An aircraft leaves a town &(28n, 66°E)
and after flying 3900km due South, it
gets to another town Y calculate,
a. The radius of the line of latitude through X
the latitude of Y Correct to the nearest
degree.
(the radius of the line of latitude through Y
(Take t=2 and R=6406 km)
​

p=4n+2 equation describes the relationship between n and p

How to find a function?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

Here the coordinates are (1,6),(2,10),(3,14),(4,18)

take two coordinates arbitrarily

ie. (1,6) and (3,14)

\(m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

\(m=\frac{14-6}{3-1}\\ = \frac{8}{2}\)

=4

we know the equation

\(y-y_{0} = m(x-x_{0} )\)

where \((x_{0},y_{0})= (1,6)\)

y-6 = 4(x-1)

y-6 = 4x-4

y = 4x-4+6

y = 4x+2

here y is the profit and x is the number of shirts

∴p=4n+2

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We will solve the differential equation and find the power series solutions for each problem.

Problem 9: y'' + (sin x)y = 0

Assuming the power series solution: y = a0 + a1x + a2x^2 + ...

Differentiating twice, we have:

y' = a1 + 2a2x + 3a3x^2 + ...

y'' = 2a2 + 6a3x + 12a4x^2 + ...

Substituting these expressions into the differential equation, we get:

2a2 + 6a3x + 12a4x^2 + ... + (sin x)(a0 + a1x + a2x^2 + ...) = 0

Grouping the terms by powers of x, we get:

a0(sin x) = 0

a1(sin x) + 2a2 = 0

a2(sin x) + 6a3 = 0

a3(sin x) + 12a4 = 0

...

From the first equation, we have a0 = 0, since sin(0) = 0. From the second equation, we have a2 = -a1(sin x)/2. From the third equation, we have a3 = -a2(sin x)/6 = a1(sin x)^2/12. From the fourth equation, we have a4 = -a3(sin x)/12 = -a1(sin x)^3/288.

Thus, we have the power series solution:

y = a1x - a1(sin x)^3/288 + ...

This solution is nontrivial, and the ratio of consecutive coefficients is:

-a1(sin x)^3/288 / (a1x) = -(sin x)^3 / (288x)

The ratio approaches zero as x approaches infinity, so the radius of convergence is infinite. Therefore, we expect the solution to be valid for all values of x.

Problem 10: e^xy'' + xy = 0

Assuming the power series solution: y = a0 + a1x + a2x^2 + ...

Differentiating twice, we have:

y' = a1 + 2a2x + 3a3x^2 + ...

y'' = 2a2 + 6a3x + 12a4x^2 + ...

Substituting these expressions into the differential equation, we get:

e^x(2a2 + 6a3x + 12a4x^2 + ...) + x(a0 + a1x + a2x^2 + ...) = 0

Grouping the terms by powers of x, we get:

a0 + (a1 + a0)x + [(2a2 + a1)x^2 + (6a3 + 2a2)x^3 + (12a4 + 6a3)x^4 + ...] = 0

Since the coefficient of x^0 is nonzero, we must have a0 = 0. Then, the coefficient of x^1 gives:

a1 + a0 = 0

a1 = 0

This means that the power series solution is identically zero, which is trivial. Therefore, we cannot form a fundamental set of solutions using power series.

Problem 11: (cos x)y'' + xy' - 2y = 0

Assuming the power series solution: y = a0 + a1x + a2x^2 + ...

Differentiating twice, we have:

y' = a1 + 2a2x + 3a3x

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Let:

Rf = Remus frogs

Jf = Julias frogs

If Remus gives a half of his frogs to Julia, what will the ratio of Julia's frogs to Remus frogs be ? so:

Therefore, the ratio will be:

Answer:

Area of a circle- pi x r square

3.14 x 2 x 2

= 3.14 x 4

= 12.56

Round off- 13

Answer:

12.7 ft^2

Step-by-step explanation:

to find the area, the equation is: r × r × π

we have the radius so we just plug the values into the equation, then into the calculator:

2 × 2 × π = 12.566 ft²

               ≈12.6 ft² (nearest tenth)

i believe that the nearest tenth is the tenths place in the decimal. hope this helped!

Answer:

you add the 11 back to the other side making it x^2+12x+11=0

then you factor it

(x+11)(x+1)

you should know what to do from here

Answer:

Step-by-step explanation:

x2 + 12x = –11

x2 + 12x +36 = –11 + 36

(x+6)^2 = -11 + 36 = 25 = (+/- 5)^2

x+6 = +/- 5

x+6 = +5  => x=-1

x+6 = -5  => x = -11

So the solution set is S = {-1, -11}

Answer:1250

Step-by-step explanation:

Answer:

the answer is 1/3

Step-by-step explanation:

\( \frac{2}{5} ( \frac{1}{3} + \frac{1}{2} ) \\ \frac{2}{5} ( \frac{1 \times 2}{3 \times 2} + \frac{1 \times 3}{ 2\times3 } ) \\ \frac{2}{5} ( \frac{2}{6} + \frac{3}{6} ) \\ \frac{2}{5} ( \frac{5}{6} ) \\ \frac{1}{3} \)

Answer:

0.3333 (repeating)

Step-by-step explanation:

used a calc

The slope and y-intercepts of each line, respectively, are:

5. m = -2; b = 6       6. m = 5/3; b = 10/3       7. m = -1/4; b = 4

Slope of a line is calculated as, m = change in y / change in x.

5. Given (2, 2) and (3, 0):

Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3

m = 2/-1

m = -2

To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:

2 = -2(2) + b

2 = -4 + b

2 + 4 = b

b = 6

6. Given (1,5) and (4, 10):

Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1

m = 5/3

To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:

5 = 5/3(1) + b

5 - 5/3 = b

b = (15 - 5)/3

b = 10/3

7. Given (8, 2) and (-8, 6):

Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8

m = 4/-16

m = -1/4

To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:

2 = -1/4(8) + b

2 = -2 + b

2 + 2 = b

b = 4

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To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Answer:

A, the correct answer is A because a dilation is when you either shrink or make the image bigger...and in this case they srunk it!

Step-by-step explanation:

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.

Given,

Function,

y = x² - 8x + 12

The supplied equation's vertex must be located.

The equation is a parabolic equation when we look at it.

We are aware that a parabolic equation's generic form is

y = x² - 8x + 12

where the parabola's vertex's x and y coordinates are denoted by h and k.

We can determine the following by comparing the aforementioned equation with the parabola's general form:

x = 4, y = 4 and h = -8

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

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Answer:

6 and 8 are corresponding.

2 and 4 is corresponding.

Step-by-step explanation:

and 2 and 7 is alternate.

3 and 6 are alternate.

The series converges because the limit of the ratio test is < 1.

To determine if the series is convergent or divergent using the ratio test, you first need to identify a_k, which is the general term of the series. In this case, a_k = 6k \(e^-^k\) . Then, evaluate the limit lim (k→∞) (a_(k+1) / a_k). If the limit is < 1, the series converges; if it's > 1, it diverges.

We have a_k = 6k \(e^-^k\). Apply the ratio test by finding lim (k→∞) (a_(k+1) / a_k) = lim (k→∞) [(6(k+1)\(e^-^(^k^+^1^)\)))/(6k \(e^-^k\))]. Simplify to get lim (k→∞) ((k+1)/k * e⁻¹). As k approaches infinity, the ratio approaches e⁻¹, which is < 1. Therefore, the series converges.

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Answer:

$39

Step-by-step explanation:

Answer:

Set costs $21 after discount

Step-by-step explanation:

$30 = 100%

$x = 100% - 30% = 70%

70% = 0.7

30(0.7) = 21

$21

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

a) a 99% confidence interval calculated from the same sample data would be longer than the 95% confidence interval, b) the statement that there is a 95% chance that µ is between 0.49 and 0.82 is incorrect

c) to compute a 90% confidence interval with a width of 2.3 and given a population standard deviation of 5.6, a sample size of approximately 71 is needed.

a) A 99% confidence interval provides a higher level of confidence compared to a 95% confidence interval. As the level of confidence increases, the width of the confidence interval also increases. This is because a higher confidence level requires a wider interval to capture a larger proportion of possible population values. Therefore, the 99% confidence interval calculated from the same sample data would be longer than the 95% confidence interval.

b) The statement that there is a 95% chance that µ (the population mean) is between 0.49 and 0.82 is incorrect. Confidence intervals are not a measure of the probability of a parameter falling within the interval. Instead, they provide a range of values within which the true parameter is likely to lie. The interpretation of a 95% confidence interval is that if we were to repeat the sampling process many times and construct 95% confidence intervals, approximately 95% of those intervals would contain the true population parameter. However, for any specific confidence interval, we cannot make probabilistic statements about the parameter's presence within that interval.

c) To compute a confidence interval with a specific width, we can use the formula:

Sample Size (n) = (Z * σ / E)^2,

where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the desired margin of error (half the width of the confidence interval). In this case, the desired confidence level is 90%, the desired width is 2.3, and the population standard deviation is 5.6. Plugging these values into the formula, we can solve for the sample size (n).

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8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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The probability of rolling an even number in at least one of the throws is 31/32 or approximately 0.969.

The probability of not rolling an even number in a single throw is 1/2, since there are three odd numbers and three even numbers on the die. Therefore, the probability of not rolling an even number in five independent throws is (1/2)^5 = 1/32.

The probability of rolling an even number in at least one of the throws is the complement of the probability of not rolling an even number in any of the five throws. So:

P(rolling an even number in at least one of the throws) = 1 - P(not rolling an even number in any of the five throws)

= 1 - (1/32)

= 31/32

Therefore, the probability of rolling an even number in at least one of the throws is 31/32 or approximately 0.969.

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The total area of the figure is 60 square centimeters.

We can see that in this figure we have 4 rectangles of 5cm by 3 cm.

Remember that the area of a rectangle is just the product between the dimensions, then the total area here is 4 times the product between the dimensions.

We will get:

Area = 4*(5cm*3cm) = 4*15cm² = 60cm²

That is the total area.

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The return predicted by CAPM for a portfolio with a beta of 0.8 is 10.8%, and the return predicted by CAPM for a portfolio with a beta of 1.5 is 15%.

The Capital Asset Pricing Model (CAPM) is a financial model that predicts what the return on an asset should be based on its expected risk and return. CAPM allows investors to calculate the expected return on a portfolio of stocks given its systematic risk.To answer this question, we need to know that the CAPM formula is:CAPM = Risk-free rate + (Beta x Market risk premium) where Beta = the systematic risk of the portfolio (measured by the beta coefficient), and the Market risk premium = (Market return - Risk-free rate).

Here are the characteristics of two portfolios, the market index, and the risk-free asset.Portfolio A:Expected Return = 11%Beta = 0.8Standard Deviation = 10%Portfolio B:Expected Return = 14%Beta = 1.5Standard Deviation = 31%Market index:Expected Return = 12%Beta = 1Standard Deviation = 20%T-bills:Expected Return = 6%Beta = 0Standard Deviation = 0%.

We can now calculate the return predicted by CAPM for a portfolio with a beta of 0.8 (Portfolio A). CAPM = Risk-free rate + (Beta x Market risk premium)Market risk premium = Market return - Risk-free rate = 12% - 6% = 6%CAPM = 6% + (0.8 x 6%) = 10.8%Therefore, the return predicted by CAPM for a portfolio with a beta of 0.8 is 10.8%.

We can also calculate the return predicted by CAPM for a portfolio with a beta of 1.5 (Portfolio B). CAPM = Risk-free rate + (Beta x Market risk premium)Market risk premium = Market return - Risk-free rate = 12% - 6% = 6%CAPM = 6% + (1.5 x 6%) = 15%Therefore, the return predicted by CAPM for a portfolio with a beta of 1.5 is 15%.In conclusion, the return predicted by CAPM for a portfolio with a beta of 0.8 is 10.8%, and the return predicted by CAPM for a portfolio with a beta of 1.5 is 15%.

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Answer:

B: y=3x+18

Step-by-step explanation:

Answer:

30 mm

Step-by-step explanation:

1 centimeter (cm) is one hundredth of a meter

1 millimeter (mm) is one thousandth of a meter

Thus one cm is 10 times bigger, so 3cm = 30mm

Correlation is a statistical measure of the relationship between two variables. It measures the strength of the association between two variables and can range from -1 to +1. There are three main types of correlations: positive, negative, and zero.

Positive correlation occurs when an increase in one variable leads to an increase in the other, and a decrease in one variable leads to a decrease in the other. An example of this would be the relationship between body weight and calorie intake; as body weight increases, calorie intake tends to increase as well.Negative correlation occurs when an increase in one variable leads to a decrease in the other, and a decrease in one variable leads to an increase in the other. An example of this would be the relationship between smoking and life expectancy; as smoking increases, life expectancy tends to decrease.

Zero correlation occurs when there is no linear relationship between two variables; they are not correlated at all. An example of this would be the relationship between gender and height; there is no linear relationship between the two variables, and so they are not correlated.

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The y-coordinate for the solution to the system of equations is -3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations. The intersection of two lines represents the system of equations' solution.

Given system of equations are,

6x + 11y = -3

4x + y = 17

To solve these equations, we must first remove x or y terms.

To do this we must make the removing term's coefficients the same.

In this case, let's remove y.

We are multiplying the second equation by 11. Then,

6x + 11y = -3

44x + 11y = 187

Now we will subtract the second equation from the first.

- 38x  = -190

x = 5

Now to find y, substitute x in any one of the equations.

6 * 5 + 11y = -3

11y = -33

y = -3

Hence the y-coordinate for the solution to the system of equations is -3.

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Step-by-step explanation:

(3760 + 4500 + 2450 + 3990) ÷ 4 = $3,675

The general solution to the given initial value problem is:

\(x_1(t) = 3c_1 * e^{6t},\\x_2(t) = 2c_1 * e^{6t}.\)

To find the general solution to the given system:

\(X' = \left[\begin{array}{ccc}12&-9\\4&0\end{array}\right]\)

Let X = [\(x_1; x_2\)] be the vector of variables, and X' represents its derivative.

The system of equations can be written as:

\(x_1' = 12x_1 - 9x_2\\x_2' = 4x_1 + 0x_2\)

To solve this system, we can rewrite it in matrix form:

X' = AX,

where A is the coefficient matrix:

\(A = \left[\begin{array}{ccc}12&-9\\4&0\end{array}\right]\)

To find the general solution, we need to find the eigenvalues and eigenvectors of matrix A.

First, we find the eigenvalues by solving the characteristic equation:

|A - λI| = 0,

where λ is the eigenvalue and I is the identity matrix.

A - λI = \(\left[\begin{array}{ccc}12-\lambda&-9\\4&-\lambda\end{array}\right]\)

Setting the determinant equal to zero:

(12 - λ)(-λ) - (-9)(4) = 0,

-λ(12 - λ) + 36 = 0,

\(\lambda^2 - 12\lambda + 36 = 0.\)

Factoring the quadratic equation:

(λ - 6)(λ - 6) = 0,

λ = 6.

Since we have repeated eigenvalue (λ = 6), we need to find the corresponding eigenvectors.

For λ = 6, we solve the equation (A - 6I)V = 0, where V is the eigenvector.

(A - 6I)V = [12 - 6 -9]\([v_1]\) = 0,

[4 -6] [\(v_2\)]

\(6v_1 - 9v_2 = 0,\\4v_1 - 6v_2 = 0.\)

We can choose \(v_1\) = 3 as a free variable.

Using \(v_1\) = 3, we get:

\(6(3) - 9v_2 = 0,\\4(3) - 6v_2 = 0.18 - 9v_2 = 0,\\12 - 6v_2 = 0.-9v_2 = -18,\\-6v_2 = -12.v_2 = 2.\)

Thus, the eigenvector corresponding to λ = 6 is V = [3; 2].

The general solution to the system is given by:

\(X(t) = c_1 * e^{6t} * V,\)

where c1 is an arbitrary constant and V is the eigenvector.

Substituting the values, we have:

\(X(t) = c_1 * e^{6t}\) * [3; 2],

or

\(x_1(t) = 3c_1 * e^{6t},\\x_2(t) = 2c_1 * e^{6t}.\)

Therefore, the general solution to the given system is:

\(x_1(t) = 3c_1 * e^{6t},\\x_2(t) = 2c_1 * e^{6t}.\)

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The lateral surface area of the triangular prism with side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters the height of the prism is 16.5 meters is 379.5 m²

Lateral surface area of prism = (a + b + c )h

a =  base side = 5m

b = base side = 8m

c = base side = 10m

h = height = 16.5 m

Lateral surface area of prism = (5 + 8 + 10)16.5

The lateral surface area of the prism = 379.5m²

The lateral surface area of the triangular prism is 379.5 m²

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Answer:

C

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

Triangle ABC matches up to EFD.  

We know both triangles have right angles and we know the distance of the hypotenuse (5 units) and one of the legs (4.5 given).  So, the justification is HL, not AAS.

Answer:

3

Step-by-step explanation:

f(x)=3x² + x-7

if f(-2)​

3(-2)²+-2-7

--> 3

Answer:

Answer 1. C

Answer 2. There's not enough information. You didn't give us the radius or diameter.

Answer 3. B

Answer 4. A

Answer 5. D

Answer 6. A

Answer 7. We can't see the gameboard. Sorry!

Answer 8. We can't see the map. Sorry!

Answer 9. A

Hope that helps! Sorry for the missings! I'm not sure for Answer 4.

Hope that helps!

Step-by-step explanation:

The value of x for equation x /45 = 3 is 135, value of expression −5.8 + (−2.5) is -8.3, the sale price is $319.20, volume of cube is 125 cubic centimeter, y = x /8 represents a proportional relationship.

An expression is combination of variables, numbers and operators.

1. The given equation is x /45 = 3

Now value of x is 45×3

x=135

3. The expression is −5.8 + (−2.5)

−5.8 −2.5

The value of expression is -8.3

4.To find the sale price  after a 20% discount, we need to subtract 20% of the original price from the original price:

20% of $399 = (20/100) x $399 = $79.80

Sale price = $399 - $79.80 = $319.20

Therefore, the sale price is $319.20.

5.  The side length of cube is 5 cm

Volume = 5³

=125 cubic centimeter

6. y = 8/ x equation represents a proportional relationship

7. 5 ft² is area of the wall will the game board cover

9. The given expression is 5 /8 x 4 /5

20/40

1/2

Hence, the value of x for equation x /45 = 3 is 135, value of expression −5.8 + (−2.5) is -8.3, the sale price is $319.20, volume of cube is 125 cubic centimeter, y = x /8 represents a proportional relationship.

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Answer:

it is answer is -3,

please mark brainlest

Answer:

It's -3

Step-by-step explanation:

You subtract by 3 every time you go down the number line. So if the highlighted line is 2 lines from 3 it is -3.