Here are some facts about units of length.
Unit
Symbol
Fact
inch
foot
ft
1 ft = 12 in
yard
yd
1 yd = 3 ft
Fill in the blanks.
3 ft =
in
8 yd =

i) the original distance when the lighthouse is due West of the ship is 7 km

ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes

iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km

To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:

i) Finding the original distance when the lighthouse is due West of the ship:

The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.

To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:

Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).

ii) Finding the time in minutes when the lighthouse is due West of the ship:

To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:

Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).

To find the time, we can use the formula:

Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).

iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:

We can use the formula for relative velocity to find the distance:

Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)

Using the values we calculated earlier, we have:

Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).

Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.

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Answer:

1) 600

2) 2460

3) 216

4) 360

if this is wrong please tell me so I can’t edit this and tell you the correct answer

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The original number is 13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 4 is an equation.

We have,

Let the number be K.

K thinks of a number, then doubles the number, and then multiplies the result by 3.

This can be written as:

(2 x k) = 2k ____(1)

3 x (2k) = 6k ____(2)

If her final number is 65 more than her original number can be written as:

6k = 65 + k _____(3)

From (3) we get,

6k = 65 + k

Subtract k on both sides.

6k - k = 65 + k - k

5k = 65

Divide both sides by 5.

5k / 5 = 65 / 5

k = 13

Thus,

The original number is 13.

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1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

Answer:

Step-by-step explanation:

If a shape is scaled by a certain scale factor then :

the area of the new shape =  (the scale factor) times (the area of the original object)

………………………

the new recreation complex was created by enlarging the old community soccer field by a scale factor of 9

Then

The area of the new recreation complex = 9² × 600 = 81×600 = 48 600 yd²

Answer:

x = 4

Step-by-step explanation:

-5/6x = -10/3

x = -10/3 / -5/6

x = 4

Topic: algebraic equations

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...

Answer:

w = 24 ft.

l = 30 ft.

Step-by-step explanation:

The formula for perimeter is P = 2l + 2w, where l is the length and w is the width.

Since the length is 6 ft longer than the width, our formula for length is l = w + 6

We can leave length in terms of width and plug it into the perimeter:

\(108=2(w+6)+2w\\108=2w+12+2w\\108=4w+12\\96=4w\\w=24\)

Now that we've found the width, we can find the width using the second formula:

\(l=24+6\\l=30\)

Answer:

The sum of the real number (a) and its opposite real number (-a) is zero

Step-by-step explanation:

5 + (-5) = 0 and (-5) + 5 = 0

or, 5 - 5 = 0 and -5 + 5 = 0

Here 5 is real number and (-5) is it's opposite real number. Sum of 5 and (-5) is zero.

Answer:115 R 11

= 115 11/20

2311 divided by 20 equals

115 with a remainder of 11

Step-by-step explanation:

The solution after divide is, 115 with remainder = 11

We have to given that,

⇒ 2311 divided by 20

Now, We can divide the numbers as,

20 ) 2311 ( 115

      - 20

------------------

          31

         - 20

         --------

            111

            100

           ----------

               11

Therefore, The solution is, 115 with remainder = 11

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Correct question is,

Find the value of 2311 divided by 20 with a reminder?

Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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The length of the rectangular shaped parking lot will be: 246 yards.

A rectangular shape has a width and a length. The perimeter of the rectangular shape is simply the sum of all its width and its length. The formula for the perimeter of the rectangular shape would therefore be:

Perimeter = 2(length + width).

Given the following:

Perimeter of the rectangular shaped parking lot = 656 yards

Width of the rectangular shaped parking lot = 82 yards

Length = x = ?

Plug in the values into the perimeter formula for a rectangular shape:

2(x + 82) = 656

Divide both sides by 2

2(x + 82)/2 = 656/2

x + 82 = 328

x + 82 - 82 = 328 - 82

x = 246

Length would need to be 246 yards.

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Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

if the total is 140 then you subtract the full value which is 40 then you have 100=2x

simply divide 100 by 2

the answer is 50

Answer:

it will be 50 hope this helps:)

Determine the slope of line passes through point (0,-5) and (-5,0).

First option is wrong.

Determine the slope for the line passes throght point (0,10) and (2,0).

Second option is wrong.

Determine the slope of line passes through point (0,-10) and (2,0).

So option 3 is correct

Answer is (0,-10) and (2,0).

Answer:

x=13/5

Step-by-step explanation:

The correct matches are: 4 in. → 10.2 cm   ,   7 kg → 15.4 lb

6 gal → 22.7 L   and  65 ft → 19.8 m.

Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.

For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.

Here are the conversions:

1 inch = 2.54 cm (approx.)

1 kg = 2.205 lb (approx.)

1 gal = 3.785 L (approx.)

1 ft = 0.3048 m (approx.)

Using these conversions, we can find the equivalent measures:

4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm

7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb

6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L

65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m

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Answer:

\(-\frac{28}{99}\)

Step-by-step explanation:

To divide a fraction by a fraction, flip the second fraction and change the divide sign into a multiplication sign.

\(\frac{4}{9}\div -\left(\frac{11}{7}\right)=\frac{4}{9} *-\frac{7}{11}\)

Multiply:

\(-\frac{4*7}{9*11}\)

\(-\frac{28}{99}\)

Answer:

The mean is 17.091

Step-by-step explanation:

The equation of the oscillating circle of the curve y = ¹/₄ x² +2 at point (2,1) is (x - 5/2)² + (y - 1)² = 1/4.

To find the equation of the oscillating circle of the curve y = ¹/₄ x² +2 at point (2,1), we need to follow these steps:

Find the first and second derivatives of the given curve:

y = ¹/₄ x² + 2

y' = ¹/₂ x

y'' = ¹/₂

Use the first and second derivatives to find the equation of the tangent line to the curve at point (2,1):

y - 1 = 1/2(x - 2)

y = 1/2 x + 0.5

Find the perpendicular bisector of the tangent line at point (2,1):

The slope of the tangent line is 1/2, so the slope of the perpendicular bisector is -2.

y - 1 = -2(x - 2)

y = -2x + 5

Find the intersection of the perpendicular bisector with the x-axis:

When y = 0, -2x + 5 = 0, so x = 5/2.

Find the center of the oscillating circle:

The center of the oscillating circle is (5/2,1).

Find the radius of the oscillating circle:

The radius of the oscillating circle is the distance between the center and the point of tangency, which is:

r = √[(2 - 5/2)² + (1 - 1)²]

r = [1/4 + 0] = 1/2.

Write the equation of the oscillating circle in standard form:

The equation of the oscillating circle is:

(x - 5/2)² + (y - 1)² = (1/2)².

Simplifying, we get:

(x - 5/2)² + (y - 1)² = 1/4.

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The complete question is below:

Find the equation of oscillating circle of curve y=1/4 x^2 +2 at (2,1)

Answer:

integrates by parts:

             U = x   dV = f''

            dU  = dx   V = f'

The integral becomes:

     x f'  - integral f' dx

 =   x  f'  -  f

limit as x->4 :   4 * f'(4) - f(4) = 4 * -3 -  7

                                  = -12-7 = -19

limit as x->1 : 1 * f'(1) - f(1) = 1 * 9 - 8 = 1

subtracting: -19-1 = -20

Step-by-step explanation:

Answer:

Dilacey took a loan of $2800

Step-by-step explanation:

P=(Simple Interest×100)/R×T

P=$420×100/10×1½

P=$42000/15

P=$2800

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

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

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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Answer:

90

Step-by-step explanation:

Since the sum of a circle is 360, just divide 360 and 1/4.

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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Answer:

its B

Step-by-step explanation:

The standard form of the expression (8x²- 3x + 3)+ (3x²- 3x + 4) - (6x² + 7)  is 5x² - 6x.

The Standard Form for writing down a polynomial is to put the terms with the highest degree.

The expression or polynomial in standard form can be represented as follows:

(8x²- 3x + 3)+ (3x²- 3x + 4) - (6x² + 7) = 8x² - 3x + 3 + 3x² - 3x + 4 - 6x² - 7

combine like terms

8x² - 3x + 3 + 3x² - 3x + 4 - 6x² - 7 = 8x² + 3x² - 6x² - 3x - 3x + 3 + 4 - 7

8x² + 3x² - 6x² - 3x - 3x + 3 + 4 - 7 = 11x² - 6x² - 6x  = 5x² - 6x

Therefore, the standard form of the expression (8x²- 3x + 3)+ (3x²- 3x + 4) - (6x² + 7)  is 5x² - 6x.

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Answer:

3×+9=5x-5

-2×=-14

×=7...thenCD=3(7)+9=30

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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