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Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

Answer:

The answer is A

Step-by-step explanation:

Just pin point each coordinate in order and connect the dots, you will get line A

Answer:

Below

Step-by-step explanation:

20 bags each 2 ft^3 = 40 ft^3

3 inches is .25 ft    

40 ft^3 / .25 ft = 160 ft^2   can be covered 3 inches deep .

L X W   has to equal 160 ft^2

Answer: 28 degrees

Step-by-step explanation:

Since angle KJL = LJM then that means angle 7x=3x+16

First we need to solve for x

7x=3x+16

4x=16

x=4

now we can input it into either equation to solve for the angle KJL

7(4)= 28 so the angle is 28 degrees

The cost to sign up for kick boxing lessons was $1.

To solve this problem, you can set up a system of linear equations to represent the given information. Let "x" represent the cost of each lesson.

Andrew paid for 5 lessons, so the total cost for his lessons was 5x.

Kara paid for 10 lessons, so the total cost for her lessons was 10x.

The total cost for both of their lessons was $113 + $188 = $301.

So, the equation for the total cost of their lessons is 5x + 10x = $301.

Combining like terms, we get 15x = $301.

Dividing both sides by 15, we get x = $20.

This means that each lesson costs $20.

To find the cost of the one-time fee to sign up, we can subtract the cost of the lessons from the total cost. The cost of the lessons was 15x = 15 * $20 = $300.

So, the cost of the one-time fee was $301 - $300 = $1.

Therefore, the cost to sign up for kick boxing lessons was $1.

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Answer:

9/2 or it can also be 4½ if not wrong.

also 4.5

Answer: x = 4.5

Step-by-step explanation:

that or 9/2 or 4 1/2 !

Answer:

Answer is in attached photo. (B)

Step-by-step explanation:

The solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:

1) Substitution Method

2) Elimination Method

Answer:

The answer is D. 393ft

Step-by-step explanation:

So if you do 62.5•2=125

Then you do 125•3.14=392.5

After that then you round 392.5 and you get 393

theres your answer.

The answer is D. 393ft is the minimum length of fencing they need to buy.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

here, we have,

radius= 62.5

So if you do 62.5•2=125

Then you do 125•3.14=392.5

After that then you round 392.5 and you get 393

hence, The answer is D. 393ft is the minimum length of fencing they need to buy.

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Answer:

$1522

Step-by-step explanation:

M = 7 + 3*J

M = 7 + 3*505

M = 7 + 1515

M = 1522

There are 2700 ways in which the teacher can select 2 students from each of the three clubs while ensuring they are different from students in other clubs.

To calculate the number of ways the teacher can select 2 students from each club while ensuring they are different from students in other clubs, we need to consider the combinations within each club and then multiply those combinations together.

Let's calculate the combinations within each club first: Club 1: 2 students selected from 10 students. Combination within Club 1: C(10, 2) = 45, Club 2: 2 students selected from 4 students. Combination within Club 2: C(4, 2) = 6. Club 3: 2 students selected from 5 students. Combination within Club 3: C(5, 2) = 10

To find the total number of ways, we multiply the combinations from each club: Total combinations = Combination within Club 1 * Combination within Club 2 * Combination within Club 3, Total combinations = 45 * 6 * 10 = 2700. Therefore, there are 2700 ways in which the teacher can select 2 students from each of the three clubs while ensuring they are different from students in other clubs.

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The radius of a sphere made of Neptunium-237 having a critical mass of about 60 kg and density of 19.5 g/cm3 is about 10.7 cm.

Neptunium-237 is a fissionable material that has a density of 19.5 g/cm³. The critical mass of this material is the minimum amount that must be brought together to initiate a nuclear chain reaction. In this case, the critical mass of Neptunium-237 is approximately 60.0 kg. We need to determine the radius of a sphere made of this material that has a critical mass.

To solve this problem, we first have to convert the density to kg/m³.19.5 g/cm³ x 1000 kg/m³ / 1 g/cm³ = 19500 kg/m³The formula for the volume of a sphere is V = 4/3πr³.To find the radius, we have to rearrange the formula to r³ = V x 3/4πr³ = m / p, where m is the mass and p is the density. r³ = (60.0 kg) / (19500 kg/m³) = 0.00308 m³r = (0.00308 m³ × 3 / 4π)1/3 = 0.107 m. Therefore, the radius of the sphere made of Neptunium-237 having a critical mass of about 60 kg and density of 19.5 g/cm³ is about 10.7 cm.

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Answer:

The volume is 1 1/15 yards^3

Step-by-step explanation:

For the volume of a rectangular prism, you use this formula: L*W*H.

In this case, we're given 2/3, 4/5, and 2.

All you have to do here is 2/3 times 2 first, and you get 4/3.

But, we're not done yet.

We also have 4/5, so we also have to multiply 4/3 by 4/5, which gives you 16/15.

It says that we can do a proper fraction or mixed number, so the answer is 1  and 1/15, or 1 1/15.

The probability of choosing two dimes consecutively without replacement is 0.196.

i.e

P (both dimes) = 0.196

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The total number of coins.

= 4 quarters + 18 dimes + 10 nickels + 8 pennies.

= 40

The probability of choosing a dime.

= 18/40

The probability of choosing a dime without replacing the first dime.

= 17/39

The probability of choosing two dimes.

= 18/40 x 17/39

= 306 / 1560

= 0.196

Thus,

P(both dimes) = 0.196

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We can see that:

1. Given

2. Definition of supplementary angles

3. Substitution Property of Equality

4. Subtraction Property of Equality

5. If two angles have the same measure, then they are congruent.

In mathematics, an angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians, and can be represented symbolically using the Greek letter theta (θ). An angle can be acute, right, obtuse, or reflex, depending on the degree of rotation. It can also be formed by the intersection of two lines or by the rotation of a line about a point.

Angles are commonly used in geometry and trigonometry to measure and describe the relationships between shapes and figures.

We see here that the above answers are correct.

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The volume of the material used to make the insulated collar is 1060.56 cubic inches.

The volume of the material used to make the insulated collar can be determined as follows.

1. Identify the given dimensions:

inner radius (r) = 3 inches,

outer radius (R) = 5 inches, and

height (h) = 21 inches.

2. Use the formula for the volume of a cylinder:

V = πr^2h.

3. Calculate the volume of the outer cylinder with radius R:

V_outer = πR^2h = 3.14 * (5^2) * 21 ≈ 1653.3 cubic inches.

4. Calculate the volume of the inner cylinder with radius r:

V_inner = πr^2h = 3.14 * (3^2) * 21 ≈ 592.74 cubic inches.

5. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the material used:

V_material = V_outer - V_inner ≈ 1653.3 - 592.74 ≈ 1060.56 cubic inches.

The volume of the material is approximately 1060.56 cubic inches, rounded to the nearest hundredth.

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The diagonal of the square bisect the angles. Therefore, the angle x in the square is 60 degrees.

A square is a quadrilateral with each angles equal to 90 degrees. The sum of angles in a square is 360 degrees.

The diagonal of a square is perpendicular to each other. It divided the square into two congruent isosceles triangle.

The diagonal of a square bisects the angles of a square. Therefore, the angles are 45 degrees each after bisection.

Hence, let's find the angle x in the square.

Therefore,

180 - 105 + x + 45  = 180

75 + x + 45 = 180

x + 120 = 180

subtract  120 from both sides of the equation

x + 120 - 120 = 180 - 120

x = 60 degrees

Therefore,

x = 60 degrees

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Answer:

25

Step-by-step explanation:

d= √l²+w²= √24²+7²= √576+49= √625= 25

Answer:

25

Step-by-step explanation:

In Pythagoras' theorem a^(2) + b^(2) = C^(2)

If we input put values, 7^(2)+24^(2)= 625

The square root of 625 is 25  

Answer:

SEVEN DOLLARS AND TWENTY-FIVE CENTS. ($7.25)

Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

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The expected number of choices needed to select the first CS PhD student is 4.

To solve this problem, we can use the concept of geometric distribution. The geometric distribution represents the number of independent and identical trials that are needed to obtain the first success, where the probability of success is p.

In this case, the probability of selecting a CS PhD student on any given trial is 50/200 = 0.25. Therefore, the number of trials needed to obtain the first CS PhD student follows a geometric distribution with p = 0.25.

The expected value of a geometric distribution with parameter p is given by E(X) = 1/p. Therefore, the expected number of choices needed to select the first CS PhD student is

E(X) = 1/p = 1/0.25 = 4

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The formulas that are typically covered in an algebra class for 6th graders may include:

1.  (a + b)^2 = a^2 + 2ab + b^2

2.  (a - b)^2  = a^2 - 2ab + b^2

3.  (a + b) (a - b)  = a^2 - b2

4.  (x + a)(x + b)  = x^2 + (a + b)x + ab

5.  (x + a)(x - b)  = x^2 + (a - b)x - ab

6.  (x - a)(x + b)  = x^2 + (b - a)x - ab

7.  (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

8. a^3 + b^3 + c^3 - 3abc = (a + b + c ) ( a^2 + b^2 + c^2 – ab – bc – ca ) + 3abc

9. a^3 + b^3 + c^3 = 3abc   (if a + b + c = 0)

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

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a) This study is observational because the researchers are observing and comparing groups based on self-reported apple consumption, without actively manipulating the variables.

b) Confounding occurs when an additional variable associated with both the exposure and outcome introduces bias. An example could be oral hygiene habits, which could confound the relationship between apple consumption and cavities.

c) No, one cannot conclude that lower cavities are solely due to eating an apple a day. Other factors or confounding variables could be at play. Experimental studies are needed to establish causality.

Let us analyze in a detailed way:

a) This study is an observational study rather than an experiment because the researchers are not actively manipulating the variables. They are observing and comparing the number of new cavities in two groups of people based on their self-reported apple consumption. The individuals in each group already have their eating habits established, and the researchers are merely observing and recording the outcomes.

b) In the context of the study, confounding refers to the presence of an additional variable that is associated with both the exposure (eating an apple a day) and the outcome (number of new cavities), leading to a potential bias in the results. It can be challenging to determine whether the observed effect is solely due to the apple consumption or if it is influenced by the confounding variable. An example of a possible confounding variable in this study could be oral hygiene habits. If individuals who eat an apple a day also have better oral hygiene practices, such as regular brushing and flossing, this could confound the relationship between apple consumption and the number of new cavities.

c) No, one cannot conclude that the lower number of cavities can be attributed solely to eating an apple a day. Even if the mean number of new cavities is significantly smaller in the group that eats an apple a day, there may be confounding factors or other variables at play that contribute to the observed difference. In order to establish a causal relationship between apple consumption and the number of new cavities, a randomized controlled trial or an experimental study would be needed, where participants are randomly assigned to the apple consumption groups and other potential confounding variables are controlled.

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An observational study is being conducted to determine if there is a difference in the number of new cavities between people who eat an apple a day and those who eat less than one apple a week. confounding is a concept in observational studies where an extraneous variable associated with both the exposure (apple consumption) and the outcome (number of new cavities) can distort the relationship. The mean number of new cavities being significantly smaller in the group that eats an apple a day does not establish causation. Additional research, such as a randomized controlled experiment, is needed to determine if the lower number of cavities can be attributed to eating an apple a day.

In this dental study, the dentists are conducting an observational study to determine if there is a difference in the number of new cavities between people who eat an apple a day and those who eat less than one apple a week. An observational study is a type of study where researchers observe and collect data on individuals without intervening or manipulating any variables. In this case, the dentists are not assigning people to specific groups or controlling their apple consumption; instead, they are simply observing and comparing the number of new cavities in two groups of people based on their self-reported apple consumption.

confounding is a concept in observational studies where an extraneous variable, known as a confounding variable, is associated with both the exposure (apple consumption) and the outcome (number of new cavities). This confounding variable can distort the relationship between the exposure and the outcome, leading to incorrect conclusions. For example, a possible confounding variable in this study could be oral hygiene habits. If people who eat an apple a day also have better oral hygiene habits, it could be the oral hygiene habits rather than the apple consumption that is responsible for the lower number of cavities.

To determine if the lower number of cavities can be attributed to eating an apple a day, additional research is needed. The mean number of new cavities being significantly smaller in the group that eats an apple a day compared to the group that eats less than one apple a week suggests an association, but it does not establish causation. Other factors, such as oral hygiene habits, diet, genetics, or socioeconomic status, could be confounding variables that contribute to the observed difference. To establish a causal relationship, a randomized controlled experiment would be necessary, where participants are randomly assigned to either eat an apple a day or not and their cavities are monitored over time.

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Yes, the distribution of heights for all adults is approximately normal because normal distribution has a bell-shaped curve. The bell curve indicates that the majority of the data points are located around the mean, with fewer data points on either side. Furthermore, normal distribution has certain characteristics that are relevant to this question.

The average height of men is 69.2 inches, while the average height of women is 63.7 inches. Therefore, we can assume that the mean height for both genders would be approximately 66.45 inches, assuming the distribution is equal (i.e., half male, half female).

If we plot the data of both males and females together, the plot will likely resemble a bell curve as per the properties of normal distribution. Since most adults would fall within the average height range, the distribution of heights for all adults is considered approximately normal. Therefore, we can conclude that the distribution of heights for all adults is approximately normal.

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The sum of the angles in triangle MNP is 180, and subtracting 135 from both sides gives 45 degrees. With the angle sum property of triangle, ∠MNP = 121°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to the given question,

45° + 90° + ∠MNP = 180°

135° + ∠MNP = 180°

∠MNP = 45°

Hence, With the angle sum property of triangle, ∠MNP = 121°.

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The approximately 99.38% of the data falls between the values 120 and 280.

To find the percentage of data that falls between the values 120 and 280, we need to find the standard scores (z-scores) that correspond to these values and use a standard normal table to find the proportion of data within this range.

First, we'll find the z-score for 120:

z = (120 - 200) / 40 = -2.5

Similarly, the z-score for 280 is:

z = (280 - 200) / 40 = 2.5

Now we can use a standard normal table to find the proportion of data between -2.5 and 2.5 standard deviations from the mean. This proportion is approximately 0.9938 or 99.38%.

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The first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs.

Let x be the number οf hοurs the first mechanic wοrked, then the number οf hοurs the secοnd mechanic wοrked wοuld be (15 - x).

The tοtal cοst οf the first mechanic wοuld be 65x, and the tοtal cοst οf the secοnd mechanic wοuld be 45(15 - x) = 675 - 45x.

Tοgether, their tοtal cοst wοuld be 65x + (675 - 45x) = 20x + 675.

We knοw that their tοtal cοst was $875, sο we can set up the equatiοn:

20x + 675 = 875

Subtracting 675 frοm bοth sides, we get: 20x = 200

Dividing bοth sides by 20, we get: x = 10

Therefοre, the first mechanic wοrked fοr 10 hοurs, and the secοnd mechanic wοrked fοr 15 - 10 = 5 hοurs .

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Using the perimeter concept, it is found that the perimeter of the polygon is of 24.1 units.

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

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

\(s^2 = 3^2 + 4^2\)

\(s^2 = 9 + 16\)

\(s^2 = 25\)

\(s = 5\)

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

\(s^2 = 5^2 + 7^2\)

\(s^2 = 25 + 49\)

\(s^2 = 74\)

\(s = 8.6\)

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

\(s^2 = 3^2 + 9^2\)

\(s^2 = 9 + 81\)

\(s^2 = 90\)

\(s = 9.5\)

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

\(P = 1 + 5 + 8.6 + 9.5 = 24.1\)

The perimeter of the polygon is of 24.1 units.

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