a rectangular box with a square base is made from 216 ft2 of material. which dimensions will result in a box with the largest possible volume?

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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The equation that models this linear function is y = 12.5x + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (44.50 - 32.00)/(3 - 2)

Slope, m = 12.5/1

Slope, m = 12.5.

At point (2, 32.00), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - 32.00 = 12.5(x - 2)

y - 32.00 = 12.5x - 25

y = 12.5x - 25 + 32.00

y = 12.5x + 7

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Complete Question:

Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. What is the equation that models this linear function?

Answer:

85 Millimeters

Step-by-step explanation:

1 centimeter is equal to 10 millimeters. Hope this helped!

someone asked tjis question before

Step-by-step explanation:

he needs 100ml to make 250ml, the explanation is somewhere on this app

Answer:

150ml

Step-by-step explanation:

250ml=100%

25ml=10%

times 25mls 6 times so that it become 60%=150ml

Aubree's car used 1 gallon to travel 30 miles.

The car used 4 gallons to travel 120 miles. We need to calculate the distance car can travel with 1 gallon of gas.

By unitary method;

The distance car can travel = (120/4)*1 =30

Aubree's car used 1 gallon to travel 30 miles.

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On 1 gallon of gas, Aubree`s car can go 30 miles.

This is a question of the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, [by dividing] and then finding the necessary value by multiplying the single unit value.

Aubree`s car used 4 gallons of gas to travel 120 miles. So, to find the miles it travelled on 1 gallon of gas. We can simply just divide the total miles the car travelled by the total litres of gas it used.

Therefore, 120/4=30 miles.

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When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.

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When Claire and Megan meet, they will be [tex]13\frac{1}{2}[/tex] miles away from the outpost. This can be solved by applying the concept of speed.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone [tex]8\frac{1}{2}[/tex] miles. When they meet, they will have gone a total of [tex]17\frac{1}{2}[/tex] miles, leaving them [tex]13\frac{1}{2}[/tex]miles away from the outpost.

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The sides 7cm , 24cm and 25cm ; forms a right angled triangle because the condition of Pythagoras Theorem is satisfied .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of hypotnuse (longest sides) is equal to the sum of the square of the other two sides .

The sides are given as ⇒ 7cm , 24cm and 25cm ;

here the longest side (hypotnuse) is = 25 cm ;

According to Pythagoras theorem ,

⇒ [tex]25^{2} =24^{2} +7^{2}[/tex] ;

⇒ [tex]625=576+49[/tex] ;

⇒ [tex]625 = 625[/tex] ;

The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Angled Triangle .

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All of the rectangles together measure 1250 meters in length.

A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.

Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:

(Rectangle width) x (Square cloth length) / (Width of square cloth)

The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.

Therefore, each rectangle is 25 meters long.

We divide the square cloth's length by each rectangle's width to get the total number of rectangles.

25m / 0.5m (50cm) = 50 rectangles.

Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:

50 m x 25 m = 1250 m

Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.

Therefore the rectangles together measure 1250 meters in length.

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maximum degree f(x) = x2 + bx + c g(x) = x3 + wx2 + yx + z [f(x)]3 - [g(x)]2 + f(x) - 1 (x2+bx+c)3 - (x3+wx2..for the given polynomial

What is a polynomial class 9?

Polynomial Definition. Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. An algebraic expression p(x) = a0xn + a1xn-1 + a2xn-2 + … an is a polynomial where a0, a1, ………. an are real numbers and n is non-negative integer.

Find the value of f(–9) and g(1) if f(x) = 8x + 6 and g(x) = 9x + 20x−2

polynomial f(x) = 8x + 6

f(–9) = 8(-9) + 6 = -66

g(x) = 9x + 20x − 2

g( 1 ) = 9( 1 ) + 20( 1 ) − 2 = 27

None of the given choices were correct (unless there's a typo error for  — it's supposed to be g( 1 ) = 27 instead of 29?) because the value are: f(–9) = -66 and g( 1 ) = 27

f(–9) and g(–1) if f(x) = –3x – 2 and g(x) = 3x³ – 24x

f(x) = –3x – 2

f(–9) = –3(–9) – 2 = 25

g(x) = 3x³ – 24x

g(–1) = 3(–1)³ – 24(–1) = 21

Therefore, : f(–9) = 25, g(–1) = 21

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Answer: 5 hardcover and 3 paperback

Step-by-step explanation: To solve, we need to keep this question in mind:

"How many books can we buy for each without going over the initiate amount [$26]?"

So, let's start with the $4 books, so knowing our multiples of 4

ex. 4, 8, 12, 16, 20, 24, 28......

So, I listed the example of the multiples. So, it can be either 20 or 24. So, it would be 20, because it is under the initiate amount AND it is less with unincluded paperback books. So, 26-20 = 6. So, if each paperback book costs $2, we need to divide 6 by 2. That's 3. So, therefore, she can buy 5 hardcovers and 3 paperbacks by spending all the money. I hope this helps!

The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N. To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N).

Reaction at Roller A:

2 m * 900 N = 1800 N

Reaction at Pin B:

3 m * 450 N + 600 N = 2450 N

To calculate the reaction at Roller A, you need to multiply the length of the roller (2 m) by the load (900 N). This gives you 1800 N.

To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N). This gives you 2450 N.

The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N.

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Answer:i had to

Step-by-step explanation: mb

Answer: it’s lar and we can’t compete against each other

Step-by-step explanation:

The cartesian equation for the curve r = 7 cos(θ) is [x -(7/2)]²+y² = 49/4, which is the equation of a circle.

Given r =7 cosθ

Multiplying throughout by ‘r’,

r² =7r cos θ --- (1)

Consider x² + y² = r² and put x = r cos θ --- (2)

x² + y² = 7x

Using completing the square method:

x² - 7x + (7/2)² + y² = (7/2)²

[x - (7/2)]² + y² = 49/4

(x - 7/2)² + (y - 0)² = (7/2)²

This is the equation of the circle with a center (7/2, 0) and radius of 7/2.

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The expression that represents the statements are

1. R = 114+P

2. M = 10+2B

3. H = 1/2M -29

Linear expressions are those statements that each term is either a constant or a variable raised to the first power.

In linear expressions, the highest power of the variable is 1.

In the first statement 'Rhona got 114 more votes Tham Petro'. Let's represent the votes for Rhona by R and for Pedro by P

therefore R = 114+ P

In the second statement 'Matt took 10 minutes longer than twice as long as Bryce took to do his assignment'

Let's represent the time it took Matt to do his assignment' by M and time it took Bryce by B.

then,

M = 10+2B

In the third statement 'A hamburger costs 29 cents less than half as much as a full meal'.

Let's represent the cost of hamburger by H and the cost of full meal' by M, then,

H = 1/2M -29

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The graph of the linear equation can be seen in the image at the end.

I assume that you want to graph the linear equation:

x + 2y = 3

To do so, you just need to find two points that lie on that line, to find them, just evaluate the linear equation in two different values of x (or y)

Remember that the point notation is (x, y)

if we use x = 0

0 + 2y = 3

2y = 3

y = 3/2 = 1.5

So we have the point (0, 1.5)

if x = 1

1 + 2y = 3

2y = 3 - 1

2y = 2

y = 2/2

y = 1

So the point is (1, 1)

Now that you have these two points, you can graph them on a coordinate axis, and connect them with a staright line.

The graph can be seen below.

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Answer: study dum ahh

Step-by-step explanation:

According to the given option +0.03 is the r values that indicates the strongest relationship between two variables. The option 3 is correct.

The strength of the association between two variables is gauged using correlation coefficients. Although there are other kinds of correlation coefficients, Pearson's is the most widely used. A correlation coefficient frequently used in linear regression is Pearson's correlation. Correlation coefficients typically lie in the range of -1.00 to +1.00.

The closest value to +1 (positive correlation) or -1 is taken into consideration as the strongest correlation, per the rule of correlation coefficients (negative correlation).

A high correlation coefficient means that one variable's value is directly correlated with another.

There is no relationship between the two variables if the correlation coefficient is zero.

A negative correlation coefficient shows an adverse relationship between the values of the two variables.

According to the given option +0.03 is the r values that indicates the strongest relationship between two variables.

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After Ms. Wilson pays her federal taxes, D. She will receive a refund of $ 258.

A tax refund is given when an individual or business overpays their taxes to the government during the year. It happens when the taxes that an individual or business paid through the year (withholding taxes or estimated taxes) are more than their actual tax liability for the year.

Going by the table, Ms. Wilson at her Single filling status was meant to pay the tax amount of $ 5, 086 in federal taxes and instead paid $ 5, 344. She will therefore get a refund of :

= 5, 344 - 5, 086

= $ 258

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The answer to the simplification is 56.

The order of precedence is the hierarchical order in which calculations are conducted. The simplest example of this is the way you always multiply before you add numbers.

In mathematics, you have BODMAS

B = Bracket

O = of

D = Division

M = Multiplication

A = Addition

S = Subtraction

From the equation;

7 x (-7 +15)

Removing the bracket

7 x (8)

Multiplying

56

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Answer:

$240

Step-by-step explanation:

To calculate the interest, you need to multiply the principal (the amount financed, $4,000.00) by the interest rate (2%) and the number of years (3).

So, the interest would be: $4,000.00 x 0.02 x 3 = $240.00

The contractor would pay $240.00 in interest over the course of the 3-year financing.

ANSWER:

STEP-BY-STEP EXPLANATION:

We must interpret each sentence mathematically, just like this:

Less then would be a subtract

Product would be a multiplication

No more than would be equal or less than

Answer:        

.2n-7≤95

.2n≤102

n≤510

hope this helps

[tex]dy/dt[/tex] for each pair of functions is [tex]4t^3 + 28t[/tex].

[tex]y[/tex] = [tex]x^2 - 2x[/tex]

[tex]x[/tex] = [tex]t^2 + 8[/tex]

[tex]y[/tex] = [tex](t^2+8)^2 - 2(t^2+8)[/tex]

[tex]dy/dt[/tex] = [tex]2(t^2+8)(2t) - 2(2t)[/tex]

         = [tex]4t^3 + 32t - 4t[/tex]

[tex]dy/dt[/tex] = [tex]4t^3 + 28t[/tex]

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.

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Answer:

Another word for the mean is "average".

Which measure of central tendency is affected by outliers? Mean.

When would you calculate an expected value? when your data points have various probabilities of occurring.

What is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3.

True or false: The mode is universally an accurate representation of data sets because it captures the number that occurs most often. False. Mode is not always an accurate representation of data sets and it may not exist in certain data sets.

Step-by-step explanation:

Answer: 10 liters

Step-by-step explanation:

Let the number of liters of 10% solution be [tex]x[/tex].

[tex]0.10x+5(0.25)=0.15(x+5)\\\\0.10x+1.25=0.15x+0.75\\\\1.25=0.05x+0.75\\\\0.05x=0.50\\\\x=10[/tex]

The solution to the linear system is [tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,\ y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]

An equation is a expression that shows the relationship between numbers and variables.

A linear system of equation:

Ax + By = C

Dx + Ey = F

Can be solved using:

[tex]x=\frac{\left[\begin{array}{cc}C&B\\F&E\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}A&C\\D&F\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]}[/tex]

Hence, for:

5x + 3y = 17

-8x - 3y = 9

[tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]

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Answer:

C

Step-by-step explanation:

Answer: 24 games

Step-by-step explanation: 60-60%=24

Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

Total investment in two accounts = $20,000

The simple interest rate for account one, x = 8%

The simple interest rate for account two, y = 10%

Total interest for a year = $1,920

Let account one = x and account two = y

x + y = 20,000 ... Equation 1

0.08x + 0.1y = 1,920 ... Equation 2

Multiply Equation 1 by 0.08

0.08x + 0.08y = 1,600 ... Equation 3

Subtract Equation 3 from Equation 2:

0.08x + 0.1y = 1,920

-

0.08x + 0.08y = 1,600

0.02y = 320

y = 16,000

= $16,000

In Equation 1, x + y = 20,000, Substitute y = 16,000:

x + 16,000 = 20,000

x = 4,000

= $4,000

Check:

From Equation 2:

0.08x + 0.1y = 1,920

0.08(4,000) + 0.1(16,000) = 1,920

320 + 1,600 = 1,920

Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.

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Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?

First account:

Second account:

For the given system of equations the value of x is 0.27 and the value of y = 2.7.

A system of equations in algebra consists of two or more equations and looks for common answers. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.

The given equations are:

-8x + 6y = 14 and

-5x + 2y = -7

For the equation -5x + 2y = -7 isolate the value of x:

-5x = 7 - 2y

x = - (7 - 2y) / 5

Substitute the value of x in the equation -8x + 6y = 14.

[tex]-8 (\frac{7-2y}{5} ) +6y =14\\\\-11.2 + 3.2y + 6y =14\\\\9.2y = 14 + 11.2\\\\y = 2.7[/tex]

Substitute the value of y in any one of the equations:

-8x + 6(2.7) = 14

-8x = 14 - 16.2

x = 0.27

Hence, the value of x is 0.27 and the value of y = 2.7.

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