The acceleration of a rocket fired vertically upwards t seconds after launch is 20+4???? m????−2 (as a rocket burns fuel it becomes lighter, so accelerates more quickly). What is the second order differential equation for the height of the rocket. ℎ′′= ___________
What is the general solution? (Please use A as the first constant of integration and B as the second):
General solution: ℎ = ___________
Use the fact that at t = 0 the rocket was on the ground and not moving to find the particular solution that gives the height of the rocket. How high was the rocket after 10 seconds? How fast was it moving then? (hint: acceleration is the rate of change of velocity. The velocity of the rocket is the rate of change of what?)
Height = ______ meters
Velocity = _______ meters/second

The value of 151.8% of £613.71 is £931.55.

An informed estimate or a flimsy explanation for a phenomena or observation that may be evaluated by more research is called a hypothesis. It serves as the basis for scientific inquiry and is often formed using known facts and observations.

A theory, on the other hand, is a proven explanation for a phenomenon or group of occurrences that has undergone significant testing and is backed by empirical data. A theory may be thought of as a framework that predicts and explains how and why things happen the way they do.

Given that, 151.8% of £613.71

To find the value, first convert the percentage to a decimal by dividing it by 100:

151.8 ÷ 100 = 1.518.

Multiply this decimal by:

£613.71: 1.518 × £613.71 = £931.55

Hence, the value of 151.8% of £613.71 is £931.55.

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If the cost of customer acquisition is $50 and the cost of customer retention is $30, then the cost of Software C would be $80,000. This is because 10,000 customers x ($50 acquisition cost + $30 retention cost) = $80,000.

Acquisition cost is the cost associated with obtaining an asset or resource. It includes the purchase price, transportation costs, installation costs, taxes, and any other associated costs.

The cost of Software C can be determined by calculating the total cost of lost customers due to software issues. To do this, companies typically look to the customer lifetime value (CLV) of each customer. CLV is the total revenue generated by a customer over the course of their relationship with the company. By multiplying the CLV by the number of unsatisfied customers, companies can get a good idea of what the cost of Software C is.

For example, if a company has 10,000 customers and their CLV is $100, then the cost of Software C would be $1,000,000. This is because 10,000 customers x $100 CLV = $1,000,000.

The cost of Software C can also be determined by looking at the cost of customer acquisition and retention.

In addition to the cost of lost customers, companies must also factor in the cost of fixing the software issue. This cost can vary depending on the complexity of the issue and the size of the company. Companies should also consider the cost of lost productivity due to the software issue, as well as any other costs associated with the issue.

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Answer:

54665655

Step-by-step explanation:

2.62 seconds before the ball Martin threw hits the ground.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared component must be included. These are also known as quadratic equations.

Let t be the time in seconds

h(t) be he height of the ball, in feet

we have

h(t) = −16t² + 40t + 5

we know that

When the ball hits the ground, the height is equal to zero

so

−16t² + 40t + 5=0

The equation solving formula for a quadratic equation of the type

at²+bt+c=0

is equal to

t=(-b±√(b²-4ac))/2a

in this problem we have

−16t² + 40t + 5=0

so

a=-16

b=40

c=5

substitute in the formula:

t = (-40±√(40²-4×40×5))/2×-16

t = (-40±√(1600-800))/-32

t=2.62sec

therefore, 2.62 seconds before the ball Martin threw

hits the ground.

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Factοring is the prοcess οf reversing the distributive prοperty sο that a pοlynοmial can be written as the prοduct οf simpler pοlynοmials is true.

Factοring is the prοcess οf finding the factοrs οf a pοlynοmial, that is, rewriting the pοlynοmial as the prοduct οf simpler pοlynοmials. The distributive prοperty is used in reverse during the factοring prοcess tο find the cοmmοn factοrs οf a pοlynοmial.

Fοr example, cοnsider the pοlynοmial expressiοn [tex]2x^2 + 6x[/tex]. We can factοr οut a cοmmοn factοr οf 2x tο get:

2x(x + 3)

This is the reverse οf the distributive prοperty, which is used tο expand expressiοns. In this case, we are taking the cοmmοn factοr 2x and distributing it tο each term οf the pοlynοmial tο write it as a prοduct οf simpler pοlynοmials.

Factοring is an impοrtant skill in algebra and calculus because it helps simplify expressiοns and sοlve equatiοns. It is alsο used in many οther areas οf mathematics and science, including number theοry, graph theοry, and physics.

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The speed of the ball thrown from third base to first base is approximately 106.1 feet/second.

From the question, we are to calculate the speed of the ball

Assuming the ball traveled in a straight line from third base to first base, we can use the distance formula to find the distance the ball traveled and then use the formula for speed to find the speed of the ball.

The diagonal of the square infield can be found using the Pythagorean theorem:

Diagonal = sqrt(90² + 90²) = 127.28 feet

Therefore, the distance the ball traveled from third base to first base is approximately equal to the diagonal of the square, which is 127.28 feet.

To find the speed of the ball, we can use the formula:

Speed = Distance / Time

Plugging in the values, we get:

Speed = 127.28 feet / 1.2 seconds

= 106.06667 feet/second

≈ 106.1 feet/second

Hence, the speed of the ball is approximately 106.1 feet/second.

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The required equivalent fractions for 1 10/15 and 9/12.

Given, two mixed fractions 1 2/3 and 3/4, determine equivalent fractions using 15 as the common denominator.

Simplification:

The process in mathematics of manipulating and interpreting functions to make a function or expression simpler or easier to understand is called simplification, and the process is called simplification.

1. Simplify fractions by canceling all common factors of the numerator and denominator and writing the fraction in its lowest/simplest form.

2. Simplify mathematical expressions by grouping and combining similar terms. This makes expressions easy to understand and solve.

According to the Question:

Here,

First

= 1 2/3

= 1+ 2 / 3

= 1 + 2 × 5 / 3 × 5

= 1 + 10 / 15

Again,

Second,

=  3 / 4

=  3 × 3 / 4 × 3

= 9/12

Thus, the required equivalent fractions for 1 10/15 and 9/12.

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Using perimeter fοrmula , 521 ft tabe is used tο cοver baseball cοurt.

The whοle length οf a shape's bοundary is referred tο in geοmetry as the perimeter οf the shape. Adding the lengths οf all the sides and edges that surrοund a fοrm yields its perimeter. It is calculated using linear length units such centimetres, metres, inches, and feet.

Here the basketball cοurt is cοmbined with twο half circle , οne circle and οne rectangle.

In the rectangle , Length = 94ft and width = 44ft.

Perimeter οf rectange = 2(length+width) = 2(94+44) = 2*138 = 276 ft.

In the half circle , Diameter = 44 ft  then radius = 44/2 = 22ft

Perimeter οf circle = πr+d = 3.14*22+44 =113.08 ft

Nοe , In the circle , Diameter = 12ft ,then radius = 12/2=6 ft.

perimeter οf circle = πd = 3.14*6=18.84 ft

Then Tοtal perimeter = 276+113.08+113.08+18.84 = 521 ft.

Hence 521 ft tabe is used tο cοver baseball cοurt.

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It has been proven that the lines bc and ad are equal.

Given that the lines ac and bd bisect each other, we can prove that the lines bc and ad are equal.

Firstly, we need to calculate the length of each side of the figure and label them accordingly. Let’s assume that the length of ac is x and the length of bd is y.

We know that the two lines ac and bd bisect each other, so the midpoint of ac and bd must be the same point, which is point c. We can use the midpoint formula to calculate the distance between points a and c:

Midpoint of ac = (x/2, 0)

Similarly, we can calculate the midpoint of bd:

Midpoint of bd = (y/2, 0)

Since the midpoints of ac and bd are the same, we have:

(x/2, 0) = (y/2, 0)

Therefore, we can calculate that x = y. This means that the lengths of ac and bd are equal and so the lengths of bc and ad must also be equal.

Therefore, bc = ad.

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The monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for it. Percentages are frequently used to represent change or growth over time and to compare two values. Finding the proportion of the quantity you are interested in to the total is necessary before you can compute a percentage. The percentage is then calculated by multiplying the ratio by 100.

For Month A the production is:

2000 + 3000 + 2000 + 3000 = 10,000

Thus, average weekly production is:

A = 10,000 / 4

A = 2500

For month B we have:

2000 + 1000 + 3000 + 0 = 6000

Average weekly crate production is:

= 6000 / 4

= 1500

The percentage decrease is given by:

percent decrease = [(original value - new value) / original value] x 100%

= [(2500 - 1500) / 2500] x 100%

= 40%

Therefore, the monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

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The equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53The y-intercept of the least squares line is given as -72.1818181818182. We have to calculate the slope of the least squares line and input the equation of the least squares line. The given data is shown below:X: 168 178 176 174 178 174 172Y: 50 57 55 55 58 54 53We know that y-intercept of the least squares line is given by b = ybar - m * xbarwhere xbar = (1/n) * ∑x and ybar = (1/n) * ∑y. Now, to calculate the slope of the least squares line, we need to calculate the value of the numerator of the following equation:Slope, m = [(n∑xy) - (∑x∑y)] / [(n∑x^2) - (∑x)^2]Here, ∑x and ∑y are the summations of x and y values, respectively. ∑xy is the sum of the products of each x and y value, and ∑x^2 is the sum of each x value squared. So, let's calculate all of these values for the given data.We have, n = 7∑x = 1202∑y = 382∑x^2 = 213468∑xy = 71848Now, substituting these values in the formula of slope, we have:Slope, m = [(7 * 71848) - (1202 * 382)] / [(7 * 213468) - (1202)^2] = 3.6000630680907Therefore, the slope of the least squares line is 3.600. Now, we can use the slope and the y-intercept to find the equation of the least squares line. Therefore, the equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

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Answer:

Step-by-step explanation:

a: in the quadratic formula, no real roots would mean b^2 - 4ac<0 because of the discriminant. b^2 is 4, so all 4c has to satisfy is that it’s greater than 4. Solving, c>1

b: casework:

Both are negative: This is impossible because square roots are always positive, so at least one would always be positive.

Both are positive: sqrt(4-4c)<2.  0<c<=1.

c. I’m not entirely sure of what you mean, but when c=0, 0 is a root of the quadratic equation, but the other root is positive 2, so no value?

d. sqrt(4-4c)>2. Another possibility is that the same thing is less than -2, but square roots are always positive. This remains true for c<0.

The number of jars of raspberry jam filled is required.

The number of jars of raspberry jam is 1/24

Fraction:

A fraction represents a part of a whole, or more generally, any number of equal parts. In common English, a fraction describes the number of parts of a certain size, such as half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator that appears above (or before a slash, such as 1⁄2) a line, and a non-zero denominator that appears. Multipliers and denominators are also used in less common fractions, including complex, complex, and mixed fractions.

According to the Question:

The number of jars of strawberry jam is 1/8 jars.

The number of jars of raspberry jam is half of the number of jars of strawberry jam.

So,

1/8 × 1/3

= 1/24

The number of jars of raspberry jam is 1/24.

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Answer:

Shape  Area (units^2)

   A          20

   B            2

   C            4

   D            6

Total =      32

Step-by-step explanation:

See the attached worksheet.  These calculations assume that the "6" is the length of the line segment as marked.  Using the expressions for areas or traingles and rectangles, as noted, each area is calculated and the sum is 32 units^2.

The prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

Prοbability is simply the pοssibility that sοmething will happen. Since we dοn't knοw hοw sοmething will turn οut, we can talk abοut the pοssibility οf οne οutcοme οr the likelihοοd οf several.

There are 10 balls in a bag with the numbers marked 1 thrοugh 10.

Nοw,

The ball with the number 1 οn it is picked in exactly 1 time

There are twο different ways tο pick the ball with the number 2.

Thus there is just οne pοssible technique tο chοοse a ball with a specific number.

There is nο lοnger a substitute.

Sο, when οne ball is taken, the tοtal number οf balls decreases by οne.

Then,

The prοbability οf selecting ball numbered 1= 1/10

The prοbability οf selecting ball numbered 2= 1/9

The prοbability οf selecting ball numbered 3= 1/8

That is dοne up tο last ball....

Last 1 is, the prοbability οf selecting ball numbered 10= 1/1

Tοtal prοbability οf chοοsing the balls in cοnsecutive οrder = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Hence, the prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

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We meet the SAS requirement for congruence because the two triangles share two congruent sides as well as the included angle.

To prove that △BEC≅△DEA, we can use the Side-Angle-Side (SAS) congruence theorem.

First, we can see that BE=ED, as both are radii of the same circle.

Secondly, angle BEC and angle DEA are both 90 degrees, as they are inscribed angles that subtend the same arc BD.

Lastly, we can see that EC=EA, as they are both radii of the same circle.

Therefore, we have the two triangles sharing two congruent sides and the included angle, satisfying the SAS criterion for congruence. Hence, we can conclude that △BEC≅△DEA.

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Answer:  960 eggs are not sold.

Step-by-step explanation:

Let t be the number of total eggs.

36%(t) = 540

0.36(t) = 540

         t = 1500

1500 - 540 = 960

Thus, the length of the other side of Ross's garden is 18 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

To find the length of the other side of Ross's garden, we can use the Pythagorean theorem.

In this case, let's assume the length of the other side of Ross's garden x.

We can set up the following equation:

x² + 30² = 33²

Solving for x, we get:

x² = 33² - 30²

x² = 1089 - 900

x² = 289

x = √289

x = 17.

Thus, the length of the other side of Ross's garden is 18 feet.

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The cost for renting a car can be represented by the equation: c = a + bm

The cost of renting a car can be expressed as a function of the number of miles driven. This function is typically linear, with a fixed cost component and a variable cost component. The fixed cost component represents the cost of renting the car regardless of the number of miles driven, while the variable cost component represents the additional cost per mile driven.

The equation that represents the cost of renting a car is c = a + bm, where c represents the total cost of renting the car, m represents the number of miles driven, a represents the fixed cost component, and b represents the variable cost component.

The equation shows that the cost of renting a car is dependent on the number of miles driven. As the number of miles driven increases, the cost of renting the car also increases, reflecting the additional variable cost per mile. By knowing the values of a and b, we can estimate the total cost of renting the car for a given number of miles.

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The given sequence is not an arithmetic sequence. Option B is correct.

Given the sequence below

-2, -8, -32, -128

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = -2

Second term = -8

Common difference = -8 -(-2) = -6

d= -32 + 8 = -24

Since the values are not equal, hence the sequence is not an arithmetic sequence.

Hence the common difference of the sequence is 8

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(a) Yes, the player makes the shot; (b) A quadratic function in standard form that models the path of the shot is: [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

(a) We need to find the x-int to see if he makes the shot at (3,0).

    so, first we factor!

[tex]y=-\frac{1}{20} (x-6)(x-3)[/tex]

0 = (x - 6) = (6, 0)

0 = (x - 3) = (3, 0)

This shows that the player makes the shot.

(b) x- int = (13, 0) and (3, 0)

    random point = (10, 1.4)

    f(x) = a(x - 13) (x - 3)

    1.4 = a(10 - 13) (10 - 3)

    1.4 = a(-3) (7)

   [tex]\frac{1.4}{-21} = \frac{-21a}{-21}[/tex]

       a = 0.06 ≈ [tex]\frac{-3}{50}[/tex]

the Quadratic function is [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

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Full Question:

A professional basketball player's shot is modeled by the function shown, where x and y are measured in feet.

a. Does the player make the shot?

b. The basketball player releases another shot from the point (13,0) and makes the shot. The shot also passes through the point (10, 1.4). Write a quadratic function in standard form that models the path of the shot.

Lauri spent 4% of 800 hours at her part time job, which is about 32 hours. The property of equality was used to solve for x.

To estimate x, we can use the property of equality. This property states that if two equations are equal, then the two sides of the equation are equal. Therefore, if we know that 4% of x is about 32 hours, we can set up an equation and solve for x. The equation is 4% of x = 32 hours. We can convert 4% to a decimal by dividing 4 by 100, which gives us 0.04. This can then be rewritten as 0.04x = 32 hours. To solve for x, we can divide both sides by 0.04. This gives us x = 800 hours. This means that if Lauri spends 4% of x hours at her part time job, then x must be 800 hours.

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The solution to the equation is x = 22.5.

To solve the equation x-9 = (3/5)x, we can first simplify the right-hand side by multiplying both sides by 5 to get rid of the fraction:

5(x-9) = 3x

An equation is a mathematical statement that indicates the equality of two expressions. Equations typically contain variables, which are represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equals sign are called the left-hand side and right-hand side of the equation.

Expanding the left-hand side, we get

5x - 45 = 3x

Next, we can simplify by subtracting 3x from both sides:

2x - 45 = 0

Adding 45 to both sides, we get:

2x = 45

Finally, dividing both sides by 2, we get:

x = 22.5

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Max worked 15 hours while John worked 10 hours

Hence, Option A is the set of values that will give PV the same value as the specified expression. N = 5, 1% = 0, PV =, PMT = 505, FV = 0, P/Y = 12, C/Y = 12, and PMT:END

Using the TVM Solver on a graphing calculator, we may identify the set of values that will give PV the same value as the supplied expression.

The sentence is as follows:

PV = ($505)((1+0.004)^0-1) / (0.004)(1+0.004)^60

If we condense this phrase, we get:

PV = -$23,724.59

Now, we can examine each set of data to determine which one yields the same PV value.

Option A: The PV is -$23,724.59 when N=5 and 1%-0.4 are used. The specified expression's value for PV is returned by this option.

Option B: The PV obtained by using N=60 and 1%-0.4 is -$153,167.63, which is not the same as the equation.

Option C: The PV obtained by using N=60 and 1%-4.8 is $18,981.10, which is not the same as the equation.

Option D: A PV of $590.68 is produced using N=5 and 1%=4.8, which differs from the stated expression.

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Answer:

Gradient of the line segment:

The gradient of a line segment is given by the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

m = (3 - 4) / (8 - 6) = -1/2

Therefore, the gradient of the line segment is -1/2.

Midpoint of the line segment:

The midpoint of a line segment is given by the formula:

((x1 + x2) / 2, (y1 + y2) / 2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

Therefore, the midpoint of the line segment is (7, 3.5).

Length of the line segment:

The length of a line segment is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

d = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(2^2 + (-1)^2) = sqrt(5)

Therefore, the length of the line segment is sqrt(5).

Answer:

To find the gradient of the line segment, we use the formula:

gradient = (change in y) / (change in x)

So, gradient = (3 - 4) / (8 - 6) = -1/2

To find the midpoint of the line segment, we use the formula:

midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

So, midpoint = ((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

To find the length of the line segment, we use the distance formula:

length = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, length = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(5)

Therefore, the gradient of the line segment is -1/2, the midpoint is (7, 3.5), and the length is sqrt(5).

Yes, Enid is correct that the distance she jogs and the number of calories she burns are in a proportional relationship. This means that as the distance she jogs increases, the number of calories she burns also increases at a constant rate.

To see this proportional relationship, we can look at the data from her last four jogs on the treadmill. Let's say that the distance she jogged is represented by x and the number of calories she burned is represented by y.

If we divide the number of calories she burned (y) by the distance she jogged (x), we should get the same constant rate for each of her four jogs.

For example, if she jogged 2 miles and burned 200 calories, the constant rate would be 200/2 = 100. If she jogged 4 miles and burned 400 calories, the constant rate would also be 400/4 = 100.

This shows that there is a proportional relationship between the distance she jogs and the number of calories she burns on the treadmill. The constant rate in this case is 100, which means that for every 1 mile she jogs, she burns 100 calories.

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Answer:

  about $10

Step-by-step explanation:

You want the difference in interest earned after 5 years between an account earning 4.3% compounded quarterly and one earning 4% compounded continuously when the investment in each is $590.

The account balance when interest is compounded quarterly for t years is ...

  A = P(1 +r/4)^(4t) . . . . . P is the principal invested at annual rate r

The account balance with interest is compounded continuously for t years is ...

  A = Pe^(rt)

The attached calculator screen shows the account balances for an investment of $590 for 5 years in accounts earning 4.3% compounded quarterly and 4% compounded continuously.

Scarlett's account, compounded quarterly, earns about $10 more interest over 5 years than does Ajay's account compounded continuously.

Answer:13

Step-by-step explanation:

The expression that corresponds to the volume of the rectangular prism is "Yes."

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

Let's determine if each expression can be used to determine the volume of the rectangular prism with dimensions 4, 6, and 2.

Expression 1: 8 × 6

To calculate the volume, we need the product of the length, width, and height. The expression 8 × 6 matches these dimensions, so the answer is Yes.

Expression 2: (2 × 4) + 6

This expression does not involve all three dimensions of the rectangular prism. It only includes the length and width, but not the height. Therefore, it cannot be used to determine the volume. The answer is No.

Expression 3: 4 × (6 × 2)

This expression involves all three dimensions of the rectangular prism: length, width, and height. It is the correct formula for calculating the volume. The answer is Yes.

Expression 4: 2 × (4 + 6)

This expression does not include all three dimensions. It only includes the length and width, but not the height. Hence, it cannot be used to calculate the volume. The answer is No.

Therefore:

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

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The complete question:

Can the following expressions be used to determine the volume of the rectangular prism in cubic inches? Please select "Yes" or "No" for each expression:

Expression 1: 8 × 6

Expression 2: (2 × 4) + 6

Expression 3: 4 × (6 × 2)

Expression 4: 2 × (4 + 6)

The length, width, and height of the prism are 4, 6, and 2 respectively.

The volume V of the cylinder can be expressed as the polynomial function: V(x) = πx³ + 30πx² + 297πx + 972π

The formula for the volume of a cylinder is given by:

V = πr²h

where r is the radius and h is the height.

In this case, the radius is x+9 units, and the height is 3 units more than the radius, which means the height is (x+9)+3 = x+12 units.

Substituting these values into the formula, we get:

V = π(x+9)²(x+12)

Expanding the square, we get:

V = π(x² + 18x + 81)(x+12)

Multiplying out the brackets, we get:

V = π(x³ + 30x² + 297x + 972)

Therefore, the volume V of the cylinder can be expressed as the polynomial function:

V(x) = πx³ + 30πx² + 297πx + 972π

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