The bearing of a fishing boat from a lighthouse is 118°.

Work out the bearing of the lighthouse from the fishing boat.

The example of an association claim is "Drinking alcohol increases cellular aging."

Cellular ageing is the term used to describe the alterations that take place in cells throughout time, which result in a decrease in function and a higher risk of disease.

Numerous things, such as oxidative stress, inflammation, and cellular damage brought on by environmental pollutants, contribute to these alterations.

Cells lose their ability to operate as they become older, which can lead to a variety of age-related illnesses and ailments, such as cancer, cardiovascular disease, and neurodegeneration.

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Answer:

because since the question is 639 / 6

we immediately know that 600 / 6 is 100

639 / 6 = 106.5

Answer:

You just need a little conversion to get the answer.

\(\frac{639}{6}=\frac{600}{6}+\frac{39}{6}\\ = 100+\frac{39}{6} >100\)

Pair 2 shows one figure rotated 180 degrees compared to the other, and translated as well. So they are congruent (ie the same).

Pair 4 shows one triangle reflected over the vertical line x = 22 to get the other triangle; which shows they are the same triangle.

The other pairs are not congruent. You can show that the areas of each figure being different is enough to prove they aren't the same figure.

Answer:

-4

Step-by-step explanation:

Rearranging the terms of this polynomial in descending order by powers of x, we get 3x2 + 5x3 − 4x4 − 7x => -4x^4 + 5x^3 + 3x^2 - 7x.

-4x^4 is the leading power of x, and -4 is the "leading coefficient" of the polynomial.

Answer:

1,666,667

Step-by-step explanation:

1000 milligrams is equal to one gram.

First, convert the mass of the grain of salt in milligrams to grams by dividing the mass in milligrams by 1000:

\(\implies \dfrac{0.06}{1000}=0.00006\; \rm g\)

To calculate how many grains of salt would be in 100 grams of sand, divide 100 g by 0.00006 g:

\(\implies \dfrac{100}{0.00006}=1,666,666.6666...\)

Therefore, there are 1,666,667 grains of salt in 100 grams of sand (to the nearest whole number).

Answer: B. Irrational

Step-by-step explanation:

the √20 is irrational because the √20 equals 4.47213595. We know that decimals or fractions are irrational, which makes the √20, 4.47213595, irrational because it is a decimal.

The total surface area of the given prism would be = 504

The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L

where a = 7

L = 14.5

Area = 2(7²) + 4 ( 7× 14.5)

= 2×49 + 4( 101.5)

= 98 + 406

= 504

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

can u include a picture of the cylinder pls luv

Step-by-step explanation:

The difference in housing prices in the fifth year is $7,125.

Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.

$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.

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solved, for  x^2+2x=35,   x=5 or x= -7

x^2+2x=35

Subtract 35 from both sides, and we get

x^2 +2x−35=0

To solve the equation, factor

x^2 +2x−35 using the formula  

x^2 +(a+b)x+ab=(x+a)(x+b).

To find a and b, set up a system to be solved.

a+b= 2

ab=−35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. List all such integer pairs that give product −35.

−1, 35

−5, 7

Calculate the sum for each pair.

−1+35=34

−5+7=2

The solution is the pair that gives sum 2, which are

a=−5

b=7

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x−5)(x+7)

To find equation solutions, solve x−5=0 and x+7=0.

x=5

x= −7

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Answer:

36

Step-by-step explanation:

Use PEMDAS:

2*10 is 20

2*2 is 4

So the equation is now

2+20+4+10=

Now add:

36

Thus the solution is 36

Hope this helps!

Answer:

Think your answer is 3 1/4

The answer of the given question based on the code is , the output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

MATLAB code:
To show that `x³ + 2x - 2` has a root between 0 and 1 and,

to find the root to 3 significant digits using the Newton Raphson Method,

we can use the following MATLAB code:  

Defining the function

f = (x)x³ + 2*x - 2;

Plotting the function

f_plot (f, [0, 1]);

grid on;

Defining the derivative of the function

f_prime = (x)3*x² + 2;

Implementing the Newton Raphson Method x0 = 1;

Initial guesstol = 1e-4;

Tolerance for erroriter = 0; % Iteration counter_while (1)

Run the loop until the root is founditer = iter + 1;

x1 = x0 - f(x0)

f_prime(x0);

Calculate the next guesserr = abs(x1 - x0);

Calculate the error if err < tol

Check if the error is less than the tolerancebreak;

else x0 = x1;

Set the next guess as the current guessendend

Displaying the resultfprintf('The root of x³ + 2x - 2 between 0 and 1 is %0.3f\n', x1));

The output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

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When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

MATLAB code:

Show that x^3 + 2x - 2 has a root between 0 and 1:

Here is the code to show that x^3 + 2x - 2 has a root between 0 and 1.

x = 0:.1:1;y = x.^3+2*x-2;

plot(x,y);

xlabel('x');

ylabel('y');

title('Plot of x^3 + 2x - 2');grid on;

This will display the plot of x^3 + 2x - 2 from x = 0 to x = 1.

Find the root to 3 significant digits using the Newton Raphson Method:

To find the root of x^3 + 2x - 2 to 3 significant digits using the Newton Raphson Method, use the following code:

format longx = 0;fx = x^3 + 2*x - 2;dfdx = 3*x^2 + 2;

ea = 100;

es = 0.5*(10^(2-3));

while (ea > es)x1 = x - (fx/dfdx);

fx1 = x1^3 + 2*x1 - 2;

ea = abs((x1-x)/x1)*100;

x = x1;fx = fx1;

dfdx = 3*x^2 + 2;

enddisp(x)

When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

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The mean of Y(n) is 0.

The mean of Z(n) is 0.

The variance of Y(n) is σ²/2.

The variance of Z(n) is (4/9)σ²/2.

Let's calculate the mean, variance, and covariance of Y(n) and Z(n) based on the given moving average processes.

Mean:

The mean of Y(n) can be calculated as:

E[Y(n)] = E[1/2(X(n) + X(n-1))]

Since X(n) is an IID(0,σ²) random variable, its mean is zero. Therefore, E[X(n)] = 0. We can also assume that X(n-1) is independent of X(n), so E[X(n-1)] = 0 as well. Hence, the mean of Y(n) is:

E[Y(n)] = 1/2(E[X(n)] + E[X(n-1)]) = 1/2(0 + 0) = 0.

Similarly, for Z(n):

E[Z(n)] = E[(2/3)X(n) + (1/3)X(n-1)]

Using the same reasoning as above, the mean of Z(n) is:

E[Z(n)] = (2/3)E[X(n)] + (1/3)E[X(n-1)] = (2/3)(0) + (1/3)(0) = 0.

Variance:

The variance of Y(n) can be calculated as:

Var(Y(n)) = Var(1/2(X(n) + X(n-1)))

Since X(n) and X(n-1) are independent, we can calculate the variance as follows:

Var(Y(n)) = (1/2)²(Var(X(n)) + Var(X(n-1)))

Since X(n) is an IID(0,σ²) random variable, Var(X(n)) = σ². Similarly, Var(X(n-1)) = σ². Hence, the variance of Y(n) is:

Var(Y(n)) = (1/2)²(σ² + σ²) = (1/2)²(2σ²) = σ²/2.

For Z(n):

Var(Z(n)) = Var((2/3)X(n) + (1/3)X(n-1))

Using the same reasoning as above, the variance of Z(n) is:

Var(Z(n)) = (2/3)²Var(X(n)) + (1/3)²Var(X(n-1)) = (4/9)σ² + (1/9)σ² = (5/9)σ².

To calculate the covariance between Y(n) and Z(n), we need to consider the relationship between X(n) and X(n-1). Since they are assumed to be independent, the covariance is zero. Hence, Cov(Y(n), Z(n)) = 0.

The mean of Y(n) and Z(n) is zero since the mean of X(n) and X(n-1) is zero. The variance of Y(n) is σ²/2, and the variance of Z(n) is (4/9)σ²/2. There is no covariance between Y(n) and Z(n) since X(n) and X(n-1) are assumed to be independent.

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The markers identified when identifying significant digits include:

Significant digits in mathematics refers to digits that  are meaningful in mathematical calculations. This implies that their position and the quantity alters the value of the number. The particular digit and the position determines whether the digit is significant or not.

Instances of digits with their locations that are significant are:

These instances results to significant digits while the instances below the digits are insignificant:

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Answer:

43.98 cm

Step-by-step explanation:

\(C=2\pi r\) where r is the radius

Plug the radius 7 cm into the equation as r

\(C=2\pi (7)\\C=14\pi \\C=43.98\)

Therefore, the circumference of the circle is approximately 43.98 cm.

I hope this helps!

The probability that a randomly selected student scored less than 82 is 0.9192 or 91.92% (rounded to two decimal places).

To find the probability that a randomly selected student scored less than 82 on an exam with a normally distributed test scores, a mean of 75, and a standard deviation of 5, you need to calculate the z-score and use a standard normal table or calculator.

The z-score formula is: (X - mean) / standard deviation

In this case, X = 82, mean = 75, and standard deviation = 5.

Z-score = (82 - 75) / 5 = 7 / 5 = 1.4

Now, use a standard normal table or calculator to find the probability associated with the z-score of 1.4. You'll find that the probability is approximately 0.9192.

To express this probability as a percentage, multiply by 100: 0.9192 * 100 = 91.92%

So, there's a 91.92% chance that a randomly selected student scored less than 82 on the exam.

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Extrapolation is a useful tool for predicting future values based on past data

Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.

In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.

Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.

Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.

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1) a. The predicted response when x∗=12.27 is y^​=140.052.  b. The 85% confidence interval for the mean response when x∗=12.27 is (125.157, 154.947).   c. The 95% prediction interval for an individual response when x∗=12.27 is (101.029, 179.075).  d. The prediction interval is wider than the confidence interval.

2) a. The predicted response when x∗=13.197 is y^​=187.845.

b. The 95% confidence interval for the mean response when x∗=13.197 is (167.726, 207.964).  c. The 95% prediction interval for an individual response when x∗=13.19 is (116.523, 259.167).  d. The prediction interval is wider than the confidence interval.

For part a, we can use the regression equation y^​=b0​+b1​x∗ to find the predicted response. Substituting the given values, we get y^​=9.3+11.6(12.27)=140.052.

For part b, we use the formula for the confidence interval for the mean response:

Mean response ± (t-critical)(Standard error)

Using the given information, we calculate the standard error using the formula sn​/√n, where n is the number of observations. The t-critical value is obtained from the t-distribution table for an 85% confidence level.

For part c, we use the formula for the prediction interval:

Mean response ± (t-critical)(Standard error) × √(1 + 1/n + (x∗-xˉ)²/SSx)

The t-critical value is obtained from the t-distribution table for a 95% confidence level. SSx is the sum of squared deviations of x values from their mean.

The calculations for part a, b, and c follow a similar process as in the previous question. The predicted response, confidence interval, and prediction interval are calculated using the given values and formulas.

For part d, we compare the widths of the confidence interval and the prediction interval. If the prediction interval is wider, it means it accounts for both the variability in the mean response and the variability in individual responses, making it wider than the confidence interval that only accounts for the mean response.

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The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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The element at the memory location that is 1 integer behind the memory location pointed to by p2.

(a) *(a1+4) - This expression evaluates to 5. It is equivalent to a1[4].

(b) a1[3] - This expression evaluates to 6, which is the value of the element at index 3 in the array a1.

(c) *p1 - This expression evaluates to 6, which is the value of the element at the memory location pointed to by p1.

(d) *(p1+5) - This expression evaluates to 1, which is the value of the element at the memory location that is 5 integers ahead of the memory location pointed to by p1.

(e) p1[-2] - This expression evaluates to 7, which is the value of the element at the memory location that is 2 integers behind the memory location pointed to by p1.

(f) *(a1+2) - This expression evaluates to 7, which is the value of the element at index 2 in the array a1.

(g) a1[6] - This expression evaluates to 3, which is the value of the element at index 6 in the array a1.

(h) *p2 - This expression evaluates to 7, which is the value of the element at the memory location pointed to by p2.

(i) *(p2+3) - This expression evaluates to 5, which is the value of the element at the memory location that is 3 integers ahead of the memory location pointed to by p2.

(j) p2[-1] - This expression evaluates to 8, which is the value of the element at the memory location that is 1 integer behind the memory location pointed to by p2.

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Answer:

x = 60.4°

Step-by-step explanation:

→ Workout BEG

180 - (110.2 + 25.6) = 44.2°

→ Find EBG

75.4

→ Now find x

x + 75.4 + 44.2 = 180

→ Simplify

x = 60.4°

Answer:

x = 60.4°

Step-by-step explanation:

DEF is a straight line , then

110.2 + ∠ BEG + 25.6° = 180°

∠ BEG + 135.8° = 180° ( subtract 135.8° from both sides )

∠ BEG = 44.2°

∠ DEB and ∠ CBE are alternate angles and are congruent , so

∠ EBG = 110.2° - 34.8° = 75.4°

Then using °°the sum of angles in a triangle = 180°

x = 180° - 44.2° - 75.4° = 180° - 119.6° = 60.4°

Answer:

x^2 - x +3, aka the last option

Step-by-step explanation: y intercept is positive in the table, and leaves us with the first option and the last option. plugging in 3 gets the right answer of 9 for the last choice and gives 15 for the first choice

The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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Answer:

it would cost $480

Step-by-step explanation:

1 poster = $6

80 posters = ?

80 posters = $6 x 80 => $480

Answer:

9/5x^3

Step-by-step explanation:

i hope that is the answer

Answer:

2 7/24 gallons

(sorry if its wrong)