From the top of a 200 foot lighthouse, the angle of depression to a ship on the ocean is 23 degrees.
How far is the ship from the base of the lighthouse?

I know I did it right by the key says its wrong. Please provide steps

By using pythagorean theorem, the length of the third side is 3 unit.

In mathematics, a number or an expression is said to be in its simplest radical form if it has no perfect square factors other than 1. For example, the square root of 12 can be simplified to 2√3 because 2 * 2 * 3 = 12, but 2 and 3 are not perfect squares. So the simplest radical form of √12 is 2√3.

what is pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as:

c^2 = a^2 + b^2

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The method that could be used instead of cross multiplication to solve the equation *3-3x+5 is distributing x + 3 and then 3x + 5 to both sides of the equation.

Instead of using cross multiplication, one alternative method to solve the equation *3-3x+5 is to distribute x + 3 and then 3x + 5 to both sides of the equation.

To explain this method, let's consider the equation step by step:

Original equation: *3-3x+5

Cross multiplication: 5(x+3) = 2(3x+5)

Distributive property: 5x + 15 = 6x + 10

Subtraction property of equality: 5x - 6x = 10 - 15

Simplification: -x = -5

Multiplication property of equality: (-1)(-x) = (-1)(-5)

Simplification: x = 5

Now, instead of cross multiplication, we can distribute x + 3 and then 3x + 5 to both sides of the equation:

Original equation: *3-3x+5

Distributive property: 5(x + 3) = 2(3x + 5)

Expanding the expressions inside the parentheses:

5x + 15 = 6x + 10

Now we can proceed with solving the equation as before:

Subtraction property of equality: 5x - 6x = 10 - 15

Simplification: -x = -5

Multiplication property of equality: (-1)(-x) = (-1)(-5)

Simplification: x = 5

By distributing x + 3 and 3x + 5 to both sides of the equation, we obtain the same result as the original method. This alternative method is another way to solve the equation without using cross multiplication.

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Answer:

actually both

Step-by-step explanation:

have a great day

If the distribution of observations were perfectly symmetrical and unimodal, option B) The mean, median, and mode would be the same.

In a perfectly symmetrical and unimodal distribution, the mean, median, and mode would be equal. This is because in such a distribution, the data would be evenly spread around a central value. The mean is calculated by summing all the observations and dividing by the total number of observations. Since the distribution is symmetrical, the sum of the observations on one side of the central value would be equal to the sum on the other side, resulting in a balanced mean.

The median is the middle value when the observations are arranged in ascending or descending order. In a symmetrical distribution, the middle value would be the same as the central value, leading to the median being equal to the mean.

The mode represents the value that appears most frequently in the distribution. In a perfectly symmetrical and unimodal distribution, all values would occur with the same frequency, resulting in multiple modes. However, since the distribution is unimodal, meaning it has only one peak, all the modes would coincide, and the mode would also be equal to the mean and median. Therefore, in a perfectly symmetrical and unimodal distribution, the mean, median, and mode would all be the same value, leading to answer B) The mean, median, and mode would be the same.

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The arithmetic mean provides a single measure for a certain population, also called the average.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The ratio of the total number of observations divided by the sum of all the given observations is known as the arithmetic mean. For instance, if the data set contains 5 observations, it is possible to get the arithmetic mean by adding all 5 of the given observations and dividing by 5.

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Answer:

y = 2x^2 + 12x + 14

Step-by-step explanation:

Write this equation in standard form.  Start by performing the exponentiation:

y = 2(x^2 + 6x + 9) - 4

Perform the indicated multiplication:

y = 2x^2 + 12x + 18 - 4, or

y = 2x^2 + 12x + 14:  This is the quadratic function in standard form.

The value of the quadratic function in standard form is,

⇒ f (x) = 2x² + 12x + 14

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = 2 (x + 3)² - 4

Now, We get;

The value of the quadratic function in standard form is,

⇒ f (x) = 2 (x + 3)² - 4

⇒ f (x) = 2 (x² + 9 + 6x) - 4

⇒ f (x) = 2x² + 18 + 12x - 4

⇒ f (x) = 2x² + 12x + 14

Thus, The value of the quadratic function in standard form is,

⇒ f (x) = 2x² + 12x + 14

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When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.

A percentage is what?

A percentage of 100 is represented as a number or ratio known as a percentage.

We've got

Take in a performance Attend a concert and a festival

Remain in state 214 and 186

Travel outside of state 391 and 59

The amount of groups planning to visit a state while attending a concert=214

The amount of groups planning to leave the state to attend a concert=391

The amount of groups planning to visit a state while attending a festival=186

The amount of groups planning to leave the state to attend a festival=59

The proportion of festival-goers that desire to travel outside of their state:

= Total number of groups from all four conditions/ Number of groups wishing to attend an event while remaining outside the state.

= 59 / ( 214 + 391 + 186 + 59 ) x 100

= 59 / 850 x 100

= 6.94%

Therefore, When considering their desire to go outside of their state, 6.94% of people say they would like to attend a festival.

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Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

The following is the provided polynomial in factored form:

5x(2x + 5)(y + 1)

The polynomial in question is 5x22xy-10y + 25x.

We can start by factoring out the biggest common factor of all the terms, which is 5, in order to factor this polynomial:

5(x²2xy - 2y + 5x)

The quadratic expression included in the parenthesis must now be factored. We can utilise the grouping approach to accomplish this:

5x(x2y + 5) = 5(x22xy - 2y + 5x). - 2y(2x + 5)

We can factor out the two terms that share the factor (2x + 5) now:

5x(2x + 5)(y + 1) = 5(x22xy - 2y + 5x)

As a result, the following is the provided polynomial's factored form:

5x(2x + 5)(y + 1)

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Permutation helps us to know the number of ways an object can be arranged in a particular manner. The correct option is D.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

The example which is an example of permutation is Selecting a first-, second-, and third-place winner at baking.

Hence, the correct option is D.

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435 miles per hour, 515 miles per hour

Step-by-step explanation:

Let us assume that plane A is traveling at 'x' miles per hour, then plane B is traveling at 'x+80' miles per hour. As the question says that one of them traveled 80 miles per hour faster than other.

After 4 hours they were 3800 miles apart.

We know that,

\( t = \frac{distance}{speed} \)

Since two planes are traveling in opposite directions, so we will add their speed.

Putting the values in the equation we get,

\(4 = \frac{3800}{x + (x + 80)} \)

Now, solving for 'x'

\(4(x + (x + 80) = 3800\)

\(4x + 4x + 320 = 3800\)

\(8x = 3800 - 320\)

\(8x = 3480\)

\(x = \frac{3480}{8} = 435\)

So the rate of plane A is 435 miles per hour and the rate of plane B is (435+80 = 515) miles per hour.

Step-by-step explanation:

Given 5x + 8 = 118 (vertically opposite angles)

\(5x + 8 = 118 \\ 5x = 118 - 8 \\ 5x = 110 \\ x = 110 \div 5 \\ = 22\)

The area of the shape is 192.5 ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The shape can be divided into parallelogram and trapezium.

area of parallelogram is expressed as;

A = base × height

A = 11 × 7

A = 77 ft²

Area of trapezium is expressed as

A = 1/2(a+b)h

A = 1/2( 8+13) 11

A = 21×11/2

A = 115.5

The area of the shape

= 77+ 115.5

= 192.5 ft²

Therefore the area of the shaded region is 192.5 ft²

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Answer:

A is true

Step-by-step explanation:

Answer:

I think it's the first one.

explanation:

Bc -4 is closer to 0 and if it is negative then the bigger the number the less value it has.

I hope this helps have an amazing day.

Answer: 3=-155.15

4=-224.05

Step-by-step explanation:

Answer: 155.15 then 223.75

Step-by-step explanation:

The solution to the system of equations is x = 7 and y = 3/2.

What is Simultaneous Equation?

Two or more algebraic equations that share variables are said to be simultaneous equations.

1) Rearrange both equations so that one variable is isolated on one side of the equation:

x/2 + y/3 = 4 --> x/2 = 4 - y/3 --> x = 8 - (2/3)y

y/4 - x/3 = 1/6 --> y/4 = 1/6 + x/3 --> y = 2/3 + (4/3)x

2) Substitute the expression for one variable into the other equation:

y = 2/3 + (4/3)x

x/2 + (2/3 + (4/3)x)/3 = 4

3) Simplify and solve for the remaining variable:

x/2 + 2/9 + (4/9)x = 4

5x/9 + 1/9 = 4

5x/9 = 35/9

x = 7

4) Substitute the value of x into one of the original equations and solve for the other variable:

x/2 + y/3 = 4

7/2 + y/3 = 4

y/3 = 1/2

y = 3/2

Therefore, the solution to the system of equations is x = 7 and y = 3/2.

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Answer:

600,000

Step-by-step explanation:

The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula \(f(x) = a(1+r)^{x}\) where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.

For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.

We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.

Answer:

y = 54x

Step-by-step explanation:

→ Divide one y value by its corresponding x values

27 ÷ 0.5 = 54

Answer:

i also needed help on this qustion and the awnser is

Step-by-step explanation:

C.

its the same problem and nothing changed besides the order↑≠≈

Answer:

The answer is C

Step-by-step explanation:

Answer:

  -145°, -325°

Step-by-step explanation:

The principal value of the arctangent of 0.7002 is 35°. The tangent function is periodic with a period of 180°, so the general solution is ...

  y = (35 +180k) degrees . . . . . where k is an integer

Values from the given list include ...

  -145°

  -325°

_____

Additional comment

  +35° and +215° would also be part of the general solution

Answer:

C. 8.9 × 10^6

Step-by-step explanation:

There isn't really much to explain, this is just how scientific notation works. It's always X.Y x 10^z power

If that didn't make sense, it's just the first number, followed by a decimal, followed by all others that are not 0, followed by 10^[the amount of 0s after]

Answer:

x=7

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

x + 2x + 69 = 90

3x + 69 = 90

3x = 21

x = 7

The number of days Henry can go on vacation is 7 days.

Given that, Henry knows it will cost $300 per day that he's on vacation plus $650 for miscellaneous activities.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of days be x.

Henry has $2750 dollars in his savings account.

So equation is 300x+650=2750

The obtained equation can be solved as follow

300x=2750-650

⇒ 300x = 2100

⇒ x = 2100/300

⇒ x = 7

Therefore, the number of days Henry can go on vacation is 7 days.

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Yes, you are right with the second option shown in the figure .

For example, 3/2 is a rational number. It denotes that the number 3 is divided by the integer 2.

second option is correct because all the other number are exceeding the number given in the question.

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The exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

To find the exact probability, we will use the properties of the normal distribution.

Let X be the random variable representing the sum of the labels on the tickets. We know that the mean of X (μ) is -581.4 and the standard deviation of X (σ) is √(17) × 4.5.

We want to find the probability that the absolute value of the difference between X and -581.4 exceeds 31.54. In other words, we want to find P(|X - (-581.4)| > 31.54).

Convert the inequality into a standard normal distribution form.

The standard normal distribution has a mean of 0 and a standard deviation of 1. To convert X to a standard normal random variable Z, we use the formula:

Z = (X - μ) / σ

In our case:

Z = (X - (-581.4)) / (√(17) * 4.5)

Calculate the Z-score.

Z = (31.54) / (√(17) * 4.5) ≈ 1.591

Find the probability using a standard normal distribution table or a calculator.

P(Z > 1.591) ≈ 0.0564 (rounded to four decimal places)

Account for both tails of the distribution.

Since we are interested in the absolute difference, we need to consider both tails of the normal distribution. Therefore, the total probability of the absolute difference exceeding 31.54 is:

P(|X - (-581.4)| > 31.54) = 2 P(Z > 1.591) ≈ 2 × 0.0564 ≈ 0.1128

So, the exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

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Answer:

3.9

Step-by-step explanation:

The answer is 0.7.

Given,

On the off chance that the odds he will get a hit is 0.3

p = 0.3,

the odds he won't are 0.7

i.e.,

q = 1 - 0.3

=0.7

What is probability ?

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Given:

Two different congruency mapping

To find:

a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up

b) a rule for congruence mapping that reflects a figure across the y-axis