30 pts if correct and will mark brainliest

Answer:

Result;

[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi[/tex]

Step-by-step explanation:

Where:

F(x, y, z) = 2(x·i +y·j +z·k) and

S: z = 0, z = 4 -x² - y²

For the solid region between the paraboloid

z = 4 - x² - y²

div F        

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)

We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

[tex]N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }[/tex]

Solving we have;

[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}[/tex]

Plugging the values for N₁ and N₂, we have

[tex]= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}[/tex]

Where:

F(x, y, z) = 2(xi +yj +zk) we have

[tex]= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA[/tex]

[tex]= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA[/tex]

[tex]= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy[/tex]

[tex]= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy[/tex]

= 32π.

Answer:

sine (x) / 14.9 = sine (71) / 25.5

sine (x) = 14.9 * sine (71) / 25.5

sine (x) = 14.088248 / 25.5

sine (x) = 0.5524803137

Angle (x) = arc sine(0.5524803137)

Angle (x) =  33.537 degrees

Step-by-step explanation:

The expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].

The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

It can be given as,

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.

For the given problem it can also be given as,

[tex]x^o=\sin^{-1}\left(\dfrac{a\sin B}{c}\right)[/tex]

Put the values,

[tex]x^o=\sin^{-1}\left(\dfrac{(14.9)\sin (71)}{25.5}\right)\\x^o=\sin^{-1}\left(0.5523\right)\\x^o=33.54^o[/tex]

Thus, the expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].

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Answer:

The answer to your question is in terms of π, Volume = 54π units³

                                                 as an exact number Volume =  169.56 units³

Step-by-step explanation:

Data

radius = 3

height = 6

π = 3.14

Process

1.- Look for the formula to calculate the volume of a cylinder

    Volume = πr²h

2.- Substitution

    Volume = π(3)²(6)

3.- Simplification

    Volume = π(9)(6)

4.- Volume in terms of π

    Volume = 54π units³

5.- As an exact number

    Volume = 54(3.14)

-Result

    Volume = 169.56 units³

Answer:

20times

Step-by-step explanation:

A fair of die has 6sides.

If 4 appears 'once' out of a 6.

Then, 4 will appear 2times out of 12 i.e

6faces = 1time

12faces = 2times.

But remember that we want to know how many times 4 will appear out of a 120

120faces = x times

Since 6faces = 1time (i.e 4 occur one time in six faces)

cross multiplying:

6 × x = 120

x = 120/6

x = 20times

This means 4 will appear 20times out of a 120

Answer: She can randomly survey 50 seventh-graders in the school.

Step-by-step explanation: To get the best result without wasting to much time means she cannot afford to survey every student. To receive the best results it should be unbiased so random is the way to go. Randomly surveying 50 girls in her school does not guarantee that those girls are all seventh graders so the best answer is She can randomly survey 50 seventh-graders in the school.

Answer:

14

Step-by-step explanation:

5x + 12 = 7x - 16

      28 = 2x

       14 = x

Angle 3's alternate interior angle is Angle 2. Angle two is equal to angle 4 (thi is just a rule in geometry). So that means Angle 3 is also equal to angle $. So just make the equations equal to eachother and solve for x as shown above.

Answer: a) 138.32 and b) 35 years approx.

Step-by-step explanation:

Since we have given that

[tex]R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}[/tex]

So, Profit is given by

[tex]Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}[/tex]

Difference in years of 1990 and 2020=30

So, Profit becomes :

[tex]P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32[/tex]

(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.

So, profit doubles , we get :

[tex]138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t[/tex]

Hence, a) 138.32 and b) 35 years approx.

Final answer:

(a) To predict the company's profit in 2020, substitute the given revenue and cost functions into the profit equation. Calculate the value of the profit at t = 30. (b) To find the time it takes for the profit to double, set the profit equation equal to twice the profit in part (a) and solve for t.

Explanation:

(a) To predict the company's profit in 2020, we need to calculate the difference between the revenue and expenses. The profit (P) is given by the equation P(t) = R(t) - C(t), where R(t) is the revenue function and C(t) is the cost function. Substituting the given functions into the equation, we have P(t) = 21.4e0.131t - 18.6e0.131t. To find the profit in 2020 (t = 30), we plug in t = 30 into the equation and calculate the value of P(30).

(b) To find the time it takes for the profit to double, we need to determine when P(t) is equal to twice the profit in part (a). We set P(t) = 2P(30) and solve for t.

Answer: 5

Step-by-step explanation:Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

7 + 8x + -2x = 37 + 2x + -2x

Combine like terms: 8x + -2x = 6x

7 + 6x = 37 + 2x + -2x

Combine like terms: 2x + -2x = 0

7 + 6x = 37 + 0

7 + 6x = 37

Add '-7' to each side of the equation.

7 + -7 + 6x = 37 + -7

Combine like terms: 7 + -7 = 0

0 + 6x = 37 + -7

6x = 37 + -7

Combine like terms: 37 + -7 = 30

6x = 30

Divide each side by '6'.

x = 5

Simplifying

x = 5

Answer:

a

Step-by-step explanation:

Answer:

A.y=5/4x

Step-by-step explanation:

Answer:

O х= -8/3 or x = 7/2

Step-by-step explanation:

6x² - 5x - 56 = 0

6x² - 21x + 16x - 56 = 0

3x(2x - 7) + 8(2x - 7) = 0

(2x - 7)(3x + 8) = 0

x = 7/2, -8/3

The solutions of the equation 6x² - 5x + 56 using the zero product property is x = -8/3 or x = 7/2.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given is a quadratic expression,

6x² - 5x = 56

We have to find the solutions using zero product property.

Zero product property states that, if a.b = 0, the either a = 0 or b = 0.

Let 6x² - 5x = 56

6x² - 5x - 56 = 0

Dividing throughout by 6,

x² - 5/6 x - 56/6 = 0

We can factorize it as (x + p)(x + q) such that pq = -56/6 and p + q = -5/6.

We know that,

8/3 × -7/2 = -56/6

8/3 - 7/2 = 16/6 - 21/6 = -5/6

So,

x² - 5/6 x - 56/6 = 0

(x + 8/3) (x - 7/2) = 0

Using zero product property,

(x + 8/3) = 0 or (x - 7/2) = 0

x = -8/3 or x = 7/2

Hence the solutions are x = -8/3 or x = 7/2.

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Answer:

y ≥ 1

Step-by-step explanation:

Hence, range of given parabola is y[tex]\geq 1[/tex]

What is parabola ?

A parabola is a curve in which all points are at the same distance from two fixed points: the focus and the origin. a constant straight line (the directrix )

How to solve?

Generic equation of parabola  y=p. (x−h[tex])^{2}[/tex]+k  where (h,k) denotes the vertex. where parabola has range y[tex]\geq 0[/tex]. but as this curve is shifted  at 0,1 hence range becomes y[tex]\geq 1[/tex]

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Answer:

98 hamburgers were sold on Friday.

Step-by-step explanation:

294/3=98

98+98=196 cheese burgers

196+98=294 hamburgers and cheeseburgers in total

98 hamburgers

Answer:

side length= 4 mm

Step-by-step explanation:

The explanation is pretty easy;

You know that to get the volume of a cube the formula is length times width times height. You also know that all sides of a cube are equal. so what multiplied by itself 3 times = 64?

That would be 4; 4 times 4 = 16 then 16 times 4 = 64

Sorry if the explanation wasn't great:(

Answer:

Using a deduction theorem of 1.01%, we can use a punnet square to help. Being that both sides of an dissociates triage is always equal to the third we can punch in the calculations and conclude that the answer is... 1 - 1 = 0

Step-by-step explanation:

Answer:

Automation means something that does not require human input, automatic.

Answer:

answer is the use of machines that function on their own.

Step-by-step explanation:

Answer:

82°

Step-by-step explanation:

By inscribed angle theorem:

[tex]m\angle QRP = \frac{1}{2} \times 164 \degree \\ \\ \huge \red{ \boxed{\therefore \: m\angle QRP =82 \degree}}[/tex]

Answer:

6 hours

Step-by-step explanation:

Make an equation

Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.

3h+12=30

Subtract 12 from both side s

3h=18

Divide both sides by 3

h=6

So, she rented  it for 6 hours

Answer:

a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Step-by-step explanation:

Answer:

Any number that can be written in fraction form is a rational number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{14k^3+7k^2}{7k^3+14k^2} =\frac{7k^2(2k+1)}{7k^2(k+2)} =\frac{2k+1}{k+2}}[/tex]

Answer:

Both Chelsea and Pedro wrote an expression that is equivalent to the original expression

Step-by-step explanation:

first simplify the expression 14k^3 + 7k^2 / 7k^3 + 14k^2 can you get Chelsea's expression. If you simplify Pedro's equation you get the same expression as Chelsea's

Answer:

y - 3 = (1/10)(x - 6)

Step-by-step explanation:

Note how x (the "run") increases by 10 and how y (the "rise") by 1.  Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is

m = rise / run = 1/10.

Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:

y - 3 = (1/10)(x - 6)

Answer:

The surface is a cylindrical surface with radius 7 units

Step-by-step explanation:

The equation is properly written as:

[tex]\rho^{2} (sin^{2} \phi sin^{2} \theta + cos^{2} \phi) = 49[/tex]

The above equation takes the form [tex]y^{2} + z^{2} = r^{2}[/tex]

Where [tex]y^{2} = \rho^{2} sin^{2} \phi sin^{2} \theta[/tex]

[tex]y = \rho sin \phi sin \theta[/tex]

and [tex]z^{2} = \rho^{2}cos^{2} \phi[/tex]

[tex]z = \rho cos \phi[/tex]

[tex]r^{2} = 49[/tex]

r = 7 units

The surface is a cylindrical surface with radius 7 units

Answer:

9

Step-by-step explanation:

X+X+1+X+2=30

3x+3=30

-3. -3

3X=27

Divide by 3

X=9

Answer:

x + (x + 1) + (x + 2) = 30

Answer:

The speed rate of the plane in still air is 1006.67 km/h

The speed rate of the wind is 246.67 km/h

Step-by-step explanation:

To answer the question, we let the speed of the plane in still air = x  km/h

Let the speed of the wind = y km/h

Therefore,

4560/(x - y) = 6 hours and

3720/(x + y) = 3 hours

4560 = 6·x - 6·y.........(1)

3720 = 3·x + 3·y ........(2)

Multiplying equation (2) by 2 and add to (1) gives

12080 = 12·x

x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h

Substituting the value of x in (1) gives

4560 = 6040 - 6·y

6·y = 1480

y = 1480/6 =  [tex]246\frac{2}{3}[/tex]

The speed rate of the plane in still air = 1006.67 km/h

The speed rate of the wind = 246.67 km/h.

Final answer:

Toby will have £4867.20 in his savings account.

Explanation:

To determine how much Toby will have in his savings account after 2 years with a 4% per annum compound interest rate, we can use the formula for compound interest:

A = P(1 + r)ⁿ

Where:

Given:

Using these values in the formula:

A = £4500(1 + 0.04)²

A = £4500(1.04)²

A = £4500(1.0816)

A = £4867.20

Therefore, Toby will have £4867.20 in his savings account after 2 years.

Answer:

Sheila earned $120 in interest.

Step-by-step explanation:

In order to calculate the interest earned by Sheila we can use the simple interest formula shown bellow:

i = P*r*t

Where i is the interested earned, P is the amount invested, r is the interest rate and t is the total time. For this case we have:

i = 800*0.03*5

i = 24*5

i = 120

Sheila earned $120 in interest.

Answer: After 5 years, Sheila earns $120

Step-by-step explanation: The calculation of simple interest is given as

Interest = P x R x T

Where P = the amount invested initially (800), R = the rate of interest earned (3% or 0.03) and T = the number of years (5) investment was held

The interest she earned can now be calculated by substituting for the known values as follows;

Interest = 800 x 0.03 x 5

Interest = 120

Therefore after 5 years, Sheila earns $120

Answer:

like 2 per minute?

Step-by-step explanation:

The rate at which customers are entering the store is calculated by dividing the number of customers by the time it took them to enter. In this case, 10 customers entered the store over 5 minutes, so the rate is 2 customers per minute.

The rate at which customers are entering the store is calculated by dividing the total number of customers by the total time it took for them to enter. Here, the total number of customers is 10, and the total time is 5 minutes. So, the calculation would be: 10 customers / 5 minutes. This equals 2 customers per minute. Therefore, the rate of customers entering the store is 2 customers per minute.

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Given Information:

Number of defective cups = 15

Total number of cups = 300

Required Information:

a) defective proportion = p = ?

b) 95% confidence interval of defective proportion = ?

Answer:

a) defective proportion = p = 0.05 = 5%

b) 95% confidence interval of defective proportion = (2.5%, 7.5%)

Step-by-step explanation:

The estimated defective proportion is given by

p = Number of defective cups/Total number of cups

p = 15/300

p = 0.05

p = 5%

The confidence interval of defective proportion is given by

[tex]CI = p \pm z\sqrt{\frac{p(1-p)}{n} }[/tex]

Where p is the defective proportion, z is the z-score corresponding to 95% confidence level and n is the total number of cups.

The z-score corresponding to 95% confidence level is 1.96

[tex]CI = 0.05 \pm 1.96\sqrt{\frac{0.05(1-0.05)}{300} }[/tex]

[tex]CI = 0.05 \pm 1.96(0.01258)[/tex]

[tex]CI = 0.05 \pm 0.025[/tex]

[tex]Upper = 0.05 + 0.025 = 0.075[/tex]

[tex]Lower = 0.05 - 0.025 = 0.025[/tex]

[tex]CI = (0.025, 0.075)[/tex]

CI = (2.5%, 7.5%)

So that means we are 95% confident that the defective proportion is between 2.5% to 7.5%.

Zack should not return this lot since the defective percentage is below 10%

Final answer:

Zack Schadek calculated the proportion of defective cups to be 5%, and then he developed a 95% confidence interval which did not surpass the 10% defectivity threshold set by his agreement with the supplier. Therefore, he should not return the lot based on this sample's data.

Explanation:

To answer the question of whether Zack Schadek should return the shipment of cups, we first need to calculate the estimated proportion defective in the population. We do this by dividing the number of defective cups by the total number of cups in the sample. In this case, it is 15 defective cups out of 300, which equals 0.05 or 5%.

Next, we will develop a 95 percent confidence interval for the proportion defective. To construct this confidence interval, the binomial distribution can be approximated by a normal distribution since np and n(1-p) are both greater than 5.  Plugging in the values, we obtain the confidence interval.

Finally, considering Zack's agreement with his supplier to return lots that are 10% or more defective, the calculated proportion defective is well below 10%. Additionally, since the confidence interval does not include 10% or higher values, Zack should not return the lot based on the data from his sample.

Answer:

(x - 2)² + (y + 8)² = 121

Step-by-step explanation:

circle: (x – h)² + (y – k)² = r²   (h , k) center        r: radius

h = 2          k = - 8          r = 11

equation: (x - 2)² + (y + 8)² = 121

The equation of circle can be determine by using general equation of circle.

The equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

Given:

The center of circle is [tex](2,-8)[/tex].

The radius is [tex]11[/tex].

Write the general equation of circle.

[tex](x-h)^2 + (y-k)^2= r^2[/tex]

Where, [tex](h,k)[/tex] is center of circle and [tex]r[/tex] is the radius of the circle.

Substitute [tex]2[/tex] for [tex]h[/tex], [tex]-8[/tex] for [tex]k[/tex] and [tex]11[/tex] for [tex]r[/tex] in above equation.

[tex](x - 2)^2 + (y + 8)^2 = 121[/tex]

Thus, the equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

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Answer:

56 player divided by 14 on each team

Step-by-step explanation:

There will be 4 teams

Answer:

1727 students

Step-by-step explanation:

Here we have the formula for sample size given as

[tex]n = \frac{p(1-p)z^2}{ME^2}[/tex]

Where:

p = Mean

ME = Margin of error = 3

z = z score

Therefore, we have

p = 150/240 = 0.625

z  at 99 % = 2.575

ME = [tex]\pm[/tex]3%

Therefore [tex]n = \frac{0.625(1-0.625)2.575^2}{0.03^2} = 1726.73[/tex]

The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.