Lucy buys a silver coat rack priced at $69.If the sales tax is 3%, how much tax will Lucy pay?

The row operations on the augmented matrix are

An augmented matrix is a matrix in which the coefficient matrix and the column matrix are written together.

Since we have the augmented matrix

[tex]\left[\begin{array}{ccc}1&3&5\\0&\frac{1}{4} &-1\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\1&\\10&\end{array}\right][/tex]

To determine the next row operations, we proceed as follows.

Since we want to convert the second element in the second row to 1, we multiply row 2 by 4,

So, R₂ → 4R₂

So, the augmented matrix becomes

[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\10&\end{array}\right][/tex]

Now, since we want to convert the first element in the third row to 0, the row operation we perform is we add 3 to row 3

So, R₃ → R₃ + 3

So, the augmented matrix becomes

[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\0&9&-8\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\13&\end{array}\right][/tex]

So, the row operations are

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Answer:

3.

Step-by-step explanation:

The answer is 3, it says "THE HEIGHT OF ORNAMENT B IS 3 TIMES LARGER THAN THE HEIGHT OF ORNAMENT A.!!!"

Answer:

E

Step-by-step explanation:

using Pythagoras' identity on the lower right triangle , with legs s and hypotenuse 2 , then

s² + s² = 2²

2s² = 4 ( divide both sides by 2 )

s² = 2 ( take square root of both sides )

s = [tex]\sqrt{2}[/tex]

The true statements are

Dilation was performed on a rectangle with a center of dilation at point V. We will evaluate the given options to determine their accuracy:

Option 1: The image is a reduction because 0 < n < 1 (True)

Explanation: Since the dilation factor is 2/5, this is less than 1, the resulting image will be smaller than the original rectangle. Therefore, this option is true.

Option 2: This is true.  Dilation preserves the proportional relationship between corresponding sides of similar shapes. Since the dilation factor is 2/5, the side lengths of the image will be two-fifths the length of the corresponding side lengths of the pre-image. Therefore, this option is true.

Option 5: is true Since the dilation factor is 2/5, the base of the image will be two-fifths the length of the base of the pre-image. This is in line with the proportional relationship preserved by dilation. Therefore, this option is true.

In summary, options 1, 2, and 5 are true, while options 3 and 4 are false.

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question

Dilation D Subscript V, two-fifths was performed on a rectangle. How does the image relate to the pre-image? Select three options. The image is a reduction because 0 < n < 1. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The angles of the image are two-fifths the size of the angles of the pre-image. The center of dilation is at point Q. The base of the image is two-fifths the size of the base of the pre-image.

Answer:

To solve the equation 3x + 6 = 34, we need to isolate x on one side of the equation.

First, we can start by subtracting 6 from both sides of the equation to get:

3x + 6 - 6 = 34 - 6

Simplifying this, we get:

3x = 28

Next, we divide both sides by 3 to isolate x:

3x/3 = 28/3

Simplifying this, we get:

x = 28/3

This is not one of the answer choices listed. However, we can approximate the answer to the nearest integer. Using a calculator, we get:

x ≈ 9.333

Rounding to the nearest integer, we get:

x ≈ 9

Therefore, the answer closest to the solution of the equation 3x + 6 = 34 is 10.

Answer:

A) [tex]x=-1\pm\sqrt{\frac{13}{6}}[/tex]

Step-by-step explanation:

[tex]\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}[/tex]

Answer:

<MON= 59°

Step-by-step explanation:

Look at the diagram what is <LON? It is the angle of the whole line. Remember when any three letters come the middle letter is the angle like here if it is asking MON it is requesting the angle O between the lines M and N. The angle between the line L and M is given so to find <MON we can simply minus <LOM with the total angle (<LON)

<MON= <LON - <LOM

= 142-83

<MON= 59°

(a) Probability that 3 balls are all white:

Step 1:

Total balls = Number of red balls + Number of white balls + Number of green balls = 7 + 12 + 4 = 23.

Step 2:

Total ways to choose 3 balls = C(23, 3) = 23! / (3 * (23-3) ) = 23 / (3 * 20) = (23 * 22 * 21) / (3 * 2 * 1) = 1771.

Step 3: Calculate the number of ways to choose 3 white balls out of 12:

Number of ways to choose 3 white balls = C(12, 3) = 12 / (3 * (12-3) ) = 12 / (3 * 9) = (12 * 11 * 10) / (3 * 2 * 1) = 220.

Step 4: Calculate the probability of selecting 3 white balls:

Probability = Number of ways to choose 3 white balls / Total ways to choose 3 balls = 220 / 1771 ≈ 0.1241.

Therefore, the probability that 3 balls drawn are all white is approximately 0.1241.

(b) Probability that 3 balls are one of each color:

Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.

Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.

Step 3: Calculate the number of ways to choose 1 ball of each color:

Number of ways to choose 1 red, 1 white, and 1 green ball = Number of red balls * Number of white balls * Number of green balls = 7 * 12 * 4 = 336.

Step 4: Calculate the probability of selecting 3 balls of different colors:

Probability = Number of ways to choose 1 ball of each color / Total ways to choose 3 balls = 336 / 1771 ≈ 0.1899.

Therefore, the probability that 3 balls drawn are one of each color is approximately 0.1899.

(c) Probability that 3 balls are of the same color:

Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.

Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.

Step 3: Calculate the number of ways to choose 3 balls of the same color:

Number of ways to choose 3 red balls = C(7, 3) = 7 / (3 * (7-3) ) = 7 / (3 * 4 ) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

Number of ways to choose 3 white balls = C(12, 3) = 220.

Number of ways to choose 3 green balls = C(4, 3) = 4.

Step 4: Calculate the probability of selecting 3 balls of the same color:

Probability = (Number of ways to choose 3 red balls + Number of ways to choose 3 white balls + Number of ways to choose 3 green balls) / Total ways to choose 3 balls = (35 + 220 + 4) / 1771 ≈ 0.1416.

Therefore, the probability that 3 balls drawn are of the same color is approximately 0.1416.

Answer:

Step-by-step explanation:

(a) Probability that 3 balls are all white:

Total number of balls = 7 red + 12 white + 4 green = 23

Number of favorable outcomes = 12 white balls

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 12 / 23

(b) Probability that 3 balls are one of each color:

Total number of balls = 7 red + 12 white + 4 green = 23

Number of favorable outcomes = 7 red balls * 12 white balls * 4 green balls

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = (7 * 12 * 4) / (23 * 22 * 21)

(c) Probability that 3 balls are the same color:

Total number of balls = 7 red + 12 white + 4 green = 23

Number of favorable outcomes = (7 red balls * 6 red balls * 5 red balls) + (12 white balls * 11 white balls * 10 white balls) + (4 green balls * 3 green balls * 2 green balls)

The installment price of the TV is $1,195.56.

To find the installment price of the TV, we need to calculate the total amount paid over the installment period.

The down payment is $60, and there are 12 monthly payments of $104.63 each.

Total amount paid over 12 months = Monthly payment x Number of payments

= $104.63 x 12

= $1,255.56

Now, we can calculate the installment price by subtracting the down payment from the total amount paid:

Installment price = Total amount paid - Down payment

= $1,255.56 - $60

= $1,195.56

Therefore, the installment price of the TV is $1,195.56.

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Answer: 7

Step-by-step explanation:

The range of a set of numbers is the difference between the highest and lowest numbers in that set.

For the given set, the highest number is 4 and the lowest number is -3.

So, the range is 4 - (-3) = 7.

Work Shown

rectangle area = length*width = 280*140 = 39,200 square cm

circle area = pi*r^2 = (22/7)*(7)^2 = 154 square cm

Divide the two areas

39200/154 = 254.54545 approximately

That rounds down to 254

Rounding to 255 will not work because there won't be enough paper for that 255th circle

The angle of intersecting chords theorem indicates that the value of x, obtained from the measure of the arc [tex]\widehat{KU}[/tex] is; x = 7

The angle of intersecting chords theorem states that the angle formed at the intersection of two chords is half the sum of the angles of the arcs intercepted by the two chords.

The angle of intersecting chords theorem indicates that we get;

The measure of the arc KU = 6·x + 8

122 = (1/2) × (6·x + 8 + 194)

Therefore; 6·x + 8 + 194 = 2 × 122 = 244

6·x = 244 - (194 + 8) = 42

x = 42/6 = 7

Therefore; m[tex]\widehat{KU}[/tex] = 6 × 7 + 8 = 50°

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Evaluating the expression results to

To simplify the given expressions, we substitute the values of A, B, C, and D into the expressions and perform the necessary calculations.

A - 2(B - A) - 3B:

Substituting the values:

8 - 2 * (10 - 8) - 3 * 10

Simplifying the expression inside parentheses

8 - 2(2) - 3 * 10

8 - 4 - 30

Performing subtraction

8 - 4 - 30

-18

Therefore, A - 2(B - A) - 3B simplifies to --18

evaluate the second expression C(4-D)+2CD:

C = 16

D = 11

Substituting the values:

16(4 - 11) + 2(16)(11)

Simplifying

16(-7) + 2(16)(11)

-112 + 352

240

Therefore, the value of the expression C(4-D)+2CD, when C = 16 and D = 11, is 240.

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To create another comic out of the scenario is as follows: An eagle is chasing a bird and spots it on top of a 10ft tree and is looking at it at an angle of elevation of 30° degrees.

To calculate the distance, the trigonometric sine law needs to be obeyed and the formula is written below as follows.

a/sinA = b/sinB

where;

a= 10ft

A= 30°

b= ?

B= 90°

That is;

10/sin30° = b/sin90°

make b the subject of formula;

b = 10×sin90°/sin30°

= 10×1/0.5

= 20ft

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The coordinates of the remaining corners are (2, 2) and (2, 10).

To find the coordinates of the remaining corners of the parallelogram, we can use the fact that the diagonals of a parallelogram bisect each other.

Let's call the point of intersection of the diagonals as (3, 4). The midpoint of one diagonal is the same as the midpoint of the other diagonal.

First, let's find the midpoint of the diagonal connecting (3, 2) and (5, 10). The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Applying this formula, we find the midpoint as (4, 6).

Since the point (3, 4) is the midpoint of the other diagonal, we can use this information to find the coordinates of the remaining corners.

If we reflect the point (4, 6) across the point of intersection (3, 4), we will obtain the coordinates of the remaining corners.

Reflecting (4, 6) across (3, 4), we get:

(4 - 2, 6 - 4) = (2, 2)

Therefore, the remaining corners of the parallelogram are (2, 2) and (2, 10).

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The similarity of the triangles cannot be determined

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

The triangles (see attachment)

The triangles are given as

FGH and JKL

Where we have

A pair of corresponding angle

Also, we have

A pair of similar side

There are no other parameters to determine if the triangles are similar or not

This means that the similarity cannot be determined

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Answer: sorry I can't help you

Step-by-step explanation:

The enclosed area can be found by plotting the given equations, finding the points of intersection, establishing the boundaries, and then calculating the integral of the difference between the two functions within these boundaries.

∫7-3[ (2-1/3*y) - (2y² - 6) ] dy

To find the enclosed area within the boundaries defined by the equations x = 2y²- 6, x = 2 – 1/3y, y= 7 and y= -3, you would firstly have to plot these equations on a plane, observe their intersection points and identify the boundaries of the area enclosed.

Then, the enclosed area can be calculated by integrating the difference between the two functions within those points where y = -3 to y = 7. Once you've done that, you calculate the definite integral of each of the functions separately from y = -3 to y = 7 and subtract the results. Here's the computation:

∫7-3[ (2-1/3*y) - (2y² - 6) ] dy

Calculating this integration will give you the area enclosed within the boundaries defined by these equations.

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This introduces some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.

We can evaluate the sampling method used for the magician's survey.

Voluntary: The survey was sent out to people who had previously attended the magician's programs. It suggests that participation in the survey is optional, meaning respondents can choose whether or not to participate. Therefore, the survey can be considered voluntary.

Ranking Preference: The survey asks participants to rank their three favorite tricks. This allows respondents to express their preferences in a specific order. It provides a clear structure for respondents to indicate their choices, making it easier for the magician to analyze the data and determine the most popular tricks.

Email Survey: The survey was conducted through email, which can be an effective method for reaching a targeted audience. However, it's important to note that the sample is limited to people who have attended the magician's programs in the past. This may introduce some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.

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The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

I thing its 7- 12 sorry if wrong

Step-by-step explanation:

Answer:

972 ft²(1 yd²/9 ft²) = 108 yd²

The smallest possible value of the entire expression is 7.5, which occurs when A = 5, B = 2, and C = 4.

We are given the three different numbers 4, and C represent three different numbers from 2 through 5 and we have to find out the smallest possible value of the entire expression 10 - A B/C.

To find the smallest possible value, we need to take the greatest value of A, the smallest value of B, and the smallest value of C.

The given number 4 is in between 2 and 5, so it cannot be the greatest value.

Therefore, A must be 5. Now, the other two numbers must be chosen from the remaining three numbers 2, 3, and 4.

We need to choose the smallest possible value of B and C to make the entire expression the smallest. The smallest value of B is 2.

Now, we need to choose the smallest possible value of C. If C is 4, then the entire expression becomes:10 - 5(2/4) = 10 - 2.5 = 7.5If C is 5, then the entire expression becomes:10 - 5(2/5) = 10 - 2 = 8

Thus, the smallest possible value of the entire expression is 7.5.

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The Algebraic expression for the costs of 4 pens and 6 rulers is:

Total cost = Cost of 4 pens + Cost of 6 rulersTotal cost = 4m + (6m - 30)Total cost = 10m - 30Hence, the algebraic expression for the costs of 4 pens and 6 rulers is 10m - 30.

Let the cost of a ruler be represented by r, then we have:

m Shillings is the cost of a pen and r Shillings is the cost of a ruler from the given information.Using the information, the cost of the ruler will be the cost of a pen minus 5.

This can be represented algebraically as:r = m - 5

To find the cost of 4 pens and 6 rulers, we can substitute the value of r from the equation above into the expression for the cost of 4 pens and 6 rulers.Cost of 4 pens = 4mCost of 6 rulers = 6r

Substituting r from the equation above into the expression for the cost of 6 rulers, we have:Cost of 6 rulers = 6(m - 5)Simplifying the expression above, we get:Cost of 6 rulers = 6m - 30

Therefore, the algebraic expression for the costs of 4 pens and 6 rulers is:

Total cost = Cost of 4 pens + Cost of 6 rulersTotal cost = 4m + (6m - 30)Total cost = 10m - 30Hence, the algebraic expression for the costs of 4 pens and 6 rulers is 10m - 30.

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Dan will pay approximately $1231.87 in cash for the fence.

To determine how much Dan will pay in cash for the fence, we need to calculate the total cost of the fence, apply the tax, and then determine the portion that will be paid with a credit card.

Dimensions of the land to be fenced: 450 ft by 280 ft

Length of a roll of fence: 60 ft

Cost of a roll of fence: $60.00

Tax rate: 9.5%

Portion to be paid with a credit card: 1/4 (or 25%)

First, let's calculate the total perimeter of the land to determine how many rolls of fence are needed:

Perimeter = 2 [tex]\times[/tex] (Length + Width)

Perimeter = 2 [tex]\times[/tex] (450 ft + 280 ft)

Perimeter = 2 [tex]\times[/tex] 730 ft

Perimeter = 1460 ft

Since each roll of fence is 60 ft long, the number of rolls needed is:

Number of rolls = Perimeter / Length of a roll

Number of rolls = 1460 ft / 60 ft

Number of rolls ≈ 24.33 rolls

Since we can't purchase a fraction of a roll, we need to round up to the nearest whole number of rolls.

Thus, we need to purchase 25 rolls.

The total cost of the fence without tax is:

Total cost = Number of rolls [tex]\times[/tex] Cost per roll

Total cost = 25 rolls [tex]\times[/tex] $60.00 per roll

Total cost = $1500.00

Now, let's calculate the tax amount:

Tax amount = Total cost [tex]\times[/tex] Tax rate

Tax amount = $1500.00 [tex]\times[/tex] 9.5% (or 0.095)

Tax amount = $142.50

The total cost including tax is:

Total cost with tax = Total cost + Tax amount

Total cost with tax = $1500.00 + $142.50

Total cost with tax = $1642.50

Finally, let's calculate the portion to be paid with a credit card and the portion to be paid in cash:

Portion paid with credit card = Portion to be paid with a credit card * Total cost with tax

Portion paid with credit card = 25% [tex]\times[/tex] $1642.50

Portion paid with credit card = $410.63

Portion paid in cash = Total cost with tax - Portion paid with credit card

Portion paid in cash = $1642.50 - $410.63

Portion paid in cash = $1231.87

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Answer:

the best value for the percentage of the area under the curve that is shaded is 68%.

Step-by-step explanation:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 170.8 min and the standard deviation is 19.7 min, we can calculate the values of U, V, and W.

U: U is one standard deviation below the mean.

U = Mean - 1 * Standard Deviation

U = 170.8 - 1 * 19.7

U ≈ 151.1

V: V is the mean.

V = Mean

V = 170.8

W: W is one standard deviation above the mean.

W = Mean + 1 * Standard Deviation

W = 170.8 + 1 * 19.7

W ≈ 190.5

Now, let's determine the best value for the percentage of the area under the curve that is shaded. Based on the empirical rule, the highest percentage that can be shaded is approximately 68% since it represents the data within one standard deviation of the mean.

Therefore, the best value for the percentage of the area under the curve that is shaded is 68%.

Answer:

The graph representing the function f(x) = −|x − 2| − 1 is a downward-opening V-shaped graph that is shifted 2 units to the right and 1 unit downward from the standard absolute value function |x|.

Step-by-step explanation:

Here is a description of the graph and its key points:

The vertex of the graph is located at the point (2, -1), which represents the minimum point of the graph.

The graph approaches negative infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

The graph is symmetric with respect to the vertical line x = 2.

Please note that I cannot display images directly, but you can search for "graph of f(x) = −|x − 2| − 1" on an online graphing tool or use a graphing calculator to visualize the specific graph.