Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.

After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?

The solution is Option B.

The rate of change of population at time t = T when the population has doubled from its initial time is P' = 2P₀ ln ( 1.09 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The formula for the population at time t is

P ( t ) = P₀ ( 1 + 9/100 )^t

P ( t ) = P₀ ( 1 + 0.09 )^t

P ( t ) = P₀ ( 1.09 )^t

Now , when population is doubled from the initial population ,

P ( t ) = 2P₀

Substituting the values in the equation , we get

2P₀ = P₀ ( 1.09 )^t

Taking logarithm on both sides of the equation , we get

log ( 2 ) = t x  log ( 1.09 )

Divide by log ( 1.09 ) on both sides of the equation , we get

t = log ( 2 ) / log ( 1.09 )

To find the rate of change , take the derivative

P'( t ) = P₀ ( 1.09 )^t ln ( 1.09 )

Now ,  we find P'(log(2)/log(1.09))

So , the equation will be

P′ ( log( 2 ) / log( 1.09 ) ) = 2P₀ln( 1.09 )

Hence , the equation will be A = 2P₀ln( 1.09 )

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Therefore , the given expression of this problem of square root

 2√2  not equal to √2.

The value that results from multiplying the square root of an integer by itself is the number.

Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.

Here,

In this case, the mathematical symbol for Root 2 is 2.

Root 2 then multiplied by Root 2.

√2 + √2 = 2√2

If we take the estimated value of 2 = 1.4142

Then

=> 2√2 = 1.4142 x 2

=> 2.8284 (approximately)

Please take note that 2 is an irrational number.

Alternatively, root2* root 2

√2 * √2 = 2

Because 2 is just the square root of 2,

Therefore,

what happens when root 2 + root 2 and root2 root 2 are different

2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)

Therefore , the given expression of this problem of square root

 2√2  not equal to √2.'

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Whole Numbers are the numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}.

Whole Numbers

Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.

Addition , Subtraction , Division and multiplication are also possible with the whole numbers as they are also numbers . Addition and Multiplication are closed which means the sum and multiplication of two numbers is also a whole number whereas Subtraction and Division are unclosed.

We know that natural numbers refer to a set of counting numbers starting from 1, 2, 3, 4 and so on. In simple words, whole numbers are a set of numbers without fractions, decimals, or even negative integers.

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The coefficient of  y² in the expression 3y²+ 4x is 3.

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.

Firstly,

The given equation is 3y²+ 4x

To find : The coefficient of y²

The coefficient is nothing but the number beside the variable.

In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.

As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of  x is 4.

Hence, the coefficient of y² in the equation is 3.

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The equation of line in slope intercept form passing through (-5,-2) and parallel to  y = -2x+1 is  y = -2x -12 .

The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .

the required line is parallel to the line with equation ⇒ y = -2x+1 ,

on comparing it with slope intercept form of line ,

we get the slope(m) as "-2"  .

the required line is passing through (-5,-2).

substituting the values , we get ;

-2 = (-2)(-5) + c ,

-2 = 10 + c ,

c = -10 -2

c = -12 .

So , the equation is ⇒ y = -2x -12 .

Therefore , the slope intercept form of the required line is y = -2x -12  .

The given question is incomplete , the complete question is

How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ?  the point is (-5,-2); and is parallel to y = -2x + 1   .

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For a w10×15 cantilevered beam of A - 36 steel subjected to loading as in the attached image, slope at B is 0.0042rad and displacement at B is 0.034ft.

For w10×15, moment of inertia I = 68.9in⁴ and for A - 36 steel, Young's modulus E = 29e3 ksi

Slope at B

θB = P₂x³/ (2EI) + P₁l³/ (2EI)

θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)

θB = 0.0042rad

Displacement at B

yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)

yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)

yB = 0.034ft

--The question is incomplete, answering to the question below--

"The W10×15 cantilevered beam is made of A - 36 steel and is subjected to the loading shown.

1. Determine the displacement at B, if P1 = 9kip and P2 = 5kip

2. Determine the slope at B, if P1 = 9kip and P2 = 5kip"

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The value of the following expression is true.

Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).

If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.

Correct Question :

Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)

a. false

b. true

c. 0

d. null

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95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

What is proportional limit?

The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.

To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:

lower confidence bound = sample mean - (t-value * standard error)

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

              [tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]

To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.

Substituting these values into the formula for the lower confidence bound, we get:

lower confidence bound = 8.52 - (1.725 * 0.19)

= 8.52 - 0.327

= 8.19

So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.

Hence,  95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.

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More than 50 in mathematical expression is written as >50.

Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.

The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].

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The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service

a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.

When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.

The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.

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Answer:

Step-by-step explanation:

a.) Correct.

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.

Whole numbers are closed under addition and multiplication. If we add and  multiply any two whole numbers, the result will be a whole number.

What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.

If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.

Therefore, whole numbers are closed under addition.

If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.

Therefore, whole numbers are closed under multiplication.

Also , Whole numbers are not closed under Subtraction and division.

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The dimensions of the rectangle is length = 5ft and width = 3ft

Define System of equation

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Let,

x = length of rectangle

y = width of rectangle

Next, set up system of equation

We have given, the length of a rectangle is 5 ft more than twice its width.

x = 2y + 5    --------(a)

Next,  The area of the rectangle is 33 ft²

xy = 33      ----------(b)

x = 33/y

substitute the value of x in eq(a)

x = 2y + 5

33/y = 2y + 5

33 = 2y² + 5y

2y² + 5y - 33 = 0

Factor it,

2y² + 11y - 6y - 33 = 0

y( 2y + 11) - 3( 2y + 11) = 0

(y - 3) (2y + 11) = 0

Split the values,

y - 3 = 0               and         2y + 11 = 0

y = 3                 and             y = -11/2 (ignore this as width cannot be -ve)

Substitute y = 3 in eq(b)

x * 3 = 33

x = 11

So, we get

length = 11 ft and width = 3 ft

Hence, the dimensions of the rectangle is length = 5ft and width = 3ft

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The value of "i" squared results in:

(-1) = i²

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

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The range is an absolute value functions is

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.

A number can never have a negative absolute value. hence the negative values will never be in the range

This makes the range to start possibly from zero, from the graph explained 0 is among the values that are in the range

Considering that absolute values are non zero and option B is the only option that does not have a negative value. This is the best option

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Answer:

The range is an absolute value functions is

B. 0 ≤ y < ∞

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Divide 500 by 40 to find the amount of buses you need

500 ÷ 40 = 12.5

BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people

you'll need 13 buses

Answer:

13 buses

Step-by-step explanation:

12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.

Equiangular triangle or Equilateral triangle have  all the sides equal and all the angles are also equal.

A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.

With each angle measuring 60 degrees, it is also known as an equiangular triangle.

An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.

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The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way.  By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.

There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:

When something is written with an an or b, it signifies that.

A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).

A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).

The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.

Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

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It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.

The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.

The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.

Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.

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Answer:

Bookcase A

Step-by-step explanation:

Bookcase A

1 half = 35 book

4 half = 140 books

So, bookcase A can hold 140 books

Bookcase B

1 half = 26 books

5 half = 130 books

So, bookcase B can hold 130 books

So, Mary should buy bookcase A

Answer:

Bookcase A is the answer

Step-by-step explanation:

Mary has 138 books

Bookcase A = 4 shelves holds 35 books per shelf

= 4 * 35=140

Bookcase B = 5 shelves holds 26 books per shelf

= 5 * 26=130

He should buy Bookcase A, it has enough space for his books

Answer:

1/256

Step-by-step explanation:

-4 times -4 times -4 times -4 = 256

A negative exponent means it's a fraction!

So, the answer is 1/256

answer :

1/256

steps:

negative exponent means it's a fraction

4^-4 =

1/4^4 :

4^4 =

4 * 4 * 4 * 4 =

256

again negative exponent means it's a fraction so

1/256

Systems of linear equations in two variables can be solved in one of four ways: by graphing; by the substitution approach; or by the elimination method and by matrix approach.

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." Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.

Given,

The four methods of solving linear equations are:

The Substitution Method

The Graphing Method.

The Addition Method, also known as the Linear Combination Method, and the Elimination Method.

The Matrix Approach

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Answer:

Step-by-step explanation:

The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.

The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.

Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.

Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.

We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:

28 = A₀ - 8 x 3

28 = A₀ - 24

A₀ = 52

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The complete question:

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?

The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔABC is given as,

AB / sin C = BC / sin A = CA / sin B

The measure of the third angle is given as,

∠A + ∠B + ∠C = 180°

35° + 90° + ∠C = 180°

∠C = 55°

Then the measure of the side c (AB) is calculated as,

AB / sin C = BC / sin A

c / sin 55° = 10 / sin 90°

c = 8.2

Then the measure of the side b (AB) is calculated as,

AC / sin B = BC / sin A

b / sin 35° = 10 / sin 90°

b = 5.7

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The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.

The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.

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The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sort the data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].

Here n = 10, So [(10/2) + (10/2 + 1)]/2.

=> Median = 8.5.

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The operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.

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Answer:

May be minus

Step-by-step explanation:

minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32

Answer:

17

Step-by-step explanation:

(9+25)/2 = 34/2 = 17

when finding a mean, you have to add all the numbers and divide the sum by the number of values given.

Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.

For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

Answer:

30 inches

Step-by-step explanation:

The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.