distribution of the work is given as:-

Monday      Tuesday        Wed      Thursday       Friday    Total

9 Hours     9 Hours          8.5         8.5                   8.5      43.5

So we have the total working hours = 43.5 hours

Weekly working hours are =40 hours

So for 40 hours she will be paid:-

Pay =40x17.50

Now extra hours or overtime is =43.5-40=3.5 hours

So the extra income will be half of the regular:-

Pay=3.5x({1}÷{2}) x17.5=$30.625

So total gross pay will be = $700+$30.625=$730.625

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The derivative of \(f(x) = 3^{3x}\) is \(9^x \cdot \ln(3) \cdot 3\).

To find the derivative of the function \(f(x) = 3^{3x}\), we can use the chain rule.

Let's denote \(u = 3x\) as the inner function.

Now, the derivative of \(3^u\) with respect to \(u\) can be expressed as \(\frac{d}{du}(3^u)\).

Applying the chain rule, we have:

\(\frac{d}{dx}(3^{3x}) = \frac{d}{du}(3^u) \cdot \frac{du}{dx}\)

To find \(\frac{d}{du}(3^u)\), we can use the natural logarithm.

\(\frac{d}{du}(3^u) = 3^u \cdot \ln(3)\)

Next, let's find \(\frac{du}{dx}\) by differentiating \(u = 3x\) with respect to \(x\):

\(\frac{du}{dx} = 3\)

Now we can substitute these values back into the chain rule equation:

\(\frac{d}{dx}(3^{3x}) = 3^u \cdot \ln(3) \cdot 3\)

Simplifying further:

\(\frac{d}{dx}(3^{3x}) = 3^{3x} \cdot \ln(3) \cdot 3\)

Finally, we can simplify the expression:

\(\frac{d}{dx}(3^{3x}) = \boxed{9^x \cdot \ln(3) \cdot 3}\)

Therefore, the derivative of \(f(x) = 3^{3x}\) is \(9^x \cdot \ln(3) \cdot 3\).

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Answer:

-3

Step-by-step explanation:

-3×(-3)×(-3)= 9×(-3)

= -27

The measurement that gives you the difference between the points on the scatterplot and the prediction line for the same value of x is the residual. Therefore, the correct answer is C. Residual.

In regression analysis, the residual represents the vertical distance between the observed data points and the corresponding predicted values on the regression line. It is calculated by taking the difference between the actual observed value and the predicted value for a specific value of the independent variable (x). The residuals provide a measure of how well the regression line fits the data, with smaller residuals indicating a better fit.

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The correct answer is (F) 8/17.

In the given triangle ΔXYZ, ∠Z is a right angle and tan X = 8/15. We are asked to find sin Y.
To find sin Y, we can use the relationship between tangent and sine. The relationship is given by the Pythagorean identity:

tan^2 Y = sec^2 Y - 1
Since ∠Z is a right angle, we can use the Pythagorean theorem to find the value of sec^2 Y.

sec^2 Y = 1 + tan^2 Y
sec^2 Y = 1 + (8/15)^2
sec^2 Y = 1 + 64/225
sec^2 Y = 289/225

Now, we can substitute the value of sec^2 Y into the equation for tangent:

tan^2 Y = sec^2 Y - 1
tan^2 Y = 289/225 - 1
tan^2 Y = 289/225 - 225/225
tan^2 Y = 64/225

Taking the square root of both sides, we get:

tan Y = √(64/225)
tan Y = 8/15

Since sine is the reciprocal of cosine, we can find sin Y using the Pythagorean identity:

sin^2 Y = 1 - cos^2 Y
sin^2 Y = 1 - (cos Y)^2
sin^2 Y = 1 - (1/cos^2 Y)
sin^2 Y = 1 - (225/289)
sin^2 Y = (289 - 225)/289
sin^2 Y = 64/289

Taking the square root of both sides, we get:

sin Y = √(64/289)
sin Y = 8/17

Therefore, the value of sin Y is 8/17.

So the correct answer is (F) 8/17.

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Using the definition of sine we obtain that sin Y = 8/17. Hence, the correct answer is (F) 8/17

To obtain sin Y,  in triangle XYZ, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Since ∠Z is a right angle (90 degrees), we have:

To obtain sin Y:

∠X + ∠Y + ∠Z = 180 degrees

∠X + ∠Y + 90 degrees = 180 degrees

∠X + ∠Y = 90 degrees

We also know that tan X = 8/15.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

In this case, we can assign the opposite side of ∠X as 8 (let's call it side X) and the adjacent side as 15 (let's call it side Y).

Therefore, we have:

tan X = 8/15

opposite/adjacent = 8/15

opposite = 8, adjacent = 15

Now, we can use the Pythagorean theorem to obtain the length of the hypotenuse, which is the side opposite the right angle ∠Z:

hypotenuse² = opposite² + adjacent²

hypotenuse² = 8² + 15²

hypotenuse² = 64 + 225

hypotenuse² = 289

hypotenuse = √289

hypotenuse = 17

Since we know the lengths of all three sides of triangle XYZ, we can now obtain sin Y using the definition of sine:

sin Y = opposite/hypotenuse

sin Y = 8/17

Therefore, the correct answer is (F) 8/17.

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Answer:

2.75cm

Step-by-step explanation:

Given data

Area of circle=  23.79cm^2

We know that the formula for the area of a circle is

Area= πr^2

Substitute

23.79=3.142*r^2

23.79/3.142= r^2

7.57=r^2

Square roo both sides

r= √7.57

r= 2.75 cm

Hence the radius is 2.75cm

a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict. b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population.

a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict.

b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population. This is because the television news program invited viewers to go to their website and indicate their opinion, which means that only a certain segment of the population who watched that particular news program and had access to the internet were able to participate in the poll. Additionally, people who feel strongly about the verdict may be more likely to participate in the poll, leading to potential bias in the sample. Therefore, it is important to acknowledge that the poll results may not be entirely representative of the entire population and should be interpreted with caution. In order to obtain a more accurate estimate of the proportion of people unhappy with the verdict in the population, a larger, more diverse and random sample should be used.

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Answer:

\(B=4^{3} feet\)

Step-by-step explanation:

The altitude of B = 16A and we now that A = 4 feet.

Finally B will be:

\(B=4^{2}*4=4^{3} feet\)

I hope it helps you!

The ratio of brown tiles to total tiles is 12 : 20, Thus, option c is correct.

When cοmparing twο quantities οf the same kind, ratiο is utilised.

Fοr twο numbers, a and b, the ratiο fοrmula is written as a: b οr a/b.

Twο οr mοre ratiοs are said tο be in prοpοrtiοn if they are all equal. Fractiοns are the fοundatiοn οf the cοncepts οf ratiο and prοpοrtiοn.

The fundamental building blοcks οf numerοus οther mathematical nοtiοns are ratiο and prοpοrtiοn.

In many everyday situatiοns, such as when cοmparing heights, weights, distances, οr times, οr when adding cοmpοnents tο a recipe, ratiο and prοpοrtiοn can be used tο help us sοlve οur difficulties.

A ratiο is a cοmparisοn between twο amοunts that is calculated by dividing οne amοunt by the οther.

Number of brown tiles = 12

Total number of tiles = 12 + 8

                                   = 20

The ratio forms is 12 : 20, Thus, option c is correct.

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Answer:

to simplify the square root of 75, first I recognize that the perfect square 25 goes into it. So 75 = 25 x 3. Therefore the square root of 75 equals the square root of 25 times the square root of 3. And that means just 5 times the square root of 3.

Step-by-step explanation:

The square root of √75 is 5√3.

The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

A radical notation is an expression that incorporates a root, such as the square or cube root.

Given:

We have to find the square root of 75.

So, we have to factories 75 as

= 25 x 3

and, the square root of 25 is 5.

Then, √75 = √( 5 x 5 x 3)

                  = 5√3.

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The shape consist of a rectangle and a semi circle

The area of a rectangle is the product of its length and width while that of a semicircle pir^2

The radius of the semicircle is = 12/2

= 6 ft

The length and width of the rectangle are 16 ft and 12 ft respectively.

Hence the area of the shape

= 12 * 16 + 3.14 *6^2

= 192 + 113.04

= 305.04 sq ft

To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.

Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.

Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.

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Answer:

1,4, 2,8, and 3,12 are all equivalent

Plzzzzz give me Brainliest!!!!!  

The terms with "x" cancel out, and we're left with:

0 = 12

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.

Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:

Slices with only pepperoni: 6 slices

Slices with only mushrooms: 10 slices

Slices with both pepperoni and mushrooms: $x$ slices

Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices

We know that the total number of slices is 12, so we can write an equation:

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.

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Answer:

6^5  * 9^5

Step-by-step explanation:

( 6*9) ^5

We know that ( ab) ^c = a^ c* b^c

6^5  * 9^5

The sets of transformations that result in the same image when performed in any order:

b two reflections over the x-axis

e two translations

Select all the sets of transformations that result in a similar image.

A) Vertical translation, reflection over y-axis- Vertical translation shift image up with some units and relection over y-axis will change its position. In this case, we get the same image.

B) Two reflections over the x-axis will result in the same image.

C) Reflection over the y-axis, dilation with center (2,2)- Reflection does not affect the size, but the dilation with center (2,2) change its size. Thus this transformation does not provide same image.

D) Translation, dilation with center (0,0) - Translation of image does not change its size. The dilation with center (0,0) change its size as the dilation performed from origin point.

E) Two translations - Translation of image only change its position and coordinate points but does not change its size and shpae. With n number of translation, the resulted image will remain same.

Thus, the sets of transformations which result in a similar image are options B and E.

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Using it's formula, the distance between the points A(13,2) and B(7,10) is of 10 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, the points are A(13,2) and B(7,10), hence the distance is given by:

\(D = \sqrt{(13 - 7)^2+(2 - 10)^2}\)

D = sqrt(100)

D = 10 units.

The distance between the points A(13,2) and B(7,10) is of 10 units.

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Answer:

H

Step-by-step explanation:

The rectangle has a length of (2x + 1) and a width of (5x - 4).

And we want to select the expression that represents the rectangle's area.

Recall that a rectangle's area is simply its length multiplied by its width. Thus:

\(A=(2x+1)(5x-4)\)

Expand by distributing:

\(A=(2x+1)(5x)+(2x+1)(-4)\)

Distribute:

\(A=(10x^2+5x)+(-8x-4)\)

Simplify:

\(A=10x^2-3x-4\)

Hence, our answer is H.

Answer:

You separate all this number then you put them in ascending order then you start to draw a line to get your median so our median is 25

Answer: C

Step-by-step explanation:

The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.

To divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.

27/22 = 1 whole number and a remainder of 5

1 × 22 = 22

27 - 22 = 5

drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}

50/22 = 2 whole number and a remainder of 6

2 × 22 = 44

50 - 44 = 6

drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}

60/22 = 2 whole number and a remainder of 16

2 × 22 = 44

69 - 44 = 16

we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.

Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.

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Answer:

C. milliliter

Step-by-step explanation:

What is the appropriate metric unit for the capacity of a bottle of ink?

See Answer

milliliters.

Joint density function is as follows: \(f(x, y) = 16y\ x3 , x > 2, 0 \leq y \leq 1\).

We need to find the marginal density function of X. Using the formula of marginal density function, \(f_X(x) = \int f(x, y) dy\)

Here, bounds of y are 0 to 1.

\(f_X(x) =\int 0 1 16y\ x3\ dyf_X(x) \\= 8x^3\)

Now, the marginal density function of X is \(8x^3\).

Marginal density function helps to find the probability of one random variable from a joint probability distribution.

To find the marginal density function of X, we need to integrate the joint density function with respect to Y and keep the bounds of Y constant. After integrating, we will get a function which is only a function of X.

The marginal density function of X can be obtained by solving this function.

Here, we have found the marginal density function of X by integrating the given joint density function with respect to Y and the bounds of Y are 0 to 1. After integrating, we get a function which is only a function of X, i.e. 8x³.

The marginal density function of X is \(8x^3\).

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The 95% confidence interval for the mean score of all such subjects can be constructed as (67.7, 84.7).

Given,

A sociologist develops a test to measure attitudes about public transportation.

Sample size, n = 27

Mean score, x = 76.2

Standard deviation, s = 21.4

z value for 95% confidence interval = 1.96

Confidence interval = x ± z (s/√n)

                                 = 76.2 ± 1.96 (21.4/√27)

                                 = 76.2 ± 8.07

                                 = (68.13, 84.27)

Hence the ideal selection of the confidence interval is (67.7, 84.7)

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We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Two positive angles coterminal with 681° are 1041° and 2001°.

Two negative angles coterminal with 681° are -599° and -1439°.

To draw each angle in standard position, we start with the positive x-axis and rotate counterclockwise by the given angle measure. The arrows indicate the direction of rotation.

To find two positive angles coterminal with 681°, we can add or subtract multiples of 360°. Adding 360° to 681° gives us 1041°, and adding another 360° gives us 2001°. So, two positive angles coterminal with 681° are 1041° and 2001°.

To find two negative angles coterminal with 681°, we can subtract multiples of 360°. Subtracting 360° from 681° gives us -599°, and subtracting another 360° gives us -1439°. So, two negative angles coterminal with 681° are -599° and -1439°.

To draw each angle in standard position, we start by placing the initial side along the positive x-axis. For angle -157°, we rotate clockwise by 157°. For angle 819°, we rotate counterclockwise by 819°. For angle 293°, we rotate counterclockwise by 293°. The arrows indicate the direction of rotation.

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