Hana is using a square piece of cardboard to make a box without a lid. She cuts 5-inch squares from each corner and folds up the edges. The finished box has a volume of 2,000 cubic inches. Which equation can be used to find the dimensions of the original cardboard piece?.

The first four terms and the hundredth term of the sequence whose nth term is given as an=n^2-3 are -2, 1, 6, 13, and 9997, respectively.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

aₙ=n²-3

a₁=-2

a₂=1

a₃=6

a₄=13

a₁₀₀=100²-3

=9997

The first four terms and the 100th term of the sequence whose nth term is given as an=n^2-3 is -2, 1, 6, 13 and 9997.

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To solve this we would divide the pirce of the soups by their container ounces

$2.38÷14=$.17 per ounce

$5.28÷30=$.176 per ounce

We do not use a thrid decmal place when talking about money so we would round $.176 (since the third decmial place is greater than or equal to 5) up to $.18

Therefore Two 14 ounce containers of soup is a better deal per ounce.

The number of children and adult that were there are 117 aand 178 respectively.

Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The recipients admission total of 560.75 dollars.

The number of children and adult can be calculated as follows;

Using equations,

let

x = number of children

y = number of adult

Therefore,

x + y = 295

1.75x + 2y = 560.75

multiply equation(i) by 2

2x + 2y = 590

1.75x + 2y = 560.75

subtract the equation

0.25 x = 29.25

x = 29.25 / 0.25

x = 117

Hence,

y = 295 - 117

y = 178

Therefore,

number of children = 117

number of adult = 178

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Answer:

Step-by-step explanation:

Ln means log to the base e and 3x+1 is an exponent

So the answer is:

4 = e^(3x+1).

The average daily balance for this month will be $1,026.45.

Your charge card's average daily balance is calculated by dividing the total balance on your card at the conclusion of each day by the length of time in a billing cycle, which can range from 28 to 31 days depending on the month. You can total the following to find your daily balance: The card's balance when the day began.

Average daily balance = (Sum of daily balance) / (Number of days)

Number of days                Balance                    Daily balance

           4                              $758                            $3,032

          12                              $879                           $10,548

          10                             $1,015                           $10,150

           5                             $1,618                            $8,090

Then the average daily balance is given as,

Average daily balance = ($3,032 + $10,548 + $10,150 + $8,090)

                                                       (4 + 12 + 10 + 5)

Average daily balance = $31,820 / 31

Average daily balance = $1,026.45

The average daily balance for this month will be $1,026.45.

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Given equation is a first-order nonlinear ordinary differential equation (ODE): y' - (x + y - 1)^2 = 0

What is differential equation ?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

This equation can be solved using various methods, such as numerical methods or analytical methods like the implicit function theorem or the method of characteristics. However, finding an exact solution can be challenging and may not always be possible.

If you would like to find an approximate solution to this ODE, you could use numerical methods such as Euler's method, Runge-Kutta method, or the finite difference method. These methods can provide a numerical approximation to the solution for a given range of x and a specified initial condition.

The given equation is a first-order nonlinear ordinary differential equation (ODE):

y' - (x + y - 1)^2 = 0

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The fundamental existence theorem guarantees that for the initial value problem dy/dt = f(t,y), y(t0)=y0, where f is a continuous function on a region containing the point (t0, y0), there exists a unique solution y(t) defined on some interval containing t0.

The fundamental uniqueness theorem guarantees that if two solutions to the initial value problem exist, they must be equal on the intersection of their domains of definition.

For the first initial value problem: dy/dt = |t| + y, y(0) = 0, the fundamental existence theorem guarantees that there exists a unique solution to the problem in some interval containing t = 0.

For the second initial value problem: dy/dt = 2t + |y|, y(0) = 0, the fundamental existence theorem guarantees that there exists a unique solution to the problem in some interval containing t = 0.

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The correct answer is log(x^(x)) = x * log(x).

The logarithmic rule states that log(a^b) = b * log(a).

So, let's apply this rule to log(x^(x)):

log(x^(x)) = x * log(x)

On the right side of the equation, x represents the exponent and log(x) represents the base.

This equation states that the logarithm of x raised to the power of x is equal to x times the logarithm of x.

Now let's simplify the other options:

x * log(x) is already simplified from the equation above, so we don't need to change it.

log(x) * log(x) is simply the logarithm of x raised to the power of 2, which is not equal to the logarithm of x raised to the power of x.

log(x) is the logarithm of x with a base of 10, and log(x) log(x) does not have a valid mathematical interpretation.

Therefore, the correct answer is log(x^(x)) = x * log(x).

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Answer:

0.6

Step-by-step explanation:

60% into a decimal is 0.6

you move the decimal two places to the left

Answer:

70

Step-by-step explanation:

Let the number we want is "x".

42 = 60% of x

42 = 60/100 x

4200 = 60 x

4200/60 = x

x= 70

The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.

The area enclosed by the curve y = -x² and y = x² - i is the difference of the areas between these two curves.

To find the area enclosed by the curve y = x², we need to find its definite integral with respect to x from -∞ to ∞.

The definite integral of y = x² with respect to x from -∞ to ∞ is:

∫[-∞,∞] x² dx = (x³/3) from -∞ to ∞

Since the definite integral of an infinite function from -∞ to ∞ is undefined, we cannot find the exact value of the area enclosed by the curve y = x².

However, we can use the definite integral of y = x² - i with respect to x from -∞ to ∞ to find the area enclosed by the curve y = x² - i:

∫[-∞,∞] (x² - i) dx = (x³/3 - i * x) from -∞ to ∞

Again, the definite integral of an infinite function from -∞ to ∞ is undefined, so we cannot find the exact value of the area enclosed by the curve y = x² - i.

Since the area enclosed by the curve y = -x² is the same as the area enclosed by the curve y = x² but with the opposite sign, the difference of the areas enclosed by the two curves is equal to 56:

Area enclosed by y = x² - i - Area enclosed by y = -x² = 56

The first equation, y = -x^2, is a parabola that opens downwards.

The second equation, y = x^2 - i, is also a parabola but is translated downward by i units.

The area enclosed by the two curves will be the difference between the area under y = -x^2 and the area under y = x^2 - i.

The area under y = -x^2 can be calculated as follows:

A = ∫[-a,a] -x^2 dx = -(1/3) x^3 |^a_-a = (1/3) a^3

Where a is the x-value at which the two curves intersect.

The area under y = x^2 - i can be calculated as follows:

B = ∫[-a,a] (x^2 - i) dx = (1/3) x^3 - i x |^a_-a = (1/3) a^3 - i a

The area enclosed by the two curves is then given by:

C = B - A = (1/3) a^3 - i a - (1/3) a^3 = -i a

Since we know that the area enclosed by the curves is 56, we can set up the equation:

-i a = 56

So,

i = -56/a

Since a value is unknown, we cannot determine the exact value of i. However, we can use this equation to find the value of i for different values of a.

Therefore, The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.

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QUESTION CORRECTION: Find the value of i for which the area enclosed by the curve =−x² and =x²− i equal to 56.

The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.

The area enclosed by the curve y = -x² and y = x² - i is the difference of the areas between these two curves.

To find the area enclosed by the curve y = x², we need to find its definite integral with respect to x from -∞ to ∞.

The definite integral of y = x² with respect to x from -∞ to ∞ is:

∫[-∞,∞] x² dx = (x³/3) from -∞ to ∞

Since the definite integral of an infinite function from -∞ to ∞ is undefined, we cannot find the exact value of the area enclosed by the curve y = x².

However, we can use the definite integral of y = x² - i with respect to x from -∞ to ∞ to find the area enclosed by the curve y = x² - i:

∫[-∞,∞] (x² - i) dx = (x³/3 - i * x) from -∞ to ∞

Again, the definite integral of an infinite function from -∞ to ∞ is undefined, so we cannot find the exact value of the area enclosed by the curve y = x² - i.

Since the area enclosed by the curve y = -x² is the same as the area enclosed by the curve y = x² but with the opposite sign, the difference of the areas enclosed by the two curves is equal to 56:

Area enclosed by y = x² - i - Area enclosed by y = -x² = 56

The first equation, y = -x^2, is a parabola that opens downwards.

The second equation, y = x² - i, is also a parabola but is translated downward by i units.

The area enclosed by the two curves will be the difference between the area under y = -x^2 and the area under y = x² - i.

The area under y = -x^2 can be calculated as follows:

A = ∫[-a,a] -x²dx = -(1/3) x³ |^a_-a = (1/3) a³

Where a is the x-value at which the two curves intersect.

The area under y = x^2 - i can be calculated as follows:

B = ∫[-a,a] (x² - i) dx = (1/3) x³ - i x |^a_-a = (1/3) a³ - i a

The area enclosed by the two curves is then given by:

C = B - A = (1/3) a³ - i a - (1/3) a³ = -i a

Since we know that the area enclosed by the curves is 56, we can set up the equation:

-i × a = 56

So,

i = -56/a

Since a value is unknown, we cannot determine the exact value of i. However, we can use this equation to find the value of i for different values of a.

Therefore, The value of i is -56/a, Since the value of a is unknown, we cannot determine the exact value of i.

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QUESTION CORRECTION: Find the value of i for which the area enclosed by the curve =−x² and =x²− i equal to 56.

The two different expressions for the total cost will be written as:-

C = 2S x 1.065

C = 0.13S + 2S

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Benita buys 2 shirts for the same price, s. The sales tax rate is 6.5%.

The two expressions for the total cost of the two shirts will be:-

C = 2S x ( 1 + 0.065)

C = 2S x ( 1.065)

The second way of writing the expression is:-

C = 2S x  0.065 + 2S

C = 0.13S + 2S

Hence, the expressions are C = 2S x 1.065 and C = 0.13S + 2S.

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The independent variable is the width of the dance floor (w), while the dependent variable is the area of the dance floor (A). Changes in w will affect the value of A.

The equation A = 25w describes the relationship between the area (A) of a rectangle dance floor and its width (w).

Thus, if the width of the dance floor is increased, the area of the dance floor will also increase.

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The numeric value of the exponential function at x = 7 is given as follows:

f(7) = -192.

The definition of an exponential function is given as follows:

y = ab^x

In which the parameters are defined as follows:

When x = 0, y = -1.5, hence the parameter a is given as follows:

y = -1.5.

When x = 2, y = -6, hence the parameter b is obtained as follows:

-1.5b² = -6

b² = 4.

b = 2.

Hence the function is defined as follows:

y = -1.5(2)^x.

Hence the numeric value at x = 7 is given as follows:

y = -1.5(2)^7

y = -192.

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Answer:So the the force between the 3rd pair of charges is maximum.Then the force between 2nd pair of charges will come.The least force is between the 1st pair of charges.

Step-by-step explanation:

STEP 1:

In the 1st pair the charges are,

The distance between them is “x”.

The force between them according to coulomb’s law will be,

The minus sign indicates the force is attractive.

The magnitude is .

STEP 2:

For the 2nd pair of charges,

The distance between them is “x”.

The force between them according to coulomb’s law will be,

The magnitude is .

STEP 3:-

For the 2nd pair of charges,

The distance between them is “x/2”.

The force between them according to coulomb’s law will be,

The magnitude is .

CONCLUSION:

The volume of the rectangular prism given the length, width and height is 6 14/27 cubic feet.

The correct answer choice is option B

Volume of a rectangular prism= length × width × height

Length= 1 5/6 ft

Width = 1 1/3 ft

Height = 2 2/3 ft

Volume of a rectangular prism= length × width × height

= 1 5/6 × 1 1/3 × 2 2/3

= 11/6 × 4/3 × 8/3

= (11 × 4 × 8) / (6 × 3 × 3)

= 352 / 54

= 6 28/54

= 6 14/27 cubic feet

In conclusion, the volume of the rectangular prism is 6 14/27 cubic feet

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Answer:

for an approximate result, divide the mass value by 28.35

so the answer is 1.058 ounces

30 grams of ounces would be 1.05822.

An ounce weighs 28 grams. A quarter ounce weighs 7 grams. A half ounce weighs 14 grams. One-eighth of an ounce weighs 3.5 grams. A gram is a unit of weight equal to one thousandth of a kilogram, whereas an ounce is a unit of mass equal to 28.35 grams.

In both the US and Imperial measurement systems, a measure of mass. An ounce is roughly the same weight as a slice of bread. 28.349523125 grams is the precise weight.

Everywhere that isn't metric, including the United States and a few other countries, uses ounces as the basic unit of mass. In actuality, 28.35 grams or such make up 1 ounce.

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The family would more likely choose the stock option, if the period of investment is 20 years,after calculating the simple & compound interest.

$999.60 is 1.02 times $980, and $1,019.59 is 1.02 times $999.60.

They may choose bonds or savings account depending on the assumptions they make about the time frame of the investment.

The value of the bonds b=1,000+20x and value of the stocks is s=980⋅(1.02)x , where x is the number of years since the investment were made.

For 10 years, the value of the bond will be

b=1,000+200=1,200 dollars.

The value of the stock will be s=980⋅(1.02)10≈1,195 dollars.

They should choose the bond option if the period of investment is 10 years.

For 20 years, the value of the bond will be

b=1000+400=1,400 dollars.

The value of the stock will be 980⋅(1.02)20=1,456980⋅(1.02)20=1,456 dollars.

So they choose the stock option, if the period of investment is 20 years.

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The complete question is attached below.

The cost of a theater ticket is an example of A. quantitative data in statistics.

Quantitative data is data with numerical value.

Quantitative data shows a certain quantity, amount, or range of values.

Nominal data classifies qualitative data according to certain categories.  It is not quantitative.

Categorical data deals with grouped data, using names and labels.

Thus, since the cost of a theater ticket is numerical, it is quantitative data instead of nominal or categorical.

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Answer:6

Step-by-step explanation:

Let the number be x.

Now, 3x+6=24

3x=24-6

3x=18

x=18/3

x=6

Answer:

6

Step-by-step explanation:

We can work the problem backwards

Since something gives 24 that means it equals 24

= 24

Something increased by 6, so something added by 6

Something + 6 = 24

Making something = x

x + 6 = 24

If we subtract 6 from both sides

x = 18

Trice a number, so divide this number by 3

x = 6

Trice of 6 is 18... 18 increased by 6 gives 24

The statement about Raj's data sets which true is The average boy plays 8.5 hours more per week than the average girl.

Technically, a dataset is a collection of related items that can be accessed individually or in certain management combinations as a single unit. Datasets can be organized into several types of data structures. Examples of dataset in the business world can be seen from names, salaries, employee contact information, to sales figures, and so on.

In conclusion, a dataset is a collection of data that is ordered and obtained from a collection of information. The collection of information itself is obtained from observation, measurement, study, or analysis to become data. Data can be facts, numbers, names, or even descriptions. Therefore, datasets are closely related to data mining activities which help data scientists analyze data into coherent information.

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The triangle PQR is an equilateral triangle

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

PQ=QR.

m/P = (2x - 26) and m/R= (x+17)

When two sides of a triangle are congruent, then the triangle is an isosceles triangle

Using the above as a guide, we have the following:

2x - 26 = x + 17 --- base angles of an isosceles triangle

So, we have

x = 43

This gives

m/P = 2 * 43 - 26 = 60

m/R= 43 + 17 = 60

If two angles of a triangle measure 60 degrees, then the third angle is 60 degrees

This implies that the triangle is an equilateral triangle

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The measure of the angle Q is 46.4°

Recall that the sum of the angles of a triangle is equal to 180 degrees

We are told that

PQ = QR

Q = 100°

As PQ and QR are equal so,

By theorem angle opposite to equal sides are equal so,

We can say that angle P = angle R = X

Therefore by angle sum  property of the triangle,

angle P + angle Q + angle R = 180°

X +(2x - 26)+ (2x - 26) = 180°

This implies that 5x-52=180

Collecting like terms

5x=180+52

5X = 232°

X =46.4°

Therefore the measure of R = 40°

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Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic equations.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.

Factoring, utilizing square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.

To factor an equation with quadratic terms:

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If the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" then , the data are considered at the nominal level of measurement .

The Level Of Measurement of a data set refers to the type of values that a variable can take and the properties that these values have.

In the survey , the respondents are identified as 1 for "yes," 2 for "no," 3 for "maybe," and 4 for "anything else."

These values are categorical, meaning they are names or labels for different categories. The data collected at this level is referred to as nominal level of measurement. This level of measurement is used when the variables are categorical and the order of the categories does not matter.

Therefore , the data collected in this survey is nominal and is used to describe categories or names, rather than numerical values.

The given question is incomplete , the complete question is

In a survey, the of respondents are identified as 1 for "yes" and 2 for "no" and 3 for "maybe" and 4 for "anything else" . the average (mean) is calculated for 665 respondents and the result is 1.5 ,

the data are at what level of measurement ?

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(a) The cardinality of A x B is 54.

(b) The cardinality of the power set P(A) is 64.

Let A and B be finite sets.

A has cardinality 6 and B has cardinality 9.

|A| = 6 and |B| = 9

A set's size, or the total number of its elements, is indicated by the set's cardinality.

(a) We have to determine the cardinality of A x B.

|A x B| = |A| x |B|

Now putting the value

|A x B| = 6 x 9

|A x B| = 54

(b) We have to determine the cardinality of the power set P(A).

|P(A)| = 2^{|A|}

Now putting the value

|P(A)| = 2^{6}

|P(A)| = 64

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The sampling distribution model for figuring out how many people in this group might not pay on time is:

E. mean = 8%; standard deviation = 1.1%.

The steps to determine the mean and standard deviation of the sampling distribution of the proportion of clients who may not make timely payments would be:

Start with the idea that 8% of the loans will have payments that are late. So the percentage of people who pay late is p = 0.08.

Calculate the sample size, which is given as n = 600.

Determine the mean of the sampling distribution. The mean of the sampling distribution of the proportion of late payments is equal to the population proportion, which is 0.08.

Find the standard deviation of the distribution of the samples. The standard deviation is discovered by taking the square root of the commodity of the sample size and the percentage of late payments in the whole population (1 - percentage of late payments in the whole population) and dividing it by the sample size:

σ = √( (p * (1-p)) / n )

σ = √( (0.08 * 0.92) / 600 ) ≈ 0.011

So, the answer will be option E. mean = 8%; standard deviation = 1.1%.

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Kayla -24

Leanne-18

Step-by-step explanation:

4+3=7

42÷7=6

6x4=24

3x6=18

Answer: Let's call the number of marbles that Kayla gets x. Then, Leanne gets 3x marbles. The total number of marbles that the girls receive is x + 3x = 4x, so 4x must equal 42 marbles:

4x = 42

Dividing both sides by 4:

x = 10.5

Since the number of marbles that each girl receives must be an integer, we round down to the nearest whole number. So, Kayla gets 10 marbles and Leanne gets 3 * 10 = 30 marbles.

Step-by-step explanation:

The required point of intersection of the two lines is (-2, 7/3).

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

The equation "y = 2/3x + 3" represents a line in the coordinate plane. It has a slope of 2/3 and a y-intercept 3. The equation "x = -2" represents a vertical line. It has no slope and the x-coordinate of all its points is -2.

Since the two equations represent lines, we can find their point of intersection by setting the two equations equal to each other and solving for y.

So, we have:

2/3x + 3 = y

and

x = -2

Substituting x = -2 into the first equation, we get:

2/3(-2) + 3 = y

Solving for y:

y = -2/3 * -2 + 3 = 4/3 + 3 = 7/3

Thus, the point of intersection of the two lines is (-2, 7/3).

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Answer: Plugging in the values x=2, y=3, and z=4 into the expression x(2y+z)², we get:

2(2(3)+4)² = 2(10)² = 2 * 100 = 200

So the expression evaluates to 200.

Step-by-step explanation:

The function y = e⁻ᵃ is a solution to the differential equation y' + y = 0 that satisfies the initial condition y(0) = 1.

Here we need to find a function that satisfies a differential equation and an initial condition.

The differential equation is given as

=> y' + y = 0.

To solve this differential equation, we need to find the general solution, which is a function that satisfies the equation for all values of t.

The characteristic equation for this equation is

=> m + 1 = 0,

which gives us m = -1 as the only solution.

This means that the general solution can be expressed as y = c1e⁻ᵃ, where c1 is an arbitrary constant.

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