The lighthouse and the boat shown below
are 24.6 km apart.
The boat is 13.5 km east of the lighthouse.
Work out the bearing of the lighthouse from
the boat.
Give your answer to the nearest degree.
|FFFFLD
Lighthouse
N
Boat
Not drawn accurately

Answer:

4/15

Step-by-step explanation:

Lets find a common denominator in order to find the total amount. There is a common denominator of 15 among 3 and 5. Therefore we will convert the fraction so they have the same denominator.

1/3 > 5/15

2/5 > 6/15

If Joy had read 5/15 of the book before reading at night, she already had the progress of being at 10/15 way through the book. At the end of the day, Joy had only 6/15 left of the book. To find the remainder, we subtract 10-6=4. This helps find the answer that Joy only read 4/15 of the book towards the end of the day.

Recall that the area of a trapezoid is equal to the average of its bases times its height.

For the trapezoids shown here, each base corresponds to the value of [tex]y=2x^2[/tex] when [tex]x[/tex] is one of the endpoints of some interval, while the height is the length of that interval.

On the interval [-2, -1], the trapezoids has bases 2(-2)² = 8 and 2(-1)² = 2, and "height" -1 - (-2) = 1. Then its area is (8 + 2)/2 × 1 = 5.

On the interval [-1, 0], one of the bases is 2(-1)² = 2 and the other is 2(0)² = 0, and the height is again 0 - (-1) = 1. Then the trapezoid's/triangle's area is (2 + 0)/2 × 1 = 1.

Then the total area under the curve [tex]y=2x^2[/tex] on the interval [-2, 0] is approximately 5 + 1 = 6.

Compare this to the actual value of the area given by the definite integral,

[tex]\displaystyle \int_{-2}^0 2x^2 \, dx = \frac{16}3 \approx 5.333\ldots[/tex]

Answer:

[tex]x=\frac{35}{9} .[/tex]

Step-by-step explanation:

[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]

Step-by-step explanation:

Since [tex]cos(\theta) = -\frac{3}{4}[/tex] we can get some information from this. First of all [tex]cos(\theta)[/tex] is defined as [tex]\frac{adjacent}{hypotenuse}[/tex]. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find [tex]sin(\theta)[/tex] to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive

Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

[tex](-3)^2 + b^2 = 4^2[/tex]

[tex]9 + b^2 = 16[/tex]

[tex]b^2 = 7[/tex]

[tex]b = \sqrt{7}[/tex]

So now we can calculate [tex]sin(\theta)[/tex].

[tex]sin(\theta) = \frac{\sqrt{7}}{4}[/tex]

Now to calculate the exact value of csc you simply take the inverse. This gives you [tex]csc(\theta)=\frac{4}{\sqrt{7}}[/tex]. Multiplying both sides by sqrt(7) to rational the denominator gives you [tex]\frac{4\sqrt7}{7}[/tex].

Now to calculate cot(theta) you  find the inverse of tan. Tan is defined as [tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)}[/tex]. So all you do is take the inverse which is [tex]cot(\theta) = \frac{cos(\theta)}{sin(\theta)}[/tex].

Plug values in

[tex]cot(\theta) = \frac{-\frac{3}{4}}{\frac{4\sqrt{7}}{7}}[/tex]

Keep, change, flip

[tex]-\frac{3}{4} * \frac{7}{4\sqrt7}[/tex]

Multiply:

[tex]-\frac{21}{16\sqrt7}[/tex]

Multiply both sides by sqrt(7)

[tex]-\frac{21\sqrt7}{112}[/tex]

This is the value of cot(theta)

Answer:

y = sin3x

Step-by-step explanation:

the equation is of the form y = sinbx

the period of the sine wave is

period = [tex]\frac{2\pi }{b}[/tex] ( b is the coefficient of x )

here period = [tex]\frac{\pi }{3}[/tex] × 2 = [tex]\frac{2\pi }{3}[/tex] , then

[tex]\frac{2\pi }{3}[/tex] = [tex]\frac{2\pi }{b}[/tex] ⇒ b = 3

y = sin3x ← equation of graph

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Explanation } }:}[/tex]

" when rays parallel to optical axis/ principal axis fall on a concave mirror it passes through focus of mirror after reflection "

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

71.4%

Step-by-step explanation:

7+3+8+3=21 total fish

7+8=15 healthy fish

15÷21=0.7142=71.4%

Answer:

10 cm

Step-by-step explanation:

Hyp = [tex]\sqrt{6^{2}+8^{2} } =\sqrt{36+64} =\sqrt{100} =10[/tex]

Hope this helps

The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

The y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero

Given the function below;

-4x + 7y = 3

For the x-intercept

-4x = 3

x = -3/4

The x-intercept is (-3/4, 0)

For the y-intercept

7y = 3

y = 3/7

The y-intercept is (0, 7/3)

Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

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Without having to raise funds externally sales could increase by $84,507.04.

Given that $4 million sales in 2021 and in end of the year total assets are $3.2, current liabilities are $500,000, payable notes are $200,000, accounts payable is $200,000 and accrued liabilities are $100,000 and in 2022 assets must increase by $.80 for every $1.00 increase in sales.

The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.

Current Year Sales = $4,000,000

Profit Margin = 3.00%

Dividend Payout Ratio = 50%

Therefore, the Retention Ratio = 50%

Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000

Last Year Total Assets = $3,200,000

Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]

= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]

= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]

= $60,000÷[$3,200,000-$300,000-$60,000]

= $80,000÷$2,840,000

= 0.02112676 or 2.112676%

Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate

= $4,000,000×2.112676%

= $84,507.04

Hence, the Increase in Sales so the company achieve without having to raise funds externally $84,507.04”

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Answer:

11:16

Step-by-step explanation:

The area of the farm that is too rough to use is 157.86

An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.

Let the total area of the farm be x.

Area of the farm, too rough to use=x/4

Area of farm kept for poultry farms=2x/5

Remaining Area=221

Thus,

[tex]x-(\frac{x}{4}+\frac{2}{5}x)=221[/tex]

[tex]\\ x-\frac{13}{20}x=221\\[/tex]

[tex]\frac{7}{20}x=221\\[/tex]

x=631.43

Area of the farm too rough to use= 631.43/4

                                                        =157.86

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Answer:

About 56%

Step-by-step explanation:

The  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

The given diagram shows two intersecting lines tangential to a circle at points A and C.

Using the theorem that states, the measure of the angle at the vertex is equal to the half of the difference of the measure of the intercepted arcs.

Mathematically;

<B = 1/2(arcADC - arcAC)

58 = 1/2(238 -x)

Hence the  equation that could be solved to find x, the measure of AC is 58 = 1/2(238 -x)

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Step-by-step explanation:

x = 145°

we don't even need the upper parallel line with the 35° angle.

it is simply based on the fact that the angles on both sides of 2 intersecting lines have to be the same (just left-right mirrored).

The graph of the given quadratic function is shown below

From the question, we are to graph the given quadratic function.

The given quadratic equation is

y = −x² −8x −7

The graph of the given quadratic function is shown below

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Step-by-step explanation:

310/100 × 72

= 223.2

using fraction × total

hope you understand.

pls like and follow :-):-)

Answer:

a

Step-by-step explanation:

y = 3x - 7 → (1)

4x - 5y = - 20 → (2)

substitute y = 3x - 7 into (2)

4x - 5(3x - 7) = - 20

4x - 15x + 35 = - 20

- 11x + 35 = - 20 ( subtract 35 from both sides )

- 11x = - 55 ( divide both sides by - 11 )

x = 5

substitute x = 5 into (1)

y = 3(5) - 7 = 15 - 7 = 8

solution is (5, 8 )

Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.

When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.

In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:

p = 10/20 = 0.5 x 100% = 50th percentile.

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Answer:

The bottom graph

Step-by-step explanation:

It shows that the kid starts 4 meters away and slowly decreases the distance for 8 seconds, pauses for 3, and moves back for 4.

Answer:

the 4th answer option

Step-by-step explanation:

the first one is looking good too, but the difference is to start at 4 meters away.

and the first graph starts at 9 meets away.

so, it is the 4th graph :

starting 4 meters away the person is coming slowly closer and closer for 8 seconds, then stands still for 3 seconds, and then walks away quickly for 4 seconds.

remember, the passing time is on the x-axis moving to the right (bigger and bigger numbers).

while the distance to the person is on the y-axis. and that value can get bigger and smaller.

The loan amount is given as $76521

We first have to calculate the total amount of tuition

6970 x 4 + 11320 x 4

= 73160

[tex]73160 (1+\frac{\frac{4.5}{100} }{12} )^1^2[/tex]

= 73160 x (1 + 0.00375)¹²

= 76520.95

Hence the new loan amount after  agrace period of 1 year = $76521

b. PV = $76521

i = [tex]\frac{4.5/100}{12}[/tex]

= 0.00375

t = 10 years

[tex]PMT[\frac{1-(1+0.00375)^-^1^2^0}{0.0375} ]= 76521[/tex]

pmt = 793. 05

The monthly payment is  $793. 05.

In ten years the total payment is 793.05 x 10 x 12

= 95166

Difference = 95166 - 76521

= $18645

In ten years her ,monthly payment on the loan would be  $18645.

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The length of the other skating surface AD of the ramp is 4√2 inches

An equation is an expression that shows the relationship between two or more numbers and variables.

Sine rule shows the relationship between the sides and angles of a triangle.

Using sine rule:

AB / sinD = AD / sinB

4/sin(30) = AD / sin(45)

AD = 4√2 inches

The length of the other skating surface AD of the ramp is 4√2 inches

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(C.) 4√2

________

I got it wrong, the correct answer was revealed <3

The component of mathematics fluency is most likely the goal of this type of assessment is Rate.

GIven,

A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems.

The component of mathematics fluency is most likely the goal of this type of assessment is Rate.

The school district is assessing the rate because they are seeing how many questions students can answer in a given time frame.

Hence, The component of mathematics fluency is most likely the goal of this type of assessment is Rate.

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Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

Answer:

Double-displacement reaction

Step-by-step explanation:

In double-displacement reaction, aka. double-replacement reaction, the cation of one compound is swapped with the cation of another. They have the general structure:

AB + CD ---> AD + CB

In this case, the silver cation (Ag⁺) from AgNO₃ is swapped with the hydrogen cation (H⁺) of HCl.

The complete balanced equation is:

HCl + AgNO₃ ---> AgCl + HNO₃

Since Jane wants to buys some lollipops, Jane has $13 dollars.

To answer the question, we need to solve simultaneous equations

Simultaneous equations are pairs of equations that contain two unknowns

Let

We know that If she buys 2 lollipops, she will have 3 dollars left, so we have that

y - 2x = 3  (1)

Also, If she wants to buy 3 lollipops, she will need 2 more dollars. So, we have that

y + 2 = 3x  (2)

So, the required simultaneous equations are

y - 2x = 3  (1)

y + 2 = 3x  (2)

From (1), x = (y - 3)/2

Substituting x into (2), we have

y + 2 = 3x  (2)

y + 2 = 3(y - 3)/2  

2(y + 2) = 3(y - 3)

2y + 4 = 3y - 9

2y - 3y = -9 - 4

-y = -13

y = -13/-1

y = 13

So, Jane has $13 dollars.

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Answer:

about 1920

step by step explanation:

40×50weeks=2000hours per year.

40×2weeks(the weeks off) = 80

2000-80= 1920hours per year

The value of the median of the distribution is closest to 5.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The median is the number at the center of a dataset when the dataset is arranged in either ascending or descending order.

The numbers arranged in ascending order is : 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9

Median = 5

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Answer:

Step-by-step explanation:

Answer:

The answer will be $3216.152

Step-by-step explanation:

If you do the 20% of $4020.19 then the answer will came $804.038 and then subtract the result from $4020.19 then it will came $3216.152 and it is the result only.