A cruise line ship left port A and traveled 80 miles due west and then 150 miles due north at this point what is the shortest distance from the cruise to port A in miles

The measure of the side length CL is equal to 9m using trigonometric ratio of cosine 60° for thy right triangle ACL

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Angle m∠BAC = 180° - (m∠C + m∠ABC)

m∠BAC = 180° - (90° + 30°)

m∠BAC = 60°

line AL is an angle bisector so;

m∠CAL = 30° and m∠BAL = 30°

which implies triangle ∆ALB is an isosceles with line LB = AL = 18m

considering the right triangle ∆ACL;

angle m∠L = 180° - (90° + 30°)

m∠L = 60°

cos 60° = CL/18 {adjacent/hypotenuse}

1/2 = CL/18m {cos 60° = 1/2}

CL = 18m/2 {cross multiplication}

CL = 9m

Therefore, the side length CL is equal to 9m using trigonometric ratio of cosine 60° for the right triangle ACL.

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Tasha has the highest batting average because 0.9(27/30) is greater than 0.8( 24/30 ) ( optionD)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The batting average for Jana is 12/15 = 0.8

The battling average for Tasha is 9/10 = 0.9

The battling average of Tasha is higher than that of Jana

0.6 can also be in form of 6/10

0.9 can also be in form of 9/10

therefore 8/10 = 24/30 and

9/10 = 27/30

Therefore Tasha has the highest batting average because 27/30 is greater than 24/30

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Answer:

27/30

Step-by-step explanation:

1. Maximum height of the Function H(t) = -12cos( πt/45 ) + 18   is  30 units.

2. For the given sinusoidal function the values of the following are as follow :

amplitude = 6ft, period = π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

Function with height 'H' is given by:

H(t) = -12cos( πt/45 ) + 18

Here 't' represents the time in seconds.

As we know that range of cosine trigonometric function is ,

-1 ≤ cosα ≤ 1

This implies cos function lies between  -1 and 1.

Replace cos( πt/45 ) by 1 or -1

For cos( πt/45 ) = 1

H(t) = -12(1) + 18

      = 6 units

For cos( πt/45 ) = -1

H(t) = -12(-1) + 18

      = 30 units

Maximum height is equals to 30 units.

Therefore, function H(t) = -12cos( πt/45 ) + 18  representing maximum height is equal to 30 units.

2. In general sinusoidal function is given by :

   y = Asin(Bx + C) + D

A is amplitude

A = High tide - low tide

   = 9 - 3 /2

   = 3ft

Time = 12:30 p.m.  - 6: 39 a.m.

        = 6 : 09 minutes

         = 6hours(approximately)

period B = 2π /T

              = 2π/6

              = π/3

Vertical shift = 9 - 3

                     = 6

Equation of the midline is

y = c

⇒ y = 6

Function is y = 3sin (π/3)x + 6

Maximum sin (π/3)x = 1

y = 9

Minimum sin (π/3)x = -1

⇒ y = 3

Therefore, the values of the following for the given function is :

amplitude = 6ft, period =  π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

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Answer: A. The distance across the lake is 626.6 m.

              B. The lake is not long enough Additional 123.4m distance will need to be set off.

Step-by-step explanation:

Note that the median in the data set given above is: 38.5.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in data collection.

Not that in the above case, the median is arrived at by finding adding the two central values (37 and 40) and dividing the result by 2. This is because the total number of data in the set is even. Where the total number of values is odd, then the central number, when the avalues are arranged in ascending order is the median.

Thus, median = 37 + 40

= 77/2

Median = 38.5

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The largest possible value for the probability of A4 is 0.1.

From the question, we have the following parameters that can be used in our computation:

A1, A2, A3, and A4, be events from a common sample space.

We know that A1 and A2 occur simultaneously with a probability of 0.1, which means that the probability of A1 or A2 occurring is 0.3

We also know that events A1, A2, and A3 each occur with probability 0.3.

So, the probability of A4 occurring is equal to 1 minus the probability of the other three events occurring.

Therefore, the largest possible value for the probability of A4 is:

P(A4) = 1 - (0.3 + 0.3 + 0.3)

P(A4) = 1 - 0.9

P(A4) = 0.1

So, the maximum value that the probability of A4 can take is 0.1.

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Answer:

22%

Step-by-step explanation:

[tex]\frac{11}{50}[/tex]  times 100% = 22%

The three lowest values of x are 30, 31 and 32.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

The statement "x is a whole number if three quarters of x is subtracted from 62. the result is less than 40" can be written as:

62 - (3/4)x < 40

- (3/4)x < 40 - 62

-3x/4 < -22

-3x < -22 × 4

-3x < -88

x > -88/-3

x > 29.33

Since x > 29.33 and x is a whole number, the three lowest values of x are 30, 31 and 32.

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Statement "B. the median is a negative number" will be correct among these options.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  that A set of data contains 10 negative numbers and 4 positive numbers.

Since the value of data is not given it can be any positive or negative numbers

mode:

A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.

Range:

When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.

Median:

The median is the value that's exactly in the middle of a dataset when it is ordered.

Thus, the Median will be negative.

Therefore, Statement "B. the median is a negative number" will be true among these options.

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Complete question:

A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?

A. The mean is a negative number.

B. The median is a negative number.

C. The mode is a negative number.

D. The range is a negative number.

Answer: 1/6

Step-by-step explanation:

2/6 - 1/6 = 1/6

According to the area the amount needed to cover the lawn with grass seed is £121.8075

In math the term called area is defined as the total space occupied by the object.

Here we have know that the Length is 100m and the Breadth is 45m :-

Then the area is calculated as,

=> A = 100 × 45 = 4500m²

Here we have to do the calculation for 3 circular pond, then it can be calculated as,

=> 1st pond = 20/2 = 10m

=> 2nd pond = 10/2 = 5m

=> 3rd pond = 5/2 = 2.5m

Then the Area of 3 circular pond is calculated as,

=> A =  (π × 10² + π × 5² + π × 2.5²)

Take the term π as common then we get,

=> A = π × ( 100 + 25 + 6.25)

Apply the value of π = 22/7, then we get,

=> A =  22/7 × (125 + 6.25)

When we simplify this one then we get

=> A = 22/7 × 131.25 = 2887.5/7

Therefore the area of the pond is  412.5m²

Now we need to do the calculation for required area for covering lawn, that can be written as

=> Required area = Area of lawn - Area of 3 circular ponds

Apply the value on it,

=> Required area = 4500 - 412.5 = 4087.5m²

As we know that packet of grass seed covers 50m, then it is simplified as,

=> Required Area = 4087.5/50 = 81.75m²

Now we need to do the calculation for cost of covering lawn is written as

=> Total cost = 81.75 × 1.49 = £121.8075

Therefore the cost of covering lawn with grass seed is £121.8075

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The y-intercept of the equation of line  y = (7/9)x + 2/3 is 2/3.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question;

y = 7/9 x + 2/3

Simplify the right hand side

y = (7/9)x + 2/3

Using the slope-intercept form, the y-intercept is 2/3.

Therefore, the y-intercept in point form is (0,2/3).

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Answer:

1.5 cups of sugar

Step-by-step explanation:

Given:

-You need a 1/4 cup of sugar for 3 cups of Kool-Aid

-You need to find the amount of sugar you need for 18 cups of liquid

Solution:

You need to find how many recipes you need

3x = 18

So x = 6

Now you need to multiply 1/4 by 6 to find the amount of sugar

That would be 6/4 which is 1.5

So you need 1.5 cups of sugar for 18 cups of Kool-Aid

The measure of an exterior angle at the fifth vertex is 62°.

A pentagon has 5 straight sides. The shape must also be closed.

A convex pentagon has no angles pointing inwards, and no internal angles can be more than 180°.

When all angles are equal and all sides are equal it is regular, otherwise, it is irregular.

The sum of exterior angles is 360°.

To know the angle of the fifth vertex add the remaining four vertexes and subtract from the sum of exterior angles.

Given 4 vertexes of the pentagon are 83°, 83°, 26°, and 46°.

By adding these we get a total of 238°

Fifth vertex=360°-238°

Fifth vertex=62°

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Answer:

4x(÷4)=36(÷4)

x=9

I hope I help you in this ans and tq.

Answer: 9

Step-by-step explanation: Because the problem is 36=4x the X next to the 4 means to multiply BUT since we don't no the answer there are many ways to solve this one way is to find what you can multiply for with or you can divide 36 and 4.

Hope fully that helps!!!

109 dollars Martin have saved before he bought the drone .

Using the conditions stated, come up with: x -68 = 41

Put the variables on the equation's left side: x = 41 + 68

Determine the difference or total: x = 109

Savings are the funds that remain after subtracting one's obligations. Cash is stored as a sort of savings.

Savings are unused funds or postponed spending. A deposit account, a pension account, an investment fund, or cash are just a few examples of ways to save money. Reducing expenses, such as recurrent fees, is a part of saving as well. The portion of money left over after paying for current expenses is what is saved. In other words, it refers to money that has been set away for use later on rather than being immediately spent. Saving enhances emotions of security and tranquilly by acting as a financial "backstop" for life's unforeseen events.

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To determine the submarine's depth, you would need to use trigonometry. The angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) form a right triangle.

You can use the tangent function (tan) to find the opposite side (depth) of the triangle, given the adjacent side (distance) and the angle.

Depth = distance * tan(angle of depression)

Depth = 500 meters * tan(40 degrees)

You can use a calculator or table to find the value of tan(40 degrees), which is approximately 0.8391.

Depth = 500 meters * 0.8391

Depth = 419.55 meters

So the submarine's depth is 419.55 meters deep.

Right triangles can be used to represent word problems involving angles of elevation and depression. When working right triangles, the trigonometric rates are used to break for the right triangle's sides and angles representing the problem.

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For the angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) the submarine's depth will be 419.55 meters

Right triangles can be used to express word problems with elevation and depression angles. When working with right triangles, trigonometric rates are employed to break for the sides and angles of the right triangle that represent the problem.

Trigonometry would be required to estimate the depth of the submarine.

Given the neighbouring side (distance) and the angle, you can use the tangent function (tan) to get the opposite side (depth) of the triangle.

Depth = distance multiplied by tan (angle of depression)

500 metre depth * tan (40 degrees)

You may determine the value of tan(40 degrees) using a calculator or a table, which is about 0.8391.

So, the value of the depth = 500 meters * 0.8391

Depth = 419.55 meters

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The domain of the function is all real numbers while the range of the function is also all real numbers.

The domain of the function t(n) = 2x + 1 is all real numbers, since there are no restrictions on the input value of x. The range of the function is also all real numbers, since adding 1 to any real number will also result in a real number. So the domain is (-infinity, infinity) and the range is (-infinity, infinity)

We have to note that in the event that we have a function such as t(n) = 2x+1, x is free to take any of the values on the real number line and this would return a value for t(n).

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An expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.

Expression

An expression refers to a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Note: -  x represents the number of tiles in a box.

A- For Bruce,

we have,

Expression = 3x + 2x + 2

Expression = 5x + 2.

For Felicia,

we have,

Expression = 5x + 5.

so, the expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.

B- no, there is no solution for X as the equations are not equal to each   other.

5x +2 = 5x + 5 (subtract 5x and 2 on both sides)

0 = 3 No solution

C-  We can conclude that someone used more tiles then the other because both equations are not equal.

D- Have 2 or 5 change because they need to be equal to each other. Its fine what you put as long as the equal sign is the same as the other side like 3 = 3 for example or 5 = 5, something like that. Once they have the same end then you can substitute the number to x.

x represents the number of tiles they used.

E- yes.

6x +2 =5x +17

6x - 5x =17 - 2

x =15

unique solution

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The resultant of the given expression after simplification is (x^2 - 12x - 8xi + 52).

In order to simplify the expression [x-(6+4i)][x-(6x4i)], we must first expand it by using the distributive property.

The first term of the first factor would be x*x = x^2,

The second term would be x*-(6-4i) = -6x - 4xi

The third term would be -(6+4i)x= -6x - 4xi.

The last term would be -(6+4i)*-(6-4i) = 6^2 - (4i)^2 = 36 + 16 = 52

Next, we would combine like terms by adding,

x^2 - 6x - 4xi - 6x - 4xi + 52 = x^2 - 12x - 8xi + 52

This would give us an expression of x^2 - 12x - 8xi + 52. This expression can't be simplified any further as it contains complex numbers.

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The factor of the given quadratic equation is (4x + 3). Option C is correct.

One way to describe the polynomial as a product of its linear parts is to factor the quadratic equation. We may use this method to locate the roots of quadratic expressions, simplify them, and solve equations.

The formula for a quadratic polynomial usually takes the form ax² + bx + c, where a, b, and c are real values. We can obtain the zeros of the quadratic equation ax² + bx + c = 0 by factoring quadratics.

Given that:

4x² + 23x + 15 = 0

By applying the distributive property, we have:

4x² + 20x + 3x + 15 = 0

Factor out the greatest common factor for each group

(4x² + 3x) + 20x + 15

x(4x + 3) + 5(4x + 3)

Factor the polynomial by factoring out the greatest common factor. 4x + 3, then we have:

(4x + 3) (x + 5)

Therefore, we can conclude that one of the factors of the quadratic expression is (4x + 3).

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Answer:

13F

Step-by-step explanation:

-15+28

Answer:

[tex]\displaystyle \frac{1}{10}(x+9)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{10}x+\frac{9}{10}=\frac{1}{10}(x+9)[/tex] because [tex]\displaystyle \frac{1}{10}(x+9)=\frac{1}{10}(x)+\frac{1}{10}(9)[/tex] by the Distributive Property

Answer:

Have a Nice Day :  ) if Incorrect sorry .

The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.

In the next 8 seconds, the ball will drop 320 meters. This can be calculated by using the equation [tex]d = (t^2) * k[/tex], where d is the distance (in meters) dropped, t is the time (in seconds), and k is a constant. Since the ball dropped 80 meters in the first 4 seconds, we have d = (4^2) * k, or k = (d/16). Plugging this value of k into the equation, we get d = (t^2) * (d/16), which simplifies to d = (t^2) * (80/16). In the next 8 seconds, t = 8, so d = (8^2) * (80/16) = 320 meters.

The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.

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If the initial position s(0) = -5 and initial velocity v(0) = -2, the position function of the object is -8cost + t^3/3 - 2t + 3. So the option D is correct.

We have to determine the position function of the object.

An object moves along a straight line with acceleration a(t) = 8cost + 2t.

Initial position s(0) = -5

Initial velocity v(0) = -2

Integration of a(t) given us s(t)

[tex]\int a(t)dt = \int (8cost + 2t) dt[/tex]

v(t) = 8sint + 2t^2/2 + C

v(t) = 8sint + t^2 + C

At v(0) = -2

v(0) = 8sin(0) + (0)^2 + C

-2 = 8 × 0 + 0 + C

C = -2

v(t) = 8sint + t^2 - 2

The integration of v(t) gives us s(t)

[tex]\int v(t)dt = \int (8sint + t^2 - 2)dt[/tex]

s(t) = -8cost + t^3/3 - 2t + D

At s(0) = -5

s(0) = -8cos(0) + (0)^3/3 - 2(0) + D

-5 = -8 × 1 + 0 - 0 + D

-5 = -8 + D

Add 8 on both side, we get

D = 3

s(t) = -8cost + t^3/3 - 2t + 3

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Answer: The best value for the cat food, milk and toys is Supermarket C. They are offering the 5 kg bag of cat food for $400 each/3 bags for $1,080, 1 litre of milk for $1100, and cat toys for $1799. Supermarket A is offering the 5 kg bag of cat food for $400 each/3 bags for $1,100, 1 litre of milk for $1,900, and cat toys for $1,900. Supermarket B is offering the 5 kg bag of cat food for $600 each/3 bags for $1,660, 1 litre of milk for $1,099, and cat toys for $2,300. Supermarket C has the lowest prices for all three items, so it is the best value.

Step-by-step explanation:

The amount of glass needed to cover a table measuring 0.8m long and 0.65m wide is (d) 0.52m²

from the question, we have the following parameters that can be used in our computation:

Length = 0.8 m

Width = 0.65 m

The area of a rectangle can be calculated using tge following equation

Area = Length * Width

substitute the known values in the above equation, so, we have the following representation

Area = 0.8 * 0.65

Evaluate

Area = 0.52

Hence, the amount is 0.52 square meters

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Answer:

13.9 miles

Step-by-step explanation:

We know

A group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream. How far did they walk altogether

8 7/10 = 87/10

5 1/5 = 26/5

87/10 + 26/5 = 87/10 + 52/10 = 139/10 = 13.9 miles

So, they walked 13.9 miles.

Answer:

yidyf

Step-by-step explanation:

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