A submarine travels 8.3 km due North from its base and then turns and travels due West for 13.9 km.
How far away is the submarine from its base?
Give your answer rounded to 1 DP

a. Covariance = 10.11
b. Correlation coefficient = 0.376

Considering the following sample data:

x 12 18 20 22 25

y 15 20 25 22 27

a. Calculation of covariance

Covariance can be calculated by the formula:

Cov (X, Y) = [Σ(X - μx) (Y - μy)] / n

where, Σ denotes the sum of, X and Y are the variables, μx and μy are the means of X and Y respectively, and n is the sample size.

x  y  x-μx  y-μy  (x-μx)(y-μy) (-)^2  (-)^2

12  15  -6.6  -5.6  37.12  43.56  31.36

18  20  -0.6  -0.6  0.36  0.36  0.36

20  25  1.4  4.4  6.16           1.96  19.36

22  22  3.4  -2.6  -8.84  11.56  6.76

25  27  6.4  2.4  15.36  41.16  5.76

Σx = 97, Σy = 109, Σ(x-μx) = 5.00, Σ(y-μy) = -2.00, Σ(x-μx)(y-μy) = 50.56

Covariance is: Cov (X, Y) = [Σ(X - μx) (Y - μy)] / n= 50.56/5= 10.11

Thus, the covariance between the variables is 10.11.

b-1. Calculation of correlation coefficient.

Correlation coefficient is a statistical measure that measures the degree to which two random variables are associated. It can be calculated by the formula:

= Cov (X, Y) /  where, Cov (X, Y) is the covariance between X and Y, σX and σY are the standard deviations of X and Y respectively.

σx2 = [Σ(x-μx)2] / (n-1)σy2 = [Σ(y-μy)2] / (n-1)σx = √[Σ(x-μx)2] / (n-1)σy = √[Σ(y-μy)2] / (n-1)

x  y  (x-μx)  (y-μy)  (x-μx)2  (y-μy)2  (-)(-)

12  15  -6.6          -5.6         43.56  31.36               1  

18  -0.6  -0.6          0.36         0.36  0.32                5

20  25    1.4          4.4          1.96          19.36               22  

22  3.4  -2.6          11.56  6.76          -8.84                25  

27  6.4  2.4          41.16  5.76          15.36

Σx = 97, Σy = 109, Σ(x-μx) = 5.00, Σ(y-μy) = -2.00, Σ(x-μx)(y-μy) = 50.56

σx2 = 30.70

σy2 = 25.70

σx = √30.70 = 5.54

σy = √25.70 = 5.07

Correlation coefficient is:

= Cov (X, Y) /  = 10.11 / (5.54*5.07)= 0.376

Thus, the correlation coefficient is 0.376.

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We have that in this case, we have that the measure of an angle on a circle is half the measure of its intercepted arc.

We have that the whole circle corresponds to a 360º, then:

because 360º - 214º = 144º

Then, the the intercepted arc by the angle K is 144º.

Then,

Answer: -2

Step-by-step explanation:

\(\frac{y2 - y1}{x2 - x1}\) = \(\frac{7-(-5)}{-4-2}\) = \(\frac{12}{-6}\) = -2

The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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Answer:

15

Step-by-step explanation:

the triangles are similar so will be the same proprotion,

I have attached a picture showing how I solved this. the second traingle is 3 times as large (15 by 12)   compared to the first triangle which is 4 by 5.

Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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Therefore, the work done in lifting the sand to a height of 18 ft is approximately 41,875.2 foot-pounds.

To calculate the work done in lifting the sand, we need to consider the weight of the sand that remains in the bag at a height of 18 ft.

Given that the bag originally weighed 144 lb, and it was half empty by the time it was lifted to a height of 18 ft, we can assume that half of the weight of the sand has been lost. Therefore, the weight of the sand remaining in the bag is 144 lb / 2 = 72 lb.

To calculate the work done in lifting the sand, we use the formula:

Work = Force × Distance

In this case, the force is equal to the weight of the sand remaining, and the distance is the height to which the sand was lifted.

The weight of the sand remaining is 72 lb, and the distance lifted is 18 ft. However, we need to convert the distance from feet to a more appropriate unit, such as joules. To do this, we need to multiply by the gravitational acceleration (approximated as 32.2 ft/s²) to obtain the distance in foot-pounds.

Distance in foot-pounds = 18 ft × 32.2 ft/s²

Now we can calculate the work:

Work = Force × Distance

= 72 lb × (18 ft × 32.2 ft/s²)

Calculating the value:

Work ≈ 72 lb × 581.6 ft·lb/s²

≈ 41,875.2 ft·lb

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The value of \(f · dr_c\) is 32π.

To find \(f · dr_c\), we need to first find the vector field f and the line integral \(dr_c.\)

The vector field f is given by:

\(f = (z − y) i + (x − z) j + (y − x) k\)

The line integral \(dr_c\) can be parameterized using the equation of the circle of radius 4 centered at (1, 1, 1) in the plane x y z = 3:

\(r(t) = 4 cos(t) i + 4 sin(t) j + (3 - 4 cos(t) - 4 sin(t)) k\), where 0 ≤ t ≤ 2π.

Taking the differential of r(t), we get:

\(dr = (-4 sin(t)) i + (4 cos(t)) j + 4 sin(t) k\)

Now we can evaluate the dot product \(f · dr\):

\(f · dr = (z − y) dx + (x − z) dy + (y − x) dz\)

\(= [(3 - 4 cos(t) - 4 sin(t)) - 4 sin(t)] (-4 sin(t)) + [4 cos(t) - (3 - 4 cos(t) - 4 sin(t))] (4 cos(t)) + [(4 sin(t) - 4 cos(t))] (4 sin(t))\)

=\(-32 sin^2(t) + 32 cos^2(t) + 0\)

\(= 32 cos^2(t) - 32 sin^2(t)\)

Since the circle is oriented clockwise when viewed from the origin, we need to reverse the direction of the parameterization by replacing t with -t. Therefore, we have:

\(f · dr_c\) = ∫\(_0^(2π) (32 cos^2(-t) - 32 sin^2(-t)) dt\)

\(=\)∫\(_0^(2π) (32 cos^2(t) - 32 sin^2(t)) dt\)

\(= 32(\)π\(cos(0) - π sin(0))\)

\(= 32\)π

Hence, the value of \(f · dr_c is 32\)π.

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The bird is 55 ft above the ground

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for the drawing.

From the drawing:

sin 30° = x/100  (opposite/hypotenuse)

x = 100 * sin 30°

x = 50 ft

height of the bird above the ground = x + 5

height of the bird above the ground = 50 + 5 = 55 ft

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Answer:

(-x - 12)

Step-by-step explanation:

(3x - 3) + (-4x - 9)

(3x-4x) + (-3-9)

-x+(-12)

(-x-12)

Answer:

English translation please.....

Answer:

A. 1/6

B. 1

Step-by-step explanation:

A. 9/j x j/54= 9/54 = 1/6

B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1

Answer:

a. 3/2

b. 1

Step-by-step explanation:

A. To simplify the expression, we can cancel out the common factor of j:

9/j * j/54 = (9/1 * 1/6) = 3/2

Therefore, 9/j * j/54 simplifies to 3/2.

B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,

(a/b) ÷ (c/d) = (a/b) x (d/c)

Using this rule, we can simplify the given expression as follows:

6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)

             = (6/8) x (4/3)  

             = 2/2

             = 1

Note that the volume   of the cuboid is approximately  1,974.08 cm³.

To find the volume of a cuboid,you need to multiply its length (L),   height (H), and width (W) together.

In this case, the length (L) is given as 19 cm, the height (H) is given as 4 cm, and the diagonal represents  the hypotenuse of a right-angled triangle formed by the length, height,and width of the cuboid.

Using the Pythagorean theorem, we can determine the width (W) of the cuboid  -

Width (W) = √(Diagonal² - Height²)

          = √(21² - 4²)

          = √(441 - 16)

          = √425

          ≈ 20.62 cm

Now that we have the values for L, H, and W, we can calculate the volume (V) of the cuboid  -

Volume (V) = Length (L) * Height (H) * Width (W)

            = 19 cm * 4 cm * 20.62 cm

            ≈ 1,974.08 cm³

Therefore, the volume of the cuboid is approximately 1,974.08 cm³.

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A centigram is 100 times larger than a milligram. So, the option b) 100 times is correct for this question.

1 centigram = 100 milligrams. A centigram is a unit of mass in the metric system, equivalent to one hundredth of a gram. A milligram, on the other hand, is a unit of mass in the metric system, equivalent to one thousandth of a gram. Therefore, a centigram is 100 times larger than a milligram. The conversion between the two units can be easily calculated as 1 centigram is equal to 100 milligrams. The use of centigrams is limited in common applications, with milligrams being the preferred unit for expressing very small masses, while grams and kilograms are used for larger masses.

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1) A Recursive formula refers always to the previous term.

2) In this Arithmetic Sequence, the common difference is 5, the first term is 12. So we can set the following Arithmetic Sequence:

Thus, this is the answer.

Answer:8755

Step-by-step explanation:100%+3%=103% in decimal form 1.03

8500x1.03=8755

Answer:

22.5% increase.

Step-by-step explanation:

Because her collection grows by 9, that means it increases by 9/40 total. As a decimal, this would be 0.225. Then, as a percent you multiply that by 100 to get 22.5%. Pilar's collection increased by 22.5%

Answer:

hahaha is

easy hmm..........

Answer:

x = 3

Step-by-step explanation:

First, distribute the -3 to each term in the parentheses. Now, you have

-6x + 24 = 2x. Add 6x to both sides, and now you have 24= 8x. Divide both sides by 8, and now you get x=3.

The required answer are k = 5/4 and k = -5/4.

To determine the values of k that make the function y = cos(kt) satisfy the differential equation 16y'' = -25y, we need to substitute y = cos(kt) into the differential equation and solve for k.

First,  find the second derivative of y = cos(kt). The first derivative is obtained by using the chain rule: y' = -ksin(kt), and the second derivative is y'' = -k^2cos(kt).

Now, substitute y = cos(kt) and y'' = -k^2cos(kt) into the differential equation 16y'' = -25y:

16(-k^2cos(kt)) = -25(cos(kt))

Simplify the equation:

-16k^2cos(kt) = -25cos(kt)

Divide both sides of the equation by cos(kt) to eliminate it:

-16k^2 = -25

Solve for k:

k^2 = 25/16

Taking the square root of both sides:

k = ±5/4

Therefore, the values of k that make the function y = cos(kt) satisfy the differential equation 16y'' = -25y are k = 5/4 and k = -5/4.

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Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

The equation of the line that passes through the points (-4, -3) and (7, 8) is:

y = x + 1

To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, which is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, let's find the slope (m) using the two given points: (-4, -3) and (7, 8).

The slope (m) is calculated as:

m = (y2 - y1) / (x2 - x1)

m = (8 - (-3)) / (7 - (-4))

m = (8 + 3) / (7 + 4)

m = 11 / 11

m = 1

Now that we have the slope (m), we can substitute one of the given points and the slope into the slope-intercept form to find the y-intercept (b).

Using the point (-4, -3):

-3 = (1)(-4) + b

-3 = -4 + b

b = -3 + 4

b = 1

Therefore, the equation of the line that passes through the points (-4, -3) and (7, 8) is:

y = x + 1

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Answer:

wrong

Step-by-step explanation:

The food truck sold 42 hamburgers and 56 hotdogs.

Let's use algebra to solve this problem. Let x be the number of hamburgers sold and y be the number of hotdogs sold. We can set up a system of equations based on the information given:

The ratio of hamburgers to hotdogs sold is 6:8, or simplified, 3:4:

x/y = 3/4

There were 14 more hotdogs sold than hamburgers:

y = x + 14

Now we can substitute the second equation into the first equation and solve for x:

x/(x+14) = 3/4

4x = 3(x+14)

4x = 3x + 42

x = 42

So 42 hamburgers were sold. We can use the second equation to find the number of hotdogs sold:

y = x + 14

y = 42 + 14

y = 56

So 56 hotdogs were sold. Therefore, the food truck sold 42 hamburgers and 56 hotdogs.

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Answer:

r = 5.6

Step-by-step explanation:

To solve this problem, we need to isolate r on one side of the equation. To do this, we need to subtract 2.3 from both sides, giving us:

2.3 + r = 7.9

r = 5.6

So, r = 5.6

Hope this helped!

Answer:

5.6

Step-by-step explanation:

2.3+r=7.9

r=7.9-2.3

r=5.6

Answer:

x= -7

Step-by-step explanation:

f(x) = -5(x+7)

0 = -5x -35

5x = -35

equals to x= -7

Answer:

a) 28

b) D

Step-by-step explanation:

a) As you can see from the diagram, in a 60-30 right triangle, the side adjacent to the 60° angle is half of the hypotenuse.

14*2=28

b) If you remember your SohCahToa, then you'll know that your trigonometric functions are:

\(sin = \frac{opp}{hyp}\\cos = \frac{adj}{hyp}\\tan = \frac{sin}{cos}\)

Now we can check each one to find the incorrect ratio:

\(sin (30^o)=\frac{4}{8}=\frac{4}{8}\\cos(60^o)=\frac{4}{8}=\frac{4}{8}\\sin(60^o)=\frac{\sqrt{48}}{8}=\frac{\sqrt{48}}{8}\\tan(30^o)=\frac{4}{\sqrt{48}}\neq \frac{\sqrt{48}}{8}\)

Answer:

∠BFC: 94 degrees

Step-by-step explanation:

∠AFB: 86 degrees

to make up a straight line you need all angles to add up to 180 degrees

180 - 86 = 94

hope this helps!   :- )

Answer:

the answer is 12

Step-by-step explanation:

I had this work sheat and got the answer from the teacher

For the volume of the prism is 1,632 cubic feet, the height of the prism is,

⇒ H = 12 feet

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

.

Given that;

The base of a rectangular prism has dimensions measuring 8 feet by 17 feet.

And, the volume of the prism is 1,632 cubic feet.

Now, We know that;

Volume of prism = B x H

Where, B is base area and H is height.

Hence, We get;

Volume of prism = B x H

1632 = 8 x 17 x H

1632 = 136 H

H =1632 / 136

H = 12 feet

Thus, For the volume of the prism is 1,632 cubic feet, the height of the prism is,

⇒ H = 12 feet

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The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

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