This is actually really confusing please help me out.

The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.

Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).

If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be

x = X + h and y = Y + k

If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.

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The length of one side of the octagon is 2.93 inches. The resulting octagon will have equal side lengths. We need to find the length of the side of the octagon.

Step 1: The square has a side length of 10 inches. So, the diagonal of the square will be 10√2 inches.

Step 2: The isosceles right triangles are congruent. Therefore, we can draw one of the triangles by cutting off one corner of the square.

The hypotenuse of the right triangle will be the side of the octagon and will be equal to the length of one side of the square minus the length of one of the legs of the right triangle. The length of each leg of the right triangle will be 10/√2.

Step 3: Using the Pythagorean theorem, we can find the hypotenuse of the right triangle. We can then subtract 10/√2 from the length of the side of the square to find the length of one side of the octagon.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a² + b² = c² Where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

Using the theorem, we can find the length of the hypotenuse of the right triangle: (10/√2)² + (10/√2)² = c²100/2 + 100/2 = c²100 = c²c = √100 = 10 inches

Step 4: To find the length of one side of the octagon, we need to subtract 10/√2 from the length of the side of the square. The length of the side of the square is 10 inches. Therefore, the length of one side of the octagon will be:10 - 10/√2 = 10 - 7.07 ≈ 2.93 inches

Therefore, the length of one side of the octagon is 2.93 inches.

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The estimated regression equation for the given data is ŷ = -0.0025 Length - 0.2171 Width - 0.0004 Weight - 0.6806 ManTran

In regression analysis, the estimated regression equation is obtained by fitting a model to the data. In this case, the equation is ŷ = -0.0025 Length - 0.2171 Width - 0.0004 Weight - 0.6806 ManTran, where ŷ represents the predicted value of the response variable (CityMPG) based on the given predictor variables (Length, Width, Weight, ManTran).

The coefficient signs in the estimated regression equation indicate the direction and magnitude of the relationship between each predictor variable and the response variable. Based on a priori expectations, negative signs were expected for Length, Width, and Weight, as these variables are typically associated with decreased fuel efficiency (lower CityMPG). However, the estimated coefficients for these variables have negative values, indicating that an increase in Length, Width, or Weight is associated with a decrease in CityMPG, which aligns with expectations.

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The given statement x y means 8 is congruent to 1 modulo 3, 1 is congruent to 2 modulo 5, and 0 is congruent to 3 modulo 2.

To show that 8 is congruent to 1 modulo 3, we need to find integers x and y such that 5x + 2y = 3k + 1 for some integer k. Let x = 1 and y = 1. Then, 5x + 2y = 5 + 2 = 7, which is not divisible by 3. Let x = 2 and y = 1. Then, 5x + 2y = 10 + 2 = 12 = 3 x 4, which shows that 8 is congruent to 1 modulo 3.

To show that 1 is congruent to 2 modulo 5, we need to find integers x and y such that 5x + 2y = 5k + 2 for some integer k. Let x = 1 and y = 0. Then, 5x + 2y = 5, which is congruent to 0 modulo 5. Let x = 0 and y = 1. Then, 5x + 2y = 2, which is congruent to 2 modulo 5. Hence, 1 is congruent to 2 modulo 5.

To show that 0 is congruent to 3 modulo 2, we need to find integers x and y such that 5x + 2y = 2k + 3 for some integer k. Let x = 0 and y = 1. Then, 5x + 2y = 2, which is not equal to 2k + 3 for any integer k. Let x = 1 and y = -2. Then, 5x + 2y = 5 - 4 = 1, which is not equal to 2k + 3 for any integer k. Let x = 0 and y = 0.

Then, 5x + 2y = 0, which is congruent to 0 modulo 2. Hence, 0 is congruent to 3 modulo 2.

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(a) The standardized score (z-score) for a baby with a birth length of 45 cm, relative to babies born after 40 weeks gestation, is approximately -2.59.

(b) The standardized score for a birth length of 45 cm for a child born one month early is approximately -1.

(c) A birth length of 45 cm is more common for babies born after 40 weeks gestation. This is because the standardized score of -2.59 indicates that the observation is farther below the mean compared to the standardized score of -1 for babies born one month early. The larger group of babies born after 40 weeks gestation makes it more likely for more babies to have shorter birth lengths in that group.

(a) The standardized score (z-score) for a baby with a birth length of 45 cm, relative to babies born after 40 weeks gestation, can be calculated using the formula:

Z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

Using the given values:

x = 45 cm

μ = 52 cm

σ = 2.7 cm

Plugging these values into the formula, we get:

Z = (45 - 52) / 2.7 ≈ -2.59

So, the standardized score for a baby with a birth length of 45 cm is approximately -2.59.

(b) To find the standardized score for a birth length of 45 cm for a child born one month early, we use the mean of that group, which is 47.7 cm.

Using the same formula:

Z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

Plugging in the values:

x = 45 cm

μ = 47.7 cm

σ = 2.7 cm

Calculating the standardized score:

Z = (45 - 47.7) / 2.7 ≈ -1

So, the standardized score for a birth length of 45 cm for a child born one month early is approximately -1.

(c) Based on the calculated standardized scores, we can determine which group a birth length of 45 cm is more common for. A lower z-score indicates that the observation is farther below the mean.

In this case, a birth length of 45 cm has a z-score of approximately -2.59 for babies born after 40 weeks gestation, and a z-score of approximately -1 for babies born one month early.

Since -2.59 is farther below the mean (0) than -1, it means that a birth length of 45 cm is more common for babies born after 40 weeks gestation. This makes sense because the group of babies born after 40 weeks gestation is much larger than the group of births that are one month early. Therefore, more babies will have short birth lengths among babies born after 40 weeks gestation.

The correct answer is (OA) A birth length of 45 cm is more common for babies born after 40 weeks gestation.

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The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

\(y=2x+3\)

Step-by-step explanation:

The slope-intercept form is \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept.

\(y=mx+b\)

Using the slope-intercept form, the slope is 2.

\(m=2\)

So in order for us to find an equation that is parallel, the slopes must be equal. We need to find the parallel line using the point-slope formula.

We use the slope 2 and a given point \((2,7)\) to substitute for x1 and y1 in the point-slope form \(y-y^1 = m (x-x^1)\), which is derived from the slope equation: \(m=\frac{y2-y1}{x2-x1}\)

Now we simplify the equation and keep it in point-slope form.

\(y-7=2\)  × \((x-2)\)

Simplify \(2\) × \((x-2)\)

\(y-7=2x-4\)

\(Rewrite.~y-7=0+0+2~x~(x-2)\)

\(Simplify~ by~adding~zeros.~y-7=2 ~x~(x-2)\)

\(Apply~the~distributive~property.~y-7=2x+2~X~-2\)

\(Multiply~2~by~-2.~y-7=2x-4\)

Last, We move all terms not containing y to the right side of the equation.

Add 7 to both sides of the equation.

\(y=2x-4+7\)

Add −4 and 7 and your answer will be: \(y=2x+3\)

The resulting expression will be \(\frac{x+2}{x-3}\\\)

Given the expression as shown in the question:

\(\frac{x-2}{x+3} + \frac{10x}{x^2-9}\)

Find the LCM of the expression to have:

\(\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}\)

Expand the expression

\(\frac{(x^2 - 5x+6+10x}{(x+3)(x-3)}\\\frac {x^2 + 5x+6}{(x+3)(x-3)}\\\)

Expand the expression

\(=\frac {x^2 + 2x + 3x +6}{(x+3)(x-3)}\\=\frac {x(x + 2) + 3(x +2)}{(x+3)(x-3)}\\=\frac{(x+2)(x+3)}{(x+3)(x-3)}\\ =\frac{x+2}{x-3}\\\)

Hence the resulting expression will be \(\frac{x+2}{x-3}\\\)

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Answer: it is close to the number 25 i think i think i think i think

Step-by-step explanation:

dvyyffffvv

Answer:

Hello,

Step-by-step explanation:

\(p-q=10\\(p-q)^2=100=p^2+q^2-2pq\ \Longrightarrow\ p^2+q^2=100+2*7=114\\\\p^3-q^3=(p-q)(p^2+pq+q^2)=10*(114+7)=10*121=1210\\\)

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

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The mom delivered a total of 283 ounces of baby.

The lucky mom gave birth to three babies, each with different weights. Baby A weighed 4 lbs and 9 oz, which is equivalent to 73 oz. Baby B weighed 7 lbs and 8 oz, which is equivalent to 120 oz.

Finally, baby C weighed 5 lbs and 10 oz, which is equivalent to 90 oz. To find the total weight of the babies, we need to add the weight of each baby together. So, 73 oz + 120 oz + 90 oz equals 283 oz. Therefore, the mom delivered a total of 283 ounces of baby.

It is important to note that delivering triplets can be challenging for the mother and the medical team. It requires careful monitoring and attention to ensure that all three babies are healthy and developing normally.  

Additionally, the mom may need additional support to manage the demands of caring for three newborns. However, despite the challenges, triplets are a special and unique blessing for families.

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For a two-dimensional potential flow, the potential is given by 1 r (x, y) = x (1 + arctan x² + (1+ y)², 2πT where the parameter A is a real number. Given potential function is;ϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πT

To find velocity components ux and uy, we need to take partial derivative of potential functionϕ(x,y) = x(1 + arctan(x² + (1+y)²))/2πTUsing the chain rule;    ∂ϕ/∂x = ∂ϕ/∂r * ∂r/∂x + ∂ϕ/∂θ * ∂θ/∂x                                                                                             = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT ∂ϕ/∂y = ∂ϕ/∂r * ∂r/∂y + ∂ϕ/∂θ * ∂θ/∂y                                                                                              = cosθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πT           - sinθ * (1/r) * x(1+arctan(x² + (1+y)²))/2πTNow, replace cosθ and sinθ with x/r and y/r respectively∂ϕ/∂x = x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT- y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [x²-y²]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT∂ϕ/∂y = y/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT + x/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT= [2xy]/(x²+y²) * x(1+arctan(x² + (1+y)²))/2πT(2) To find stagnation point, we have to find (x,y) such that ux = uy = 0 and ϕ(x,y) is finite. Here, from (1) we get two equations;  x(1+arctan(x² + (1+y)²))/2πT= 0 and  x(1+arctan(x² + (1+y)²))/2πT + y(1+arctan(x² + (1+y)²))/2πT= 0For (1), either x=0 or arctan(x² + (1+y)²) = -1, but arctan(x² + (1+y)²) can't be negative so x=0. Thus, we get the condition y= -1  from (2)So, stagnation point is (0, -1).(3) For the far field, pressure is p, density is P. In potential flow, we have;  P = ρv²/2 + P0,  where P0 is constant pressure. Here, P0 = P and v = ∇ϕ   so, P = ρ[ (∂ϕ/∂x)² + (∂ϕ/∂y)² ]/2Using expressions of ∂ϕ/∂x and ∂ϕ/∂y obtained above, we can find pressure at (0,-2).(4) Given flow is around a cylinder. For flow around cylinder, stream function can be written as;   ψ(r,θ) = Ur sinθ (1-a²/r²)sinθTo find centre and radius of the cylinder, we find point where velocity is zero. We know that ψ is constant along any streamline. So, at the boundary of cylinder, ψ = ψ0, and at the centre of the cylinder, r=0.Using stream function, it is easy to show that ψ0= 0.So, at boundary of cylinder; U(1-a²/R²) = 0, where R is radius of cylinder, which gives R=aSimilarly, at centre; U=0To find the resulting force on the cylinder, we first have to find the lift and drag coefficients;  C_d = 2∫_0^π sin²θ dθ = π/2   and  C_l = 2∫_0^π sinθ cosθ dθ = 0We know that C_d = F_d/(1/2 ρ U²L) and C_l = F_l/(1/2 ρ U²L)where L is length of cylinder.So, F_d = π/2 (1/2 ρ U²L) and F_l= 0. Thus, the resulting force is F= (π/2) (1/2 ρ U²L) at an angle 90° to the flow direction.

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Using these values, we can write Bernoulli's equation as: P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

(1) To determine the expression for the velocity components ux and uy, we can use the relationship between velocity and potential in potential flow:

ux = ∂Φ/∂x

uy = ∂Φ/∂y

Taking the partial derivatives of the potential function Φ(x, y) with respect to x and y:

∂Φ/∂x = (1+arctan(x^2+(1+y)^2)) - x * (1/(1+x^2+(1+y)^2)) * (2x)

∂Φ/∂y = -x * (1/(1+x^2+(1+y)^2)) * 2(1+y)

Simplifying these expressions, we have:

ux = 1 + arctan(x^2+(1+y)^2) - 2x^2 / (1+x^2+(1+y)^2)

uy = -2xy / (1+x^2+(1+y)^2)

(2) To find the value of A such that the point (x, y) = (0,0) is a stagnation point, we need to find the conditions where both velocity components ux and uy are zero at that point. By substituting (x, y) = (0,0) into the expressions for ux and uy:

ux = 1 + arctan(0^2+(1+0)^2) - 2(0)^2 / (1+0^2+(1+0)^2) = 1 + arctan(1) - 0 = 1 + π/4

uy = -2(0)(0) / (1+0^2+(1+0)^2) = 0

For the point (x, y) = (0,0) to be a stagnation point, ux and uy must both be zero. Therefore, A must be chosen such that:

1 + π/4 = 0

A = -π/4

(3) To determine the pressure at the point (0, -2), we can use Bernoulli's equation for potential flow:

P + 1/2 * ρ * (ux^2 + uy^2) = constant

At the far field, where the velocity is assumed to be zero, the pressure is constant. Let's denote this constant pressure as P_far.

At the point (0, -2), the velocity components ux and uy are:

ux = 1 + arctan(0^2+(1-2)^2) - 2(0)^2 / (1+0^2+(1-2)^2) = 1 + arctan(5) - 0 = 1 + arctan(5)

uy = -2(0)(-2) / (1+0^2+(1-2)^2) = 4 / 3

Using these values, we can write Bernoulli's equation as:

P + 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2) = P_far

Solving for P at the point (0, -2), we have:

P = P_far - 1/2 * ρ * ((1 + arctan(5))^2 + (4/3)^2)

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Answer:

The optimal price should be $10 which will result in maximum revenue.

Step-by-step explanation:

y = [5+ 0.5x] [ 300 - 30x]

y = 1500 - 150x + 150x - 15x^2

y = 1500 - 15x^2

x^2 = 1500 /15

x = \(\sqrt{100}\)

x = 10

The value of the expression after evaluating it according to the values of c and d is 42.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Since, no expression is given, let us assume that the expression is

c + d / 4

Now we have to evaluate the value of the expression according to the values of c and d,

For that, we will simply put the given values in the expression and solved it accordingly,

Put c = 36 and d = 24 in the expression we assumed,

c + d / 4 = 36 + 24/4

= 36 + 6 = 42

Hence, the value of the expression after evaluating it according to the values of c and d is 42.

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Given relation between height and time is:

Now put the value of h=85 ft in given relation:

Solving it for t:

The probability of rolling a number greater than or equal to 2 is 5/6.

There are six possible outcomes when rolling a standard six-sided die: 1, 2, 3, 4, 5, or 6. Since we want to know the probability of rolling a number greater than or equal to 2,

we need to count the number of outcomes that satisfy this condition. These outcomes are: 2, 3, 4, 5, and 6. There are five such outcomes out of a total of six possible outcomes, so the probability of rolling a number greater than or equal to 2 is:

5/6

In other words, there is a 5 in 6 chance, or approximately 83.3% chance, that Fabian will roll a number greater than or equal to 2 when he rolls a standard six-sided die.

we can think of the six-sided die as a fair game where each of the six outcomes is equally likely. Since we want to roll a number greater than or equal to 2,

we are essentially saying that we want to win this game if we roll any of the five numbers: 2, 3, 4, 5, or 6. Since there are five winning outcomes and only one losing outcome (rolling a 1), the probability of winning this game is 5/6.

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E = nhν refers to the energy (E) of a photon in terms of Planck's constant (h), the frequency (ν) of the photon, and a positive integer (n) that represents the quantum number of the photon.

The equation E = nhν is derived from the quantum theory of light, which states that light is composed of particles called photons. Each photon carries a discrete amount of energy that is directly proportional to its frequency. Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.

In the equation, the quantum number (n) represents the number of energy quanta or "packets" that make up the total energy of the photon. The value of n can be any positive integer, such as 1, 2, 3, and so on.

The equation E = nhν allows us to calculate the energy of a photon based on its frequency and quantum number. By multiplying the frequency by the quantum number and then scaling it by Planck's constant, we obtain the total energy of the photon.

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The volume of the solid generated when the region in the first quadrant is: V ≈ 183.78

The disc method, the shell method, and Pappus' centroid theorem can all be used to calculate volume. In many academic disciplines, such as engineering, medical imaging, and geometry, revolution volumes are used. Integration can be used to determine the area of a region bounded by a known curve.

Because we are only revolving the region in the first quadrant, the x values range from x = 0 to x = 3.

Because of the rotation is about the vertical line x = -1, the radius of the cylindrical shell at x is r = x + 1.

The height of the cylindrical shell at x is h = \(x^{2}\)

We can now create our integral equation to find the volume:

\(V =2\pi\int\limits^a_b {rh} \, dx =2\pi\int\limits^3_0 {(1+x)x^2} \, dx \\\\V =2\pi\int\limits^3_0 {(x^{2} +x^3)} \, dx\)

We can now integrate and evaluate to find the volume of the solid.

\(V=2\pi(\frac{x^3}{3}+\frac{x^4}{4} )|^3_0\\\\V = 2\pi(\frac{27}{3}+\frac{81}{4} )\\\\V=\frac{117\pi}{2}\)

V ≈ 183.78

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The given question is incomplete, complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded above by the curve y =\(x^{2}\), below by the x-axis, and on the right by the line x = 3, about the line x = −1

Answer: the answer is B

Step-by-step explanation:

The x axis cannot have the same number. -2 and -2 are the same so you would have to replace one of them with a different number that is not used in the x axis.

Answer:

$52.60

Step-by-step explanation:

$13.15 x 4 = $52.60

the slopes would look like this

Answer:

part 11

Step-by-step explanation:

B

Step-by-step explanation:

hope that help!

There are some means for value. There are:

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Answer:

P(lollipop) = 7/21 = 1/3

Answer:

3.9x + 0.8y

Step-by-step explanation:

Simplify:

-Chetan K