A boat heading out to sea starts out at Point AA, at a horizontal distance of 787 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 13^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 2^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

The volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.

What is volume?

Any three-dimensional solid's volume is simply the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.

We are given that two balloons have a total volume of [tex]\frac{3}{5}[/tex] gallon.

Let the volume of balloon A be x and the volume of balloon B be y.

So, we get

x + y = [tex]\frac{3}{5}[/tex]

Also, it is given that the difference of their volumes is [tex]\frac{1}{5}[/tex] gallon and Balloon A has a greater volume than Balloon B.

So, we get another equation as

x - y = [tex]\frac{1}{5}[/tex]

Now, on adding both the equations, we get

⇒ 2x = [tex]\frac{4}{5}[/tex]

Now, on solving we get

⇒ x = [tex]\frac{2}{5}[/tex]

Now, on substituting the value of x in the equation, we get

⇒ [tex]\frac{2}{5}[/tex] + y = [tex]\frac{3}{5}[/tex]

⇒ y = [tex]\frac{1}{5}[/tex]

Hence, the volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.

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n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))

       2 [cos(alpha) sin(alpha) + cos(4 alpha) sin(2 alpha) + cos(9 alpha) sin(3 alpha) + ... + cos(n^2 alpha) sin(n alpha)]

     = [sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)].

        sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)

     = (sin(2 alpha) - sin(2n^2 alpha))/(1 - sin(2 alpha))

     = (2 sin(n^2 alpha) cos(n^2 alpha))/(2 cos(alpha) - 1)

     = [sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)

        [sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)

        sin(2n^2 phi/2008) = k(2 cos(alpha) - 1)

        cos(90 - 2n^2 phi/2008) = k(2 cos(alpha) - 1)

       90 - 2n^2 phi/2008 = ±arccos(k(2 cos(alpha) - 1))

       n^2 = (2008/4phi)[90 ± arccos(k(2 cos(alpha) - 1))]

       n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))

We can find the smallest positive integer n by incrementing the value of k starting from 1 until ceil(k^2*alpha) is greater than or equal to n.

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Answer:

Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.

The expression -5 + 28p9q5 - 12pq + 7 is equivalent to 7. Since all the terms except the last one contain variables, we can use algebra to solve for the value of the expression.

Algebra is a branch of mathematics which deals with the manipulation of equations, inequalities, and other mathematical expressions. Algebra is used to solve equations, simplify expressions, and model real-world problems.

To begin, we can add -5 and 7 to obtain 2. This means that the expression is now equal to 2 + 28p9q5 - 12pq. We can then simplify this expression by combining like terms.

Since 28p9q5 and -12pq are both products of the same variables, we can add them together. When we do so, we obtain 16p9q5, which means that the expression is now equal to 2 + 16p9q5.

Finally, we can simplify the remaining term by breaking down the product. We can divide 16 by 8 to obtain 2, and then divide 9 by 3 to obtain 3. This means that the expression is now equal to 2 + 2p3q5. Since there are no more terms to simplify, we can conclude that the answer is 2.

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A patient's probability of recovering is 0.8, so the likelihood that they won't is 0.2.

The probability that a patient will recover from a stomach disease is 0.8. Assume that 20 persons have reportedly got this illness.

Let X = # of recoveries out of 20 patients who caught the condition while PMF for X and resolve issues. Imagine that a 20-person sample was chosen at random.

Here, Bernoulli trials are applicable.

Recall that the chance of k successes in n trials using the Bernoulli approach is given by:

P(k)=( n/k )p (power k) * (q power n−k)

where q=1-p is the probability that an attempt would fail

where q=1-p is the probability that an attempt would fail

Here, let's make recovery a success. Hence, p = 0.8, q = 0.2, and n = 20

The probability that at least 10 recoveries will occur is

P(X10) = P(10) + P(11) + P(12) +... + P (20)

The complete question will be:

The probability that a patient recovers from a stomach disease is 0.8. Suppose twenty people are known to have contracted this disease. What is the probability that at least ten recover?

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The gorilla has a heart rate that is four times faster than the chimpanzee's when they are resting.

Expression in math is a combination of numbers, variables, operations and/or symbols that represent a value, quantity or an equation. It can either be a single term, or several terms connected by mathematical operations such as addition, subtraction, multiplication and division. Expressions are typically used in equations, formulas and problems to help solve them.

To calculate the heart rate of the gorilla, we use the power function given: H(m) = 240m. Substituting in m = 200, we get H(200) = 240(200) = 48,000 beats per minute.

To calculate the heart rate of the chimpanzee, we use the same power function: H(m) = 240m. Substituting in m = 50, we get H(50) = 240(50) = 12,000 beats per minute.

Therefore, the gorilla has a heart rate that is four times faster than the chimpanzees when they are resting.

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Answer: x = squrt (1/20

Step-by-step explanation:

Answer:

12x - 6

Step-by-step explanation:

[tex] \rm \: 4 + 5(3x - 2) - 3x[/tex]

[tex] \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)[/tex]

[tex] \rm= 12x - 6 \: \sf (combine \: like \: terms)[/tex]

[tex] \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)[/tex]

[tex] \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)[/tex]

[tex] \rm \:= 12x - 6 \: \sf (simplify)[/tex]

Answer:

angle "E" =70°

Step-by-step explanation:

<ABC=<ADC

<ADC=<EAD (alternate angles)

<EAD=<DEA (because /DA/=/DE/

and <DEA=angle E, therefore answer=70°

The average number of customers in the West End Donut Shop simultaneously is 30, which is obtained by using the arrival rate and service rate formulas for a queueing system.

To find the average number of customers in the shop simultaneously, we can use the concept of the arrival rate and the service rate.

The arrival rate is the rate at which customers arrive at the shop, and can be calculated as:

arrival rate = number of customers / time

arrival rate = 2400 customers / 10 hours

arrival rate = 240 customers per hour

The service rate is the rate at which customers are served by the shop, and can be calculated as:

service rate = 60 minutes / 5 minutes per customer

service rate = 12 customers per hour

Using the formula for the average number of customers in a queueing system, we get:

average number of customers = arrival rate / (service rate - arrival rate)

average number of customers = 240 / (12 - 240/60)

average number of customers = 240 / 8

average number of customers = 30

Therefore, on average, there are 30 customers in the West End Donut Shop simultaneously.

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Step-by-step explanation:

The factors of 9x² +49y² are:

D. (3x + 7y)(3x + 7y) and C. (3x - 7y)(3x - 7y)

We can use the identity:

a² + b² = (a + b)(a - b)

To factor the expression 9x² + 49y², let a = 3x and b = 7y. Then we have:

9x² + 49y² = (3x)² + (7y)² = (3x + 7y)(3x - 7y)

So the factors of 9x² + 49y² are (3x + 7y) and (3x - 7y). We can see that these factors are not prime, as they can be factored further into (3x + 7y)(3x + 7y) and (3x - 7y)(3x - 7y).

Answer:

x = the unknown number. Its square is x2. The sum of a number and its square is 12:

x + x²= 12

Putting the quadratic into standard form:

x2 + x - 12 = 0

(x+4)(x-3) = 0

x = -4 and 3

Let's check x=-4:

x + x2 = 12

(-4) + (-4)2 = 12

-4 + 16 = 12

12 = 12

Now let's check x= 3:

x + x2 = 12

3 + 32 = 12

3 + 9 = 12

12 = 12

Yup, they both work. There are two answers, x = -4 and x = 3

The independent variable in this hypothesis is the method of studying, specifically whether students engage in spaced learning or cramming.

In the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam, the independent variable is the method of studying.

This variable is independent because it is being manipulated and controlled by the researcher. In this case, the researcher is comparing two different methods of studying and measuring the effect on exam performance.

Spaced learning involves breaking up the study time into smaller, more manageable chunks over a period of time, such as a week. Cramming, on the other hand, involves trying to learn all the material in a short period of time, such as the night before the exam.

The dependent variable in this hypothesis is exam performance, which is expected to be better for students who engage in spaced learning compared to those who cram.

The hypothesis suggests that the method of studying has a causal relationship with exam performance, but it is the independent variable, the method of studying, that is being manipulated to test this hypothesis.

Therefore the independent variable in the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam is the method of studying, specifically whether the student engages in spaced learning or cramming.

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The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.

First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.

To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:

Dose = Desired dose / Stock strength

Where:

Desired dose is 0.175 mg

Stock strength is 0.05 mg/mL

So, substituting the values into the formula:

Dose = 0.175 mg / 0.05 mg/mL

Dose = 3.5 mL

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Answer: y - 10.26

Step-by-step explanation: Add 5.4 on both sides and that leaves you with y

The maximum number of 12-ton trucks that the cargo ship can carry per trip is 750. This is obtained by solving the linear programming problem subject to the given constraints.

Let's denote the number of 5-ton trucks and 12-ton trucks that the cargo ship carries by x and y, respectively. Then, we can write the following two constraints based on the requirements.

x + y ≥ 750 (constraint 1: the ship must carry at least 750 trucks)

5x + 12y ≤ 5000 (constraint 2: the total weight of the trucks can be at most 5,000 tons)

We want to maximize the number of 12-ton trucks y, subject to these two constraints.

To solve this problem, we can use linear programming techniques.

The feasible region is the set of all (x,y) pairs that satisfy the two constraints

The feasible region is bounded by the x-axis, the y-axis, and the two lines 5x + 12y = 5000 and x + y = 750.

We want to find the point in the feasible region where the number of 12-ton trucks y is maximized. This point will lie on one of the corners of the feasible region.

We can calculate the coordinates of the corners of the feasible region by solving the system of equations formed by the two constraint lines:

x + y = 750      (equation 1)

5x + 12y = 5000      (equation 2)

Multiplying equation 1 by 5, we get:

5x + 5y = 3750        (equation 3)

Subtracting equation 1 from equation 2, we get:

7y = 1250

y = 178.57 (rounded to 2 decimal places)

Substituting this value of y into equation 1, we get:

x = 571.43 (rounded to 2 decimal places)

The coordinates of this corner point are (571.43, 178.57).

Similarly, we can calculate the coordinates of the other corner points:

(750, 0), (500, 250), and (0, 750)

We can now evaluate the objective function (the number of 12-ton trucks y) at each of these corner points:

At (571.43, 178.57), y = 178.57

At (750, 0), y = 0

At (500, 250), y = 250

At (0, 750), y = 750

The maximum value of y is 750, which occurs at the point (0, 750).  

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First we have to remember what the perimeter of a rectangle is. The perimeter is the outside edges of the rectangle, think of it as the fence around a yard. This means that the perimeter of a rectangle or a square has four sides: two widths and two lengths.

This problem tells us that the length of this rectangular parking lot is 98m. Since this parking lot is a rectangle, each of the parallel lengths are the same size. Therefore, each length is 98m and that takes care of 196m of the perimeter [tex](98\text{m} \times 2)[/tex].

To find the width, we know that the lengths take up 196m of the total 364m of the perimeter which leaves 168m for the widths. Again, since this parking lot is a rectangle, each parallel width is the same size so we can find one width by dividing the left over perimeter by 2: [tex]168\text{m} \div 2 = \bold{84m}[/tex].

I hope that helps!

If the number of samples is doubled, the new confidence interval would be 9.61, 10.39 or narrower (smaller) while keeping the same confidence level.

. When calculating the confidence interval, the standard error is used, along with the sample mean and the critical value from the distribution. If we have a larger sample size, we can be more confident in our estimate of the population parameter because the sample mean will more closely resemble the population mean. As a result, the confidence interval can be narrower, indicating a higher degree of precision. For Example:Suppose a sample of 50 was taken, and the mean weight of an object was 10 grams with a standard deviation of 2 grams.

At a 95 percent confidence level, the confidence interval for the mean weight would be 10 ± (1.96)(2/√50) = (9.15, 10.85)Now suppose that the sample size is doubled to 100. The standard error will be cut in half, i.e., 2/√100 = 0.2. As a result, the new confidence interval would be 10 ± (1.96)(0.2) = (9.61, 10.39). Notice that the new confidence interval is narrower, indicating a higher degree of precision while keeping the same confidence level.

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P(t) = 5(1 + 0.125)^t

where P(t) is the population of fruit flies after t days.

Answer:

Step-by-step explanation:

The probability that at most one sample is mutated in 10 samples is 0.746.

To calculate this probability, we use the binomial distribution formula.

The binomial distribution formula is used to calculate the probability of a certain number of successes (in this case, samples that are mutated) in a certain number of trials (10 samples). We need to find the probability of 1 success or fewer in 10 trials.

This is equal to P(x<=1) = 1 - P(x>1), where x is the number of successes.

For this calculation, we need the following parameters: n = 10 (number of trials), p = 0.15 (probability of a single sample being mutated), and x = 1 (number of successes). So, P(x<=1) = 1 - P(x>1) = 1 - P(x = 2) - P(x = 3) - P(x = 4) - P(x = 5) - P(x = 6) - P(x = 7) - P(x = 8) - P(x = 9) - P(x = 10).

The probability of at most one sample being mutated in 10 samples is calculated by adding the individual probabilities of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 samples being mutated, which equals 0.746.

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the t-score for a 99.8% confidence interval with a sample size of 5 is 4.604.

The t-score for a 99.8% confidence interval with a sample size of 5 can be found using a t-distribution table or calculator.

Since we have a sample size of 5, the degrees of freedom (df) will be n - 1 = 4.

From the t-distribution table or calculator, the t-score for a 99.8% confidence interval with 4 degrees of freedom is approximately 4.604.

Therefore, the t-score for a 99.8% confidence interval with a sample size of 5 is 4.604.

the complete question is :

what is the value of the t score for a 99.8% confidence interval if we take a sample of size 5?

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Answer:

2.80

Step-by-step explanation:

It asks to find the shipping and handling price.

The first step is take that percentage, 20% and convert into decimal form. Then you need to multiply that by the original price. So it would be 0.2 x 14.

That gives you 2.80 which is the shipping and handling price. That's all you have to do.

The perimeter of parallelogram ABCD in which AM ,BN are angle bisector and DM = 4ft and MN = 3ft  is: P = 2(AB + BN) = 2(2 + 2) = 8 ft.

Perimeter is the total length of the boundary or the distance around the edge of a two-dimensional shape such as a polygon or a circle.

To find the perimeter of parallelogram ABCD, we need to find the length of each side of the parallelogram.

Since AM and BN are angle bisectors of parallelogram ABCD, we know that they intersect at the diagonals' midpoint. Therefore, we can say that DM = MB and MN = NA.

Using this information, we can label the sides of the parallelogram as follows:

AB = CD = x (opposite sides of a parallelogram are equal)

AM = MC = BM = MD = x/2 (diagonals of a parallelogram bisect each other)

BN = ND = NA = NC = y (angle bisectors of a parallelogram bisect opposite angles and sides)

DM = 4 ft and MN = 3 ft (given)

Since DM = MB, we can write:

x/2 + 4 = y + 3

x/2 - y = -1

Since BM = MC, we can write:

x/2 + y = x

y = x/2

by substituting-

x/2 + 4 = x/2 + 3

x = 2

Therefore, AB = CD = 2 ft and BN = ND = NA = NC = x/2 = 1 ft.

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Answer:

domain is [-11 , -3]

Step-by-step explanation:

domain is x

range is y

x values are from -11 to -3

The score located 2 standard deviations below the mean is 100. This score can be found by subtracting 2 standard deviations (20) from the mean (120).

The normal distribution is a bell-shaped curve that is symmetrical around the mean. This means that if you calculate the number of standard deviations away from the mean, you can use the same number to calculate how many standard deviations away from the mean the score is.

For example, in this question, the mean is 120 and the standard deviation is 10. To find the score located 2 standard deviations below the mean, subtract 2 standard deviations from the mean. This means the score is 120 - 20 = 100.

In general, the formula for calculating the score located x standard deviations away from the mean is:

Score = Mean + (x * Standard Deviation)

For example, to find the score located 4 standard deviations away from the mean, the formula is:

Score = Mean + (4 * Standard Deviation)

In this example, the score is 120 + (4 * 10) = 160.

In summary, to find the score located x standard deviations away from the mean, use the formula:
Score = Mean + (x * Standard Deviation)

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The distance between points B and C on the graph is equal to: D. √34 units.

In Mathematics, Pythagorean's theorem is represented by the following mathematical expression:

c² = a² + b²

Where:

a, b, and c represent the side length of any right-angled triangle.

In order to determine the distance between points B and C in right-angled triangle ABC, we would have to apply Pythagorean's theorem.

BC² = AB² + AC²

BC² = 5² + 3²

BC² = 25 + 9

BC² = 34

BC = √34 units.

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a) The probability of hitting the black circle inside the target is closer to zero.

b) The probability of hitting the white portion inside the target is closer to one.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the region is given as follows:

10² = 100 units squared.

The black circle has a radius of one unit(as the diameter is of 2 units), hence it's area is given as follows:

A = 3.14 x 1²

A = 3.14 units squared.

Then the probability of hitting the black circle is of:

3.14/100 = 0.0314 -> closer to zero.

The probability of hitting the white circle is given as follows:

1 - 0.0314 = 0.9686 -> closer to one.

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Answer: 41$

Step-by-step explanation:

This is because 5x6=30 (To find how much money is made)

then 11+30=41 (add both amounts)