The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.15 gallons. A previous study found that for an average family the variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water

Therefore, 2 with an exponent of 0 is equal to 1.

When a number is raised to an exponent of 0, the result is 1. This applies to any non-zero number, including 2. Therefore, 2 with an exponent of 0 is equal to 1.

The reason is that any number raised to the power of 0 is 1. This is because any number multiplied by 1 is itself, and any number raised to the power of 1 is itself. Therefore, raising a number to the power of 0 is the same as multiplying it by 1, so the result is 1.

It is also important to note that a number raised to the power of 1 is the number itself, so 2^1=2, 2^2=4, 2^3=8 and so on.

Therefore, 2 with an exponent of 0 is equal to 1.

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There are one combination of choosing all 8 from 8 items when the order does not matter.

Therefore the answer is 1.

The number of combinations of 8 items is given by the formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of items and k is the number of items in each combination.

In this case, we want to find the number of combinations of 8 items, so n = 8 and k = 8.

Plugging these values into the formula, we get:

C(8, 8) = 8! / (8!(8-8)!) = 8! / (8!(0!))

= 8! / 8! = 1.

So, there is only 1 combination of 8 items when k = 8.

It's important to note that a combination is a set of items in which the order doesn't matter, so the order of the items in the set doesn't affect the number of combinations. If you want to find the number of permutations, in which order matters, it would be 8! (8 factorial) = 8x7x6x5x4x3x2x1 = 40320.

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Answer:

apples don't grow on maple trees

Step-by-step explanation:

The discriminant value associated with this quadratic equation when it has zero real number solutions is -5.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

In a quadratic equation when the discriminant is 0 we get one real solution.

In a quadratic equation when the discriminant is positive we get two real solutions.

In a quadratic equation when the discriminant is negative we get a complex solution.

A complex solution is not a real solution.

So,

The discriminant value must be -5.

Thus,

The discriminant value associated with this equation is -5.

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Answer: It’s A: -5

Step-by-step explanation:

on edge 2020

(Took test)

The base value of a number can be changed by using a base conversion calculator. This calculator can convert a number from one base to any other base. It can also be changed manually by using the rules of base conversion.

Base conversion is the process of changing a number from one numerical base to another.

This can be done manually by using the rules of base conversion or by using a base conversion calculator. When using a calculator, the user will enter the number, the current base, and the desired base and the calculator will output the number in the desired base.

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Margaret is incorrect because the given information does not include enough details to determine if the quadrilateral WXYZ is a parallelogram.

To prove that a quadrilateral is a parallelogram, the four sides must be equal in length and the opposite angles must be congruent. The given information does not include any measurements or angles, so it is not possible to determine if the quadrilateral is a parallelogram.

No, 144 inches of tape is not enough to finish the job. The hazard sign has two identical parallelogram-shaped stripes, and each stripe will require more than 144 inches of tape to outline. The area of a parallelogram can be calculated using the formula A = bh, where b is the base and h is the height. In order to determine how much tape is needed to outline the stripes, the base and height of the parallelograms must be known.

There is not enough information to prove that a quadrilateral is a parallelogram, as all four sides must be equal in length and the opposite angles must be congruent. Additionally, 144 inches of tape is not enough to outline the hazard sign's two identical parallelogram-shaped stripes, as the base and height of the parallelograms must be known in order to calculate the area.

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The simplified expressions are given as follows:

1. 3n³/8 + 2.

2. 2.4y² + 7.6y - 0.5.

The expressions are simplified combining the like terms.

The first expression is given as follows:

(7/8)n³ + 2 - (1/2)n³.

The like terms are given as follows:

Hence the simplified expression is:

3n³/8 + 2.

The second expression is defined as follows:

1.4y² + 3.6y + 8y - 0.5 - 4y + y².

The like terms are given as follows:

Hence the simplified expression is:

2.4y² + 7.6y - 0.5.

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The expression 3x − 6 = 2(x + 4) has one solution of x which is 10

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph

For the given problem, 3x − 6 = 2(x + 4) the solution is sort as thus

3x − 6 = 2(x + 4)

expanding the parenthesis

3x − 6 = 2x + 4

collecting like terms by subtracting 2x from both sides and adding 6 on both sides will result to the equation below

3x - 2x = 6 + 4

x = 10

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Point P lies between Q and R

Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.

Given here:  Points P, Q, and R are collinear, with PQ=5, PR=7, and QR=12

Clearly we can observe that QR = PQ+PR

                                                 12=5+7

And the three points are collinear therefore we can deduce that Point P must lie between the two points Q,R.

Hence, Point P lies between Q and R

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Where while feeding a patient, Nadine, a nurse's aide, twists her upper body as she turns to retrieve a piece of tissue to help the patient wipe hands. She sprains her neck muscles and so has to leave work and go home to rest. Note that Nadine could have correctly turned the body using the principles of body mechanics: "by moving her feet and hips along with the upper body" (Option D)

Employee well-being depends on maintaining good body mechanics at work. Every employee should adhere to the four body mechanics principles. They are as follows:

When these body mechanics principles are followed, employees are less likely to get injured at work and are more productive.

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Answer:

(1, -2)

The solution to a system of equations is the point where the 2 lines intersect.

Examine the graph. Where do the 2 lines intersect?

(1,-2)

The answer is:

Work/explanation:

This system has been solved by the graphing method; both equations have been graphed, and to find the solution, I need to find the point where both graphs intersect. And the graphs are the lines.

The x co-ordinate of the point is the solution for x, and the y co-ordinate of the point is the solution for y.

In our case, the lines intersect at (1, -2), which means that the value of x is 1, and the value of y is -2.

The solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

To solve the inequality 2y – 4x < 8, we can start by isolating y by adding 4x to both sides:

2y < 4x + 8

then divide both sides by 2:

y < 2x + 4

This is the solution in slope-intercept form (y = mx + b), where the slope is m = 2 and the y-intercept is b = 4.

To graph the solution, you can pick a few x-values and substitute them into the inequality to find the corresponding y-values.

You can use x = -2, x = -1, x = 0, x = 1, x = 2, for example and find the y-values for each x, y < 2* -2 + 4 = 0, y < 2* -1 + 4 = 2, y < 20 + 4 = 4, y < 21 + 4 = 6 and y < 2*2 + 4 = 8.

Then plot those points on a coordinate plane and draw the line that goes through them, and shade the half-plane that is below the line

Hence, the solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.

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The Triangle with length of the sides as 10.2 cm 5.8 cm and 4.5 cm is possible.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b ≥   c. The basic tenet of the theorem is that a straight line connects any two places.

Given:

Sides of triangle is: 10.2 cm 5.8 cm and 4.5 cm

Now, using Triangle inequality "the sum of two sides is greater than the third side of the triangle."

Suppose such a triangle is possible.

4.5 + 5.8 > 10.2

5.8 + 10.2 > 4.5

10.2 + 4.5 > 5.8

Hence, the triangle is possible.

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Answer: If it took Luca 20 minutes to walk to the park and his estimate was 25% more than that, we know that the estimate was 20 * 1.25 = 20 + (20 * 0.25) = 20 + 5 = 25 minutes.

So Luca estimated that it would take him 25 minutes to walk to the park.

Step-by-step explanation:

Noah's total score is 17 out of 20 since he answered 3 questions wrong.

A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.

Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.

Given that,

Total multiple choice questions = 20

The score of answering one question correctly = 1

Total number of questions Noah wrongly answered = 3

Therefore, his score out of 20 = 20 - 3 = 17

Thus, Noah's total score is 17 out of 20 since he answered 3 questions wrong.

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Answer:

median = 4

Step-by-step explanation:

On the box plot the median is represented by the vertical line inside the box.

That is the median = 4

The slope of the line is 60 The bus is traveling at a speed of 60 miles per hour.

A line's steepness is determined by its slope. Slope can be computed mathematically as "rise over run" (change in y divided by change in x). In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). Its y value of the y intercept point is represented by b in the equation.

Given that,

A line begins at ordered pair (0, 0) and goes through ordered pair (1, 60) and ordered pair (2, 120).

Slope of the line (m) = (y₂ - y₁) / (x₂ - x₁)

m = 120 - 60 / 2 - 1

m = 60

thus, slope of the line = 60

The bus is travelling at a speed of 60 miles per hour.

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Answer: The student got the wrong answer. ✅

Step-by-step explanation: When you add 364 and 728 together, you get 1092. To make it easier to understand, it is like having 3 piles of 100, 6 piles of 10, and 4 ones on one side, and 7 piles of 100, 2 piles of 10, and 8 ones on the other side, when you put them together you get 10 piles of 100, 8 piles of 10 and 12 ones.

To find the biggest number they have in common, you can divide both numbers by 2 and you get 182 and 364.

So the correct way to rewrite 364 + 728 is 364 * (3+2) ✅

Answer:

ewd

Step-by-step explanation:

ewddew

The equation y = 2x + 2 is a function. This can be determined by observing that for each x-value, there is exactly one corresponding y-value. In other words, the graph of the equation passes the vertical line test, which states that a graph represents a function if no vertical line intersects the graph more than once.

Additionally, as the given points (1,0), (0,2), (1,4), (2,6) all fall on the same line, all with a slope of 2 and y-intercept of 2, so this confirms that the equation is indeed a function.

Answer:

3:8

Step-by-step explanation:

The total number of t-shirts is 16. Out of the 16 t-shirts, 6 are blue. We can write this as 6:16, or 6 out of 16. You can simplify this further by dividing the ratio by 2 to get 3:8. I hope this helps!

The division is performed by dividing the dividend by the divisor. This helps to find the quotient and remainder.

Along with addition, subtraction, and multiplication, the fourth main operation in mathematics is division. There are five main division techniques used in arithmetic calculations: long division, short division, dividing fractions, dividing exponents, and dividing decimals.

For example, to divide 500 by 5 we use the following steps using short division. Here, the divisor is 5 and the dividend is 500.  Doing the division we get, the quotient is 100, and the remainder is 0. This is represented in the attached image. Here, the answer for the division of 500 by 5 is 100.

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Answer:

Succeeded because you did the correct research and made educated investments in a reliable company.

Failed because you did not do good and deep research and invested in an unreliable company.

Answer:

Question 2 :  
[tex]\boxed{-35}[/tex]

Question 3:
[tex]\boxed{7}[/tex]

Question 4:
[tex]\boxed{-5}[/tex]

Question 5:
[tex]\boxed{-5}[/tex]

Step-by-step explanation:

The easiest points to take on the line are those where x =0, y = 35 (0,35) and x = 7, y =0 (7,0)

Question 2.
We can see that between these two points, the y value decreases linearly from 35 to 0. So the rise between (0, 35) and (7,0) = [tex]0 -35 = -35[/tex]

Question 3

[tex]\textrm{Between (0, 35) and (7,0) the x value increases from 0 to 7 so the run is 7}[/tex]

Question 4

[tex]\dfrac{rise}{run}= \dfrac{-35}{7}= -5}[/tex]

Question 5

Slope is the same as rise over run

We can also write this as
[tex]\dfrac{0-35}{7-0} = \dfrac{-35}{7} = -5[/tex]

Though not asked for, the equation of the line is
[tex]y = -5x + 35[/tex]

In mathematics, the image of a function is the algebraic set of all output values it may generate. Real image and Virtual Image.

More generally, evaluating a given function

f at each element of a given subset

A of its domain produces a set, called the "image of

A under (or through) f

f". Likely, the inverse image (or preimage) of a given subset.

B of the codomain of f

f, is the set of all elements of the domain that map to the members of B.

Both Image and inverse image may also be defined for general binary relations, not just functions.

Image In common language an image is a picture or other visual way of showing something. But in mathematics it is another name for Range of a Function

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The value of n is -1 < n < -4.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-4>n or 3n+1>-2

now, solving the above inequality

3n+1>-2

3n > -2-1

3n > -3

n > -1

So, the value of n varies -1 < n < -4.

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Number of functions. It is an important topic in sets and relation. A relation in which each input has a specific output is called a function. If f is a function from set A to set B, then each element of A will be plot with only one element in B.

1. Number of possible functions: If a set A has j elements and set B has k elements, then the number of functions possible from A to B is j ^k.

2. Number of Injective Functions (One to One): If set A has j elements and set B has k elements, j ≥k, then the number of injective functions or one to one function is given by j! / (j-k)!

3. Number of Bijective functions: If there is bijection between two sets A and B, then both sets will have the same number of elements. If n(A) = n(B) = m, then number of bijective functions = m!

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After dilatation, the vertices of polygon ABCD with vertices at A (4, 6), B (2, 2), C (4, 2), and D (4, 4) will be

Dilation is a transformation technique that can either enlarge or reduce the preimage depending on the scale factor.

The following is the dilation transformation rule:

(x, y) with r as the scaling factor (rx, ry)

Using a similar process for the given issue, we have for r = one fourth

preimage    dilation                   image

A(-4, 6)   → (1/4 * -4, 1/4 * 6) →   A'(-1, 1.5)

B(−2, 2)   → (1/4 * -2, 1/4 * 2) →  B'(-0.5, 0.5)

C(4, −2)  → (1/4 * 4, 1/4 * -2) →   C'(1, -0.5)

D(4, 4)   → (1/4 * 4, 1/4 * 4)   →  D'(1, 1)

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