Leroy is building a slide for his kids. If the ladder is 5 feet tall and he wants the bottom of the slide to be 12 feet from the ladder, how long does the slide need to be?

The set builder form of the sets are

1) { | = ², where is a positive integer between 1 and 9}

2) { | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

3) { | = 3, where is a positive integer between 1 and 6}

In set-builder notation, we use the curly brackets {} to enclose the elements of a set, and a rule or condition to define the elements that belong to the set.

Let's look at each of the sets given and express them in set-builder form:

{1, 4, 9,……..81}

This set contains the perfect squares of the numbers 1 to 9. To express it in set-builder notation, we can use the following rule:

{ | = ², where is a positive integer between 1 and 9}

{1, 5, 25, 125, 625, 3125}

This set contains the powers of 5, starting from 5⁰=1 up to 5⁵=3125. To express it in set-builder notation, we can use the following rule:

{ | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

{3, 6, 9, 12, 15, 18}

This set contains the multiples of 3, from 3 to 18. To express it in set-builder notation, we can use the following rule:

{ | = 3, where is a positive integer between 1 and 6}

In this rule, we multiply 3 by the positive integers 1 to 6 to obtain the elements of the set.

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Complete Question:

Express the following sets in set-builder form.

1. {1, 4, 9,……..81}

2. {1, 5, 25, 125, 625, 3125}

3. {3, 6, 9, 12, 15, 18}

Answer:

x's will eliminate because they have opposite coefficients

Step-by-step explanation:

Because the x's have opposite coefficients, they will eliminate when the given system of linear equations (2-var) are summed up

Answer:

x's will eliminate because they have opposite coefficients.

Step-by-step explanation:

Why the other choices are incorrect:

y's will eliminate because they have opposite coefficients - not true, they don't have opposite coefficients.

x's will eliminate because you always have to solve for x first - you can solve for y too.

y's will eliminate because why not - isn't a good explanation.

To evaluate the integral 4 cos x^2 dx dy dz, 2y by changing the order of integration, we first need to determine the limits of integration.

Integrating with respect to x first, we have:
∫∫∫ 4 cos x^2 dx dy dz, 2y
= ∫∫ [2 sin x^2]y=0 to y dz, 2y
= ∫ [2 sin x^2]z=0 to z dz, 2y
= 2y ∫ [sin x^2]z=0 to z dz

Next, integrating with respect to z, we have:
2y ∫ [sin x^2]z=0 to z dz
= 2y [cos x^2]z=0 to z
= 2y [cos z^2 - 1]
Finally, integrating with respect to y, we have:

∫∫∫ 4 cos x^2 dx dy dz, 2y
= ∫∫ 2y [cos z^2 - 1] dy dz
= ∫ [y^2(cos z^2 - 1)]z=0 to z dz
= ∫ y^2(cos z^2 - 1) dz
Therefore, we have changed the order of integration from dx dy dz, 2y to dz dy dx, and the new limits of integration are:
0 ≤ z ≤ √(π/2)
0 ≤ y ≤ √(π/2 - z^2)
0 ≤ x ≤ √(π/2 - y^2 - z^2)

We can now evaluate the integral using these new limits and the equation we derived earlier:
∫∫∫ 4 cos x^2 dx dy dz, 2y
= ∫∫∫ 4 cos x^2 dz dy dx, 2y
= ∫ from 0 to √(π/2) ∫ from 0 to √(π/2 - z^2) ∫ from 0 to √(π/2 - y^2 - z^2) y^2(cos z^2 - 1) dx dy dz
= -4/3π
Therefore, the value of the integral is -4/3π.
To evaluate the integral by changing the order of integration, first, we need to rewrite the given integral in the correct notation. Unfortunately, the provided integral seems to have some errors or missing information, making it difficult to give a complete answer.

Please provide the correct integral and the limits of integration for each variable (x, y, and z) so I can assist you better.

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The median for the number of pencils can be found by locating the middle value on the dot plot, which appears to be 3 pencils.

The dot plot displays the number of pencils each boy has at his desk in class. By locating the middle value of the data on the dot plot, the median number of pencils can be determined to be 3.

This indicates that half of the boys have 3 pencils or fewer, while the other half have 4 pencils or more.

The dot plot provides a visual representation of the distribution of the data and allows for easy identification of the median value.

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The number of bases, faces, edges and vertices are;

7. 2, 4, 6, 6

8. 6, 5, 10, 10

9. 1, 4, 5, 5

10. 1, 5, 7 , 7

11. 1, 5, 7, 7

12. 1, 3, 4 , 4

To determine the number, we need to take the following into considerations;

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The magnitude of vector v is 4 and the direction is 125 degrees.

Given that vector u has a magnitude of 2 and a direction of 55 degrees, we can determine the magnitude and direction of vector v.

To find the magnitude of vector v, we can use the equation:

|v| = |-2u|

Since u has a magnitude of 2, we can substitute it into the equation:

|v| = |-2 * 2|

|v| = |-4|

|v| = 4

The magnitude of vector v is 4.

To find the direction of vector v, we can note that multiplying a vector by -1 (in this case, multiplying u by -2) reverses its direction. So the direction of v is the exact opposite of the direction of u.

Since the direction of u is 55 degrees, the direction of v is 55 degrees in the opposite direction. In the interval of 0 degrees ≤ θ < 360 degrees, the direction of v can be expressed as:

θ = 180 - 55

θ = 125 degrees

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The probability of selecting a brown M&M from this bag is 0.

Since there are no brown M&Ms mentioned in your bag, the probability of selecting a brown M&M is 0. In probability terms, we can express this as:

Probability of selecting a brown M&M = Number of brown M&Ms / Total number of M&Ms

There are 0 brown M&Ms, and there are a total of 4 green + 6 yellow + 7 purple + 3 red = 20 M&Ms in the bag. So the probability is:

Probability = 0 / 20 = 0

Thus, the probability of selecting a brown M&M from this bag is 0, meaning it's impossible with the given information.

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The normal distribution curve gives useful information regarding the distribution of students' grades, such as the average grade, the dispersion of grades, the likelihood of receiving a specific grade, and the presence of any outliers.

The normal distribution curve generated by the educator offers multiple insights into the distribution of academic achievement among her pupils. The analysis of the curve yields various informative data such as:

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The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum fo angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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The annual compound rate of return on this 20-year zero coupon bond is 6%. To calculate the annual compound rate of return, we need to use the following formula:

Annual Compound Rate of Return = (Face Value / Purchase Price)^(1/Number of Years) - 1

Here, the face value of the bond is $1000, the purchase price is $500, and the bond has a term of 20 years. Substituting these values in the above formula, we get:

Annual Compound Rate of Return = (1000/500)^(1/20) - 1

Simplifying this expression, we get:

Annual Compound Rate of Return = 1.06 - 1

Annual Compound Rate of Return = 0.06 or 6%

Therefore, the annual compound rate of return on this 20-year zero coupon bond is 6%.

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The price of the medium pizza without the coupon is approximately $14.74.

To find the original price of the pizza without the coupon, we can use the following formula:

Original Price = Discounted Price / (1 - Discount Percentage)

In this case, the discounted price is $10.32 and the discount percentage is 30% or 0.3. Plugging the values into the formula:

Original Price = $10.32 / (1 - 0.3)

Original Price = $10.32 / 0.7

Original Price ≈ $14.74

So, the price of the medium pizza without the coupon is approximately $14.74.

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Answer:

Step-by-step explanation:

True

The phrase "putting the cart before the horse" refers to doing things in the wrong order or prioritizing less important tasks over more crucial ones.

In the context of the puzzle time question, the answer is: You should never put the cart before the horse, as it is essential to follow the proper sequence of actions to achieve the desired outcome effectively.

In the context of the puzzle time question, the phrase "putting the cart before the horse" implies that it is crucial to follow the proper sequence of actions or steps to solve the puzzle correctly.

By prioritizing less important tasks or skipping essential steps, the desired outcome may not be achieved, and the solution may be flawed.

To effectively solve the puzzle, it is essential to understand and follow the rules, guidelines, and necessary steps in the correct order. This ensures that each action builds upon the previous one and leads to a coherent solution.

By doing so, you avoid the mistake of putting the cart (less important tasks) before the horse (more crucial steps), leading to a successful and accurate solution.

In summary, the phrase "putting the cart before the horse" emphasizes the importance of following the correct sequence of actions or steps in any given task, including solving puzzles. It serves as a reminder to prioritize tasks appropriately to achieve the desired outcome effectively.

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Answer:

3

√

10

√

5

Step-by-step explanation:

Point estimate of μ  [tex]26.15[/tex]

99% confidence interval: [tex](24.213, 28.087)[/tex]

Margin of error:[tex]1.437[/tex]

The point estimate of  (population mean) is calculated by finding the sample mean , which is the average of the given sample data. Adding up all the observations and dividing by the sample size (18), we get:

To make a 99% confidence interval for we can use the t-distribution and the sample mean. Since the sample size is 18, we have (18 - 1) = 17 degrees of freedom. Using a t-distribution table or a calculator, we find the critical value for a 99% confidence level and 17 degrees of freedom to be approximately 2.898.

Next, we calculate the standard error (SE) using the sample standard deviation (s) divided by the square root of the sample size .Assuming the population standard deviation is unknown, we estimate it using the sample standard deviation, which is approximately 3.858.

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u = 28.8

The 99% confidence interval for μ is (27.01, 30.59).

28.4 + 27.3 + 25.5 + 25.5 + 31.1 + 23.0 + 26.3 + 24.6 + 28.4 + 37.2 + 23.9 + 28.7 + 27.9 + 25.1 + 27.2 + 25.3 + 22.6 + 22.7 = 518.3

The sample mean (or the point estimate of μ) is:

518.3 / 18 = 28.8

Calculate each data point's deviation from the mean, square it, and then sum up these values.

(28.4-28.8)² + (27.3-28.8)² + (25.5-28.8)² + (25.5-28.8)² + (31.1-28.8)² + (23.0-28.8)² + (26.3-28.8)² + (24.6-28.8)² + (28.4-28.8)² + (37.2-28.8)² + (23.9-28.8)² + (28.7-28.8)² + (27.9-28.8)² + (25.1-28.8)² + (27.2-28.8)² + (25.3-28.8)² + (22.6-28.8)² + (22.7-28.8)²

= 116.4

Divide by (n - 1), where n is the number of observations. In this case, n = 18, so n - 1 = 17.

So, the variance (s²) is 116.4 / 17 = 6.85 (approximately)

s = √6.85 = 2.62

CI = x ± (t * (s/√n))

CI = 28.8 ± (2.898 * (2.62/√18))

CI = 28.8 ± 1.79

So, the 99% confidence interval for μ is (27.01, 30.59).

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The height of a 16-year-old boy in the 96th percentile is approximately 73.8 inches. Rounded to the nearest inch, the answer is 74 inches.

To find the z-score associated with the 96th percentile, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given distribution to a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, we want to find the z-score associated with the 96th percentile. The 96th percentile is the value below which 96% of the observations fall. We can find this value by using a standard normal table or a calculator. Using a calculator, we get:

invNorm(0.96) ≈ 1.75

This means that the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:

x = μ + z * σ

where x is the value we want to find, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the z-score we just found.

In this case, we have:

x = 68.3 + 1.75 * 2.9 ≈ 73.8

Thus, 74 inches is the conclusion.

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Answer:

Step-by-step explanation:

Since AB is parallel to DE, we know that:

(ABC + BCD) = (CDE + EDC)

Substituting the given values, we get:

800 + BCD = 280 + EDC

Simplifying, we get:

BCD = EDC - 520

We also know that:

(BCD + CDE + DCE) = 180

Substituting BCD = EDC - 520 and CDE = 280, we get:

(EDC - 520 + 280 + DCE) = 180

Simplifying, we get:

EDC + DCE - 240 = 0

EDC + DCE = 240

Now we can solve for DCE in terms of BCD:

DCE = 240 - EDC

DCE = 240 - (BCD + 520)

DCE = 760 - BCD

Substituting this expression for DCE into the equation (BCD + CDE + DCE) = 180, we get:

BCD + 280 + (760 - BCD) = 180

Simplifying, we get:

1040 - BCD = 180

BCD = 860

Therefore, (DCB) = 180 - (BCD + CDE) = 180 - (860 + 280) = -960. However, since angles cannot be negative, we can add 360 degrees to this value to get:

(DCB) = -960 + 360 = -600

Therefore, (DCB) = -600 degrees.

Each cuboid has a total of 12 cubes, but they have different shapes and sizes. The table is attached below.

A cube is a three-dimensional geometric shape that has six equal square faces, 12 equal edges, and eight vertices (corners). All the angles between the faces and edges of a cube are right angles (90 degrees), and all the edges are of equal length. A cube is a special type of rectangular prism where all the sides are equal in length, making it a regular polyhedron.

Sure, here's a table showing the possible dimensions of the four different cuboids that can be made with 12 cubes:

Cuboid Length Width Height

A                1       2 6

B                1       3 4

C                2       2 3

D                1        1 12

Note that the dimensions are given in terms of the number of cubes in each direction. For example, cuboid A has a length of 1 cube, a width of 2 cubes, and a height of 6 cubes.

Therefore, Each cuboid has a total of 12 cubes, but they have different shapes and sizes.

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The difference in volumes between the sphere and the cylinder is approximately 3619.14 cubic cm.

We need to find the difference in volumes between a sphere and a cylinder with the same radius (12 cm) and the cylinder has a height of 12 cm.

Step 1: Find the volume of the sphere.
The formula for the volume of a sphere is V_sphere = (4/3)πr³.
V_sphere = (4/3) × 3.14 × (12 cm)³
V_sphere = (4/3) × 3.14 × 1728 cm³
V_sphere ≈ 9047.78 cm³

Step 2: Find the volume of the cylinder.
The formula for the volume of a cylinder is V_cylinder = πr²h.
V_cylinder = 3.14 × (12 cm)² × 12 cm
V_cylinder = 3.14 × 144 cm² × 12 cm
V_cylinder ≈ 5428.64 cm³

Step 3: Find the difference in volumes.
Difference = V_sphere - V_cylinder
Difference = 9047.78 cm³ - 5428.64 cm³
Difference ≈ 3619.14 cm³

The difference in volumes between the sphere and the cylinder is approximately 3619.14 cubic cm.

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Hunter has 32 different possible outcomes if he rolls a pyramid-shaped die with four sides, spins a spinner with four equal-sized sections, and flips a coin.

There are different methods to approach this problem, but one possible way is to use the multiplication principle of counting, which states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks in sequence.

In this case, Hunter has three tasks: rolling the die, spinning the spinner, and flipping the coin.

For the first task, rolling the die, there are four possible outcomes.

For the second task, spinning the spinner, there are four possible outcomes as well.

For the third task, flipping the coin, there are two possible outcomes.

Using the multiplication principle, the total number of possible outcomes is:

4 x 4 x 2 = 32

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Answer: 6

Step-by-step explanation:

So, he wears the shirt 10 out of 20 days.

10 days is half of 20 days.

This means he wears the shirt approximately half of the time, by the logic of 10/20 days.

So, now we apply this to 12 days.

What's half of 12? 6.

This means that he most likely wears the green shirt on 6 out of the 12 days.

In the given square ERTN, the length of the side NT is found to be equal to 25.

The square ERTN has ER = 5x and RT = 10x - 25. Because it is a square, the sides will be equal in magnitude. So, we can write,

Length of ER = Length of RT

5x = 10x - 25

5x = 25

x = 25/5

x = 5

So, the length of ER will be 5(5) = 25 and the length of RT will be 10(5)-25 = 25.

So, finally the length of NT would also be equal to 25.

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Answer:

13, 2x^2 - 98 = 0 ........ given

2x^2= 98 ........ take to tge left side no.98

x^2 = 98/2 = 49 ..... multiple both side by radical

x = √49 = 7 ........ simplify

17, 4x^2 + 10 = 11

4x^2 + 10 = 11 4x^2 = 11- 10 = 1

4x^2 + 10 = 11 4x^2 = 11- 10 = 1 x^2 = 1/4

4x^2 + 10 = 11 4x^2 = 11- 10 = 1 x^2 = 1/4 x = √1/4 = 1/2

Answer:

Step-by-step explanation:

The gold vein is at (-3,9) and the farthest gold dust strike is at (33,9). The distance between the two points is 36 miles.

The manager will need to pay $244.95 to purchase the silverware, including sales tax.

What is decimal?

Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

According to the given information:

If the silverware costs $230 and the sales tax is 6.5%, we need to calculate the amount of tax that will be added to the cost of the silverware:

Tax = 6.5% of $230 = 0.065 x $230 = $14.95

So the total cost of the silverware including tax is:

$230 + $14.95 = $244.95

Therefore, the manager will need to pay $244.95 to purchase the silverware, including sales tax.

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we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

To compare the rates of participation in sports among the three grades, we can convert each percentage or fraction to a decimal and then compare the values.

Grade 6: 0.872

Grade 7: 0.87 (87% converted to decimal)

Grade 8: 0.875 (7/8 converted to decimal)

Therefore, we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

Answer:

Grade 8 had the greatest rate of participation.

Grade 6 had the least rate of participation.

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To optimize the given function e - 222 - 4xy - 2y^2 subject to the constraint 0x^2 - 4xy + ly^2 = 10, we'll first set up the Lagrange function L(x, y, λ) as follows:

Langrange- L(x, y, λ) = e - 222 - 4xy - 2y^2 + λ(0x^2 - 4xy + ly^2 - 10)
Now, we'll get the partial derivatives of L with respect to x, y, and λ and set them equal to zero:
Step:1. ∂L/∂x = -4y - λ(-4y) = 0
Step:2. ∂L/∂y = -4x - 4y - 2λy = 0
Step:3. ∂L/∂λ = 0x^2 - 4xy + ly^2 - 10 = 0
These three equations represent the system of equations we need to solve to find the critical points. To reiterate, the equations are:
1. -4y + 4yλ = 0
2. -4x - 4y - 2λy = 0
3. -4xy + ly^2 - 10 = 0

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Answer:

B

Step-by-step explanation:

15 pounds and 5 pounds per day so to figure out how many days you do division. The equation is 15÷5=3 so the answer is 3 days.

Soloman's attempt to construct a triangle similar to triangle XYZ by making angles X' and Y' half the measures of angles X and Y, respectively, does not result in a similar triangle.

For two triangles to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be equal. In this case, the angle measures of triangle X'Y'Z' are not congruent to the angle measures of triangle XYZ.

Since angle X' is half of angle X and angle Y' is half of angle Y, the measures of angles X' and Y' are not congruent to the measures of angles X and Y, respectively. Therefore, the triangles are not similar.

If Soloman had made all three angles of triangle X'Y'Z' proportional to the angles of triangle XYZ, then the triangles would have been similar according to the Angle-Angle (AA) similarity theorem.

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