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Final answer:

The piecewise function, using the Heaviside function, is defined as 0 for t < 0, t^2 for t in [0, 1], and t for t > 1.

Explanation:

The piecewise function can be defined using the Heaviside function.

We know that the Heaviside function, H(x), is defined as:

H(x) = 0 for x < 0

H(x) = 1 for x ≥ 0

Using the Heaviside function, the piecewise function can be written as:

f(t) = 0 for t < 0

f(t) = t2 for t ∈ [0, 1]

f(t) = t for t ≥ 1

The answer is for this problem is 10

Find A ∩ B is any numbers that are in both sets

they booth have 6 & 12 so the answer is: {6, 12}

Answer:

6,12

Step-by-step explanation:

The volume of the rectangular prism completely packed with 200 cubes of edge length 1/5in is approximately 1600 cubic inches.

The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism. In this case, the prism is completely packed with cubes of edge length 1/5in. Since there are 200 cubes, the length, width, and height of the prism would be the number of cubes in each respective direction. Therefore, the volume of the rectangular prism is:

(200 cubes in length) x (200 cubes in width) x (200 cubes in height) x (1/5in cube)^3

To simplify the calculation, we can express the volume in terms of the number of cubes:

200 x 200 x 200 x (1/5)^3 in³

Converting the units, we find that the volume of the rectangular prism is approximately 1600 cubic inches.

The Boardman family's walking speed is 1.4 miles per hour, which is calculated by dividing the distance walked (2/5 mile) by the time it took (2/7 hour).

A unit rate defines how many units of the first type of quantity correspond to one unit of the second type of quantity. In this case, we need to find out how many miles they walk in one hour.

To calculate the unit rate, we divide the distance by the time. They walked 2/5 of a mile in 2/7 of an hour. Setting up the division, we have:
(2/5) miles / (2/7) hours = (2/5) × (7/2) miles per hour = 7/5 miles per hour

After simplifying, we get that the Boardman family's walking speed is 1.4 miles per hour.

x + 6 =y

8 =2y ........ y = 8/2 = 4

4+6 =10

John is four & Jose is 10

the answer to Give the angle measure represented by 2 rotations clockwise. it's A. -720 on edge

The translation of the statement '55 times what number is 1265?' into an equation is '55 * x = 1265', which, with 'dot' finding use as multiplication, matches with the provided option A) 55 dot x = 1265.

The question asks for the translation of the problem statement into an equation. The phrase '55 times what number is 1265?' implies multiplication. Specifically, 55 is being multiplied by an unknown number (which we can denote by 'x'), and the result of this multiplication is 1265. Therefore, the correct translation of this problem into an equation would be 55 * x = 1265 or in the provided options A) 55 dot x = 1265 where 'dot' indicates multiplication.

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To solve this, we need to use the z statistic. The formula for z score is:

z = (x – u) / s

where x is sample value = less than 90, u is the sample mean = 90.6, s is the standard deviation = 17.2

z = (90 – 90.6) / 17.2

z = -0.035

From the standard distribution tables:

P (z = -0.035) = 0.4860

Therefore there is about 48.60 % chance that it will be less than 90 pounds

If the number of samples is increased, this actually leads to a reduction in error of the distribution. This is because of the relationship between variation and sample size which has the formula of:

σx = σ / sqrt (n)

So from the formula we can actually see that the variation and sample size is inversely proportional.

Which means that increasing the sample size results in a reduction of variation.

Answer:

It will have less variation

Increasing the sample size causes the confidence interval to narrow, decreases the standard deviation, and makes the sample mean distribution more normal. This leads to more accurate and reliable estimates of the population parameters.

The effect of increasing the sample size in a distribution of sample means primarily involves the confidence interval, the standard deviation, and the progress towards a normal distribution.

Firstly, increasing the sample size reduces the error bound, leading to a narrower confidence interval. This means that the calculated mean is likely to be more accurate representation of the true population mean.

Secondly, as the sample size increases, the standard deviation, which is a measure of spread or dispersion in the data, decreases. So, larger sample sizes result in lesser variability.

Finally, per the central limit theorem, an increased sample size makes the distribution of sample means get closer to a normal distribution, regardless of the population's initial distribution. This property is valid as long as the sample size is large enough (generally taken as 30 or more).

Thus, larger sample sizes tend to provide more accurate and reliable estimates of the population parameters.

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(2x² +3x -4) + (8 -3x) + (-5x² +2)

= x²(2 -5) +x(3 -3) +(-4 +8 +2)

= -3x² +6

_____

The process here is called "collecting terms", which means you add the coefficients of "like" terms. Terms are "like terms" when they have the same constellation of variables. Here, there are three different kinds of like terms:

• x² terms

• x terms

• constants

This process is an application of the distributive property, as you can see on the second line of the solution above.

The rational number equivalent to the given expression is 50 5/9.

The given expression is [tex]69\frac{2}{9} -31\frac{1}{9} -(-12\frac{4}{9} )[/tex].

To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator.

Now, [tex]69\frac{2}{9} -31\frac{1}{9} +12\frac{4}{9}[/tex]

[tex]=(69-31+12)(\frac{2}{9}-\frac{1}{9}+\frac{4}{9})[/tex]

=50 5/9

Therefore, the rational number equivalent to the given expression is 50 5/9.

To learn more about the rational number visit:

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The area of the square dance floor when each side is increased by one foot becomes 441 square feet. Since 441 is an integer, the new area is a rational number because it can be expressed as a fraction with a non-zero denominator.

The question pertains to the change in area of a square dance floor when each side of the square is increased by one foot. Given that the initial area is 400 square feet, we understand that the dimensions of the dance floor are 20 feet by 20 feet, since 20 * 20 = 400. If each side of the square increases by one foot, the new dimensions of the square will be 21 feet by 21 feet, resulting in a new area of 441 square feet.

To answer the question as to whether the new area is a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, with a denominator that is not zero. Given that 441 is an integer, and the area can be written as 441/1, the new area of the dance floor is indeed a rational number.

Final answer:

The question involves creating unordered lists with various bullet options such as disc, square, circle, and triangle. While disc, square, and circle are commonly available, the triangle may need to be created as a custom bullet option in advanced editors. The process includes selecting the Bullets icon in the Paragraph section and choosing or customizing the bullet style.

Explanation:

The question refers to the process of creating unordered lists in document editing or web development environments, where you have the option to format lists using different types of bullets. When you want to organize information without a specific order of importance, an unordered list can be used. These lists are often formatted with bullet points to improve readability and structure.

Steps to Create an Unordered List with Different Bullet Options:

Go to the Home menu item.

In the Paragraph section, select the Bullets icon for unordered lists.

To choose a different bullet format, select the arrow beside the icon.

Select a format from the format Library that appears in the drop-down menu. Common bullet styles include disc, square, and circle. However, the question mentions 'triangle' which is not a standard option in most document editors but can be created as a custom bullet in some advanced editing tools.

Using different bullet styles like disc, square, and circle can help distinguish or organize your content more effectively. While the 'triangle' option might not be directly available, it represents the possibility to define new custom bullets, adding a unique aspect to your document's design.

We can solve this problem using the binomial probability equation:

P = [n! / (n – r)! r!] p^r q^(n – r)

where the variables are:

n = total number of questions = 10

r = number of correct = at least 5

p = probability of success = 0.5

q = probability of failure = 0.5

So what we have to do is to calculate for P for r = 5 to 10

when r = 5

P =  [10! / (10 – 5)! 5!] 0.5^5 0.5^(10 – 5)

P = 0.246

when r = 6

P =  [10! / (10 – 6)! 6!] 0.5^6 0.5^(10 – 6)

P = 0.205

when r = 7

P =  [10! / (10 – 7)! 7!] 0.5^7 0.5^(10 – 7)

P = 0.117

when r = 8

P =  [10! / (10 – 8)! 8!] 0.5^8 0.5^(10 – 8)

P = 0.044

when r = 9

P =  [10! / (10 – 9)! 9!] 0.5^9 0.5^(10 – 9)

P = 9.766 x 10^-3

when r = 10

P =  [10! / (10 – 10)! 10!] 0.5^10 0.5^(10 – 10)

P = 9.766 x 10^-4

So the probability that her score will be at least 5 is:

P (r≥5) = 0.246 + 0.205 + 0.117 + 0.044 + 9.766 x 10^-3 + 9.766 x 10^-4

P (r≥5) = 0.623

So about 62.3% chance.


You can do the same for the other item quiz, just set the value of n

Final answer:

When randomly guessing on true-false quizzes, the probability of getting at least a 50% grade on a three-item quiz is 0.5, on a four-item quiz is 0.6875, and on a five-item quiz is also 0.5.

Explanation:

Calculating the probability of getting at least 50% on a true-false quiz when randomly guessing involves understanding the binomial probability distribution. For a true-false quiz, each question has two possible outcomes, from which we can calculate the likelihood of each score.

Answer:

Step-by-step explanation:

Okay. So first 8.25 * 20 = 165. Then you multiply 165 by 3 (165*3). 165 * 3 = 495.

Dan will earn $495 in three weeks.