Diana looks up at an angle of 57 and sees a hot air balloon 150 meters away. To the nearest meter, what is the value of x,
the height of the hot air balloon above Diana's head? (Show work on paper)

To apply the Divergence Theorem, we need to first find the divergence of the vector field F:

div(F) = ∂/∂x(x²) + ∂/∂y(-y²) + ∂/∂z(z²)

= 2x - 2y + 2z

Next, we find the bounds for the region D by setting the two plane equations equal to each other and solving for z:

9 - x - y = 6 - x - y

z = 3

So the region D is bounded below by the xy-plane, above by the plane z = 3, and by the coordinate planes x = 0, y = 0, and z = 0. Therefore, we can set up the integral using the Divergence Theorem as follows:

∫∫F · dS = ∭div(F) dV

= ∭(2x - 2y + 2z) dV

= ∫₀³ ∫₀^(3-z) ∫₀^(3-x-y) (2x - 2y + 2z) dz dy dx

We can simplify this integral using the limits of integration to get:

∫∫F · dS = ∫₀³ ∫₀^(3-x) ∫₀^(3-x-y) (2x - 2y + 2z) dz dy dx

= ∫₀³ ∫₀^(3-x) [(2x - 2y)(3-x-y) + (2/3)(3-x-y)³] dy dx

= ∫₀³ [∫₀^(3-x) (2x - 2y)(3-x-y) dy + ∫₀^(3-x) (2/3)(3-x-y)³ dy] dx

Evaluating the two inner integrals, we get:

∫₀^(3-x) (2x - 2y)(3-x-y) dy = -x²(3-x) + (3/2)x(3-x)²

∫₀^(3-x) (2/3)(3-x-y)³ dy = (2/27)(3-x)⁴

Substituting these back into the integral and evaluating, we get:

∫∫F · dS = ∫₀³ [-x²(3-x) + (3/2)x(3-x)² + (2/27)(3-x)⁴] dx

= 9/5

Therefore, the net outward flux of the vector field F across the boundary of the region D is 9/5.

Learn more about  Divergence Theorem  from

https://brainly.com/question/17177764

#SPJ11

Answer:

12

Step-by-step explanation:

12:18=2:3 multiply by four to get 8 as the first term

8:12

8:x

so x is 12.

*this could be wrong so check my work

Answer:

x = 12

Explanation:

8 : x

12 : 18

to find the value of x, we need to convert 12 into 8. since they both have a common factor of 4, we can divide 12 by 3 to get 4, and then multiply it by 2 to get 8. in numerical terms, this is:

12 ÷ 3 = 4

4 × 2 = 8

now, we can do the same for 18.

18 ÷ 3 = 6

6 × 2 = 12

thus, 12 : 18 is equivalent to 8 : 12. x = 12.

Answer: 250 mL Juice container

Step-by-step explanation:

Given

Half liter juice costs $2.86 i.e.

[tex]\dfrac{1}{2}\ L\rightarrow\$2.86\\\\1\ L\rightarrow\dfrac{2.86}{\frac{1}{2}}=\$5.72\\\\5\ L\rightarrow\$28.6[/tex]

A 250 mL juice costs $1.05 i.e.

[tex]250\ mL=0.25\ L\rightarrow \$1.05\\\\1\ L\rightarrow \dfrac{1.05}{0.25}=\$4.2\\\\\Rightarrow 5\ L\rightarrow \$21[/tex]

The cost of 250 mL Juice packet is low for 5 L quantity, therefore, Cierra must buy 250 mL Juice container

When x = 5, y = -1

When x = 6, y = 0

When x = 9, y = 1

When x = 14, y = 2

Answer:

a=7

Step-by-step explanation:

These two angles are complementary and the sum of their measures is 90°.

Therefore, we can create the equation: (5a+3)+52=90.

1. combine like terms. the equation becomes 5a+55=90.

2. -55 to both sides of the equation. the equation becomes 5a=35.

3. /5 to both sides of the equation. we can reach the conclusion that a=7

Answer:

It is complementary since their sum is equal to 90°

Answer:

Option A

Step-by-step explanation:

The total shipping cost given was  $7.02.

C = 7.02

Solve for 'w'.

[tex]C = $3.50 + $0.55w\\\\7.02=3.50+0.55w\\\\3.52=0.55w\\\\\boxed{6.4=w}[/tex]

Hope this helps.

Answer:

[tex]CI = (0.028636,0.071364)[/tex]

I am 95% confident that the true proportion of couples where the wife is taller than her husband is captured in the interval (.028, .071)

Step-by-step explanation:

Given

[tex]n = 400[/tex]

[tex]x = 20[/tex] --- taller wife

[tex]y = 380[/tex] --- shorter wife

Required

Determine the 95% confidence interval of taller wives

First, calculate the proportion of taller wives

[tex]\hat p = \frac{x}{n}[/tex]

[tex]\hat p = \frac{20}{400}[/tex]

[tex]\hat p = 0.05[/tex]

The z value for 95% confidence interval is:

[tex]z = 1.96[/tex]

The confidence interval is calculated as:

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

[tex]CI = 0.05 \± 1.96* \sqrt{\frac{0.05 (1 - 0.05)}{400}}[/tex]

[tex]CI = 0.05 \± 1.96 * \sqrt{\frac{0.0475}{400}}[/tex]

[tex]CI = 0.05 \± 1.96 * \sqrt{0.00011875}[/tex]

[tex]CI = 0.05 \± 1.96 * 0.01090[/tex]

[tex]CI = 0.05 \± 0.021364[/tex]

This gives:

[tex]CI = (0.05 - 0.021364,0.05 + 0.021364)[/tex]

[tex]CI = (0.028636,0.071364)[/tex]

Answer:

FV= $1,045.96

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $575.75

Number of periods (n)= 15*5= 60 months

Interest rate (i)= 0.12 / 12= 0.01

To calculate the future value (FV), we need to use the following formula:

FV= PV*(1+i)^n

FV= 575.75*(1.01^60)

FV= $1,045.96

a. the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%. b. the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces. c. the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.

(a) The probability that the weight of a randomly selected candy bar is less than 8 ounces can be found by calculating the cumulative probability using the Normal distribution. Given that the distribution of weights is Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces, we want to find P(X < 8), where X represents the weight of a candy bar.

Using the properties of the Normal distribution, we can standardize the variable X using the formula Z = (X - μ) / σ, where Z is the standard normal random variable, μ is the mean, and σ is the standard deviation.

For our case, we have Z = (8 - 8.1) / 0.1 = -1.

Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -1 is approximately 0.1587. Therefore, the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%.

(b) The mean of the sampling distribution of the sample mean can be calculated as the same as the mean of the population, which is 8.1 ounces.

The standard deviation of the sampling distribution of the sample mean, also known as the standard error of the mean, can be calculated using the formula σ / sqrt(n), where σ is the standard deviation of the population and n is the sample size.

In our case, the standard deviation of the population is 0.1 ounces, and the sample size is 40 candy bars. Therefore, the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces.

(c) To find the probability that the mean weight of the forty candy bars is less than 8 ounces, we can again use the properties of the Normal distribution. Since the mean and standard deviation of the sampling distribution are known, we can standardize the variable using the formula Z = (X - μ) / (σ / sqrt(n)).

In this case, we have Z = (8 - 8.1) / (0.0159) ≈ -6.29.

Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -6.29 is extremely close to 0. Therefore, the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.

(d) The answers to (a), (b), and (c) would not be affected if the weights of chocolate bars produced by this machine were distinctly non-Normal. This is because of the Central Limit Theorem, which states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of the sample mean approaches a Normal distribution.

In our case, we have a sufficiently large sample size of 40, which allows us to rely on the Central Limit Theorem. As long as the sample size is large enough, the sampling distribution of the sample mean will still be approximately Normal, even if the population distribution is non-Normal.

Therefore, we can still use the Normal distribution to calculate probabilities and determine the mean and standard deviation of the sampling distribution, regardless of the population distribution being non-Normal.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

Answer:

30

Step-by-step explanation:

Angles on a straight line are equal to 180°

180°-120°= 60°

Sum of Co interior angles are equal to 180°

180°-60° =120°

90°+60°+ x = 180°

((180° - 90° - 60°= 30°))

{{{ THE BOLDED CHARACTERS SHOULD BE SMALL. }}}

SEQUENCE: 6, 18, 54, 162

18/6 = 3

54/18 = 3

162/54 = 3

then, r (common ratio) = 3

_________________________________________

RECURSIVE RULE: r = 3

an = a(n - 1) × r       [formula]

ANSWER: an = a(n - 1) × 3

_________________________________________

ITERIATIVE RULE: r = 3, a1 = 6

an = a1 × r^(n - 1)       [formula] [ ^(n-1) is an exponent]

ANSWER: an = 6 × 3^(n - 1)

Answer:

DTI ratio in percentage = 42.36

Step-by-step explanation:

Annual salary = $47334

This means that gross monthly pay = 47334/12 = $3944.5

Now,

Total monthly debt payments = 1115 + 336 + 112 + 108 = $1671

Debt to income ratio = (1671/3944.5) × 100% = 42.36%

Since we are told not to put the % symbol, then answer is 42.36

Answer: Let’s assume that the bacteria population grows exponentially according to the formula P(t) = P0 * e^(kt), where P0 is the initial population, k is the growth rate, t is time in hours, and e is the mathematical constant approximately equal to 2.71828. We know that at time t = 0, the population is P(0) = 1000. After one hour, the population is P(1) = 8000. We can use this information to solve for the growth rate k. Substituting the values into the formula, we get: 8000 = 1000 * e^(k * 1) Dividing both sides by 1000, we get: 8 = e^k Taking the natural logarithm of both sides, we get: ln(8) = k Now that we have solved for k, we can use the formula to find out when the population will reach 15000. 15000 = 1000 * e^(ln(8) * t) Dividing both sides by 1000, we get: 15 = e^(ln(8) * t) Taking the natural logarithm of both sides, we get: ln(15) = ln(8) * t Dividing both sides by ln(8), we get: t = ln(15)/ln(8) ≈ 1.71 hours So it will take approximately 1.71 hours for the bacteria population to reach 15000. Received message.

Answer:

15π cm²

Step-by-step explanation:

The total lateral area of a cone

= πr√h² + r²

= √h² + r² = l

h = Height = 4cm

r = radius = 3cm

Hence:

= π × 3 √4² + 3²

= 3π × √16 + 9

= 3π × √25

= 3π × 5

= 15π cm²

The given equation, X = 36y², represents a parabola. In standard form, the equation can be rewritten as y² = (1/36)x. The vertex (V) is located at the origin (0, 0), the focus (F) is at (0, 1/4), and the directrix (d) is the horizontal line y = -1/4.

To rewrite the equation X = 36y² in standard form, we divide both sides by 36 to get y² = (1/36)x. This form represents a parabola with its vertex at the origin (0, 0).

In standard form, the equation of a parabola can be written as y² = 4px, where p is the distance from the vertex to the focus and also the distance from the vertex to the directrix. In this case, p = 1/4.

Therefore, the vertex (V) is located at (0, 0), the focus (F) is at (0, 1/4), and the directrix (d) is the horizontal line y = -1/4.

Learn more about parabola here:

https://brainly.com/question/11911877

#SPJ11

Answer:

the amount that necessary to fund is $2,671.61

Step-by-step explanation:

The computation of the amount is shown below;

Given that

PMT = $270

NPER = 6 × 2 = 12

RATE = 6.2% ÷ 2 = 3.1%

FV = $0

The formula is shown below:

=-PV(RATE;NPER;PMT;FV;TYPE)

After applying the above formula the present value is $2,671.61

hence, the amount that necessary to fund is $2,671.61

To approximate the area of the region bounded by the graph of f(t) = cos(t/2 - 3π/8) and the t-axis on the interval [3π/8, 11π/8] using 4 subintervals, we can use the midpoint rule.

The width of each subinterval is (11π/8 - 3π/8) / 4 = π/2.

We can calculate the height of each rectangle by evaluating the function at the midpoint of each subinterval.

The midpoints of the subintervals are:

t₁ = 3π/8 + π/4 = 5π/8

t₂ = 5π/8 + π/4 = 7π/8

t₃ = 7π/8 + π/4 = 9π/8

t₄ = 9π/8 + π/4 = 11π/8

Calculating the corresponding heights:

f(t₁) = cos(5π/16 - 3π/8)

f(t₂) = cos(7π/16 - 3π/8)

f(t₃) = cos(9π/16 - 3π/8)

f(t₄) = cos(11π/16 - 3π/8)

Now we can calculate the area of each rectangle by multiplying the width by the height.

Area of rectangle 1: (π/2) * f(t₁)

Area of rectangle 2: (π/2) * f(t₂)

Area of rectangle 3: (π/2) * f(t₃)

Area of rectangle 4: (π/2) * f(t₄)

Finally, we can approximate the total area by summing up the areas of all the rectangles:

Approximate area = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3 + Area of rectangle 4

Please note that I cannot provide the exact numerical values as the calculation involves trigonometric functions and the specific values of π/8.

Learn more about  midpoint of each subinterval from

https://brainly.com/question/31433004

#SPJ11

Answer:

Equally Likely

Answer:

It's correct.

Step-by-step explanation:

- - - - - - - - - - - - - - - - - - - -

The minimum sample size needed is 423.

To find the minimum sample size needed to estimate the population proportion with a given level of confidence and a desired margin of error, we can use the formula:

n = (Z^2 * p * q) / E^2

where:

n is the minimum sample size

Z is the Z-score corresponding to the desired confidence level

p is the estimated proportion of the population

q is 1 - p (complement of the estimated proportion)

E is the desired margin of error

In this case, the researcher wants to estimate the population proportion of adults who eat fast food four to six times per week with a 90% confidence level and an accuracy within 2% (margin of error of 0.02).

Since the estimated proportion is not given, we can use a conservative estimate of p = 0.5, which maximizes the sample size. This is because when the estimated proportion is unknown, assuming p = 0.5 results in the largest sample size required.

The Z-score corresponding to a 90% confidence level is approximately 1.645.

Plugging the values into the formula:

n = (1.645^2 * 0.5 * 0.5) / 0.02^2

n ≈ 422.94

Rounding up to the nearest whole number, the minimum sample size needed is 423.

Know more about the sample size click here:

https://brainly.com/question/31734526

#SPJ11

Answer:

The degrees of freedom, Df = The number of bags produced on Monday - 1

Step-by-step explanation:

The number of degrees of freedom is the limiting number of values that are logically not influenced by other values such that they are capable of having variation

The degrees of freedom = The sample size - 1 = N - 1

Therefore, the degrees of freedom, Df = The number of bags produced on Monday - 1

Answer:

696 39/100 meters

Step-by-step explanation:

Ben needs to replace two sides of his fence. One side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?

Side A = 367 9/100 meters

Side B = 329 3/10 meters

How much fence does Ben need to buy?

Total fence Ben needs to buy = Side A + side B

= 367 9/100 + 329 3/10

= 36709/100 + 3293/10

= (36709+32930) / 100

= 69639/100

= 696 39/100 meters

Ben needs to buy 696 39/100 meters

Answer: Evaluate the findings to compare to his hypothesis

Step-by-step explanation: Since the biologist already has the findings and has a hypothesis, he now has to compare both of them together.

Step-by-step explanation:

just put the ratios into a fraction if x:y then x/y

A.)6/1=6

B.)12/2=6

C.)4/24=1/6

D.)48/8=6

E.)18/3=6

F.)1/6

24/4=6 so A, B, D, and E are equivilant to the ratio 24/4

Hope that helps :)

Answer:

6:1 ,12:2, 48:8

Step-by-step explanation:

24:4

24 ÷ 4 =6 and 4÷4 =1

6:1

24:4

24÷2 =12 , 4÷2=2,

12:2

48:8

24×2=48, 4×2=8

48:8

The parametric representation for the surface is x = ρsin(φ)cos(θ), y = ρsin(φ)sin(θ), z = ρcos(φ) with the restrictions 0 ≤ ρ ≤ 2, 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π/4.

To find a parametric representation for the surface that lies above the cone z = √(x² + y²) and is part of the sphere x² + y² + z² = 4, we can express the surface in terms of spherical coordinates.

In spherical coordinates, the sphere x² + y² + z² = 4 can be represented as:

ρ² = 4

ρ = 2

Since we want to consider only the part of the sphere above the cone, we restrict the values of ρ to be between 0 and 2.

The cone z = √(x² + y²) in spherical coordinates is expressed as:

z = ρcos(φ)

Combining these equations, we can find the parametric representation for the desired surface:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

However, we need to restrict the values of ρ and φ to only the part of the surface above the cone. This means that ρ should range from 0 to 2, and φ should range from 0 to the angle that corresponds to the cone z = √(x² + y²).

Let's find the range of φ by substituting the equation for the cone into the equation for z:

z = ρcos(φ)

√(x² + y²) = ρcos(φ)

Since x² + y² = ρ²sin²(φ) (using the spherical coordinate expressions for x and y), we can rewrite the equation as:

√(ρ²sin²(φ)) = ρcos(φ)

ρsin(φ) = ρcos(φ)

tan(φ) = 1

Solving for φ, we find φ = π/4.

Therefore, the parametric representation for the surface is:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

with the restrictions:

0 ≤ ρ ≤ 2

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π/4

Learn more about parametric here

https://brainly.com/question/30451972

#SPJ11

Answer:

well religion does not work here sorry

Step-by-step explanation:not everyone prays im sorry

Answer:

im confused

Step-by-step explanation:

dont delete this