A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 13°
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22°
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

Answer:

11700 m²

Step-by-step explanation:

Split the shape in two. One rectangle 150x30 and one triangle 180x80.

Find the areas of both and add them:

A = bh + 1/2bh

A = 150(30) + 1/2(180)(80)

A = 4500 + 7200

A = 11700

Answer:

-84

Step-by-step explanation:

Let the number be x. Then we have,

[tex]\frac{x}{-7}[/tex] (the quotient of a number and -7)

[tex]\frac{x}{-7}-2[/tex] (decreased by 2)

[tex]\frac{x}{-7}-2=10[/tex] (is 10)

Now we can solve for x,:

[tex]\frac{x}{-7}-2=10[/tex]

[tex]\frac{x}{-7}=12[/tex]

[tex]x=-84[/tex]

So, the original number is -84

Answer:

-84

Step-by-step explanation:

[tex]\frac{n}{-7}[/tex] -2 = 10

add 2 to each side to get:

[tex]\frac{n}{-7}[/tex] = 12

multiply each side by -7 to get:

n = -84

Answer:

x >= 1/5

Step-by-step explanation:

2 + 5x >= 3

5x >= 1

x >= 1/5

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

As we observe the points, we can conclude that :

Translation along x axis is ~

[tex]\qquad \sf  \dashrightarrow \: 1 - ( - 3)[/tex]

[tex]\qquad \sf  \dashrightarrow \:1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 \: \: units \: \: towards \: \: left[/tex]

Translation along y axis ~

[tex]\qquad \sf  \dashrightarrow \: - 8 - ( - 13)[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 8 + 13[/tex]

[tex]\qquad \sf  \dashrightarrow \:5 \: \: units \: \: towards \: \: down[/tex]

So, same goes with translation of (-5 , 9)

[tex]\qquad \sf  \dashrightarrow \: x \: \:coordinate = - 5 - 4 = - 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: y \: \:coordinate = 9 - 5 = 4[/tex]

So, the required coordinates of the image under same translation is ~

[tex]\qquad \sf  \dashrightarrow \:(-9, 4)[/tex]

Answer:

Please help look at the image I need help with number 4. I already did the line plot for number 3 and the data in on the chart. Thank you! :)

Answer:

the regions whose populations have 9 as the power include Africa and Asia.

Step-by-step explanation:

Answer:

africa and asia

Step-by-step explanation:

Answer:

Aviva deposited $4,000

Step-by-step explanation:

Given:

Solving:

We'll create an equation to find the amount of money Aviva deposited.

D = 240(50/3)

D = the amount of money she has deposited.

50/3 represents 94% of D.
Since 240 is 6% of the deposit Aviva has deposited, multiplying 50/3 by 240 will equal 100% of D.

Solve:

4,000 = 240(50/3)

The amount of money Aviva deposited is $4,000.

*This is one method to solve.

Ratio compares two quantities. The amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.

Given to us

The solubility of calcium carbonate is 14.

We know that to dissolve 14 milligrams of calcium carbonate we will need 1 liter of water. therefore, the ratio of water and calcium carbonate can be written as,

[tex]\rm \dfrac{calcium\ carbonate}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]

We need to find the amount of water needed to dissolve 14 grams of water, therefore, we will convert grams to milligrams,

1 gram = 1000 milligram

14 gram = 14,000 milligram

Using the same ratio,

[tex]\rm \dfrac{14,000\ milligram}{water} = \dfrac{14\ milligram}{1\ liter}[/tex]

[tex]\rm {water} = \dfrac{14000\ milligram \times 1\ liter}{14\ milligram}[/tex]

water = 1000 liters

Hence, the amount of water that will be needed to dissolve 14 grams of calcium carbonate is 1000 liters.

Learn more about Ratio:

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Answer:

B. card I'' increased by 1.2986 = 13 more than card H's

Step-by-step explanation:

Answer:

4 and 5

Step-by-step explanation:

Answer:

Answer: ¾

Step-by-step explanation:

» From the trigonometric identities:

[tex]{ \tt{ \sin {}^{2} \theta + \cos {}^{2} \theta = 1 }}[/tex]

» Substitute to the formular:

[tex]{ \tt {( \frac{ \sqrt{7} }{4} )}^{2} + { \cos }^{2} \theta = 1 } \\ \\ { \tt{ \frac{7}{16} + { \cos}^{2} \theta = 1 }} \\ \\ { \tt{ \cos {}^{2} \theta = 1 - \frac{7}{16} }} \\ \\ { \tt{( \cos\theta) {}^{2} = \frac{9}{16} }} \\ \\ { \tt{ \sqrt{ {( \cos \theta}^{2}) } = \sqrt{( \frac{9}{16}) } }} \\ \\ { \tt{ \cos \theta = \frac{ \sqrt{9} }{ \sqrt{16} } }} \\ \\ { \boxed{ \tt{ \cos \theta = \frac{3}{4} }}}[/tex]

According to the given confidence interval, we have that:

a) Since 12 ounces is part of the confidence interval, the interval does not provide convincing evidence that the true mean volume is different than 12 ounces.

b) Since 12 ounces is part of the confidence interval, the interval provides convincing evidence that the true mean volume is 12 ounces.

It is being tested if the true mean volume is different of 12 ounces, hence:

In this problem, the interval is (11.97, 12.05), hence it provides convincing evidence that the true mean volume is 12 ounces, and basically, item a is False and item b is True.

You can learn more about confidence intervals at brainly.com/question/16236451

Answer:

[tex]4p^2q-4q+8p[/tex]

Step-by-step explanation:

[tex](12p^2q+p-3pq^2)-(4q-7p+8p^2q-3pq^2)[/tex]

Apply rule [tex]-(-a)=a[/tex] and [tex]-(a)=-a[/tex]:

[tex]\implies 12p^2q+p-3pq^2-4q+7p-8p^2q+3pq^2[/tex]

Collect like terms:

[tex]\implies 12p^2q-8p^2q-3pq^2+3pq^2-4q+7p+p[/tex]

Combine like terms:

[tex]\implies 4p^2q-4q+8p[/tex]

Answer:

-4

Step-by-step explanation:

(-12) - (-5) = -7

-7 + 3 = -4

Answer:

-4

Step-by-step explanation:

HOPE IT HELPED U

Answer:D

Step-by-step explanation:

D

Answer:

I think the answer is letter C.15

Correct me if im wrong

#Thank you

Answer:

1.4

Step-by-step explanation:

= 7/5 × 2/2

= 14/10

=1.4

Answer:

8 • 20m - 29

Step-by-step explanation:

this might be right

Answer:

   -2.5 m/s^2

Step-by-step explanation:

From 2 seconds to 8 seconds (the last 6 seconds), the speed decreased from 15 m/s to 0. The average acceleration is ...

  (-15 m/s)/(6 s) = -2.5 m/s^2

[tex] \frac{5}{6} [/tex]

The total percent of decrease in price of the shares of Selena's stock which Selena first buys and then sold is 11.5 percent.

Percentage decrease in a number is the ratio of total decrease in the original value of a number to the decreased value in the percentage form.

Given information-

The total stock buy by the Selena in $32.

The total stock sold by the Selena in $28.32.

As the total stock buy by the Selena in $32, and the total stock sold by the Selena in $28.32. Thus the total decrease in the price of stock is,

[tex]C_s=32-28.32\\C_s=3.68[/tex]

Thus the total decrease in the price of stock is $3.68.

As the cost price of the stock is $32 and the total decrease in the price of stock is $3.68. Thus the total percent of decrease in the price of the stock is,

[tex]\Delta C_s=\dfrac{3.68}{32}\times100\\\Delta C_s=11.5[/tex]

Thus the total percent of decrease in the price of the stock is 11.5 percent.

Learn more about the percentage decrease here;

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Velocity can be represented in horizontal and vertical components

The horizontal component form of the velocity is 12.5 mph

The given parameters are:

Velocity = 25 mph

Angle = 60 degrees

The horizontal component form of the velocity is then calculated as:

[tex]v_x = 25 * \cos(60)[/tex]

Evaluate the product

[tex]v_x = 12.5[/tex]

Hence, the horizontal component form of the velocity is 12.5 mph

Read more about velocity at:

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Answer:

14 pints were drank

Step-by-step explanation:

22 pints - 8 pints =

Answer:

14 pints

Step-by-step explanation:

22 - 8 is 14 pints, now just convert the pints to cups, that would be 28 cups since 1 pint is 2 cups so 14 x 2 is 28, hope this helps

The length of the other leg of the right triangle is; 89.44 centimetres

According to the question;

By the Pythagoras theorem;

Hence, It follows that;

Find the square root of both sides of the equation;

x = 89.44 centimeters

Read more on Pythagoras theorem;

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Answer:

the zeroes are -2 and 8

Step-by-step explanation:

[tex]-x^2 +6x+16\\\implies -(x^2-6x-16)\\\implies -(x+2)(x-8)[/tex]

Therefore, the zeroes are -2 and 8

Congruent triangles have congruent corresponding sides and angles, while similar triangles may or may not be congruent

The congruence statement is given as:

ΔPOG ≅ ΔSOR

The above means that:

Points P, O and G correspond to the points S, O and R

Hence, the corresponding side of PO in ΔPOG ≅ ΔSOR is SO

The congruence statement is given as:

ΔPOG ≅ ΔSOR

Hence, the congruent triangles are ΔPOG ≅ ΔROS

In figure 2, we have:

2 congruent sides, and 1 congruent angle between the congruent sides

Hence, the congruence postulate is SAS

The congruence statement is given as:

ΔABC ≅ ΔXYZ

The above means that:

Point A corresponds to the point X

Hence, the congruent angle of <A is <X

Read more about congruent triangles at:

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Answer:

Step-by-step explanation:

Quotient meaning:

Equation:

Solve:

Multiples:

Answer:

Answer:

634

Step-by-step explanation:

Answer:

Angle C prime

Step-by-step explanation:

First design and sketch it:

Make a rectangle with corners C D E and F. 90 degrees each. Now rotate it 45 degrees to the left. Angle D is diagonally from Angle C.

I hope this helps! :)

Answer:

15 children

Step-by-step explanation:

30÷2

=15

therefore there is 15 adults and 15 children