35. State the domain and range for each function. (MAFS.912.F-IF.2.4)

Therefore, the total cost of the knives is $50.

Arithmetic is the fundamental of mathematics that includes the operations of numbers. These operations are addition, subtraction, multiplication and division. Arithmetic is one of the important branches of mathematics, that lays the foundation of the subject 'Maths', for students.

The total cost of the knives is $50.

What is being offered in the television ad?

A set of knives is being offered in the television ad. The knives are being sold for $20 down and $5 a month for six months.How to determine the total cost of the knives?To calculate the total cost of the knives, we will use the formula:

Total cost = Down payment + Monthly payment × Number of monthsTotal cost

= $20 + $5 × 6 = $20 + $30

= $50

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The correct answer is D. No; the correct distance is 1 1/12 miles, because 1/4 + 2/3 = 4/12 + 8/12 = 12/12 = 1 1/12.

To solve this problem, we first need to convert the mixed numbers to fractions. 1 4 = 4 12 and 2 3 = 8 12. Then, we can add the fractions together. 4 12 + 8 12 = 12 12 = 1 1 12.

Therefore, Brandon is incorrect. He walks a total of 1 1/12 miles, not 11 1/2 miles.

To calculate the amount of sand Maija should order, we need to find the volume of the sandbox. The sandbox is in the shape of a cube, so its volume is determined by multiplying the length, width, and height.

Given that the sides of the square sandbox are 2 feet long and the desired depth of the sand is 1.55 feet, we can calculate the volume as follows:

[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]

Since all sides of the sandbox are equal in length (2 feet), the formula simplifies to:

[tex]\[ \text{Volume} = \text{Side}^3 \][/tex]

Substituting the values:

[tex]\[ \text{Volume} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.55 \, \text{ft} \][/tex]

[tex]\[ \text{Volume} = 6.2 \, \text{cubic feet} \][/tex]

Therefore, Maija should order 6.2 cubic feet of sand for her sandbox.

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A manufacturing company has determined that the daily revenue R(n) in thousands of dollars is given by the formula R(n) = 12n - 0.6n where n represents the number of palettes of product sold (0 < n < 500).

If the company wishes to make a revenue of 45 thousand dollars, we are supposed to find the number of palettes of product sold .Solution :Let us substitute the value of R(n) = 45 in the given equation and solve for n45 = 12n - 0.6n45 = 11.4n, n = 3.9474Hence, the manufacturing company has to sell either 3 or 4 palettes of product to make $45.000.

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The formula of height h = (3v) / (π * r^2)To find the height (h) of a cone given the volume (v) and the radius of the base (r), we can rearrange the equation v = (π * r^2 * h) / 3.

By multiplying both sides by 3 and dividing by π * r^2, we isolate the variable h and obtain the formula h = (3v) / (π * r^2). Substituting the appropriate values for volume and radius into this equation allows us to calculate the height of the cone.

To solve for the height (h) in the equation v = (π * r^2 * h) / 3, we first multiply both sides by 3 to eliminate the fraction. This results in the equation 3v = π * r^2 * h. Next, we isolate the variable h by dividing both sides of the equation by π * r^2, giving us the formula h = (3v) / (π * r^2). By substituting the known values for volume (v) and radius (r) into this equation, we can calculate the height (h) of the cone. It is important to ensure that the units for volume and radius are consistent and compatible to obtain the correct result.

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The side lengt of the square is approximately 1839 feet.

To find the length in feet of the side of a square with an area of 1.00 acre, we need to convert the acreage to square feet.

Given:

1 acre = 640 acres/mile² (640 acres in a square mile)

1 mile = 5280 feet (conversion factor from miles to feet)

To convert acres to square feet, we can multiply by the conversion factor:

1 acre = 640 acres/mile² * 1 mile² * 5280 feet

Simplifying the units:

1 acre = 640 * 5280 square feet

Now, to find the length of the side of the square, we can take the square root of the area:

Side length = √(1 acre * 640 * 5280 square feet)

Calculating:

Side length ≈ √(1 * 640 * 5280) ≈ √3379200 ≈ 1839.29 feet

Rounding to the nearest foot, the length of the side of the square with an area of 1.00 acre is approximately 1839 feet.

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The value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

The value of y can be determined by using the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). In this case, we have the points (7, 4) and (3, y), with a slope of 1/4. Plugging in the values, we get (y - 4) / (3 - 7) = 1/4. Simplifying this equation, we have (y - 4) / (-4) = 1/4. Cross-multiplying, we get -4(y - 4) = 1(-4), which simplifies to -4y + 16 = -4. Solving for y, we subtract 16 from both sides, giving us -4y = -20. Dividing by -4, we find y = 5.

To summarize, the value of y in the pair of points (7, 4) and (3, y), lying on the same line with a slope of 1/4, is y = 5. This is obtained by setting up and solving an equation using the slope formula.

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1. One of the planes parallel to plane WXT is the plane WXY.2. Two segments parallel to VU are AB and CD.3. Two segments parallel to SW are PQ and RS.4. Two segments skew to XY are QR and PS.5.

Two segments skew to VZ are RT and PU.A plane parallel to plane WXT:Consider the following figure below: Here, WX is parallel to YZ. Now, any plane which passes through any of the point, say X and Y, which lie on the line WX and YZ respectively, will be parallel to plane WXT. One of such plane is plane WXY.

Two segments parallel to VU:Segments AB and CD are parallel to VU in the following figure below:Two segments parallel to SW:Segments PQ and RS are parallel to SW in the following figure below:Two segments skew to XY:Segments QR and PS are skew to XY in the following figure below:Two segments skew to VZ:Segments RT and PU are skew to VZ in the following figure below:

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Emily can walk 3/4 of a mile in 1/4 of an hour. At the same rate, time taken to walk 1 mile =1/3 of an hour.

Mathematical representation

We know that, Emily can walk 3/4 of a mile in 1/4 of an hour.

Meaning,

Time taken to walk 3/4 of a mile = 1/4 of an hour

Distance covered = 3/4 mile

We need to find the time taken by Emily to walk 1 mile.

The rate is defined as the distance covered in unit time. So,

                        Rate = Distance / Time

We know that Rate of Emily = 3/4 ÷ 1/4

                                              = 3/4 × 4/1

                                              = 3 miles/hour

The rate of walking is 3 miles/hour.

Now we can find the time taken to walk 1 mile using rate formula.

             Distance = Rate × Time

We have to walk 1 mile and the rate of walking is 3 miles/hour.

             Time = Distance / Rate

Time taken to walk 1 mile = 1 / 3 = 1/3 hour.

So, the answer is option C.

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Answer:

for 1.

Step-by-step explanation:

the formula is pir2h

John recorded 5 heads and flipped a coin 9 times. The ratio of heads to tails recorded by John is 5:4.

John flipped a coin 9 times and recorded 5 heads. To determine the ratio of heads to tails, we need to compare the number of heads to the number of tails. Since John recorded 5 heads, the remaining flips would be tails.

Therefore, the number of tails recorded would be 9 - 5 = 4. The ratio of heads to tails recorded by John is thus 5:4, which means for every 5 heads, there were 4 tails. This ratio represents the relative frequency of heads and tails in John's coin flips.

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The surface area of a sphere is 4πr2, where r is the radius of the sphere. The cost of a sphere is 2 per square foot, so the cost of a sphere with radius r is 8πr2. Selim can spend 20 per sphere, so he can purchase a sphere with radius r such that 8πr2≤20. This inequality can be solved for r to get r≤8π20​​=2π5​​. The diameter of a sphere is 2r, so the maximum diameter of the spheres Selim can purchase is 22π5​​=10π​≈3.162 feet.

This means that the expression 10x² + 2x - 8  completely factored as 2(5x - 2)(x + 2).

The correct factored form of the expression 10x² + 2x - 8 is:

2(5x - 2)(x + 2).

To factor the quadratic expression completely for common factors first that the coefficient 2 is a common factor in all three terms. After factoring out 2, left with (5x² + x - 4).

An factor the trinomial (5x² + x - 4). However, this trinomial cannot be factored further using integer coefficients.

So, the factored form of the expression is 2(5x - 2)(x + 2).

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Mrs. Rodriguez sold 128.8 ounces of popcorn.We know that each bag of popcorn weighs 2.3 ounces. Therefore, to find out the total amount of popcorn Mrs. Rodriguez sold in 56 bags, we need to multiply 2.3 by 56. That is;2.3 × 56 = 128.8Therefore, there are 128.8 ounces of popcorn in 56 bags

We are given that Mrs. Rodriguez is selling popcorn at the snack stand. Each bag holds 2.3 ounces of popcorn. In one hour, she sold 56 bags of popcorn. Our task is to find out how many ounces of popcorn are in 56 bags.In order to find out how many ounces of popcorn are in 56 bags, we need to first find out the weight of one bag of popcorn. We are told that each bag holds 2.3 ounces of popcorn. So, we have:

Weight of one bag of popcorn = 2.3 ounces Now, we can use this information to calculate the total weight of popcorn Mrs. Rodriguez sold in 56 bags. To do this, we need to multiply the weight of one bag of popcorn (2.3 ounces) by the number of bags she sold (56). That is;Weight of 56 bags of popcorn = 2.3 × 56= 128.8Therefore, Mrs. Rodriguez sold 128.8 ounces of popcorn in one hour.

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Based on the information, the probability is 1/144, or approximately 0.0069.

Each number cube has 12 possible outcomes, as there are 12 faces labeled from 1 to 12.

The probability of rolling an 11 on one number cube is 1 out of 12, as there is only one face labeled 11 out of the 12 possible outcomes.

Since the two number cubes are rolled simultaneously, the total number of possible outcomes is the product of the possible outcomes for each cube, which is 12 * 12 = 144.

The number of favorable outcomes, in this case, is 1, as both number cubes need to show 11.

Therefore, the probability that both number cubes land with the number 11 facing up in one roll is:

Number of favorable outcomes / Total number of possible outcomes

= 1 / 144

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Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

To determine Jen's average speed for the entire round trip, we need to calculate the total distance traveled and the total time taken.

Let's assume the distance between Boston and Cape Cod is "d" miles.

For the outbound trip from Boston to Cape Cod, Jen traveled at a speed of 60 mph. The time taken for this leg of the trip is given by:

Time = Distance / Speed

Time = d / 60

For the return trip, it took Jen 3 times longer due to heavy traffic. Therefore, the time taken for the return trip is 3 times the time taken for the outbound trip:

Time for return trip = 3 * (d / 60) = (3d) / 60

The total time for the round trip is the sum of the outbound and return trip times:

Total Time = d / 60 + (3d) / 60 = (d + 3d) / 60 = 4d / 60 = d / 15

The total distance for the round trip is twice the distance from Boston to Cape Cod:

Total Distance = 2d

Now, we can calculate Jen's average speed by dividing the total distance by the total time:

Average Speed = Total Distance / Total Time

Average Speed = 2d / (d / 15)

Average Speed = 2 * 15

Average Speed = 30 mph

Therefore, Jen's average speed for the entire round trip, including the outbound and return trips, is 30 mph.

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The Apostle Paul demonstrates humility in Acts 15:36-39 and 2 Timothy 4:11 through his willingness to resolve differences. In these passages, Paul's actions and attitudes reflect his humility and his desire for reconciliation and unity among believers.


In Acts 15:36-39, Paul and Barnabas had a disagreement regarding taking John Mark on a missionary journey. Barnabas wanted to bring John Mark along, but Paul did not because John Mark had previously left them on a previous journey. Despite the disagreement, Paul shows humility by accepting Barnabas' decision and allowing him to take John Mark as his companion, while Paul chooses Silas as his own companion. This act demonstrates Paul's willingness to prioritize unity and reconciliation over personal preferences.

In 2 Timothy 4:11, Paul shows humility by reconciling with John Mark. He requests Timothy to bring Mark with him because Paul considers Mark to be helpful in his ministry. This shows a change in Paul's attitude towards Mark, indicating that he was willing to put aside any past differences and extend forgiveness and acceptance. Paul's willingness to reconcile and work alongside Mark reveals his humility and his understanding of the importance of resolving differences for the sake of the Gospel and the unity of believers.

Overall, both passages highlight Paul's humility through his willingness to resolve differences and prioritize unity, showcasing his desire for reconciliation and harmony among fellow believers.

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The dimensions of the rectangle are 16 inches in width and 24 inches in length.

Let's assume the width of the rectangle is x inches. According to the problem, the length is 8 inches greater than the width, so the length can be represented as (x + 8) inches.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 384 square inches. So, we can set up the equation:

Length * Width = Area

(x + 8) * x = 384

Expanding the equation:

x^2 + 8x = 384

Rearranging the equation to solve for x:

x^2 + 8x - 384 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring it, we find:

(x - 16)(x + 24) = 0

So, x = 16 or x = -24.

Since dimensions cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 16 inches.

Substituting this value back into the equation for the length:

Length = x + 8 = 16 + 8 = 24 inches

Hence, the dimensions of the rectangle are 16 inches in width and 24 inches in length, which gives an area of 384 square inches.

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Therefore, the answer rounding to the nearest tenth is d. 5.3.

To convert 1 gallon to liters, we multiply by the conversion factor of 3.79 L/gal.

1 gal. * 3.79 L/gal = 3.79 L

Now, to find the equivalent of 20 liters, we can set up a proportion:

1 gal / 3.79 L = x gal / 20 L

Cross-multiplying and solving for x, we get:

x = (1 gal / 3.79 L) * 20 L = 20 / 3.79 gal

Rounding to the nearest tenth, we have:

x ≈ 5.3

Therefore, the answer is d. 5.3.

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The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18

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

8, 10, 12, 14, 16,.

In the above sequence, we have

First term, a(1) = 8

And we have the common difference to be

d = 2

So, we have

a(n) = a(n - 1) + 2

The next term of the sequence is

Next = 16 + 2

Evaluate

Next = 18

Hence, the recursive formula for the sequence is a(n) = a(n - 1) + 2

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The mean rainfall for the highland storms is 15.27 millimeters, and the mean rainfall for the lowland storms is 12.05 millimeters.

In the dot plots, each dot represents the rainfall total for a spring storm in either the highland or lowland areas. To find the mean rainfall, we calculate the average of all the rainfall values in each plot.

For the highland storms, the mean is 15.27 millimeters, which indicates that, on average, the rainfall for the spring storms in the highland areas is 15.27 millimeters.

For the lowland storms, the mean is 12.05 millimeters, suggesting that the average rainfall for the spring storms in the lowland areas is 12.05 millimeters.

These values provide a measure of the central tendency or average rainfall for the respective areas and can help in comparing the rainfall patterns between the highlands and lowlands.

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To determine the measure of angle DAB, we need to use the congruence of quadrilaterals ABCD and AMCG.

Quadrilateral ABCD is congruent to quadrilateral AMCG.

Since the two quadrilaterals are congruent, their corresponding angles are equal. Therefore, we can write:

m∠DAB = m∠MAC

However, the measure of angle MAC is not given in the given information. Therefore, without additional information, we cannot determine the exact measure of angle DAB.

The options provided in the question do not correspond to the measure of angle DAB. Therefore, the correct answer cannot be determined based on the given information.

It is important to have additional information about the measures of angles or the side lengths in order to determine the measure of angle DAB accurately.

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Cindy has scores of 72, 82, 83 and 89 on her Biology tests. Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

Cindy's current average score in Biology is:

(72 + 82 + 83 + 89) / 4 = 81.5

Since the final exam counts as two tests, we can calculate the total number of points Cindy can earn in the course as follows:

Total points = 4 tests + 2 tests = 6 tests

To earn a C in the course, her average score must be between 77 and 84. Let's assume she needs to score x on her final exam to achieve a C. Then her total points would be:

Total points = 72 + 82 + 83 + 89 + x + x

Simplifying this equation, we get:

Total points = 326 + 2x

To earn a C, Cindy's average score must be between 77 and 84. Therefore, we can set up an inequality:

77 <= (326 + 2x) / 6 <= 84

Multiplying both sides by 6, we get:

462 <= 326 + 2x <= 504

Subtracting 326 from all sides, we get:

136 <= 2x <= 178

Dividing by 2, we get:

68 <= x <= 89

Therefore, Cindy must score between 68 and 89 on her final exam to earn a C in Biology.

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a) The gradient of the line passing through the points (0,6) and (3,0) is -2. b) The gradient of the line perpendicular to this line is 1/2. c) The equation for the line passing through point a and perpendicular to the line ab can be determined using the point-slope form of a linear equation.

a) To find the gradient (slope) of the line passing through (0,6) and (3,0), we use the formula: gradient = (change in y) / (change in x). Substituting the coordinates, we get (-6) / (3-0) = -2.

b) The gradient of a line perpendicular to another line is the negative reciprocal of the original gradient. Therefore, the gradient of the line perpendicular to the given line is 1/2.

c) To find the equation of the line passing through point a and perpendicular to line ab, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is point a and m is the gradient of the perpendicular line. Substituting the values, we get y - 6 = (1/2)(x - 0), which simplifies to y = (1/2)x + 6.

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Given a quadrilateral ABCD, with the sides AB and DC parallel and equal in length. Let us denote angle BAD as ∠α and angle ADC as ∠β. Now, we have to find the values of the variables x and y such that ABCD is a parallelogram.

Parallelogram has a pair of parallel sides. So, we have AB ∥ CD. It is given that ∠α = ∠β and AB = CD. So, by angle-angle-side rule, the two triangles ABD and DCA are congruent.

In triangle ABD, we have:∠DAB = 180° - ∠α = 180° - ∠β (as ∠α = ∠β)⇒ ∠DAB + ∠CDA = 180° (linear pair of angles)⇒ ∠CDA = ∠β.In triangle DCA, we have:∠CDA = ∠β (as obtained above)⇒ ∠CAD = ∠α (as ∠α = ∠β)⇒ ∠BDC = 180° - ∠α = 180° - ∠β (linear pair of angles)⇒ ∠BDC = ∠DAB.In quadrilateral ABCD, the adjacent angles are supplementary. So, we have:∠BDC + ∠BCD = 180° (adjacent angles are supplementary)⇒ ∠DAB + ∠BCD = 180° (as ∠BDC = ∠DAB)⇒ ∠BCD = 180° - ∠DAB.In triangle ACD, we have:∠C = ∠C (common)⇒ ∠CAD + ∠BCD = 180° (angles of a triangle add up to 180°)⇒ ∠α + (180° - ∠DAB) = 180°⇒ ∠α + ∠β = 180°.

Now, we can solve for x and y.In triangle ABD, we have:AB = BD⇒ 3x = 21 - x⇒ 4x = 21⇒ x = 21/4.In triangle DCA, we have:CD = DA⇒ 3y = 22 - y⇒ 4y = 22⇒ y = 11/2. Therefore, the value of x is 21/4 and the value of y is 11/2.

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1: The number closest to zero is not always the least.

2: The number farthest from zero is not always the greatest.

3: The number farthest right is not always the least.

4: The number left is always the least.

The first statement, "The number closest to zero is always the least," is not necessarily true.

It depends on whether the numbers being compared are positive or negative.

For example, -2 is closer to zero than -4, but it is actually greater than -4.

The second statement, "The number farthest from zero is always the greatest," is also not necessarily true.

Just like the first statement, it depends on whether the numbers being compared are positive or negative.

For example, -5 is farther from zero than -3, but -3 is actually greater than -5.

The third statement, "The number farthest right is always the least," is definitely not true.

The direction of the number line (left or right) has nothing to do with whether a number is greater or lesser than another number.

That leaves us with the fourth statement, "The number left is always the least."

This statement is true! On a number line going from negative to positive numbers, the numbers to the left of zero (the negative numbers) are always less than the numbers to the right of zero (the positive numbers).

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Let x be the number of regular bouquets and y be the number of mini bouquets the florist makes.so the florist makes 5 regular bouquets and 15 mini bouquets

Then we can write the following system of equations based on the given information:

6x + 2y = 60

(since each regular bouquet has 6 roses and 2 peonies)

2x + 2y = 40

(since each mini bouquet has 2 roses and 2 peonies)We can use any method to solve this system of equations, but we will use the substitution method. We will solve the first equation for y in terms of x:y = 30 - 3xSubstitute this expression for y into the second equation and solve for

x:2x + 2(30 - 3x) = 402x + 60 - 6x = 40-4x = -20x = 5Substitute x = 5 into the expression we found for y:y = 30 - 3(5) = 15

Therefore, the florist makes 5 regular bouquets and 15 mini bouquets. Another method to solve the system of equations is by graphing: Graph the two equations on the same set of axes and find the intersection point. The x-coordinate of the intersection point will give us the number of regular bouquets, and the y-coordinate will give us the number of mini bouquets. We can see that the intersection point is (5, 15), which agrees with the solution we found using the substitution method.

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To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.

The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).

To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):

0.45 * 40 = 0.5x + 0.25(40 - x)

Simplifying the equation:

18 = 0.5x + 10 - 0.25x

Combining like terms:

0.25x = 8

Dividing both sides by 0.25:

x = 32

Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.

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The dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.

To find the dimensions of the bedroom in the blueprint, we can use the given scale of 1/4 in = 3 ft.

First, let's convert the dimensions of the actual bedroom into feet:

Length of the actual bedroom = 16 in * (1 ft / 12 in) = 16/12 ft = 4/3 ft

Width of the actual bedroom = 12 in * (1 ft / 12 in) = 12/12 ft = 1 ft

Now, let's use the scale to find the dimensions of the bedroom in the blueprint:

Length of the bedroom in the blueprint = Length of the actual bedroom * Scale

Length of the bedroom in the blueprint = (4/3 ft) * (1/4 in / 3 ft)

Length of the bedroom in the blueprint = 4/3 * 1/12

Length of the bedroom in the blueprint = 4/36

Length of the bedroom in the blueprint = 1/9 ft

Width of the bedroom in the blueprint = Width of the actual bedroom * Scale

Width of the bedroom in the blueprint = (1 ft) * (1/4 in / 3 ft)

Width of the bedroom in the blueprint = 1 * 1/12

Width of the bedroom in the blueprint = 1/12 ft

Therefore, the dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.

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The work done is 400.0 Joules A force of 80 Newtons pushes a 50-kilogram object across a level floor for 8.0 meters.

To find the work done, we can use the formula:work = force x distance x cos(theta)where force is 80 N, distance is 8.0 m, and theta is the angle between the force and the displacement. Since the force is applied in the direction of motion, theta is 0° and cos(0°) is 1.

we can simplify the formula as:work = force x distance x cos(theta)work = 80 N x 8.0 m x cos(0°)work = 640.0 JHowever, we need to check the units of our answer to make sure they are in Joules (J). The units of force are Newtons (N), the units of distance are meters (m), and the units of cos(theta) are dimensionless. Therefore, our answer is in Joules (J).So, the work done is 640.0 Joules.

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