Given lines
�
,
�
,
l,m,and
�
n are parallel and cut by two transversal lines, find the value of
�
x. Round your answer to the nearest tenth if necessary.

The total cubic centimeters of space the tissue box requires is 500 cubic centimeters, under the condition that the box is half full.

The volume of a cube is evaluated by multiplying its length by its width by its height. If all sides of a cube are equal,

we can use the formula

V = s³

here

s = length of one side of the cube.

If we let s be the length of one side of the cube and V be its volume,

V = s³

If we know that the tissue box is half full, then let us consider that half of its volume is occupied by tissues. Then

V' = 0.5 × V

Staging V = s³ in the equation

V' = 0.5 × s³

s = 10 cm (given)

V' = 0.5 × 1000 = 500 cubic centimeters

Hence, if Patrick's tissue box has a volume of 1000 cubic centimeters and it is half full, then the tissues occupy 500 cubic centimeters of space.

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The complete question is

Patrick buys a tissue box in the shape of a cube of side 10 centimeters. How many cubic centimeters of space do the tissues occupy if the box is half full? Show all work

Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

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The value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

To evaluate the definite integral 2t sin(-9t)dt using integration by parts, we first need to choose u and dv.

Let u = 2t and dv = sin(-9t)dt. Then du/dt = 2 and v = (-1/9)cos(-9t).

Using the integration by parts formula ∫udv = uv - ∫vdu, we can evaluate the definite integral as follows: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - ∫(-2/9)cos(-9t)dt

Next, we need to evaluate the integral on the right-hand side.

Let u = -2/9 and dv = cos(-9t)dt. Then du/dt = 0 and v = (1/9)sin(-9t).

Using integration by parts again, we get: ∫cos(-9t)dt = (1/9)sin(-9t) + ∫(1/81)sin(-9t)dt = (1/9)sin(-9t) - (1/729)cos(-9t)

Substituting this result back into the original equation, we get: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - [(-2/9)(1/9)sin(-9t) + (2/9)(1/729)cos(-9t)]

Now, we can evaluate the definite integral by plugging in the limits of integration (0 and π) and simplifying:

∫π0 2t sin(-9t)dt

= [-2π/9 cos(-9π)] - [(-2/9)(1/9)sin(-9π) + (2/9)(1/729)cos(-9π)] - [(-2/9)cos(0)]

= [-2π/9 cos(9π)] - [(-2/9)(1/9)sin(9π) + (2/9)(1/729)cos(9π)] - [(-2/9)cos(0)]

= [-2π/9 (-1)] - [(-2/9)(1/9)(0) + (2/9)(1/729)(-1)] - [(-2/9)(1)]

= (2π/9) + (2/6561) + (2/9) = 5.25π

Therefore, the value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

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The concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon

We can use the formula:

(concentration of salt in tank) * (gallons of water in tank) = (total pounds of salt in tank)

To solve this problem. At the beginning, the tank contains 500 gallons of salt-free water, so the total pounds of salt in the tank is 0. After 10 minutes, 20 gallons of brine have entered the tank, and 20 gallons of the mixture have left the tank. As a result, the amount of water in the tank remains constant at 500 gallons.

The amount of salt that enters the tank in 10 minutes is:

(0.25 lb/gal) * (2 gal/min) * (10 min) = 5 lb

The total pounds of salt in the tank after 10 minutes is:

0 + 5 = 5 lb

Therefore, the concentration of salt in the tank at the end of 10 minutes is

(concentration of salt in tank) * (500 gallons) = 5 lb

Solving for the concentration of salt in the tank, we get:

concentration of salt in tank = 5 lb / 500 gallons

Simplifying this expression, we get:

concentration of salt in tank = 0.01 lb/gal

Therefore, the concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon.

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Step 1: Find the cost of 1 pie

1 pie = 4 cups of fruit + 1 pie crust

1 pie = 4(0.75) + 1(2.50)

1 pie = 3 + 2.50

1 pie = 5.50

Step 2: Find the amount of money a baker makes by selling 1 pie

1 pie cost = 5.50

1 pie revenue = 10.25

1 pie profit = 4.75

Step 3: Find the amount of money a baker makes by selling 10 pies

1 pie profit = 4.75

10 pies profit = 47.5

Answer: $47.50

Hope this helps!

The lowest score that would achieve an A is 10.

To find the lowest score that would achieve an A, we need to find the score corresponding to the 7th percentile of the distribution of scores.

First, we need to find the z-score corresponding to the 7th percentile. We can use a z-table or a calculator to find this value.

The z-score corresponding to the 7th percentile is approximately -1.44. This means that a score at the 7th percentile is 1.44 standard deviations below the mean.

We can use the formula for z-score to find the raw score corresponding to this z-score:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Plugging in the values we have:

-1.44 = (x - 46) / 25

Multiplying both sides by 25:

-36 = x - 46

Adding 46 to both sides:

x = 10

Therefore, the lowest score that would achieve an A is 10.

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The amount of cashews needed to be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately is 10 pounds.

To solve this problem, we need to use the equation:

$3(20) + 6x = 4(20 + x)$

where x is the number of pounds of cashews needed.

First, we simplify the equation by multiplying:

$60 + 6x = 80 + 4x$

Then we isolate x by subtracting 4x from both sides and subtracting 60 from both sides:

$2x = 20$

Finally, we solve for x by dividing both sides by 2:

$x = 10$

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________________________________

________________________________

The decision of how to divide a whole into fractional parts and where to begin and end a number scale depends on the context and purpose.

when dividing a whole into fraction parts, the decision of how to divide it depends on the context and the specific problem being solved. For example, if a pizza needs to be divided among 4 people, it would make sense to divide it into 4 equal parts or fourths. If a recipe calls for 1/3 cup of flour, then the whole cup would be divided into 3 equal parts or thirds.

Regarding number scales, they can begin and end at different points depending on the context and purpose. For example, a temperature scale could start at 0 degrees and end at 100 degrees for Celsius, or start at 32 degrees and end at 212 degrees for Fahrenheit.

A financial scale could start at negative numbers for debts and end at positive numbers for assets. In general, number scales are designed to provide a clear and consistent way of measuring and comparing quantities in a particular context.

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The volume of the figure, which is made up of 2 rectangular prisms, would be 276 cm ³.

The figure shown is made up of two rectangular prisms which means that we can find the volume of the entire figure by finding the volumes of the rectangular prisms and then adding up these volumes to find the total volume.

Volume of the first rectangular prism:

= Length x Width x Height

= 10 x 6 x 3

= 180 cm ³

Volume of the second rectangular prism:

= Length x Width x Height

= 4 x 6 x 4

= 96 cm ³

The total volume of the figure:

= 180 + 96

= 276 cm ³

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To maximize the revenue, we need to find the maximum value of the revenue function.

The revenue function, R(x), is given by the product of the price per bolt (p) and the number of bolts sold (x thousand), which is R(x) = p * x.

Given the price function p = 82 - 26x,

we can substitute this into the revenue function:

R(x) = (82 - 26x) * x

Now, we need to find the maximum value of R(x). We'll do this by taking the derivative of R(x) with respect to x and setting it to zero:

R'(x) = d/dx[(82 - 26x) * x] R'(x) = 82 - 52x

Now, we set R'(x) = 0 and solve for x: 0 = 82 - 52x 52x = 82 x = 82 / 52 x ≈ 1.58

So, approximately 1.58 thousand (or 1580) bolts must be sold to maximize revenue in the hardware store.

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We get:

[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]

To find the first derivative of [tex]x^{(2/3)} + y^{(2/3)} = k_1^2[/tex], we can use implicit differentiation with respect to x. Taking the derivative of both sides, we get:

[tex](2/3)x^{(-1/3)} dx/dx + (2/3)y^{(-1/3)} dy/dx = 0[/tex]

Simplifying and solving for [tex]dy/dx[/tex], we get:

[tex]dy/dx = - (x/y)(y/x)^{(-2/3)} = - (x/y) (y/x)^{(2/3)}[/tex]

which can also be written as:

[tex]dy/dx = - (y/x)^{(1/3)}[/tex]

To find the first derivative of [tex]x cos(k_1 x + k_2 y) = y sin x[/tex], we can also use implicit differentiation with respect to x. Taking the derivative of both sides, we get:

[tex]cos(k_1 x + k_2 y) - x k_1 sin(k_1 x + k_2 y) = y \cos x[/tex]

Solving for y' (i.e., [tex]dy/dx[/tex]), we get:

[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]

Note that we could have also solved for x' (i.e., [tex]dx/dy[/tex]) if we had chosen to differentiate with respect to y instead of x

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Answer:

-----------------------------

The measure of the angle formed outside of circle is half the difference of major and minor arc measures.

It means the measure of angle T is:

The measure of the angle indicated in the diagram is 50 degrees.

What is Tangent ?

In geometry, the tangent is a trigonometric function that relates the opposite side and adjacent side of a right triangle. More specifically, for a given angle θ, the tangent of θ (denoted by tan θ) is defined as the ratio of the length of the opposite side to the length of the adjacent side of the right triangle containing that angle.

In the given figure, the two lines are tangent to the circle with center O. Let's call the point where the two lines intersect point P.

We know that the angle formed by a tangent line and a radius of a circle is always 90 degrees. Therefore, we can draw a radius OP from the center of the circle to point P and we know that angle POQ (where Q is the point where the radius intersects the circle) is 90 degrees.

We also know that angle OPQ is 40 degrees (as given in the diagram).

Since the sum of the angles in a triangle is 180 degrees, we can find angle OQP as follows:

angle OQP = 180 - angle OPQ - angle POQ

= 180 - 40 - 90

= 50 degrees

Therefore, the measure of the angle indicated in the diagram is 50 degrees.

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In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman

so 5 from 14 is given by :

= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]

which is :

14 x 13 x 11 = 2002

combinations of 5 from 7 is :

(9x8x7x6x5) / (5x4x3x2x1)

[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]

which is :

7 x 3= 21

so the final answer is 2002 - 21 = 1981.

Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.

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There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

Let's denote the number of $2 coins as x, the number of $1 coins as y, and the number of quarters as z.

We need to find all the possible combinations of x, y, and z that satisfy the equation:

2x + y + 0.25z = 2.50

Here's the corrected organized list of combinations:

(1, 0, 2) → $2 + $1 + $0 = $2.50

(0, 2, 2) → $0 + $2 + $0.50 = $2.50

(0, 1, 6) → $0 + $1 + $1.50 = $2.50

(0, 0, 10) → $0 + $0 + $2.50 = $2.50

There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

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The explanation of the continuous range is added below

Continuous ranges are expressed in inequality notation because they represent a set of infinitely many numbers between two endpoints.

Inequality notation allows us to describe this range using mathematical symbols to show that the values can be any number between the two endpoints, including the endpoints themselves.

For example, a continuous range might be described as "all real numbers between 0 and 1, including 0 and 1".

This can be expressed in inequality notation as 0 ≤ x ≤ 1, where x is a real number.

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You must begin to brake 234643.2 feet from the intersection.

In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).

Based on the information provided above, the speed of this car is represented by the following equation;

s = √(30fd)

Where:

By substituting the given parameters, we have:

20 = √(30(0.3)d)

400 = 9d

d = 400/9

d = 44.44

Conversion:

1 mile = 5,280 feet.

44.44 miles = 234643.2 feet.

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So, the final answer is:

(1/2)(-√(4 - x^2) / x) + C. To evaluate the integral ∫dx / (x^2√(4-x^2)), we will use the trigonometric substitution x = 2sin(θ). This substitution is chosen because it simplifies the expression under the square root, as 4 - x^2 becomes 4 - 4sin^2(θ) which can be factored into 4cos^2(θ).

Now, we need to find dx in terms of dθ. Differentiating x with respect to θ, we get:

dx/dθ = 2cos(θ) => dx = 2cos(θ)dθ

Substituting x = 2sin(θ) and dx = 2cos(θ)dθ into the integral:

∫(2cos(θ)dθ) / ((2sin(θ))^2√(4(1-sin^2(θ))))
= ∫(2cos(θ)dθ) / (4sin^2(θ)√(4cos^2(θ)))

Simplifying the integral, we get:

= (1/2) ∫(cos(θ)dθ) / (sin^2(θ)cos(θ))
= (1/2) ∫dθ / sin^2(θ)

Now, use the identity csc^2(θ) = 1/sin^2(θ) and integrate:

= (1/2) ∫csc^2(θ) dθ
= (1/2)(-cot(θ)) + C

To find cot(θ), we draw a right triangle with the opposite side x, the adjacent side √(4 - x^2), and the hypotenuse 2:

cot(θ) = adjacent / opposite = √(4 - x^2) / x

So, the final answer is:

(1/2)(-√(4 - x^2) / x) + C

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The value of p is x-5/48x³ On the interval [−4,4] we know that x and x² are orthogonal.

The p-value, under the assumption that the null hypothesis is true, is the likelihood of receiving findings from a statistical hypothesis test that are at least as severe as the observed results. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.

P-value is frequently employed by government organisations to increase the credibility of their research or findings. The U.S. Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero. The Census Bureau has also established guidelines that specify which p-values are acceptable.

<p, x> = [tex]\int\limits^2_{-2} {x(x+ax^2+bx^3)} \, dx[/tex]

[tex]= \int\limits^2_{-2} {x^2} \, dx +a\int\limits^2_{-2} {x^3} \, dx +b\int\limits^2_{-2} {x^4} \, dx[/tex]

Right so the middle integral is zero already since you said x and x² are orthogonal,

= 2([tex]\int\limits^2_0 {x^2} \, dx +b\int\limits^2_0 {x^4} \, dx[/tex])

[tex]=2(\frac{x^3}{3} +\frac{bx^5}{5} )^2_0[/tex]

b = -5/12.

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The interquartile range of 58,55,54,61,56,54,61,55,53,53 is 6.

To find the interquartile range (IQR), we first need to find the first and third quartiles of the data set. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set. The IQR is then the difference between Q3 and Q1.

To find Q1 and Q3, we first need to put the data set in order from lowest to highest:

53, 53, 54, 54, 55, 55, 56, 58, 61, 61

The median of the entire data set is the average of the two middle numbers, which in this case is (55 + 56) / 2 = 55.5.

To find Q1, we need to find the median of the lower half of the data set, which includes the numbers 53, 53, 54, 54, 55. The median of this lower half is the average of the two middle numbers, which is (53 + 54) / 2 = 53.5.

To find Q3, we need to find the median of the upper half of the data set, which includes the numbers 56, 58, 61, 61. The median of this upper half is the average of the two middle numbers, which is (58 + 61) / 2 = 59.5.

Now that we have Q1 and Q3, we can calculate the IQR as:

IQR = Q3 - Q1 = 59.5 - 53.5 = 6

Therefore, the interquartile range of the given data set is 6.

The IQR is a useful measure of variability because it is not influenced by outliers or extreme values in the data set, unlike the range or standard deviation. The IQR gives us an idea of the spread of the "middle" 50% of the data, which can help us understand the distribution of the data and identify any potential skewness or outliers.

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The Unique or Many for each description by placing a check or X in the appropriate box is given below.

We are given that;

Measurements=  30°, 60°, 90°

Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4.

Now,

If three angle measures are given, and they add up to 180 degrees, then there are infinitely many similar triangles with those angle measures, but they differ in size. This is called the AAA (angle-angle-angle) similarity criterion.

If two angles and a non-included side are given, then there may be zero, one, or two possible triangles with those measurements, depending on the length of the side and the position of the angles. This is called the AAS (angle-angle-side) or SSA (side-side-angle) criterion.

Using criteria, we can fill in the table as follows:

Conditions | Unique | Many Side lengths 3 cm, 6 cm, 7 cm | ✓ | Angle measures 30°, 60°, 90° | | ✓ Angle measures 35º, 35°, 110° | | ✓ Side lengths 5 cm, 5 cm, 5 cm | ✓ | Side lengths 3 in and 4 in with an included 95° angle | ✓ |

Therefore, by the angle the answer will be given.

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The standard deviation of the shoe size data for the math class is 1.5. Standard deviation is a measure of how spread out the data is, and it is calculated by taking the square root of the variance.

Calculate the difference between each shoe size and the mean (7.5)

if the shoe sizes in the class are 6, 7, 8, 9, 10

The differences from the mean are (-1.5), (-0.5), 0.5, 1.5, 2.5

Square each difference

(-1.5)² = 2.25

(-0.5)² = 0.25

0.5² = 0.25

1.5² = 2.25

2.5² = 6.25

Add up all the squared differences

2.25 + 0.25 + 0.25 + 2.25 + 6.25 = 11.25

Divide the sum of squared differences by the number of shoe sizes (n):

11.25 / 5 = 2.25

Take the square root of the result to get the standard deviation

√(2.25) = 1.5

Therefore, the standard deviation of the shoe size data for the math class is 1.5.

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In a school, a teacher surveys 50 randomly selected 6th grade students and 50 randomly selected 7th grade students. c) More seventh-graders than sixth-graders enjoy horror films.

The first statement is false as the total 6th graders which like horror and comedy movie is 19 + 9 = 28 students which is more than 6th graders who like action movies which is 22, hence the first statement is false. this is interpreted from given data set.

The second statement is also false as it says that 6th graders prefer comedy films to action films, whereas 7th graders prefer action films but from the data given, it can be seen that the number of 6th graders who like comedy films is same as the number of 7th graders who like action movies which is 19, hence statement is false.

The third statement is true as 6th graders who like horror movies is 9 while 7th graders who like horror movies is 14 and hence, the statement is true.

Fourth statement is also false as 17, 7th graders like comedy movies in contrast to 14, 7th graders who like horror movies.

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Correct question:

A teacher conducts a survey of 50 randomly selected 6th grade and 50 randomly selected 7th grade students in a school. The survey asks the students about the type of movies they like to watch. The table shows the number of students who selected each type of movie. Select the correct statement.

a) 6th graders like action movies more than horror and comedy movies.

b) 6th graders like comedy movies more than 7th graders like action movies.

c) More 7th graders than 6th graders like horror movies.

d) 7th graders like horror movies more than comedy movies.

The estimate from direct proportionality is higher than the prediction from KLEIBER's law.

a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.

b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.

The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.

This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.

Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.

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We can use the Pythagorean theorem to find the distance between the game store and the skate park.

Let's call the distance between the game store and the skate park "d". Then we have:

d^2 = (distance between school and game store)^2 + (distance between school and skate park)^2

d^2 = 7.3^2 + 8.7^2

d^2 = 106.18

d ≈ 10.3

Therefore, the game store is approximately 10.3 kilometers from the skate park.

Answer:

3x

Step-by-step explanation

Answer:

That's the correct order.

Step-by-step explanation:

2x+20+5=55

2x+25=55

2x=30

x=15

Answer:

B

Step-by-step explanation:

3x 5

_ + _

4 2

The amount of compound remaining from a 75-ounce sample after three weeks is 0.52 oz. The correct option is c) 0.52 oz.

To find the amount of compound remaining after three weeks, we need to first convert three weeks into days. Since one week is equal to seven days, three weeks is equal to 21 days. The exponential decay function is given by: N = [tex]N0e^(-kt)[/tex]

Where N is the amount of compound remaining after time t, N0 is the initial amount of compound, k is the decay constant, and t is time. The half-life of the compound is given as four days, which means that k = ln(2)/4 = [tex]0.1733 day^-1.[/tex]

Substituting the values, we get: N =[tex]75e^(-0.1733*21[/tex]. N = 0.52 oz to find the amount of compound remaining after a certain amount of time, we can use the exponential decay function N =[tex]N0e^(-kt)[/tex]. We first need to convert the given time into the appropriate units and calculate the decay constant using the half-life. We can substitute the values to find the answer.

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The option that represents the resulting transformation is: Option C

A reflection over line is defined as a transformation in which each point of the original figure which is also called the pre-image possesses an image that is the essentially the same distance from the reflection line as the original point, but then is on the opposite side of the line. In a reflection, the image is the same size and shape as the pre-image.

Now, looking at the letter Q, when we reflect it once, it should be the mirror image but when reflect it the second time about same line, it becomes exactly the original copy.

Thus, we can conclude that Option C represents the resulting transformation.

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