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Answer:

Step-by-step explanation:

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Using a two-way table and conditional percentages, the depression datanle available in the Data section below should be used.

The depression datanle should be analyzed using a two-way table and conditional percentages, to answer the research question: "Which of the drugs (if either) was more successful in preventing the recurrence of depression relative to the placebo?"

The table should show the number of patients who took the drugs and those who took the placebo, and the number of patients who had a recurrence of depression and those who didn't have a recurrence of depression after taking the drugs or placebo, respectively.Then, conditional percentages should be calculated for each group of patients who took the drugs and those who took the placebo.

These conditional percentages should be calculated by dividing the number of patients who didn't have a recurrence of depression by the total number of patients who took the drugs or placebo for each group. Finally, the percentage difference should be calculated between the two conditional percentages for the drug and placebo groups. The group with the highest percentage difference is the one that was more successful in preventing the recurrence of depression relative to the placebo.

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The 85% confidence interval that the true mean number of words a third grader can read per minute is between 30.131 and 30.869.

To create a confidence interval for the mean number of words a third grader can read per minute, an educational psychologist wishes to know the mean number of words a third grader can read per minute. She intends to produce an estimate at an 85% level of confidence.

For a sample of 146 third graders, the mean words per minute read was 30.5. Assume a population standard deviation of 3.1.

To create a confidence interval, the following formula can be used:

µ±z_α/2*σ/√n

Here, we are given the following details:

Sample size: n = 146

Mean: µ = 30.5

Population standard deviation: σ = 3.1

Level of confidence: α = 1 - 0.85 = 0.15

We need to determine the critical value of z_α/2.

α/2 ⇒ 0.15/2 ⇒ 0.075

Using a standard normal distribution table, we find that the value of z_0.075 is 1.44.

Confidence Interval: µ ± z_α/2*σ/√n

⇒ 30.5 ± 1.44 × (3.1/√146)

⇒ 30.5 ± 0.369

Thus, the confidence interval for the mean number of words a third grader can read per minute is (30.131, 30.869).

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Accοrding tο the percentage calculatiοn, 45% οf 60 is 27. Thus, D is the cοrrect οptiοn.

A number οr ratiο that can be expressed as a fractiοn οf 100 is referred tο as a percentage in mathematics. If we need tο calculate a percentage οf a number, we shοuld divide it by its entirety and then multiply it by 100. The percentage therefοre refers tο a part per hundred. Per 100 is what the wοrd percent means. The letter "%" stands fοr it.

A part οf a whοle expressed in hundredths,

Tο find 45% οf 60, we can multiply 60 by 0.45:

45% οf 60 = 0.45 × 60 = 27

Therefοre, 45% οf 60 is 27. Answer: 27

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For example, to achieve a sum of $100,000 in 10 years with an initial investment of $10,000, the annual rate of return r required would be:

r =[tex](1/10) ln(100,000/10,000) = 0.069.[/tex]

a) The differential equation which models the rate of change of the sum with respect to time (t) is given by:

dS/dt = rS

where S is the sum and r is the annual rate of return.

b) The formula for the sum can be obtained by solving the differential equation:

S = S0ert

where S0 is the initial investment.

c) To determine the value of r which will provide the desired sum in a given amount of time, we can rearrange the equation above to give:

[tex]r = (1/t) ln(S/S0)[/tex]

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Answer: You cannot

Step-by-step explanation:

5/34 is considered a proper fraction, it is impossible to convert it into an improper fraction.

The slant height of given square pyramid is √45 inch.

A square pyramid is a geometric solid that has a square base and four triangular faces that meet at a common vertex. It belongs to the family of pyramids, which are three-dimensional shapes that have a palled the apex.

With the help of the Pythagoras theorem, we can find out the slant height of pyramid using the formula:

[tex]s^{2} =H^{2} +(\frac{a}{2} )^{2}[/tex]

Here, height of square pyramid is H.

take an equilateral triangle, where a triangle has all sides are equal.

so, the height of the triangle (h) = [tex]\sqrt{a^{2} + (\frac{a}{2}) ^{2} }[/tex] = [tex]\sqrt{6^{2} + (\frac{6}{2}) ^{2} }[/tex] = √45 inch

the height of the square pyramid (H) is:

[tex]H^{2} + (\frac{a}{2}) ^{2} } = h^{2}[/tex]

[tex]H^{2} = (\sqrt{45} )^{2} - (\frac{6}{2}) ^{2} }[/tex]

H = 6 inch

The slant height of pyramid using the formula:

[tex]s^{2} =6^{2} +(\frac{6}{2} )^{2}[/tex] = 36 + 9 = 45

s = √45 inch

Therefore, the slant height of given square pyramid is √45 inch.

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The set of integers that represents a debit of $10 and a credit of $6 would be  option 1. {-10, 6}.

An integer is a mathematical object that represents a whole number, either positive, negative or zero, without any decimal or fractional part. Integers include the natural numbers (1, 2, 3, ...), their negative counterparts (-1, -2, -3, ...) and the number zero (0).

In this case, a debit of $10 means that $10 has been spent or taken out of the account, which is represented by the negative integer -10. A credit of $6 means that $6 has been added to the account, which is represented by the positive integer 6.

Therefore, the set {-10, 6} represents a debit of $10 and a credit of $6.

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The complete question is:

Which set of integers represents a debit of $10 on a number line, and the credit of $6?

Answer:

enjoy your weekend bud , both answers and solutions ares given , if you didn't understand anything lmk with a message and ill be happy to explain

Hence The solution set is {x | x ∈ ℝ, x ≈ 2.91 or x ≈ -0.51}.

In algebra Any equation that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a is not equal to zero is known as a quadratic equation.

How do you determine a set of  solution?

first of all you must enter each value from the domain into the equation to obtain the corresponding range values before you can determine the solution set of an equation with a specified domain. From these values, make ordered pairs, and then write them as a set.

The given quadratic equation is ,

25 [tex]x^2[/tex]= -60 x +37

or 25 [tex]x^2[/tex]+60 x - 37=0

to compare  a quadratic equation of the form of [tex]ax^2 + bx + c = 0,[/tex]

than  we get:

a = 25, b = -60, c = -37

We know that the quadratic formula is

x=[tex]\frac{-b ± \sqrt{(b^2 - 4ac)})}{2a}[/tex]

These values are substitute the quadratic formula than we get,

[tex]x=\frac{ 60± \sqrt{(60^2 - 4*25*37)})}{2*25}\\x=\frac{ 60± \sqrt{(3600+3700)})}{2*25}\\x=\frac{ 60± \sqrt{7300)})}{50}\\\\x=\frac{ 60± 85.38}{50}\\\\x=\frac{ 60+ 85.38}{50} or x=\frac{ 60-85.38}{50}\\x=2.91 or x= -0.51\\[/tex]

The solution set is {x | x ∈ ℝ, x ≈ 2.91 or x ≈ -0.51}.

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As the density of Mercury is higher than that of both Copper and Zinc, so both the new & old penny will float on mercury.

By dividing the object's mass by its volume, we may determine the density of metal.

Mass/volume equals density.

For ex, the object would have a density of 0.284 per cubic inch if its mass were 7.952 pounds and its volume were 28 cubic inches.

Now here in the given question,

Density of copper = 8.8g/cm³

Density of zinc = 7.2g/cm³

Here, both the densities are lesser than that of mercury.

Hence, both the metal pennies will float when dropped into a beaker of mercury.

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Answer:

The missing information for the proof is:

- Point D' will coincide with point D, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).

- Point C" will coincide with point C, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).

- Angle ADC will be taken onto angle ACD, since they are corresponding parts under the same reflection. Therefore, they are congruent.

All pοssible angles (in degrees) with a cοsine value οf 0.74 are:

42.47° + 360n and 137.53° + 360n, where n is an integer.

Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It is used tο sοlve prοblems in variοus fields, including physics, engineering, and astrοnοmy.

The cοsine functiοn is pοsitive in the first and fοurth quadrants, sο we can restrict οur attentiοn tο angles between 0 and 360 degrees in thοse quadrants.

Tο find the angles with cοsine 0.74, we can use the inverse cοsine functiοn (alsο called arccοsine οr cοs⁻¹) οn a calculatοr. In degrees, we have:

cοs⁻¹(0.74) ≈ 42.47° and cοs⁻¹(-0.74) ≈ 137.53°

The cοsine functiοn has a periοd οf 360 degrees, sο we can add οr subtract multiples οf 360 degrees tο these angles tο get all pοssible angles with cοsine 0.74. In general, the angles are given by:

θ = cοs⁻¹(0.74) + 360n and θ = cοs⁻¹(-0.74) + 360n, where n is an integer.

Sο, all pοssible angles (in degrees) with a cοsine value οf 0.74 are:

42.47° + 360n and 137.53° + 360n, where n is an integer.

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The solution is x = 8.

The solution to the equation 2ln(x) = ln(4) + ln(16) should be determined, taking into account any extraneous solutions. The steps to accomplish this are as follows:2ln(x) = ln(4) + ln(16)ln(x^2) = ln(4*16)ln(x^2) = ln(64)By taking the exponential of both sides, this expression can be resolved.x^2 = 64x = ±8Since the natural logarithm is only defined for positive numbers, only the positive value of x is taken into account. Therefore, the solution is x = 8.The process of checking for extraneous solutions involves substituting the answer obtained into the original equation and evaluating it to see whether it is accurate or not.2ln(8) = ln(4) + ln(16)The above equation can be simplified to become: ln(64) = ln(64)The answer is consistent. As a result, the solution is accurate and does not include any extraneous values. The solution is x = 8.

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Using the laws of logarithms, the value of x is 1024

We are given the equations:

log x = 1,000,000,000

log₂ x = 10

Using the definition of logarithms, we know that log x = y is equivalent to x = 10^y. Therefore, we can rewrite the given equations as:

x = 10^1,000,000,000

x = 2^10

We can use a calculator to find that 10^1,000,000,000 is an extremely large number (a "googol" is a 1 followed by 100 zeroes, and this number is much larger than a googol). However, we can simplify the expression x = 2^10 by calculating 2^10, which is 1024.

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The ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

We can use the Pythagorean theorem to determine if the ladder will reach 7 feet high. Let's let x be the height that the ladder reaches, as shown in the diagram below:

According to the Pythagorean theorem, we have:

[tex]$\begin{align*}x^2 + 6^2 &= 10^2 &= 100 - 36 &= 64 \x &= \sqrt{64} \x &= 8\end{align*}[/tex]

Therefore, the ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.

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The answer is 3.18.

The given equation is sin(4x)cos(6x) − cos(4x)sin(6x) = -0.9. To find the smallest positive solution, we can use the following identities: sin(A + B) = sinAcosB + cosAsinBcos(A + B) = cosAcosB - sinAsinBWe can rewrite the given equation using these identities as follows:sin(4x + 6x) = -0.9sin(10x) = -0.9sinx = -0.09We need to solve for the smallest positive value of x. To do this, we can find the value of x in the interval [0, 2π] such that sinx = -0.09.Using a calculator, we get:x ≈ 3.176 rad ≈ 181.97°The smallest positive solution in degrees is 181.97°. To get the answer to 2 decimal places, we can round off the value of x to 2 decimal places, giving:smallest positive solution ≈ 3.18 rad (to 2 decimal places) or ≈ 181.97° (to 2 decimal places)Thus, the answer is 3.18.

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You can use 3599 red tiles. If you have used 121 blue tiles.

To begin, find out how many total tiles are in the square by squaring the number of tiles along one side. Then subtract the number of tiles in the two diagonals of the square, which are all blue, to get the number of red tiles. Let us try to solve the problem. Given that the tiles are square and congruent, they must have identical dimensions. Let us assume that the length of one side of the square tile is x.

Therefore, the length of each side of the square can be determined by dividing the number of tiles by the length of the side of the square. The total number of tiles in the square can be calculated by squaring the number of tiles along one side. Consider the following equation: Let x be the length of each side of the square tile.

Then, the total number of tiles that make up the square can be determined using the following equation:

Total number of tiles in square = [tex]x^2[/tex]

We know that all the tiles are congruent squares, except those that are blue, which are located on the two diagonals. This means that there are 2 diagonals of blue tiles, and the remaining tiles are red. To determine the number of blue tiles in the two diagonals, use the following formula:

Length of diagonal = √2 x side length

Since the diagonals pass through opposite corners of the square, they must be equal in length. The total number of blue tiles, 121, is equal to twice the number of blue tiles in one diagonal. Use the following formula to determine the number of blue tiles in one diagonal: 121 / 2 = 60.5 The answer is rounded up to 61.

Using the Pythagorean Theorem, the length of the diagonal of each blue tile can be calculated. The following equation can be used: Side of square = x

Length of diagonal of one blue tile = x√2

The number of blue tiles in one diagonal is the length of the diagonal divided by the length of the diagonal of one blue tile. This can be expressed as a formula:x / (x√2) = number of blue tiles in one diagonal

Simplify the formula:

x / (x√2) = number of blue tiles in one diagonal

Multiply both sides by √2 and simplify:(√2 / 2) = number of blue tiles in one diagonal

This indicates that each diagonal has a total of 61 blue tiles. Because the two diagonals have a total of 122 blue tiles, the number of red tiles is equal to the total number of tiles minus the total number of blue tiles. The following equation can be used to calculate the number of red tiles:([tex]x^2[/tex]) - 122 = number of red tiles

Substitute 61 for x: [tex](61)^2[/tex] - 122 = 3721 - 122 = 3599.

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0.55 = 55% probability of experiencing neither of the side effects.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

Venn diagrams are diagrams used to visually describe sets, relationships between sets, and operations carried out on them. John Venn (1834–1883) invented the Venn diagram, which makes use of circles (overlapping, intersecting, and non–intersecting) to show the relationship between sets. A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it.

The "or probability" is given by:

P(A∪B)=P(A)+P(B)-P(A∩B)

P(N)=0.2 , P(D)=0.4 and P(N∩D)=0.15

The "at least one" probability is:

0.2+0.4-0.15=0.45

Hence, the "neither" probability is:

1-0.45=0.55

0.55 = 55% probability of experiencing neither of the side effects.

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1. Find the length of DE. 2. Calculate the length of BD. 3. Add BD and EC to get AD.

To find the length of AD, the following steps can be followed:

1. To find the length of DE, the Pythagorean theorem can be used. It states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the triangle is DEBC.

Therefore, DE2 = (12)2 + (10)2 = 144 + 100 = 244.

Taking the square root of 244 gives the length of DE as 15.722.

2. The length of BD can then be calculated as 12, since it is already given in the figure.

3. To find the length of AD, the lengths of BD and EC can be added together. That is, AD = BD + EC = 12 + 10 = 22.

Therefore, the length of AD is 22.

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the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it is approximately 0.2679, or 26.79%.

To find the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it, we need to know how many table-tennis balls with "1" and "B" there are and the total number of table-tennis balls.

The probability of Steven selecting a "1" on his first pick is:

P(1 on first pick) = 3/8

The probability of Steven selecting a "B" on his second pick, given that he has already selected a "1", is:

P(B on second pick | 1 on first pick) = 5/7

The probability of Steven selecting a "1" and a "B" in sequence is the product of these two probabilities:

P(1 and B) = P(1 on first pick) * P(B on second pick | 1 on first pick)

= (3/8) * (5/7)

= 0.267857

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The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is [tex]V = \pi r^2h,[/tex] where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by [tex]= \pi r^2h.[/tex]

The volume of the cone is given by V_cone = [tex](1/3)\pi r^2h.[/tex]

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = [tex]\pi r^2h[/tex] and V_cone = [tex](1/3)\pi r^2h.[/tex]

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = [tex]((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3[/tex]

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

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The correct answer is "56."

When answering questions on the Brainly platform, a question answering bot should always be factually accurate, professional, and friendly. Additionally, they should be concise and avoid providing extraneous amounts of detail. They should also not ignore any typos or irrelevant parts of the question, and they should not repeat the question in their answer. Instead, they should use their own words to provide a step-by-step explanation of how to solve the problem.In this case, we are given information about two different diet plans and asked to determine which one is more likely to result in a monthly weight loss of over 7 kg. We are also given information about the length of human pregnancies and asked to estimate how many out of 791 randomly selected newborn babies this month in UAE would be premature.Diet Plan A advertises an average monthly weight loss of 4.5 kg with a standard deviation of 1.4 kg, while Diet Plan B claims an average monthly weight loss of 5.5 kg with a standard deviation of 0.84 kg. To determine which diet plan is more likely to result in a monthly weight loss of over 7 kg, we can use z-scores and the normal distribution.

We can calculate the z-score for Diet Plan A as follows:z = (7 - 4.5) / 1.4 = 1.79We can calculate the z-score for Diet Plan B as follows:z = (7 - 5.5) / 0.84 = 1.79Since both z-scores are the same, both diet plans are equally likely to result in a monthly weight loss of over 7 kg. Therefore, the correct answer is "Both plans are the same."To estimate how many out of 791 randomly selected newborn babies this month in UAE would be premature, we can use z-scores and the normal distribution. We know that births that occur before 245 days are considered premature, and we know that the length of human pregnancies is normally distributed with a mean of 267 days and a standard deviation of 15 days. We can calculate the z-score for a pregnancy length of 245 days as follows:z = (245 - 267) / 15 = -1.47We can use a z-score table to find that the area to the left of a z-score of -1.47 is 0.0708. Therefore, the proportion of pregnancies that result in premature births is approximately 0.0708. To estimate the number of newborn babies out of 791 that would be premature, we can multiply 0.0708 by 791:791 × 0.0708 ≈ 56Therefore, we would expect about 56 out of 791 randomly selected newborn babies this month in UAE to be premature. We should round our answer to the nearest whole number, which is 56. Therefore, the correct answer is "56."

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The manager's claim that fewer than 750 damaged computer displays are produced daily is accurate, thus yes. A hypothesis theory can help us with this.

We need to conduct a hypothesis test to establish whether the manager's assertion is likely to be accurate. The null hypothesis, labelled H0, is that the fraction of damaged computer displays manufactured each day is 750/10,000 = 0.075. The proportion being less than 0.075 is the alternative hypothesis, labelled Ha.

The test statistic, which gauges how far the sample proportion deviates from the null hypothesis proportion assuming the null hypothesis is true, can be calculated using the sample data. Here is how the test statistic is computed:

p is the sample proportion of faulty, and z = (p - p0) / (p0(1-p0)/n) computer monitors, n is the sample size, and p0 is the null hypothesis proportion.

In this instance, n = 290, p = 9/290 = 0.031, and p0 = 0.075.

These variables are plugged in, and the result is: z = (0.031 - 0.075) / (0.075(1-0.075)/290) -4.50

The test statistic reveals how far the sample percentage deviates from the null hypothesis proportion by how many standard deviations. The test statistic's absolute value should be higher if there is more evidence arguing against the null hypothesis.

The likelihood of seeing a test statistic that is as extreme or more extreme than the one we computed assuming the null hypothesis is true is known as the p-value, and it may be determined using a conventional normal distribution. As the alternative hypothesis in this situation is that, we are interested in the left tail of the distribution. The proportion is lower than the proportion under the null hypothesis.

The p-value, which can be calculated or calculated using statistical tools, is about 0.000003. Due to the extremely low p-value, it is extremely unlikely that the sample proportion will be as extreme as or more extreme than 0.031, if the null hypothesis is correct.

The maximum probability of rejecting the null hypothesis when it is true is called the significance level, and it is typically used to compare the p-value to. The usual ranges for are 0.05 and 0.01. We reject the null hypothesis and come to the conclusion that there is evidence against it if the p-value is less than. If not, we are unable to reject the null hypothesis and come to the conclusion that there is insufficient evidence. to dismiss it.

If we apply = 0.05 in this instance, the p-value is significantly lower than. As a result, we reject the null hypothesis and come to the conclusion that there is evidence to support a daily production rate of fewer than 0.075 defective computer displays. The manager's assertion that fewer than 750 damaged computer displays are manufactured each day is in conflict with this.

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Therefore , the solution of the given problem of inequality comes out to be three individuals are listed as not purchasing either a dress or a coat.

Despite the fact that algebra lacks a comparable symbol, its distinction can be expressed by a pair or collection for numbers. Equilibrium is typically followed by equity. The ongoing disparity in norms is what causes inequality. Disparity and fairness are not synonymous. Even though the components are typically not connected or situated closely together, that was our most popular symbol.

Here,

The 120 customers who frequent the store are represented by the rectangle in the Venn diagram.

The "C" circle stands for those who purchase a coat, and the "D" circle for those who purchase a frock.

The individuals who purchase both a dress and a coat are represented by the area inside the overlap of the two circles. 19 less the number of individuals who purchase both a coat and a dress equals the number of people who only purchase a coat. 14 less the number of people who purchase both a parka and a dress equals the number of people who only purchase a dress.

Three individuals are listed as not purchasing either a dress or a coat.

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Answer:

4.5 m^3

Step-by-step explanation:

Volume = length × breadth × height

= 5m × 1.2m ×(75÷100)m

= 4.5 m^3

The values that complete the equations so that each statement is true are presented as follows;

No solution

6 - 3 + 4·x + 1 = 4·x + 4

One solution

6 - 3 + 4·x + 1 = 3·x + 3

Infinitely many solutions

6 - 3 + 4·x + 1 = 4·x + 4

A linear equation is the equation of a straight line. The degree of a linear equation is the first degree, therefore, the highest power of the variables in a linear equation is 1.

The equation 6 - 3 + 4·x + 1, can be simplified as follows;

6 - 3 + 4·x + 1 = 4 + 4·x

A system of linear equations have no solutions when they have the same slope and different y-intercept.

The slope of the equation, y = 4 + 4·x is 4, and the y-intercept of the equation is 4, therefore the equation will have no solution, when we have;

The slope (the coefficient of x) of the equation on the right hand side is 4, and the y-intercept, the constant term differs from 4

Therefore the equation has no solution, is of the form;

When those the equation; 6 - 3 + 4·x + 1 = 4·x + 4

A system of linear equation has one solution when they have different slopes, therefore, the system will have one solution when we have;

6 - 3 + 4·x + 1 = 4·x + 4 = 3·x + 3

A system of equations have infinitely many solutions when the slope and the y-intercept on the left and right hand side of the equation are the same, therefore, we get;

The equation will have infinitely many solutions when the equations are;

6 - 3 + 4·x + 1 = 4·x + 4

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Answer: Monomial

!!Not 100% sure!!

Answer: The answer is Monomial because the expression, 2x is 1 term.

The solution of the equation is as follows:

[tex]\frac{8^{x} }{2^{y} } = 2^{12}[/tex]

Therefore, the answer is A.

The equation 3x - y  = 12. Let's find the value of [tex]\frac{8^{x} }{2^{y} }[/tex] as follows:

Let's apply the exponential law to solve the expression as follows:

Therefore, when dividing exponential values with the same base, we have to subtract the exponents.

Hence,

[tex]\frac{a^{x} }{a^{y} } = a^{x-y}[/tex]

Therefore,

[tex]8^{x} = 2^{3x}[/tex]

Hence,

[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} }[/tex]

Applying the law,

[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y}[/tex]

Using substitution,

3x - y = 12

Therefore,

[tex]\frac{8^{x} }{2^{y} } = \frac{2^{3x} }{2^{y} } = 2^{3x - y} = 2^{12}[/tex]

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