An average clementine is shaped like a sphere and has a diameter of 3. 5 inches. What is the volume of the fruit? Use 3. 14 for pi. Round your answer to the nearest hundredth

Answer:

I cant read all of that. Im sure others ant either.

Step-by-step explanation:

Answer:

i cant read it for some reason, can you type it?

Step-by-step explanation:

Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

a)  the potential function f(x, y) is given by: f(x, y) = \((1/3)x^3y^3 + (1/12)x^3y^3\) + \(h(x) = (5/12)x^3y^3 + h(x)\)

b) To evaluate the integral, we substitute the limits of t into the expression and compute the result. The integral represents the work done by the vector field F along the curve C.

a) To find a potential function f such that F = ∇f, we need to find a function f such that its partial derivatives with respect to x and y are given by the components of F.

So, we have:

∂f/∂x =\(x^2y^3\)

∂f/∂y =\(x^3y^2\)

Integrating the first equation with respect to x gives:

f = \((1/3)x^3y^3 + g(y)\)

where g(y) is an arbitrary function of y. Now, we differentiate this expression with respect to y and equate it with the second equation to solve for g(y):

∂f/∂y =\(x^3y^2 = 3x^2y^2g'(y)\)

So, g'(y) =\(x^3/3.\)Integrating both sides with respect to y, we get:

g(y) = \((1/12)x^3y^3 + h(x)\)

where h(x) is an arbitrary function of x. Therefore, the potential function f(x, y) is given by:

f(x, y) = \((1/3)x^3y^3 + (1/12)x^3y^3 + h(x) = (5/12)x^3y^3 + h(x)\)

b)  To evaluate ∫C ∇f · dr along the given curve C, we substitute the parametric equations of C into the gradient of f and take the dot product with the tangent vector of C.

The parametric equations of C are:

x = \(t^3 - 2t\)

y =\(t^3 + 2t\)

The gradient of f is:

∇f = (∂f/∂x)i + (∂f/∂y)j

=\((x^2y^3)i + (x^3y^2)j\)

Taking the dot product with the tangent vector of C:

dr/dt = (∂x/∂t)i + (∂y/∂t)j

= \((3t^2 - 2)i + (3t^2 + 2)j\)

∇f · dr = \((x^2y^3)(3t^2 - 2) + (x^3y^2)(3t^2 + 2)\)

Substituting the parametric equations of C into the expression, we have:

∇f · dr = (\((t^3 - 2t)^2(t^3 + 2t)^3)(3t^2 - 2) + ((t^3 - 2t)^3(t^3 + 2t)^2)(3t^2 + 2\))

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(a) The potential function f(x,y) for the given vector field F(x,y) = x²y³i + x³y²j is f(x,y) = 1/4x³y⁴ + 1/4x⁴y³ + C, where C is a constant.

To find the potential function f(x,y) such that F = ∇f, we need to find a function whose gradient is equal to F. In this case, F(x,y) = x²y³i + x³y²j.

To obtain f(x,y), we integrate each component of F with respect to its corresponding variable. Integrating x²y³ with respect to x gives us 1/4x³y⁴ + g(y), where g(y) is an arbitrary function of y. Similarly, integrating x³y² with respect to y gives us 1/4x⁴y³ + h(x), where h(x) is an arbitrary function of x.

To find the potential function f(x,y), we need to choose g(y) and h(x) such that their partial derivatives with respect to y and x, respectively, cancel out the remaining terms. In this case, g(y) = 0 and h(x) = 0.

Therefore, the potential function f(x,y) for F(x,y) is f(x,y) = 1/4x³y⁴ + 1/4x⁴y³ + C, where C is the constant of integration.

(b) Using the potential function f(x,y) obtained in part (a), we can evaluate the line integral ∫C ∇f ⋅ dr along the given curve C.

The curve C is defined as r(t) = ⟨t³ - 2t, t³ + 2t⟩, 0 ≤ t ≤ 1.

To evaluate the line integral, we substitute the parametric equations of C into ∇f and dr, and then perform the dot product and integration.

∫C ∇f ⋅ dr = ∫₀¹ (∇f) ⋅ (r'(t) dt)

Since ∇f = ⟨∂f/∂x, ∂f/∂y⟩ and r'(t) = ⟨dx/dt, dy/dt⟩, we have:

∫C ∇f ⋅ dr = ∫₀¹ (⟨∂f/∂x, ∂f/∂y⟩) ⋅ (⟨dx/dt, dy/dt⟩) dt

Using the given potential function f(x,y) from part (a), we can calculate the partial derivatives ∂f/∂x and ∂f/∂y. Then we substitute the parametric equations of C and perform the dot product to evaluate the integral.

The exact calculation of the integral requires finding the explicit form of f(x,y) and performing the integration over the interval [0,1].

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Answer:

31-m

Step-by-step explanation:

Hope this helps!

Answer:

31 - m

Step-by-step explanation:

Expressions don't have the equal sign, equations do.

The sample mean is the best estimate of the population mean.

Option (C) is correct.

What is a sample mean?

The sample mean is a statistic obtained by calculating the arithmetic average of the values of a variable in a sample. If the sample is drawn from probability distributions having a common expected value, then the sample mean is an estimator of that expected value.

The concept used in this situation is an estimation.

The estimation in statistics is nothing but a data analysis framework that uses a combination of confidence intervals, effect sizes, and meta-analysis.

In this process we plan the experiments, analyze the data and interpret the results.

1. An estimate is a value that is based on some data and has been adjusted using statistical estimation.

2. An estimate of a population is expressed in two ways such as point estimation and interval estimation.

3. A point estimate of the population is defined as a single value of the statistic.

4. The interval estimate of the population is defined as the population parameter that lies between two numbers.

Step: 1

From the information, observe that the sample mean is not the best point estimate for the following measures.

1. Population standard deviation.

2. Population median

3. Sample standard deviation.

The sample mean is not a best-point estimate of the population standard deviation, population median, and sample standard deviation.

Since the sample means is not an unbiased estimate of these measures.

That is, the expectation of the sample mean value is not equal to the population standard deviation, population median, and sample standard deviation values.

From the information, observe that the sample mean is given and the sample mean is the best point estimate to the population mean.

The sample mean is the best point estimate of the population mean.

Since the sample mean is an unbiased estimator for the population.

Hence, the sample mean is the best estimate of the population mean.

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Answer:

m= 4/3

Step-by-step explanation:

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer:

\(m = 2017\)  and \(m = -1000\)

Step-by-step explanation:

Given equations are (I am hoping it is 1017 as written by you)

From the first equation we get

\(mx-1000=1017 \\\\\rightarrow mx = 1017 + 1000\\\\\rightarrow mx = 2017\\\\\rightarrow m = 2017/x\dots [1]\)

From the second equation we get
\(1017=m-1000x\\\\m-1000x = 1017\\\\m = 1000x + 1017 \dots[2]\)

Equating [1] and [2] we get

\(\dfrac{2017}{x} = 1000x + 1017\\\\\)

Multiply above equation throughout by x to get

\(2017 = 1000x^2+ 1017x\\\)

Subtract 2017 from both sides:
0 = 1000x^2 + 1017x - 2017\\\\

Switching sides:

\(1000x^2 + 1017x - 2017 = 0\\\\\)

This is a quadratic equation in x which can be solved by the quadratic formula, completing the square or factorization

Let's choosing factoring to solve
\(1000x^2 + 1017x - 2017 = 0\) can be factored as

\(\left(1000x^2-1000x\right)+\left(2017x-2017\right) = 0\)\\\\

Factor out 1000x from the first term and 2017 from the second term:

\(\rightarrow 1000x(x - 1) + 2017(x -1) = 0\)\\\\

Factor out common term x - 1:
\(\left(x-1\right)\left(1000x+2017\right)\\\\\)

This means either \(x - 1 = 0 \;or\; 1000x + 2017 = 0\)

giving two possible solutions

\(x - 1 = 0 \rightarrow \boxed{x = 1}\)

and

\(1000x + 2017 = 0 \rightarrow 1000x = - 2017 \rightarrow \boxed{ x = -\dfrac{2017}{1000}}\)

Use these two values of x in equation 1 to solve for possible values of m

At x = 1
\(m = \dfrac{2017}{1} = 2017\)

At
\(x = -\dfrac{2017}{1000}\)

\(m = \dfrac{2017}{-\dfrac{2017}{1000}}\)

When dividing by a fraction, just multiply the numerator by the reciprocal of the denominator
\(\dfrac{a}{\dfrac{b}{c}}=\dfrac{a\cdot \:c}{b}\)

\(m =\dfrac{2017}{-\dfrac{2017}{1000}}\\\\\\= -\dfrac{2017\cdot \:1000}{2017}\\\\\\= - 1000\)

So the possible values of m are
\(\text{m = 2017 \;and\; m = -1000}\)

Answer:

61 seats.

Step-by-step explanation:

This is an example of an arithmetic sequence.

The formula for this is an = a + (n - 1)d

Where an is the number of seats in the 19th row, a is the number of seats in the first row, n is the 19th row, and d is the common difference.

We can calculate the common difference by finding how many extra seats there are from the first row to the second. 27 - 25 = 2. So, with each additional row, there are two more seats.

a19 = 25 + (19 - 1) * 2

a19 = 25 + 18 * 2

a19 = 25 + 36

a19 = 61

So, there are 61 seats in the 19th row.

Hope this helps!

Answer:

i think 61 i hope im right

Step-by-step explanation:

Step-by-step explanation:

what do you mean ? what needs to be done ?

solve the equation for x ?

(x+1)² + (x-8)² = 0

x² + 2x + 1 + x² -16x + 64 = 0

2x² - 14x + 65 = 0

the formula to solve such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 2

b = -14

c = 65

x = (14 ± sqrt(196 - 520))/4 = (14 ± sqrt(-324))/4 =

= (14 ± 18i)/4 = (7 ± 9i)/2

remember that the is no real solution to a square root of a negative number. sqrt(-1) is called I. and all numbers that are combinations with I are called complex numbers.

x1 = (7 + 9i)/2

x2 = (7 - 9i)/2

a is answer please tell brinlest answer

Answer:

£16 : £144

Step-by-step explanation:

Sum the parts of the ratio, 1 + 9 = 10 parts

Divide quantity by 10 to find the c=value of one part of the ratio

£160 ÷ 10 = £16 ← value of 1 part of the ratio , thus

9 parts = 9 × £16 = £144

The surcharge for each additional point after 6 is $25 per point.

This means that if you accumulate 7 points within 3 years, you will be subject to a surcharge of $175 ($150 for the first 6 points and $25 for the additional point).

If you accumulate 8 points within 3 years, the surcharge will be $200 ($150 for the first 6 points and $50 for the additional two points), and so on.

This information is based on the New Jersey Motor Vehicle Commission's (NJMVC) point system. The NJMVC assigns points for various traffic violations, such as speeding, reckless driving, and failure to yield.

If you accumulate too many points within a certain period of time, your driving privileges may be suspended or revoked.

It's important to note that the NJMVC point system is just one example of how states in the US handle driver's license points and surcharges. Each state has its own system, so it's important to check with your local Department of Motor Vehicles (DMV) or equivalent agency to understand how points and surcharges work in your area.

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Answer:

4

Step-by-step explanation:

6-4=2

2x5=10

10+2=12

12 divided by 3=4

She put 4 in each book.

the table shown is a relation between the side lengths of a regular octagon and its perimeter

so, the easiest way to find the ratio is.

Step 1

divide the perimeter by the length of the side

so, the factor is 8, it means that you need take the length and multiply by 8 to obtain the perimeter

Step 2

find the misssing values

so, the numbers in the table must be 72 and 96.

Answer:

C

Step-by-step explanation:

After 2 hours, the bacteria count will be 12.

Answer:

9 plus 11 plus 12 =

Step-by-step explanation:

x is 22

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

We have to find the equation of a circunference with:

As it is a circunference that passes through a point, we know that the distance between the center and the point must be the radius, as all points in a circunference are at the same distance from the center.

We will find then the radius, by calculating the distance:

Now, this means that the radius is √90.

We use the standard form for the equation of a circle:

where (h,k) is the center of the circle. In this case,

And replacing, we obtain that the equation of the circle is:

(a) Expected hourly income ≈ 24.6747 $US/hour.

(c) Liters of gasoline to fill the tank ≈ 60.56656 liters.

(d) Price of gas in $US/gallon ≈ 4.9498 $US/gallon.

(e) Cost to fill the tank ≈ 90.2714 €.

(f) Number of full days depends on the daily commuting distance. Divide the daily commuting distance by 320 miles to get the number of full days.

To solve the given problems, we'll use the provided information and formulas for conversions.

(a) To calculate your expected hourly income in US dollars, we'll use the exchange rate of 1€ = 1.2993 $US:

Expected hourly income = Wage per hour in euros × Exchange rate

                     = 19 €/hour × 1.2993 $US/€

                     ≈ 24.6747 $US/hour

Therefore, your expected hourly income is approximately 24.6747 $US/hour.

(c) To determine how many liters of gasoline it will take to fill the car's empty tank, we need to know the conversion factor between US gallons and liters. 1 US gallon is approximately equal to 3.78541 liters.

Liters of gasoline to fill the tank = Tank capacity in US gallons × Conversion factor

                                  = 16 US gallons × 3.78541 liters/US gallon

                                  ≈ 60.56656 liters

Therefore, it will take approximately 60.56656 liters of gasoline to fill the car's empty tank.

(d) To find the equivalent price of gas in US dollars per gallon, we need to convert the price from euros per liter to US dollars per gallon. We'll use the conversion factor of 1 US gallon ≈ 3.78541 liters.

Price of gas in $US/gallon = Price of gas in euros per liter × (1€ / 1.2993 $US) × (3.78541 liters / 1 US gallon)

                         = 1.49 €/liter × (1/1.2993) $US/€ × (3.78541 liters / 1 US gallon)

                         ≈ 4.9498 $US/gallon

Therefore, the equivalent price of gas is approximately 4.9498 $US/gallon.

(e) To calculate the cost in euros to fill the tank, we'll multiply the number of liters required to fill the tank by the price of gas in euros per liter:

Cost to fill the tank = Liters of gasoline to fill the tank × Price of gas in euros per liter

                    = 60.56656 liters × 1.49 €/liter

                    ≈ 90.2714 €

Therefore, it will cost approximately 90.2714 euros to fill the tank.

(f) Given that the car averages 20 miles per gallon, we can calculate how many miles you can commute before needing to refill the tank:

Miles per full tank = Tank capacity in US gallons × Miles per gallon

                  = 16 US gallons × 20 miles/US gallon

                  = 320 miles

If you commute a distance of 320 miles per full tank, the number of full days you can commute before refilling the tank depends on your daily commuting distance. Divide your daily commuting distance by 320 miles to find the number of full days:

Number of full days = Daily commuting distance (miles) / Miles per full tank

                  = Daily commuting distance (miles) / 320 miles

This calculation requires your daily commuting distance to provide an exact answer.

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The maximum volume of the box that can be constructed from the square sheet of metal is V = (x/2)^2 * (x - 2(x/2)) = x^3/8.

Let's assume that the original square sheet of metal has a side length of 'x'. We will cut squares of length 'y' from each corner of the sheet to form the metal box.

The length of the base of the box will be (x-2y) and its width will also be (x-2y), as two squares of length 'y' have been removed from each side of the square sheet. The height of the box will be 'y', as this is the size of the square that was cut out from each corner.

Therefore, the volume of the box can be expressed as V = (x - 2y)^2 y.

Taking the derivative of V with respect to y

dV/dy = 4y(x - 3y)(x - 2y)

Setting dV/dy to zero, we get:

4y(x - 3y)(x - 2y) = 0

This equation has three solutions: y=0, y=x/3, and y=x/2.

The first solution, y=0, corresponds to not cutting any squares from the corners of the sheet and therefore does not result in a box. The second solution, y=x/3, gives a volume of V=(x/3)^2(x-2x/3)=x^3/27, and the third solution, y=x/2, gives a volume of V=(x/2)^2(x-x)=x^3/4.

Therefore, the maximum volume of the box is obtained when y = x/2. In this case, the dimensions of the box are:

length = width = x - 2y = x - x = 0

height = y = x/2

However, since the box cannot have zero length or width, this means that the maximum volume occurs when y=x/2 is at the edge of the feasible region. Therefore, we should choose y=x/2 as the size of the squares to be cut out and the dimensions of the resulting box are:

length = width = x - 2y = x - x = 0

height = y = x/2

So, the maximum volume of the box that can be constructed from the square sheet of metal is V = (x/2)^2 * (x - 2(x/2)) = x^3/8.

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The variance of X is 0.09.

Formula used: Variance is the square of the standard deviation. T

he formula to calculate variance of a discrete random variable X is given by:

Var(X) = E[X²] - [E(X)]²Calculation:

P(B) = 0.2P(A)

= 0.5P(AB) =

0.1

By definition,

P(A U B) = P(A) + P(B) - P(AB)

⇒ P(A U B) = 0.5 + 0.2 - 0.1

⇒ P(A U B) = 0.6

Now,E[X] = E[1B + ?]

⇒ E[X] = E[1B] + E[?]

Since 1B can have two values 0 and 1.

So,E[1B] = 1*P(B) + 0*(1 - P(B))

= P(B)

= 0.2P(A/B)

= P(AB)/P(B)

⇒ P(A/B)

= 0.1/0.2

= 0.5

So, the conditional probability distribution of ? given B is:

P(?/B) = {0.5, 0.5}

⇒ E[?] = 0.5(0) + 0.5(1)

= 0.5⇒ E[X]

= 0.2 + 0.5

=0.7

Now,E[X²] = E[(1B + ?)²]

⇒ E[X²] = E[(1B)²] + 2E[1B?] + E[?]²

Now,(1B)² can take only 2 values 0 and 1.

So,E[(1B)²] = 0²P(B) + 1²(1 - P(B))= 0.8

Also,E[1B?] = E[1B]*E[?/B]⇒ E[1B?] = P(B)*E[?/B]= 0.2 * 0.5 = 0.1

Putting the values in the equation:E[X²] = 0.8 + 2(0.1) + (0.5)²= 1.21Finally,Var(X) = E[X²] - [E(X)]²= 1.21 - (0.7)²= 0.09

Therefore, the variance of X is 0.09.

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Answer:

10 batches - they only have 10 eggs, so they can't make any more batches without them

Answer:

Decimal and fractions numbers are non-integers

Step-by-step explanation:

The answer is the third choice because integers are whole numbers that can be positive, negative, or zero. -1.3, however, is not a whole number, so it is not an integer. The reason is the third choice as decimals and fractions are not integers. Hope it helps!

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

25

Step-by-step explanation:

do 60 and multipy it by 5 then 5/12

and turn it into a proper fraction

Answer:

25

Step-by-step explanation:

60 × \(\frac{5}{12}\) = \(\frac{300}{12}\)= 25

The area of the region bounded by the parabola y=2-x^2, and the lines x-y=0 and 2x-y=0 is 2.667 square units.


To find the area, we set up a double integral over the given region. The region is bounded by the curves y=2-x^2, x-y=0, and 2x-y=0. We need to determine the limits of integration for x and y. The parabola intersects the x-axis at x=-2 and x=2.

The line x-y=0 intersects the parabola at x=-1 and x=1. The line 2x-y=0 intersects the parabola at x=-√2 and x=√2. Therefore, the limits for x are -√2 to √2, and the limits for y are x-y to 2-x^2. Integrating the constant 1 over these limits, we obtain the area as approximately 2.667 square units.

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Answer:

4

Step-by-step explanation:

Answer:

64 %

Step-by-step explanation:

( 16 / 25 ) x 100

= ( 16 x 100 ) / 25

= 16 x 4

= 64 %