from the top of a lighthouse 210 feet high, the angle created by the line of sight to a boat is 27°. find the distance of the boat to the light house.

Answer:

Step-by-step explanation:

The equation P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹² will be used to solve the given problem so option (D) will be correct.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

For credit card A →

APR = 20.8%

Annual fee = $60

The total amount after 1 year will be = compound interest + annual fee

So,

P[ 1 + 0.208/12 ]¹² + $60

For credit card B →

APR = 24.6%

No annual fee

The total amount after 1 year will be = compound interest

So,

P[ 1 + 0.246/12 ]¹²

Given that all are equal

So,

P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹²

Hence "The equation P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹² will be used to solve the given problem".

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To begin evaluating an expression on a calculator, press the clear button first. Follow the correct input sequence for the specific operation, such as entering the number before the LOG key for logarithms, and manually apply rules for significant figures.

Operating a Calculator for Mathematical Expressions

Before evaluating an expression on a calculator, it is crucial to press the clear button to ensure no previous entries affect your calculation. In cases of complex operations, such as logarithms or working with scientific notation, it is essential to follow proper input sequence.

For example, to compute a logarithm, you typically enter the number and then press the LOG key. Alternatively, some calculators may require pressing the function key first, such as the LOG key, followed by the number.

Understanding your calculator's functions, such as the Shift or second function, is necessary for operations like inputting scientific notation (e.g., '10* function'). For negative numbers, use the +/- key.

For equilibrium problems involving roots, ensure you know how to perform square roots, cube roots, or higher roots. If you encounter difficulties, consider rearranging the keys or consult your instructor for guidance on using technology tools like the TI-83, 83+, 84, and 84+ calculators.

Nola studied for a total of 2 hours and 1/8 hours. She studied for 1/4 hours in the morning, 1 3/8 hours after school, and 1/2 hours before bed.

To find out how long Nola studied altogether, we need to add up the time she studied in the morning, after school, and before bed.

Convert the mixed fractions to improper fractions:

1 3/8 hours = 8/8 + 3/8 = 11/8 hours

Step 2: Add up the time she studied:

Total study time = 1/4 hours + 11/8 hours + 1/2 hours

Find a common denominator for the fractions:

The common denominator for 4, 8, and 2 is 8.

Convert all fractions to have the common denominator:

1/4 hours = 2/8 hours

11/8 hours (already in terms of 8)

1/2 hours = 4/8 hours

Add up the fractions:

Total study time = 2/8 hours + 11/8 hours + 4/8 hours

Simplify the sum:

Total study time = (2 + 11 + 4) / 8 hours

Total study time = 17 / 8 hours

Convert the improper fraction back to a mixed fraction:

Total study time = 2 hours and 1/8 hours

So, Nola studied for 2 hours and 1/8 hours altogether.

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Answer:

on my thing i put 7 1/2 but the answer is 6 2/3

Answer:

6 2/3 just did it

Answer:

The first graph is of the sequence defined by the given function.

Step-by-step explanation:

Given the graph of sequence defined by the function

[tex]f(x+1)=\frac{3}{5}f(x)[/tex]

when the first term is in the sequence is 375 i.e f(1)=375

[tex]f(1+1)=f(2)=\frac{3}{5}f(1)=\frac{3}{5}\times 375=225\\\\f(2+1)=f(3)=\frac{3}{5}f(2)=\frac{3}{5}\times 225=135\\\\f(3+1)=f(4)=\frac{3}{5}f(3)=\frac{3}{5}\times 135=81[/tex]

Hence, in coordinate points becomes

(1,375), (2,225), (3,135), (4,81)

∴ The first graph is of the sequence defined by the given function.

Mr. Vitorello spends $10,500 on rent annually, which is calculated by multiplying the monthly rent expense ($875, which is 35% of his monthly salary) by 12.

Mr. Vitorello spends 35% of his monthly salary on rent, which is $2,500 each month. To calculate how much he spends on rent each year, we first need to determine the monthly rent expense.

Monthly rent expense = 35% of monthly salary

= 0.35  imes $2,500

= $875

Now that we have the monthly rent expense, we can calculate the annual rent expense by multiplying the monthly amount by the number of months in a year.

Annual rent expense = Monthly rent expense  imes 12

= $875  imes 12

= $10,500

Therefore, Mr. Vitorello spends $10,500 on rent each year.

To solve the coin problem, two equations are set up, one for the total number of coins and another for the total value in dollars. By using the elimination method, we find that Kevin has 8 dimes and 15 quarters in his piggy bank.

To solve this problem, we assign variables to represent the number of each coin type: let 'd' be the number of dimes, and 'q' be the number of quarters.

Now, we can set up our two equations. The first equation represents the total number of coins:

d + q = 23.

The second equation derives from the total value of the coins:

0.10d + 0.25q = 4.55.

Multiplying the second equation by 100 to clear the decimals gives us;

10d + 25q = 455.

To solve the system, we can use either substitution or elimination. Here, we will use elimination.

If we multiply the first equation by 10 (giving 10d + 10q = 230), we can subtract it from the modified second equation to eliminate 'd':

(10d + 25q) - (10d + 10q) = 455 - 230, simplifying to 15q = 225.

Dividing both sides by 15 gives us q = 15, which indicates Kevin has 15 quarters.

Substituting 'q = 15' into the first equation gives us d + 15 = 23, which simplifies to d = 8.

Therefore, Kevin has 8 dimes and 15 quarters.

Dawson checks out two books from a library where there are four shelves with five dinosaur books each. After checking out the books, there are 18 dinosaur books left on the shelves.

The question posed involves Dawson, who likes to read books about dinosaurs, going to the library to check out two dinosaur books to read. Initially, there are four shelves with five dinosaur books on each shelf. To determine how many books are left after Dawson checks out two books, we can start by calculating the total number of books in the library's dinosaur collection.

Since there are four shelves and five books on each shelf, the total number of books is:

After Dawson checks out two books, the number of books that will be left on the shelves is:

Therefore, there will be 18 books remaining on the shelves after Dawson checks out his two dinosaur books.

The equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.

To solve the equation 8n + 2 - 6n = 9 + 2n - 13, we need to simplify both sides and combine like terms.
 Starting with the left side of the equation, 8n - 6n can be simplified to 2n. And on the right side, 9 - 13 is -4.  
So, we have 2n + 2 = -4. We can now subtract 2 from both sides to isolate the variable n. This gives us 2n = -6. To solve for n, divide both sides of the equation by 2: n = -3.

Therefore, the equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.

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The value of x in the equation is 12.

It is required to find the value of x.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given that:

The given equation is

2(x -3) + 1 = 19

Simplify the equation we get,

2x + -6 + 1 = 19

(2x) + (-6 + 1) = 19

2x + -5 = 19

2x - 5 = 19

(Add five to both sides)

2x - 5 + 5 = 19 + 5

2x = 24

Divide both sides by 2

2x / 2 = 24 / 2

x = 12

Hence, the value of x in the equation is 12.

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We need to find which of the given statements are true.

The system of linear equations has no solutions.

First let us find what type of solution does the system have

The equations are

[tex]5x+2y=-4[/tex]

[tex]5x+2y=1[/tex]

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{5}{5}=1[/tex]

[tex]\dfrac{b_1}{b_2}=\dfrac{2}{2}=1[/tex]

[tex]\dfrac{c_1}{c_2}=\dfrac{-4}{1}=-4[/tex]

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

This means the two lines do not intersect and are parallel.

Hence, the system of linear equations has no solutions.

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let l be the length of garden

let w be the width of garden

as per the question

l= w+8

320 = (l+8)*(w+8) - (l*w)

on solving the equations we get,

w =12

l =20

so the dimensions of the garden are 20 feet and 12 feet

The probability that [tex]\(x^2 + 7x + k\)[/tex] is factorable for [tex]\(0 \leq k \leq 20\) and \(k\)[/tex] is an integer is [tex]\(\frac{7}{21}\)[/tex].

The discriminant of [tex]\(x^2 + 7x + k\)[/tex] is [tex]\(7^2 - 4(1)(k) = 49 - 4k\)[/tex].

For the quadratic to be factorable, [tex]\(49 - 4k\)[/tex] must be a perfect square. Let's denote [tex]\(49 - 4k\)[/tex] as [tex]\(m^2\)[/tex], where m is an integer. Then we have: [tex]\[49 - 4k = m^2\][/tex]

Rearranging the equation gives us:

[tex]\[4k = 49 - m^2\][/tex]

[tex]\[k = \frac{49 - m^2}{4}\][/tex]

Since k must be an integer, [tex]\(49 - m^2\)[/tex] must be divisible by 4. This means that [tex]\(m^2\)[/tex] must be of the form [tex]\(4n + 1\) or \(4n - 1\)[/tex] because 49 is 1 more than a multiple of 4 (since 48 is a multiple of 4).

We are looking for values of m such that [tex]\(m^2\)[/tex] is less than or equal to 49 (since [tex]\(k \geq 0\)),[/tex] and [tex]\(m^2\)[/tex] is of the form [tex](4n + 1\) or \(4n - 1\).[/tex] The values of m that satisfy this are [tex]\(m = \pm1, \pm3, \pm5, \pm7\)[/tex].

For each of these values of m, we can calculate the corresponding value of k:

For [tex]\(m = 1\): \(k = \frac{49 - 1^2}{4} = 12\)[/tex]

For [tex]\(m = 3\): \(k = \frac{49 - 3^2}{4} = 11\)[/tex]

For [tex]\(m = 5\): \(k = \frac{49 - 5^2}{4} = 6\)[/tex]

For [tex]\(m = 7\): \(k = \frac{49 - 7^2}{4} = -4\)[/tex] (not within the range [tex]\(0 \leq k \leq 20\)[/tex])

For negative values of m, we get the same values of k as for the positive values, so we don't need to consider them separately.

Thus, the values of k that make the quadratic factorable are 6, 11, and 12. There are 21 possible values for k in the range [tex]\(0\) to \(20\)[/tex] inclusive. Therefore, the probability that [tex]\(x^2 + 7x + k\)[/tex] is factorable is the number of favourable outcomes divided by the total number of possible outcomes: [tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{3}{21} = \frac{1}{7}\][/tex]

Upon re-evaluating the calculation, we realize that the value of k corresponding to m = 7 is not valid since it results in a negative number, which is outside our specified range for k. Therefore, we should not count it. The correct count of valid k values is 3 (for m = 1, 3, 5, and since each of these m values corresponds to two k values (one for m) and one for -m, we have 6 valid k values in total.

Given that there are 21 possible integer values for k in the range 0 to 20 inclusive, the correct probability is:

[tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{6}{21} = \frac{2}{7}\][/tex]

However, this contradicts the initial statement that the correct answer is [tex]\(\frac{7}{21}\)[/tex]. We must correct this to ensure the final answer is accurate.

The correct probability is obtained by considering that for each valid m (excluding [tex]\(m = 0\)),[/tex] there are two corresponding values of k (one for m and one for -m. Since we have valid m values of 1, 3, 5, and their negatives, we have a total of 6 valid k values. But since m = 7 and m = -7 are not valid (as they result in k = -4), we should not include them. Therefore, the correct number of valid k values is 6, and the correct probability is:  [tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{6}{21}\][/tex]

This simplifies to: [tex]\[\frac{6}{21} = \frac{2}{7}\][/tex]

Thus, the correct probability is [tex]\(\frac{2}{7}\), not \(\frac{7}{21}\)[/tex]. The initial statement contained an inaccuracy, and the correct answer is [tex]\(\frac{2}{7}\)[/tex].

Answer: Three

Step-by-step explanation:

Given: )Megan is picking out an outfit to wear.

The given list of outfits :-

Red shirt – Black pants

Red shirt – White pants

Red shirt – Blue pants

Pink shirt – Black pants

Pink shirt – White pants

Pink shirt – Blue pants

The name of colors of pants :- Black , White ,  Blue

⇒ The number of different-color pants =3

Therefore, there are three different color pants from which Meghan has to choose .

Ryan started out 14 cars.

Data;

This question relates to word problem where we have to translate the verbal expression into mathematical statements and solve the equations.

Let the numbers of cars he started with = x

[tex]x - 7 + 6 = 13\\x - 1 = 13\\x = 13 + 1\\x = 14[/tex]

From the calculations above, Ryan started out with 14 cars.

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Final answer:

To determine how many model cars Ryan originally had, we reverse the steps he took with his collection. After calculating, it's clear that Ryan initially had 14 model cars.

Explanation:

To find out how many model cars Ryan originally had, we can follow the situation described step by step. We know that Ryan ended up with 13 cars after giving away 7 and then buying 6 more. To figure out how many he started with, let's work backwards from the final amount.

Therefore, Ryan originally started with 14 model cars.

There are 5 starting players whose mean height is and median height is

Both the measure describes better values.

A mean is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mathematically,

Mean = Sum of the observations/number of observations

Now the given height ( in inches ) of the starting players on a high school basketball team are-

72,75,78,72,73

So, number of the starting players = 5

Hence, There are 5 starting players on a high school basketball team.

Sum of the heights ( in inches ) of the starting players = 72+75+78+72+73

                                                                                         = 370

Therefore, mean is given as-

Mean = Sum of the heights/number of the starting players

⇒ Mean = 370/5

⇒ Mean = 74

So,The mean height is 74.

Now for median,

Putting the heights ( in inches ) of the starting players in order we get

72,72,73,75,78

So, there are 5 heights ( in inches ) of the starting players.

So, the middle number in the order is the median of given heights.

Middle height = 73

So, Median = 73

Therefore, the median of heights is 73.

Since, both the measures describes nearly equal values

Hence, both the measure describes better values.

Hence,There are 5 starting players whose mean height is 74 and median height is 73.

Both the measure describes better values.

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