The total weight of all the students in a class is 3,159 lb. The mean weight of the students is 117 lb. How many students are there in the class?

To evaluate the iterated integral ∫∫∫ R x[tex]y^{2}[/tex] dz dy dx over the given region R in cylindrical coordinates, we first convert the limits of integration and the integrand to the cylindrical form. Then we evaluate the integral using the appropriate transformations and calculations.

In cylindrical coordinates, we express points in three-dimensional space using the variables (ρ, θ, z), where ρ represents the distance from the origin to a point projected onto the xy-plane, θ denotes the angle measured counterclockwise from the positive x-axis to the projection of the point onto the xy-plane, and z represents the height of the point above or below the xy-plane.

To evaluate the given iterated integral, we begin by transforming the limits of integration. The outermost integral corresponds to the variable ρ, which ranges from 0 to 1. The next integral corresponds to θ and remains unchanged since the region R does not involve any angular restrictions. The innermost integral corresponds to z and ranges from the lower limit of √(1 - [tex]x^{2}[/tex]) to the upper limit of √(1 - [tex]x^{2}[/tex]), as determined by the given limits of integration.

Next, we convert the integrand, [tex]xy^2[/tex], to cylindrical coordinates. The variable x is replaced by ρcosθ, and y is replaced by ρsinθ, giving us [tex]ρ^3cosθsin^2θ[/tex].

With the limits of integration and the integrand expressed in cylindrical coordinates, we proceed to evaluate the iterated integral. Following the order of integration, we integrate ρ from 0 to 1, θ from 0 to 2π, and z from √(1 - [tex]x^{2}[/tex]) to -√(1 -[tex]x^{2}[/tex]). The integration of ρ yields [tex]ρ^4[/tex]/4, the integration of θ results in 2π, and the integration of z simplifies to 0.

Finally, we substitute the limits of integration and perform the calculations: (∫(0 to 1) [tex]ρ^4[/tex]/4 dρ) * (2π) * (0). Evaluating the integral of[tex]ρ^4[/tex]/4 yields 1/20, and multiplying this by 2π and 0 gives us the final result of 0.

Therefore, the evaluated iterated integral in cylindrical coordinates is 0.

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Answer: 1047.2

Step-by-step explanation:

V=(4/3)(pi)(r^3)

V=(4/3)(pi)(5^3)

=523.6

Since there are 2 pinatas, you multiply 523.6 by 2.

=1047.2

The function [tex]√(x^3 - 8)[/tex] at each x value is 0.25 * [-1.902 - 1.609].  The interval [2, 3] into subintervals and apply the respective formulas.

To approximate the integral ∫[2 to 3] √(x^3 – 8) dx using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule, we need to divide the interval [2, 3] into subintervals and apply the respective formulas. Let's compute the approximations for each rule.

Step 1: Determine the subinterval width, h.

We can calculate h using the formula:

h = (b - a) / n

Given:

a = 2

b = 3

Let's use different values of n for each rule.

For Trapezoidal Rule, let's set n = 4.

For Midpoint Rule, let's set n = 4.

For Simpson's Rule, let's set n = 2.

Step 2: Compute the approximations for each rule.

Using the Trapezoidal Rule:

Approximation = (h / 2) * [f(a) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(b)]

For n = 4:

h = (3 - 2) / 4 = 0.25

Approximation = (0.25 / 2) * [f(2) + 2f(2.25) + 2f(2.5) + 2f(2.75) + f(3)]

Evaluate the function √(x^3 - 8) at each x value:

f(2) ≈ √(2^3 - 8) ≈ -2

f(2.25) ≈ √(2.25^3 - 8) ≈ -1.726

f(2.5) ≈ √(2.5^3 - 8) ≈ -1.414

f(2.75) ≈ √(2.75^3 - 8) ≈ -1.125

f(3) ≈ √(3^3 - 8) ≈ -0.464

Approximation = (0.25 / 2) * [-2 + 2(-1.726) + 2(-1.414) + 2(-1.125) + (-0.464)]

≈ (0.125) * [-2 - 3.452 - 2.828 - 2.25 - 0.464]

≈ (0.125) * [-11.994]

≈ -1.49925

Using the Midpoint Rule:

Approximation = h * [f(x1) + f(x2) + ... + f(xn)]

For n = 4:

h = (3 - 2) / 4 = 0.25

Approximation = 0.25 * [f(2.125) + f(2.375) + f(2.625) + f(2.875)]

Evaluate the function √(x^3 - 8) at each x value:

f(2.125) ≈ √(2.125^3 - 8) ≈ -1.902

f(2.375) ≈ √(2.375^3 - 8) ≈ -1.609

f(2.625) ≈ √(2.625^3 - 8) ≈ -1.335

f(2.875) ≈ √(2.875^3 - 8) ≈ -1.073

Approximation = 0.25 * [-1.902 - 1.609]

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Answer:

(1,5) because, before it was at (3,8) and  

3 – 2 = 1      

8 – 3 = 5

For further explanation:

(3,8) / (2,3) = (1,5)

2 for 2 units left and 3 for 3 units down

the answer would be b on scholar

Answer:

3 (x² + 5) (x - 2)

Step-by-step explanation:

3x³- 6x² + 15x - 30

=> 3 (x³ - 2x² + 5x - 10)

=> 3 [x²(x - 2) + 5 (x - 2)]

=> 3 (x² + 5) (x - 2)

Answer:

16

Step-by-step explanation:

p=k√q

8=k√25

8=k5

k=8/5

p when q=100

p=8/5*√100

p=8/5*10

p=16

The proportion of Shohei Ohtani's hitting the ball (batting average) decreased from 2018 to 2019. In 2018, Ohtani hit the ball 103 times out of 195 at-bats, resulting in a batting average of approximately 0.528.

In 2019, he hit the ball 54 times out of 179 at-bats, yielding a batting average of approximately 0.302. To determine whether Ohtani's batting average decreased from 2018 to 2019, we compare the proportions of hitting the ball in each year. Using a 1% significance level and assuming the Central Limit Theorem conditions hold, we can conduct a hypothesis test. The null hypothesis (H0) states that there is no difference in Ohtani's batting average between 2018 and 2019, while the alternative hypothesis (Ha) suggests a decrease in batting average.

To test the hypotheses, we can use a two-sample z-test for proportions. We calculate the sample proportions for hitting the ball in each year: p1 = 103/195 ≈ 0.528 in 2018 and p2 = 54/179 ≈ 0.302 in 2019. The standard error for the difference in proportions is given by the formula sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)), where n1 and n2 are the sample sizes.

Next, we calculate the test statistic z using the formula z = (p1 - p2) / sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)). The calculated z-value can be compared to the critical z-value at the 1% significance level (zα/2) to determine if we reject or fail to reject the null hypothesis.

In this case, the z-value is negative, indicating that the proportion of hitting the ball decreased from 2018 to 2019. By comparing the calculated z-value to the critical z-value, we can conclude that the decrease in Ohtani's batting average is statistically significant.

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Answer:

8!

Step-by-step explanation:

Answer) 8!

Explanation) i dont have one :')

Answer:

i think ist D correct me if im wrong

Step-by-step explanation:

Answer:

22.7

Step-by-step explanation:

if ∡M is 90° then you can do:

sin 65 = h/25

h = 25(sin 65°)

h = 22.65

Answer:

X>8

Step-by-step explanation:

Open circle, going towards larger numbers, meaning it is greater than eight but not equal to.

Answer:

3.14 square inches or π square inches

Step-by-step explanation:

The radius of a circle is 1 inch. What is the area?

r=1 in

The formula for the area of a circle is given as:

πr²

The radius (r) = 1 inch

Hence,

Area of the circle = π × 1²

= 3.1415926536 square inches

Approximately = 3.14 square inches or we can say that the Area of the circle = π square inches

If differential equation is 3(1+x^2)dy/dx = 2xy(y^3-1) then exponential is |y^3-1| = Ce^(x^2).

To solve the given differential equation, we can begin by separating the variables. We divide both sides of the equation by 2xy(y^3-1) to get:

3(1+x^2)dy/dx = 2xy(y^3-1)

(3(1+x^2))/(2xy(y^3-1)) dy = dx

Next, we integrate both sides with respect to their respective variables. On the left side, we integrate with respect to y, and on the right side, we integrate with respect to x:

∫(3(1+x^2))/(2xy(y^3-1)) dy = ∫dx

After evaluating the integrals, we obtain:

ln|y^3-1| = x^2 + C

Where C is the constant of integration. Finally, we can exponentiate both sides of the equation:

|y^3-1| = e^(x^2+C)

|y^3-1| = Ce^(x^2)

Here, Ce^(x^2) represents the constant of integration. Since the absolute value can be positive or negative, we consider both cases and solve for y to obtain the general solution.

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Answer:

3.9mm

Step-by-step explanation:

Answer:

*Pew Pew*

Step-by-step explanation:

Answer: 180 ft^3

Step-by-step explanation:

Answer: 180 ft is the answer

Step-by-step explanation:

The solution to the initial value problem [tex]cos^{2xsinx}dy/dx + cos^{3(x)}y = 5, y(\pi/3) = 4[/tex], involves solving the given differential equation and applying the initial condition.

To solve the differential equation, we can use an integrating factor. The integrating factor for the given equation is [tex]e^{\int{cos^3x} \, dx}[/tex]. Integrating [tex]cos^3(x)[/tex] gives us (1/4)(3sin(x) + sin(3x)).

Multiplying the entire equation by the integrating factor, we get [tex](1/4)(3sin(x) + sin(3x)) * cos^2(x)sin(x) * dy/dx + (1/4)(3sin(x) + sin(3x)) * cos^3(x) * y = 5 * (1/4)(3sin(x) + sin(3x))[/tex]

Simplifying, we have [tex](3sin(x) + sin(3x)) * cos(x)sin^2(x) * dy/dx + (3sin(x) + sin(3x)) * cos^3(x) * y = 5 * (3sin(x) + sin(3x))/4[/tex]

This equation can be rewritten as [tex]d/dx[(3sin(x) + sin(3x)) * cos^2(x) * y] = 5 * (3sin(x) + sin(3x))/4[/tex].

Integrating both sides with respect to x, we obtain [tex](3sin(x) + sin(3x)) * cos^2(x) * y = 5 * (3sin(x) + sin(3x))/4 * x + C[/tex], where C is the constant of integration.

Applying the initial condition y(π/3) = 4, we can substitute x = π/3 and y = 4 into the equation to find the value of C.

By substituting the values, we get [tex](3sin(\pi /3) + sin(3\pi/3)) * cos^2(\pi/3) * 4 = 5 * (3sin(\pi/3) + sin(3\pi/3))/4 * (\pi/3) + C[/tex]

Simplifying and solving for C, we can determine the value of C.

Finally, we can substitute the value of C back into the equation to obtain the solution to the initial value problem.

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Answer:

C. y = -x + 2

Step-by-step explanation:

Sana nakatulong

Answer:

The mode is 23

Step-by-step explanation:

Answer:This seems easy! do u want help on how to do the answer or r u just looking for the answer????/

Step-by-step explanation:

Answer:

slope-intercept form: y= -5/4x-1

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Given information: Consider a binomial distribution. About 47% of Salinas residents bank entirely online.

A random sample of 62 residents is selected. Find the probability that less than 21 bank entirely online. The given data follows binomial distribution with n = 62 and p = 0.47

Let X be the random variable representing the number of residents bank entirely online. Then X ~ B(62, 0.47) We need to find the probability that less than 21 bank entirely online. P(X < 21) = P(X ≤ 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20Using binomial probability distribution, P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = ∑P(X = x) , where x = 0, 1, 2, 3, ... 20P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)P(X ≤ 20) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = 20)

Now, we can use a calculator or software to find this sum. Using software or calculator, P(X ≤ 20) = 0.0251Therefore, the probability that less than 21 bank entirely online is 0.0251. Hence, the correct option is 0.0251.

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The subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].

To determine if the described set is a subspace, we need to check if it satisfies three conditions: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let's consider the subset of [tex]R^{3}[/tex] consisting of vectors of the form (a, b, c), where a = b = c.

Closure under addition: Let (a₁, b₁, c₁) and (a₂, b₂, c₂) be two vectors in the subset.

Their sum is (a₁ + a₂, b₁ + b₂, c₁ + c₂).

Since a₁ = b₁ = c₁ and a₂ = b₂ = c₂, we have (a₁ + a₂, b₁ + b₂, c₁ + c₂) = (a₁ + a₁, b₁ + b₁, c₁ + c₁) = (2a₁, 2b₁, 2c₁).

Since 2a₁ = 2b₁ = 2c₁, the sum is also in the subset.

Closure under scalar multiplication: Let (a, b, c) be a vector in the subset and let k be a real number.

The scalar multiple k(a, b, c) is (ka, kb, kc). Since ka = kb = kc, the scalar multiple is also in the subset.

Contains the zero vector: The zero vector is (0, 0, 0). Since 0 = 0 = 0, it is in the subset.

Therefore, the subset satisfies all three conditions, it is a subspace of [tex]R^{3}[/tex].

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Answer:

B

Step-by-step explanation:

cus thats the formula

Answer:

A is the answer.

Step-by-step explanation: It would go up about 2.2 i hope i helped! <3

Answer: A is your answer

Step-by-step explanation:

Answer:

400

1.05

Step-by-step explanation:

The athlete should take the second offer.

It is given by the formula,

A = P(1+r)ⁿ

where A is the value after n period of time, P is the initial amount, and,

r is the rate of increment or decrement.

Now, Total amount = $400,000(1+5%)⁷

                    = $400,000(1+0.05)⁷

                    = $400,000(1.4071)

                    = $562840.17

Now, the total amount that the pro-athlete will get in 8 years is,

Total amount = $425,000(1+4%)⁷

                    = $425,000(1+0.04)⁷

                    = $425,000(1.3159)

                    = $559,271

Since the total amount that the athlete will get in the next 8 years is more for the second offer, the athlete should take the second offer.

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Answer:

9/100 is the answer i believe

Answer:

the answer is 9/100

Step-by-step explanation:

9 ÷ 100= 0.09