A mouse is moving through a maze and must make four turns where it can go either left or
right. The mouse will escape the maze if it makes three lefts and one right, in any order.
(a) To the right, draw a tree diagram
of all possible routes the mouse
could take.
(b) Using your tree diagram, create
an organized list of the routes. For
example, a route of right, left, left,
right could be listed as RLLR.
(C) What is the probability the mouse
escapes the maze if all turns are
randomly made?

Answer: No they are not

Step-by-step explanation:

Distribute the 4 from the left equation into the parenthesis.

you would get 20k - 12

that is not equivalent to 14k - 8

Answer:

  C = (-1, -2)

  D = (2, 0)

Step-by-step explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

  E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

  C = 2E -A = 2(0, 2) -(1, 6)

  C = (-1, -2)

and

  D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

  D = (2, 0)

The displacement of the man from Noth east of A from C is 12.2 km.

The displacement of the man is the distance between his initial position at A and final position at C.

The angle formed at position B is calculated as follows;

θ = 30⁰  + 90⁰

θ = 120⁰

The displacement of the man is calculated by applying cosine rule as follows;

d² = 8² + 6² - 2(8 x 6) cos (120)

d² = 148

d = √148

d = 12.2 km

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Using given function 9(x) = ln(3x+11), gl (x) B) 3(-3x + 11)^-1.

We are given 9(x) = ln(3x+11) and we need to find gl(x).

First, we can use the chain rule to differentiate ln(3x+11):

d/dx [ln(3x+11)] = 1/(3x+11) * d/dx [3x+11] = 3/(3x+11)

Now, we can use the given equation 9(x) = ln(3x+11) to find d/dx [9(x)]:

d/dx [9(x)] = d/dx [ln(3x+11)] = 3/(3x+11)

Therefore, gl(x) = d/dx [9(x)] / 3(x) = 3/(3x+11) * 1/3 = (3(-3x+11))^-1.

Therefore, the correct answer is B) 3(-3x+11)^-1.

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Approximately 21.3 percent of the total items sold were baseball items.

Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:

300 - 5 = 295

We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:

0.20 * 295 = 59

Therefore, the total number of baseball and football items sold is:

59 + 5 = 64

The percentage of total items sold that were baseball items is:

(64 / 300) * 100% = 21.3%

Therefore, approximately 21.3 percent of the total items sold were baseball items.

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Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.

A three-dimensional object's volume is a measurement of how much space it takes up. It is a real-world physical number that can be expressed in cubic measurements like cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3). Physics, chemistry, architecture, and mathematics all use the idea of volume extensively. Volume is frequently used to refer to the amount of space that an object or substance takes up, for instance the amount of a container, the volume of either a liquid, or the quantity of a gas. Depending on an object's shape, a different formula is required to determine its volume.

given

The formula V = (1/3)r2h, where V is the volume, r is the radius of the base, and h is the height, can be used to determine the volume of a cone.

Hence, by multiplying the circumference by two, we can determine the radius of the base:

12π / 2π = 6

Thus, the base's radius is 6 cm.

Also, we are informed that the cone's volume is 96. As a result, we can get the height using the following formula for a cone's volume:

V = (1/3)r2h

96 = (1/3)(6/2)h

96 = 36 h

96 / 36 = 8/3

Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.

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Answer:

Step-by-step explanation:

First, let's simplify the numerator:

3^6 - 3^8 = 729 - 6561 = -5832

Now, let's simplify the denominator:

9^4 - 9^2 = 6561 - 81 = 6480

So, the expression simplifies to:

(-5832) / 6480 = -0.9

a. The tube dilution in tubes 1, 3, and 5:
- Tube 1: 1:5 (1 ml serum + 4 ml saline)
- Tube 3: 1:125 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2 x 1:5 dilution from Tube 3)
- Tube 5: 1:3125 (1:125 dilution from Tube 3 x 1:5 dilution from Tube 4 x 1:5 dilution from Tube 5)

b. The solution dilution in tubes 1, 2, and 7:
- Tube 1: 1:5
- Tube 2: 1:25 (1:5 dilution from Tube 1 x 1:5 dilution from Tube 2)
- Tube 7: 1:78125 (1:3125 dilution from Tube 5 x 1:5 dilutions for Tubes 6 and 7)

c. The total volume and solution dilution in tube 10 before transfer:
- Total volume: 3 ml (2 ml saline + 1 ml transferred from Tube 9)
- Solution dilution: 1:1953125 (1:78125 dilution from Tube 7 x 1:5 dilutions for Tubes 8, 9, and 10)

d. The amount or volume of serum in tube 6 before transfer and after transfer:
- Before transfer: 0.00064 ml (2 ml x 1:3125 dilution from Tube 5)
- After transfer: 0.00032 ml (1 ml x 1:3125 dilution from Tube 5, as half the volume was transferred to Tube 7)

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We know that both np and nq are greater than or equal to 10, it is appropriate to use a normal distribution to model the sampling distribution of p^ in this case.

(a) To calculate the mean and standard deviation of the sampling distribution of p^, we'll use the formulas:

Mean (μ) = p
Standard deviation (σ) = √(p*q/n)

where p is the proportion of individuals with allergies (0.12), q is the proportion of individuals without allergies (1 - p = 0.88), and n is the sample size (100).

Mean (μ) = 0.12
Standard deviation (σ) = √(0.12 × 0.88 / 100) = 0.02887

(b) The standard deviation of 0.02887 in this context represents the variability in the proportions of individuals with allergies that we would expect to observe in different random samples of 100 adult patients each. It quantifies the dispersion of p^ around the true population proportion.

(c) To determine if it's appropriate to use a normal distribution to model the sampling distribution of p^, we can check if both np and nq are greater than or equal to 10:

np = 100 × 0.12 = 12
nq = 100 × 0.88 = 88

Since both np and nq are greater than or equal to 10, it is appropriate to use a normal distribution to model the sampling distribution of p^ in this case.

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The expression for the area of the triangle is given as follows:

A = 6x² - 7x - 3.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the expression for the area of the triangle is given as follows:

A = 0.5(4x - 6)(3x + 1)

A = 0.5(12x² - 14x - 6)

A = 6x² - 7x - 3.

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Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.

Let x be the time (in minutes) that Norma and David spent crawling to the barn, and y be the time (in minutes) they spent hopping back to the house. We know that:

x + y = 7 (the total time they spent on the round trip was 7 minutes)

300x + 400y = distance to the barn and back (since their speeds are given in centimeters per minute, the product of their speeds and the time spent crawling or hopping gives the distance in centimeters)

We want to find x, the time they spent crawling to the barn. We can solve for x by rearranging the first equation as x = 7 - y, and substituting into the second equation:

300(7 - y) + 400y = distance to the barn and back

2100 - 300y + 400y = distance to the barn and back

100y = distance to the barn and back - 2100

y = (distance to the barn and back - 2100)/100

Now we need to find the distance to the barn and back. They crawled to the barn at 300 cm/min, so the distance they crawled is 300x cm. They hopped back to the house at 400 cm/min, so the distance they hopped is 400y cm. The total distance to the barn and back is:

distance to the barn and back = 300x + 400y

= 300x + 400[(distance to the barn and back - 2100)/100] (substituting the expression we found for y)

= 300x + 4(distance to the barn and back - 2100)

Simplifying and solving for distance to the barn and back, we get:

distance to the barn and back = 5400/7 cm

Finally, we can substitute this value into the expression we found for y, and solve for x:

y = (distance to the barn and back - 2100)/100

= (5400/7 - 2100)/100

= 24/7

x = 7 - y

= 7 - 24/7

= 37/7

Therefore, Norma and David crawled for 37/7 minutes, or approximately 5.29 minutes.

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The set of ordered pairs that does NOT represent a function is option B) (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)

  A function is a term that do not have two different outputs that is (y) for the same input(x).

Note that

For option A: The x values are {0,2,4,-2,5} Here none of the x values are repeated, So, it represents a function.

For option B: The input value 2 is linked with two different output values (2 and 7), so this set of ordered pairs does not stand a function.

Based on the explanation of the function given above, if x=2, the 'y' can not be equal to 2, 7. So, this is not a function.

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2x+14=30

2x =30-14

2x=16

x =8

Answer:

8

Step-by-step explanation:

Twice means 2 so twice a number,n, means 2 times n thus 2n

sum means add so, 2n + 14

"is" means equal so 2n + 14 = 30

Solve for n:

2n=16

N=8

She requires 55 consecutive successful throws to get a success rate of 60%

The number of successful throws she made is 8 out of 50

Now to calculate the percentage we will use the formula

[tex]\frac{8}{50} X 100 = 16[/tex]

According to the problem, she needs to make her success percentage 60% and for that, we need to estimate the number of consecutive successful throws. Hence the new equation will be

[tex]\frac{8+x}{50+x} X 100 = 60[/tex]

[tex]or, \frac{8+x}{50+x} = 0.6[/tex]

This is the equation concerned.

Now,to solve this, we will take the denominator on the other side will give us

[tex]or, 8+x = 0.6(50+x)[/tex]

[tex]or, 8+x = 30+ 0.6x[/tex]

[tex]or, x - 0.6x = 30 -8[/tex]

[tex]or, 0.4x= 22[/tex]

or, x = 55

Hence we see that she requires 55 consecutive successful throws to get a success rate of 60%

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Complete Question

A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.

(a) Write an equation to represent this situation.

(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?

To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:

7² + 2² = x²

Simplifying this equation, we get:

49 + 4 = x²

53 = x²

To find the value of x, we need to take the square root of both sides:

√53 = x

So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.

In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.

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In Option 1, the arrival rate remains constant at 13 customers per hour. This means that, on average, 13 customers arrive at the checkout lane every hour, following a Poisson probability distribution.

However, the service rate in Option 1 increases to 30 customers per hour. This improvement is achieved by hiring a second person to assist the cashier in bagging groceries while the main cashier is occupied with entering cost data and collecting money from the customer. This essentially speeds up the overall service process, allowing more customers to be served within the same time frame.

The service rate of 30 customers per hour indicates that, on average, the cashier and the assistant can complete the checkout process for 30 customers in an hour. The service times still follow an exponential probability distribution, but with a faster rate of service compared to the initial service rate of 20 customers per hour.

By implementing Option 1, the manager aims to reduce the waiting time prior to the checkout process to no more than five minutes, thereby improving overall customer satisfaction and efficiency at Pete's Market.

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The product of (8-6b)(5-3b), using the distributive property of multiplication is [tex]18b^2 - 54b + 40[/tex].

This problem is actually an algebraic expression involving variables and constants. To find the product of (8-6b)(5-3b), we need to use the distributive property of multiplication.

We can start by multiplying 8 by 5, which gives us 40. Next, we multiply 8 by -3b, which gives us -24b. Then, we multiply -6b by 5, which gives us -30b. Finally, we multiply -6b by -3b, which gives us[tex]18b^2[/tex].

Putting all of these terms together, we get:
(8-6b)(5-3b) = [tex]40 - 24b - 30b + 18b^2[/tex]

Simplifying this expression, we can combine the like terms -24b and -30b to get -54b. So the final answer is:
(8-6b)(5-3b) = [tex]18b^2 - 54b + 40[/tex]

Therefore, the product of (8-6b)(5-3b) is  [tex]18b^2 - 54b + 40[/tex].

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The planes intersect at the point (-19/21, -11/14, 1).

To determine how, if at all, the planes intersect, we need to solve the system of equations given by the three planes:

[2T/3A] 2x + 2y + z - 10 = 0

5x + 4y - 4z = 13

3x – 2z + 5y - 6 = 0

We can use elimination to solve this system. First, we can eliminate z from the second and third equations by multiplying the second equation by 2 and adding it to the third equation:

5x + 4y - 4z = 13

6x - 4z + 10y - 12 = 0

11x + 14y - 12 = 0

Next, we can eliminate z from the first and second equations by multiplying the first equation by 2 and subtracting the second equation from it:

4x + 4y + 2z - 20 = 0

-5x - 4y + 4z = -13

9x - y - 6z - 20 = 0

Now we have two equations in three variables. To eliminate y, we can multiply the second equation by 14 and subtract it from the first equation:

11x + 14y - 12 = 0

-70x - 56y + 56z = -182

-59x - 42z - 12 = 0

Finally, we can substitute this expression for x into one of the previous equations to find z:

3(59/42)z - 12/42 - 2y - 10 = 0

177z - 60 - 84y - 420 = 0

177z - 84y - 480 = 0

Now we have two equations in two variables, z and y. We can solve for y in terms of z from the second equation:

y = (177/84)z - (480/84)

Substituting this expression for y into the third equation, we can solve for z:

177z - 84[(177/84)z - (480/84)] - 480 = 0

177z - 177z + 480 - 480 = 0

This equation simplifies to 0=0, which means that z can be any value. Substituting z=1 into the expression for y, we get:

y = (177/84)(1) - (480/84) = -11/14

Substituting z=1 and y=-11/14 into the expression for x, we get:

x = (59/42)(1) - (12/42) + 2(-11/14) + 10 = -19/21

Therefore, the planes intersect at the point (-19/21, -11/14, 1).

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The perimeter of Rebakh's new mural is 9 meters.

Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.

So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.

Therefore, the perimeter of Rebakh's new mural is 9 meters.

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The mean number of points Kathleen made is 38.

To calculate the mean number of points Kathleen made, we will use the following terms: mean, sum, and total number of assignments.

The mean is the average value of a set of numbers. To find the mean, we need to sum all the given values and then divide the sum by the total number of values in the set.

Kathleen's assignment scores are 29, 38, 45, 42, and 36 points. To find the sum, we add these numbers together: 29 + 38 + 45 + 42 + 36 = 190 points.

Now, we need to determine the total number of assignments. Kathleen has completed five assignments. So, we will divide the sum of her points (190) by the total number of assignments (5) to find the mean.

Mean = Sum / Total number of assignments
Mean = 190 / 5
Mean = 38

The mean number of points Kathleen made on her assignments is 38 points. This indicates that on average, she scored 38 points per assignment. Calculating the mean gives us a general idea of her performance across all assignments, allowing us to gauge her overall progress.

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2 cos x - 1 = 0, cos x = 1/2, and x = π/3 or 5π/3. These are the critical numbers of g(x) on (0,7). the absolute maximum value of g(x) on (0,7) is √3 - π/3 and the absolute minimum value is -√3 - 5π/3.

To find the critical numbers for g(x) = 2sin(r) - r on the interval (0, 7), follow these steps:
1. Find the derivative of g(x): g'(x) = 2cos(r) - 1
2. Set the derivative equal to zero: 2cos(r) - 1 = 0
3. Solve for r: r = cos^(-1)(1/2)
Now, find the absolute maximum and minimum values for g(x) on the interval (0, 7):
1. Evaluate g(x) at the critical numbers: g(cos^(-1)(1/2)) = 2sin(cos^(-1)(1/2)) - cos^(-1)(1/2)
2. Evaluate g(x) at the endpoints of the interval: g(0) = 2sin(0) - 0, g(7) = 2sin(7) - 7
3. Compare the values from steps 1 and 2 to find the maximum and minimum values.
The critical numbers for g(x) = 2sin(r) - r on the interval (0, 7) are r = cos^(-1)(1/2). The absolute maximum and minimum values for g(x) on the interval (0, 7) can be found by comparing g(cos^(-1)(1/2)), g(0), and g(7).

To find the critical numbers of g(x) = 2 sin x - x on (0,7), we first need to find its derivative:
g'(x) = 2 cos x - 1
Setting g'(x) = 0, we get:
2 cos x - 1 = 0
cos x = 1/2
x = π/3 or 5π/3
These are the critical numbers of g(x) on (0,7).

To find the absolute maximum and minimum values of g(x) on (0,7), we need to evaluate g(x) at the critical numbers and at the endpoints of the interval (0,7).
g(0) = 0
g(π/3) = 2 sin(π/3) - π/3 = √3 - π/3
g(5π/3) = 2 sin(5π/3) - 5π/3 = -√3 - 5π/3
g(7) = 2 sin(7) - 7
To determine the absolute maximum and minimum values, we compare these values:
The absolute maximum value is √3 - π/3, which occurs at x = π/3.
The absolute minimum value is -√3 - 5π/3, which occurs at x = 5π/3.
Therefore, the absolute maximum value of g(x) on (0,7) is √3 - π/3 and the absolute minimum value is -√3 - 5π/3.

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Answer:

(-2,-8)

Step-by-step explanation:

First, we have to make these linear equations into standard form:

-3x+y=-2

and

9x-y=-10

Now we tell my using elimination method, we can cross out the y variables because when added(y+(-y)) is just 0, so we just cross them out

Add liked terms

6x=-12

Solve for X:

X=-2

Plug 2 for X in any equation (lets do -3x+y=-2)

Plug in -2 for X:

-3(-2)+y=-2

Thus we get 6+y=-2

Solve for Y:

y=-8

Now that we have both our variables, we know that the answer is (-2,-8)

Check the picture below.

Answer:

Locker and Phone number

Step-by-step explanation:

Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter

The correct answer is C.

The cost of membership is fixed at $50 per year, and the cost of purchasing games is $60 each. If you purchase up to 6 games a year, the cost of each purchase will be $60, and the total cost of membership and games will be $50 + ($60 x number of games purchased).

The function that relates the number of games purchased to the total cost is:

Total cost = 50 + 60(number of games purchased)

Now, let's consider the options provided:

A. Domain: All real numbers

Range: All real numbers

This is not a valid option since the domain and range are not restricted to the given context.

B. Domain: {50, 110, 170, 230, 280, 340}

Range: {0, 1, 2, 3, 4, 5, 6}

This option does not represent the relationship between the number of games purchased and the total cost correctly.

C. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {50, 110, 170, 230, 290, 350, 410}

This option correctly represents the relationship between the number of games purchased and the total cost. The domain represents the number of games purchased (up to 6), and the range represents the total cost (membership fee + cost of games).

D. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {60, 160, 210, 270, 320, 380}

This option represents the cost of games purchased only, and does not include the cost of membership.

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1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²), the power and multiplication law is not used correctly.

2. (y⁵/x²)*(y¹⁰/x³), the power and multiplication law is not used correctly.

3.  y⁷/x⁴ * y¹⁰/x³,  the multiplication law is not used correctly.

The exponents are simplified as follows; (using power exponents)

1. (x⁻²y⁵)²*(x⁻³y⁸/x⁻⁶y⁻²)

= (x⁻⁴y¹⁰)*(x⁻⁹y¹⁰)

= x⁻¹³y²⁰

2. (y⁵/x²)*(y¹⁰/x³) (simplify using multiplication and division rule)

(y⁵/x²)*(y¹⁰/x³)

= (y⁵x⁻²)*(y¹⁰x⁻³)

= y¹⁵x⁻⁵

3. y⁷/x⁴ * y¹⁰/x³ (simplify using multiplication and division rule)

y⁷/x⁴ * y¹⁰/x³

= (y⁷x⁻⁴)(y¹⁰x⁻³)

= y¹⁷x⁻⁷

4. y¹⁷/x⁷ (This expression is simplified correctly)

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The mean number of people in passenger cars on the highway is 1.7 (approximately 2).

The mean of a probability distribution function is also known as Expectation of the probability distribution function.

The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.

Thus E(x) can be calculated as,

E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5

where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway

⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)

⇒ E(x) = 1.7

Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.

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The volume of the solid is 32/15 cubic units.

To find the volume of the solid, we need to integrate the area of each square cross section perpendicular to the x-axis over the interval [a, b], where a and b are the x-coordinates of the intersection points of f(x) and g(x):

First, we find the intersection points of the two functions:

x²+1 = 2x+1

x² - 2x = 0

x(x-2) = 0

x = 0 or x = 2

So, a = 0 and b = 2.

Next, we find the side length of each square cross section. Since the cross section is a square, the side length is equal to the difference between the y-coordinates of the functions f(x) and g(x) at each x:

Side length = f(x) - g(x) = (x²+1) - (2x+1) = x² - 2x

Finally, we integrate the area of each square cross section over the interval [0, 2] to get the volume of the solid:

V = ∫[0,2] (x² - 2x)² dx

V = ∫[0,2] (x⁴- 4x³ + 4x²) dx

V = [1/5 x⁵ - 1 x⁴ + 4/3 x³] [0,2]

V = (1/5 x⁵ - 1 x⁴ + 4/3 x³)|[0,2]

V = (1/5(2⁵) - 1(2⁴) + 4/3(2³)) - (1/5(0⁵) - 1(0⁴) + 4/3(0³))

V = (32/5 - 16/3)

V = 32/15

Therefore, the volume of the solid is 32/15 cubic units.

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3.75 kg of meat will cost 712.50, The correct answer is option (c).To determine how much 3.75 kg of meat will cost at ?190.00 per kilogram, you'll need to perform a multiplication using the given weight and price per kilogram, we need to :

1. Identify the weight of the meat: 3.75 kg.
2. Identify the cost per kilogram: ?190.00.
3. Multiply the weight (3.75 kg) by the cost per kilogram (?190.00).

3.75 kg × ?190.00/kg = 712.50
So, 3.75 kg of meat will cost ?712.50, which corresponds to option (c) in your list of possible answers. Remember to always check your calculations and units when solving problems like this to ensure accuracy.

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