Which is the correct formula to calculate the volume of a sphere?
a.
Four-thirds pi r squared
c.
One-third pi r cubed
b.
Four-thirds pi r cubed
d.
4 pi r cubed



Please select the best answer from the choices provided


A
B
C
D

Not a

Answer;

22.88m

Explanation

The formula for finding the area of the trinagle is expressed as;

a and b arethe sides of the triangle

theta is the central angle between the sides

Given

a = 12m

b = 7m

theta = 33 degrees

Substitute the given values into the formula as shown;

Hence the area of the triangle to the nearest hundredth is 22.88m

The equation that describes the simple harmonic motion of the particle is:

x = 7 * sin(2t + φ)

The equation that describes the simple harmonic motion of a particle moving uniformly around a circle can be represented as:

x = A * sin(ωt + φ)

In this equation:

x represents the displacement of the particle at time t.

A represents the amplitude of the motion.

ω represents the angular frequency or angular speed of the motion.

t represents time.

φ represents the phase constant.

In the given scenario, the particle is moving uniformly around a circle of radius 7 units, with an angular speed of 2 radians per second. In circular motion, the displacement can be represented by the arc length along the circumference of the circle.

Since the angular speed is 2 radians per second, the angular frequency (ω) is also 2 radians per second.

Since the particle is moving uniformly, the amplitude of the motion (A) is equal to the radius of the circle, which is 7 units.

The phase constant (φ) determines the initial position of the particle at t = 0.

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Answer:

answer is 42 in²

:-)))

....

Answer:

4

Step-by-step explanation:

\(\sqrt{16}\) = 4

Answer:

4.

Step-by-step explanation:

The square root of 17 is 4.12...

square root of 16 is 4

The answer is ⟨y(x) = (-1/27)(5 - 3x)^9 + C, where C is an arbitrary constant⟩.

The given differential equation is:

y' = (5 - 3x)^8

We can separate the variables and integrate both sides:

dy/dx = (5 - 3x)^8

dy = (5 - 3x)^8 dx

Integrating both sides, we get:

∫dy = ∫(5 - 3x)^8 dx

y = (-1/27)(5 - 3x)^9 + C

where C is an arbitrary constant of integration.

Therefore, the general solution of the differential equation is:

y(x) = (-1/27)(5 - 3x)^9 + C

where C is an arbitrary constant.

Hence, the answer is ⟨y(x) = (-1/27)(5 - 3x)^9 + C, where C is an arbitrary constant⟩.

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The upward unit normal to the surface 7cos(xy) = \(e^(^8^z^)\)- 13 at (7, π, 0) is (0, 0, 1/√2).

To find the upward unit normal to the surface, we need to calculate the partial derivatives of the given surface equation with respect to x, y, and z.

Starting with the given equation: 7cos(xy) = \(e^(^8^z^)\)- 13, we differentiate it partially with respect to x, y, and z.

Evaluating these partial derivatives at the point (7, π, 0), we have:

Next, we construct the normal vector by normalizing the vector (0, 0, 8) to obtain the unit normal vector: (0, 0, 1).

Therefore, the upward unit normal to the surface at (7, π, 0) is (0, 0, 1).

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the volume of the solid below the paraboloid z = 48 - \(3x^2 - 3y^2\) in polar coordinates is 640π cubic units.

To find the volume of the solid below the paraboloid given by the equation z = 48 - \(3x^2 - 3y^2\) using polar coordinates, we need to express the equation in terms of polar variables.

In polar coordinates, we have x = rcosθ and y = rsinθ, where r represents the distance from the origin and θ is the angle with the positive x-axis.

Substituting these values into the equation of the paraboloid, we get:

z = 48 - 3(rcosθ\()^2\) - 3(rsinθ\()^2\)

z = 48 - 3\(r^2(cos^2\)θ + \(sin^2\)θ)

z = 48 - \(3r^2\)

Now, the volume of the solid can be expressed as a triple integral in polar coordinates:

V = ∬D (48 - 3\(r^2\)) r dr dθ

The region D in the xy-plane corresponds to the projection of the solid. Since the solid extends infinitely in the z-direction, the limits of integration for r and θ will be the same as the limits for the entire xy-plane.

Assuming we integrate over the entire xy-plane, the limits of integration will be:

0 ≤ r < ∞

0 ≤ θ < 2π

Now, we can evaluate the triple integral:

V = ∫₀²π ∫₀ᴿ (48 - 3r^2\(r^2\)) r dr dθ

To find the value of R, we need to determine the radius at which the paraboloid intersects the xy-plane. In this case, when z = 0:

0 = 48 - 3r^2

3r^2 = 48

r^2 = 16

r = 4

Therefore, the limits of integration become:

0 ≤ r ≤ 4

0 ≤ θ < 2π

Now, we can calculate the volume:

V = ∫₀²π ∫₀⁴ (48 - 3\(r^2)\) r dr dθ

Integrating with respect to r first:

V = ∫₀²π [(24\(r^2 - r^4/2\))] from 0 to 4 dθ

V = ∫₀²π [(\(24(4)^2 - (4)^4/2\))] dθ

V = ∫₀²π [(384 - 64)] dθ

V = ∫₀²π (320) dθ

V = 320∫₀²π dθ

V = 320(θ) from 0 to 2π

V = 320(2π - 0)

V = 640π

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Regression analysis is a statistical technique used to predict the value of a quantitative variable based on another quantitative variable i.e., the given statement is true.

Regression analysis is widely used when there is an interest in understanding how one quantitative variable, known as the dependent variable or response variable, is influenced by another quantitative variable, known as the independent variable or predictor variable.

The goal is to establish a mathematical relationship between the variables that can be used for prediction and inference.

In regression analysis, a model is built based on the observed data to estimate the relationship between the variables. The model takes into account the variability in the data and provides insights into the strength and direction of the relationship.

By analyzing the model's coefficients, such as the slope and intercept, predictions can be made about the dependent variable's values for different levels of the independent variable.

Regression analysis allows for the assessment of the significance of the relationship, the quantification of the effect of the predictor variable on the response variable, and the estimation of the prediction accuracy.

It provides a valuable tool for making informed decisions, conducting research, and understanding the underlying factors that contribute to the variability of the dependent variable.

Therefore, it is true that regression analysis is useful when predicting the value of a quantitative variable based on another quantitative variable.

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If the size of an object doubles, the new distance needs to be square root of 2 times the original distance to keep the same angular size.

To relate the size of an object (x) to the distance to the object (d), you can use the small-angle formula. This formula is θ = x/d, where θ represents the angular size of the object.

If the size of an object doubles, you need to find the new distance (c) in order to keep the angular size the same.

To calculate the new distance (c), you can rearrange the small-angle formula. Since the angular size (θ) remains the same, the new size of the object will be 2x.

So, the equation becomes θ = 2x/c.

To find the new distance (c), you need to solve for c. Rearrange the equation as c = 2x/θ.

Now you can plug in the values for the new size of the object (2x) and the angular size (θ) to calculate the new distance (c).

Remember to use consistent units for accurate results.

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The numerical length of VX is undefined

The given parameters are

VX = 4x

VW = 3x

WX = 5x

Point W is on line segment VX

So, we have

VX = VW + WX

This gives

4x = 3x + 5x

Evaluate

4x= 8x

The above equation is false

Hence, the numerical length of VX is undefined

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Answer:

-52, I think

Step-by-step explanation:

1. We should understand that question is missing, but, the amount 1 that Mia has to pay back if she takes the loan will be Loan amount plus the interest on it.

2. The banks 2 and other financial institutions did offer cash loans to people that did not apply for it because they knew that had favorable credit worthiness, that is, they repay loan as at when due.

Creditworthiness is how a lender determines whether you will default on your debt obligations or whether you are creditworthy. Creditors consider your creditworthiness before approving new credit for you.

Several factors influence it, including your repayment history and credit score. When determining the likelihood of default, some lending institutions consider available assets as well as the number of liabilities you have.

The credit report shows how much debt you have, as well as the high balances, credit limits, and the current balance of each account. It will also flag any relevant information for the potential lender, such as past due amounts, defaults, bankruptcies, and collection items.

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Answer:

x(x-9)+7(x-9)

x²-9x+7x-63

x²-2x-63

The standard deviation of this dataset isapproximately 76.88 rounded to one decimal place. To find the standard deviation of this dataset, we first need to find the mean:

\(Mean = (120 + 60 + 250 + 120 + 200) / 5 = 150\)

Next, we need to find the deviation of each data value from the mean:

120 - 150 = -30
60 - 150 = -90
250 - 150 = 100
120 - 150 = -30
200 - 150 = 50

We then square each deviation:

(-30)^2 = 900
(-90)^2 = 8100
100^2 = 10000
(-30)^2 = 900
50^2 = 2500

We then find the sum of the squared deviations:

900 + 8100 + 10000 + 900 + 2500 = 23600

Next, we divide the sum of squared deviations by the number of values minus 1:

\(23600 / 4 = 5900\)

Finally, we take the square root of this value to find the standard deviation:

sqrt(5900) = 76.81

Rounding to one decimal place, the standard deviation of this dataset is 76.8.

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Answer:

40%

Step-by-step explanation:

it's easiest to get a percentage from 100, multiplying 25 by 4 gives you 100 so if you do that then multiply 10 by four to make the equation even that will give you the answer

Answer:

125

Step-by-step explanation:

5x5=25

then 25x5=125

Answer:

125

Step-by-step explanation:

5*5= 25

25*5= 125

I hope this helps!!!!

a) The electric field (Erec) and potential (V) at Prec (0,0,1) if rho_s = rho_o within region (1 ≤ r_c ≤ 2, 0 ≤ Φ ≤ 2π), and rho_s = 0 elsewhere are Erec = 0 and V = 0.

b) The electric field (Erec) and potential (V) at Prec (0,0,1) if rho_s = rho_o within region (1 ≤ r_c ≤ 2, 0 ≤ Φ ≤ π/2), and rho_s = 0 elsewhere are Erec = 0 and V = 0.

a) In this case, the surface charge density rho_s is nonzero only within the region defined by 1 ≤ r_c ≤ 2 and 0 ≤ Φ ≤ 2π. Since the point Prec is located at z = 1, which is above the plane z = 0, the contribution of rho_s to the electric field and potential at Prec is zero. This is because the electric field due to a surface charge distribution is perpendicular to the surface, and since Prec is located above the surface, there is no electric field contribution from rho_s. Similarly, since the electric field is zero, the potential is also zero at Prec.

b) In this case, the surface charge density rho_s is nonzero within the region defined by 1 ≤ r_c ≤ 2 and 0 ≤ Φ ≤ π/2. Again, since the point Prec is located at z = 1, above the plane z = 0, the contribution of rho_s to the electric field and potential at Prec is zero. This is because the electric field due to a surface charge distribution is perpendicular to the surface, and since Prec is located above the surface, there is no electric field contribution from rho_s. Consequently, the potential at Prec is also zero.

In both cases, the contributions from the surface charge distribution rho_s to the electric field and potential at Prec are zero due to the specific location of Prec with respect to the surface charge distribution.

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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The correct answer is: c. The n-th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1.

This statement indicates that there is a correlation or relationship between consecutive error terms, where the n-th error term can be predicted based on the previous error term. In a simple linear regression model, the error terms are assumed to be independent and have no correlation with each other.

However, if there is a correlation between the error terms, it violates the assumption of independence, which can lead to biased and unreliable regression results. Therefore, this condition suggests that the result from the simple linear regression model could be potentially misleading.

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In a similar polygon, corresponding sides are proportional. Therefore, the proportion that must be true when polygon ABCD is similar to polygon PQRS is d. CD:AB = PQ:RS.

This means that the ratio of the length of side CD to the length of side AB in polygon ABCD should be equal to the ratio of the length of side PQ to the length of side RS in polygon PQRS. It is important to note that the order of the sides matters in the proportion.

In this case, CD corresponds to PQ, and AB corresponds to RS. By setting up this proportion, we can compare the lengths of corresponding sides in similar polygons and establish the relationship between them.

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Answer: she would be 19 years old right now.

Step-by-step explanation:

14 years plus another 5 equals 19 years.

Answer: 13

Step-by-step explanation:

Answer: Therefore, we need to choose the smaller positive value of x:

x ≈ 1.8/8 = 0.225 inches

So, each side should be shortened by approximately 0.225 inches.

Step-by-step explanation:

Let's call the amount by which each side is shortened "x". After the board is shortened on all sides by "x", its new dimensions will be (12-2x) inches by (8-2x) inches. The area of the new board will be:

(12-2x)(8-2x)

We want this area to be 45 square inches, so we can set up the equation:

(12-2x)(8-2x) = 45

Expanding the left side of the equation, we get:

96 - 40x + 4x^2 = 45

Rearranging and simplifying, we get a quadratic equation:

4x^2 - 40x + 51 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 4, b = -40, and c = 51. Plugging in these values, we get:

x = [40 ± sqrt((-40)^2 - 4(4)(51))] / (2(4))

x = [40 ± sqrt(136)] / 8

x ≈ 3.3/8 or x ≈ 1.8/8

However, we can see that if we choose x = 3.3/8 (approximately 0.4125 inches), then the new dimensions of the board would be negative, which does not make sense. Therefore, we need to choose the smaller positive value of x:

x ≈ 1.8/8 = 0.225 inches

So, each side should be shortened by approximately 0.225 inches.

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Answer:

\(f = k \frac{qq}{ {r}^{2} } \: \: \: \: \times {r}^{2} \\ f {r}^{2} = kqq \: \: \div qq \)

\( \frac{f {r}^{2} }{qq} = k\)

this is answer A

The formula that represents the equation, when solved for k is → k = Fr²/qQ

Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the magnitude of charge on the objects and inversely proportional to the square of the distance between the two objects. Mathematically -

F = kqQ/r²

where -

k = 1/4πε₀

Given is the mathematical representation of Coulomb's law as -

F = kqQ/r². This formula relates the force 'F' between two charges → q and Q, which are a distance of 'r' units apart.

We have the following expression -

F = kqQ/r²

Rearranging the equation -

kqQ = Fr²

k = Fr²/qQ

Therefore, the formula that represents the equation, when solved for k is → k = Fr²/qQ

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A 95% confidence interval for the calorie count of the snack bars is (135.88, 167.24).

We will construct a 95% confidence interval for the calorie count of the snack bars using the given sample data and population standard deviation (σ=24).

Step 1: Calculate the sample mean (x)

x = (149+145+140+160+149+153+131+134+153) / 9

x = 1364 / 9

x = 151.56

Step 2: Find the z-score for a 95% confidence interval

The z-score for a 95% confidence interval is 1.96 (from the standard normal table).

Step 3: Calculate the standard error (SE)

SE = σ / √n

SE = 24 / √9

SE = 24 / 3

SE = 8

Step 4: Calculate the margin of error (ME)

ME = z-score * SE

ME = 1.96 * 8

ME = 15.68

Step 5: Construct the confidence interval

Lower limit = x - ME = 151.56 - 15.68 = 135.88

Upper limit = x + ME = 151.56 + 15.68 = 167.24

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The one-sample chi-square test is used to determine whether the distribution of a single categorical variable significantly differs from what would be expected by chance. The statement is True.

The one-sample chi-square test is a statistical test used to determine if there is a significant difference between the observed frequency and the expected frequency in a single categorical variable. It compares the observed frequency distribution of a variable to the expected frequency distribution, assuming that the null hypothesis is true.

This test compares observed frequencies to expected frequencies and calculates a chi-square statistic to assess the significance of the difference.

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we have that

First

Rotate 180 degrees clockwise about the origin

the rule is

S(x,y) --------> S'(-x,-y)

Second

translated 6 units to the left

the rule is

S'(-x,-y) -----> S''(-x-6,-y)

Third

Reflect across the line y=x

the rule is

the x-coordinate and y-coordinate change places

S''(-x-6,-y) ------> S''''(-y,-x-6)

therefore

Answer:

77 this answer is rounded to the nearest tenth

Step-by-step explanation:

The formula for the are of a circle is A=πr² so thats π7² which is equaled to about 153.9 since this is a semicircle you'd divide that by two giving you 76.96902.