lee has $\frac{5}{7}$ of a gallon of water. he gives $\frac{1}{2}$ of a gallon of water to his dog, gilligan. what fraction of the amount of water that lee had originally did he give to gilligan?

The set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

You must take the following actions to determine the standard deviation of a set of observations:

Mean: (32 + 28 + 29 + 30 + 31) / 5 = 30

Deviations: 32 minus 30 = 2, 28 minus 30 = 2, 29 minus 30 = 1, 30 minus 30 = 1, etc.

Squared deviations are as follows: 22 = 4, (-2)2 = 4, (-1)2 = 1, and 02 = 0.

Sum of squared deviations: (Sum of squared deviations) / (number of observations) = 10 / 5 = 2

Standard deviation is square root of sum of squared deviation.

so, [tex]\sqrt{2}[/tex] is 1.41.

As a result, the set of observations (32, 28, 29, 30, and 31) has a 1.41 standard deviation.

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Answer: 12 m

Step-by-step explanation:

Answer:

  b)  process b

Step-by-step explanation:

You have 2 of machine A, each of which can do its process in 1 minute; 1 of machine B, which takes 2 minutes to do its process; and 3 of machine C, each of which takes 3 minutes to do its process.

In 6 minutes, the 2 of machine A can produce 2 × 6/1 = 12 units.

In 6 minutes, the 1 of machine B can produce 1 × 6/2 = 3 units.

In 6 minutes, the 3 of machine C can produce 3 × 6/3 = 6 units.

Process B produces the fewest units in equivalent time, so process b is the bottleneck.

__

Additional comment

The production quantity of a given machine is ...

  (production time)/(time/unit) = units

This will be multiplied by the number of machines doing the process.

For comparison purposes, we used a production time of 6 minutes here.

Answer:

Equations of parallel and perpendicular lines The equation of a straight line is represented as \ (y=ax+b\) which defines the slope and the \ (y\)-intercept. Here \ (a\) represents the slope of the line. Since two parallel lines never intersect and have the same slope, their slope is always equal.

Step-by-step explanation:

Answer:

2) y ≥ 2x - 3

Step-by-step explanation:

3 and 4 would be eliminated because the line does not intersect at (0, 2), but rather (0, -3).

Answer: One solution

Step-by-step explanation:

Answer:

Domain:

[tex]0 \leqslant x \leqslant 4[/tex]

Range:

[tex]0 \leqslant x \leqslant 64[/tex]

The interpretation of the x-intercept in the context of the given problem is: B. After 16 months, the business will have $0 remaining in their technology budget.

To find the x-intercept of an equation, substitute the value of y = 0, and solve for x. It is the value of x when y or the output = 0.

Given the equation, T(x) = −135x + 2160, where T(x) is the amount of money remaining in the budget for technology, and x is the number of months, the x-intercept would be the number of months that the business will have $0 in their budget for technology.

To find the x-intercept, substitute T(x) = 0, into T(x) = −135x + 2160:

0 = −135x + 2160

135x = 2160

Divide both sides by 135

135x/135 = 2160/135

x = 16

This means after 16 months, the technology budget that the company will have remaining is $0.

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Subtraction property of equality is B, -4.

What is subtraction property?

The Subtraction Property of Equality states that if two expressions are equal, then the same expression minus any number will also be equal. In other words, if a = b, then a - c = b - c. This property is important in algebra, as it allows us to solve equations by subtracting the same number from both sides. This property is also known as the Subtraction Property of Equality or the Subtraction Property of Equality of Two Values. It is an important concept that allows us to solve equations, and it is used in all levels of mathematics.

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The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from 0 to 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. A value of 0.5 or higher is considered a strong correlation.

The correlation coefficient is calculated by taking the covariance between two variables and dividing it by the product of the standard deviations of the two variables. The formula is as follows:

r = covariance(x,y) / (stdDeviation(x) * stdDeviation(y))

The correlation coefficient is a statistical measure used to quantify the strength of the linear relationship between two variables. It takes a value between 0 and 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. The correlation coefficient is calculated by taking the covariance between the two variables and dividing it by the product of their standard deviations. A negative correlation coefficient means that as one variable increases, the other decreases. A value of 0.5 or higher is considered a strong correlation. The correlation coefficient can be used to determine the strength of the relationships between variables, whether they are linear or non-linear. It is an important tool for data analysis and can help to identify relationships between different variables.

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Answer:

There isn't enough information to solve for x.

Step-by-step explanation:

The way the statement of similarity is written, we get this proportion:

TY/CH = TL/CK = YL/HK

Replace segment names with lengths:

TY/10 = 25/CK = (4x - 1)/(x + 5)

There isn't enough information to solve for x.

The number of days it will take Sharon to hit her target 700 points is 21 days

490 + 10g = 700

Subtract 490 from both sides

10g = 700 - 490

10g = 210

divide both sides by g

g = 210 / 10

g = 21

Therefore, it will take Sharon 21 days to meet her target points.

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The multiplicative rate of change of the exponential function represented in the table is given as follows:

1.5.

For an exponential function, when x is increased by one, the output variable y is multiplied by a constant, called multiplicative rate of change of the exponential function.

Then, given a table of values, the rate of change is obtained by the division of two outputs(output with the greater input divided by output with the smaller input) when their inputs have a difference of 1.

Thus, for the table, the rate of change is obtained as follows:

6.75/4.5 = 1.5.

(the difference of the inputs is of 2 - 1 = 1).

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(4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

What does greater than (>) mean ?

Greater than means that the variable or number is more than the given limit. On the other hand, greater than or equal to states that the number or variable is either equal to or more than the given limit. The greater-than symbol is represented as >, whereas the greater than or equal to sign is represented as ≥.

Given :

(4,3)

(4,4)

(0,-4)

(4,3.9)

(0,0)

Since , all the ordered pairs are in the (x,y) form , we can clearly see that (4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

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Yes, it is generally considered appropriate for a 12-year-old to learn algebra. Algebra is a branch of mathematics that involves working with variables and equations to solve problems. It is usually introduced to students in middle school or junior high school, which is around the age of 12 or 13.

According to studies, depending on the teaching technique and intellectual maturity: between 5 and 13. Algebra is a theoretical algebra with fewer techniques for demonstrating tangible lessons.

A youngster who develops abstract comprehension at a young age might learn extremely quickly, but a pupil who has difficulties with abstract notions may struggle well into their adolescence.

It is crucial to recognize that each student learns at a different rate and may have distinct arithmetic talents and weaknesses. It is critical that students receive the necessary support and adjustments in order to study algebra and excel in their math studies.

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The x and y intercepts of the graphed function are (–1, 0) and ( 0,-3 ) respectively.

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A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .

A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.

Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.

In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.

A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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Answer:

-3/2

Step-by-step explanation:

Let's call the number we're trying to find "x". When we double x and then subtract 3, we get 2x-3. The statement says that this is the same as if we had quadrupled x, which would be 4x. We can set these two expressions equal to each other to create an equation:

2x - 3 = 4x

We can solve this equation by first adding 3 to both sides to get rid of the negative number:

2x - 3 + 3 = 4x + 3

This simplifies to:

2x = 4x + 3

We can now subtract 4x from both sides to get rid of the 4x term:

2x - 4x = 4x + 3 - 4x

This simplifies to:

-2x = 3

Finally, we can divide both sides by -2 to solve for x:

(-2x) / (-2) = 3 / (-2)

This simplifies to:

x = -3/2

Therefore, the number we were trying to find is -3/2.

Answer:

Let's call the number we're trying to find "x". If we double x and then subtract 3, we get the expression 2x - 3. If we quadruple x instead, we get the expression 4x. We are looking for a value of x that makes these two expressions equal, so we can set them equal to each other and solve for x:

2x - 3 = 4x

To solve this equation, we can first combine like terms on each side by adding 3 to both sides and then dividing both sides by 2:

2x - 3 + 3 = 4x + 3

2x = 4x + 3

Combining like terms on the left side gives us:

2x - 4x = 4x + 3 - 4x

0 = 3

This equation is clearly false, since no value of x can make 0 equal to 3. Therefore, there is no solution to this problem, and the original number cannot be determined.

In general, if you are trying to solve a problem involving algebraic equations and you end up with a false equation (like 0 = 3 in this case), it means that there is no solution to the problem. This can happen for a variety of reasons, but in this case it is because the original problem statement was not possible or did not make sense.

Step-by-step explanation:

To rewrite an expression in equivalent form, you can use the distributive property, combine like terms, apply the commutative property, or use identities to simplify and rearrange the expression.

The distributive property states that multiplying a term and a sum of two or more terms is the same as multiplying each individual term and then adding the products together. It can be used to simplify expressions by breaking down larger terms into smaller ones. For example, 8(x + 2) can be rewritten as 8x + 16.Combining like terms is another way to rewrite expressions in equivalent form. This involves adding (or subtracting) two or more terms with the same variables. For example, 5x + 3x can be rewritten as 8x.The commutative property states that changing the order of two numbers or variables does not change their value. This can be used to rearrange expressions in equivalent forms. For example, 5x + 2y can be rewritten as 2y + 5x.Finally, identities are equations that are always true. They can be used to simplify and rearrange expressions in equivalent form. For example, (x + y)2 can be rewritten as x2 + 2xy + y2 using the identity (x + y)2 = x2 + 2xy + y2.

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Answer:

Below

Step-by-step explanation:

The height of the candle DEPENDS on how many hours it has burned.

Dependent variable = height

Independent = hours

The principal of account A is $3 and the principal of account B is $4, Account B had the greater principal.

What is principal?

The principal is the sum that was first invested or borrowed from the bank. P stands for the principal. Rate: Rate is the interest rate at which the main sum is loaned to a person for a specific period of time; it may be 5%.

Given $15.75 in interest in Account A with interest rate 3.0% and $28.00 in interest in Account B with interest rate 4.0% after 21 months.

The formula of simple interest is I = PRT.

For account A:

R = 3.0% = 0.03

T = 21 month = 21/12 year

I = $15.75

P = I/RT

P = 15.75/ (0.03 × (21/12))

P =$3

For account B:

R = 4.0% = 0.04

T = 21 month = 21/12 year

I = $28.00

P = I/RT

P = 28.00/ (0.04 × (21/12))

P =$4

The principal of account B is more than that of account A.

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The set of all the real numbers are written as R.

The term set in set theory can be written as the well-defined collection of objects called elements or members of the set.

Here we have to find the way to write all real numbers.

Here we have considered that all the real numbers are collectively put on to the set.

And the set that contain all the real numbers are called R.

We all know that the real number contain all the number like negative , positive numbers.

So, Here we consider that if the domain of a function is all real numbers, then here we can represent this using interval notation as (−∞,∞).

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Answer:

Step-by-step explanation:

answer is 3 because formula of mean is Mean = {Sum of Observation} ÷ {Total numbers of Observations}.

so 1+2+3+4+5=15/5=3

so 3

The mean or arithmetic mean* is represented with this symbol [tex]\boldsymbol{\sf{\overline{x}}}[/tex], and it is calculated by adding all the data, and dividing them in total, by the total number of data there is.

The mode of 1,2,3,4,5 is 3✅.

Let x be the coefficient of y^2 in the expression 2x^2y+10xy^2-5y^2. So x=5.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.

As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

The given algebraic expression is 2yx^2+10xy^2-5y^2.

The terms are xy^2, yx^2 any y^2

So the co-efficient of y^2 is 5.

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Answer: The first one is correct

Step-by-step explanation: 4x(-2)=-8; The car used 8 gallons of gasoline.

The graph of the given function is attached below.

What is a absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x > 0 and f(x) = -x if x 0.

Given function is g(x)= - 2|x -5|-4.

Finding some points on the graph:

Putting x = 5

g(5)= - 2|5 -5|-4

g(5) = -4

Putting x = 0

g(0)= - 2|0-5|-4

g(0) = -2 ×5 - 4

g(0) = -14

Putting x = 10

g(10)= - 2|10 -5|-4

g(10) = -2 ×5 - 4

g(10) = -14

The points on the graph are ( 5,-4), (0,-14), (10,-14).

Plot the points and joint them.

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Answer:

$12

Step-by-step explanation:

given:

Stefan sells jin a bicycle for $114 and a helmet for $18.

we're gonna add to get the total cost 114 + 18 = $132

The total cost is 110% of what he spent originally to buy the bike and helmet.

divide 110% by 100 to get the answer in decimal which if you calculate is 1.1

now we're gonna make a simple equation and assume what Stefan spends originally is x

1.1 * x = 132

1.1x = 132

(now we want x to be alone so we can find its value so divide both sides by 1.1 (division is the opposite of multiplication if, for example, we have 1.1 - x   1.1 is positive so take it to the other side it'll be negative))

after dividing x=120

therefore, he originally spent $120

and to find how much money Stefan made we're gonna subtract 132-120 = $12

Stefan made $12

We can solve this question using Linear equations . The answer for the question is Option B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

So in the given question the motorboat is 55 km from the shore.

  SO y =55 when x=0

  where y is the distance and x is time.

   after 12 minutes it is 19km from the sea shore.

  So y=-3x +55 is the equation.

We can solve this question using Linear equations . The answer for the question is Option B.

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