From the observation deck of a skyscraper, Valeria measures a 67^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 945 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.

solution 1

[tex]\dashrightarrow \sf 6\dfrac{2}{6} *1\dfrac{1}{2}[/tex]

[tex]\dashrightarrow \sf \dfrac{38}{6} *\dfrac{3}{2}[/tex]

[tex]\dashrightarrow \sf \dfrac{114}{12}[/tex]

[tex]\dashrightarrow \sf 9\dfrac{6}{12}[/tex]

solution 2

[tex]\dashrightarrow \sf 5\dfrac{2}{3} *\dfrac{3}{4}[/tex]

[tex]\dashrightarrow \sf \dfrac{17}{3} *\dfrac{3}{4}[/tex]

[tex]\dashrightarrow \sf 4\dfrac{3}{12}[/tex]

Answer:

Question 3) -- C -- 9  6/12

Question 4) -- C -- 4  3/12

Step-by-step explanation:

Hope this helps

Answer:

Solution

A=2(wl+hl+hw)=2·(4.9×10-3·5.2×10-3+9.1×10-3·5.2×10-3+9.1×10-3·4.9×10-3)≈2.3478×10-4m²

Step-by-step explanation:

The sampling method that ensures the  accuracy and generalizability of findings is a random sampling.

The term random samping is a sampling technique in which the participants are selected in a random manner from the population. The sample is selected in such a way that it is representative of the entire population.

The sampling method that ensures the  accuracy and generalizability of findings is a random sampling.

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Answer: [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

The equation is in the slope-intercept format of y=mx+b

In this format the slope is m

In this case m is [tex]\frac{3}{4}[/tex]

Answer:

  f(7) = 1.08

Step-by-step explanation:

The recursive formula can be used with the given value to find the desired value.

__

Given:

  f(n) = 0.3×f(n-1) . . . . . where f(5) = 12

The next term in the sequence is ...

  f(6) = 0.3×f(5) = 0.3(12) = 3.6

  f(7) = 0.3×f(6) = 0.3(3.6) = 1.08

Answer:

I thank it is D

Step-by-step explanation:

See analyris

[tex]Hlug\ in\ the\ value\ of \left.\ t.\right\}[/tex]

[tex]The\ infital\ ampunt\ in\ the\ sample:[/tex]

[tex]t=0_{-1}\ \ \ \ \ f(t)=39\omega\bullet(\frac{1}{2})^\frac{0}{14}[/tex]

                        [tex]=3900\ g.[/tex]

[tex]Ater\ bo\ busis.[/tex]

[tex]t=6,\ \ \ \ \ A(t)=2900\times(\frac{1}{2})^\frac{60}{14}[/tex]

                       [tex]=3900\times(\frac{1}{2})^\frac{30}{7}[/tex]

                       [tex]\approx 209.[/tex]

I hope this helps you

:)

Answer:

150 miles

Step-by-step explanation:

If they've completed 60% and have covered 90 miles

We can say

60% = 90 (miles)

We can work out 10% by dividing by 6 on both sides

10% = 15

100% is just 10 times larger

100% = 150

The trip (100% completion) is 150 miles

After one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

It is defined as the systematic way of representation of loan payments according to the time in which the principal amount and interest mentioned in a list manner.

We have a table given that showing a  first segment of a five-year amortization schedule that has a 5-year amortization schedule and the amount of interest paid for months 1 through 12.

As the loan amount is not mentioned in the question, we are assuming the loan amount is $1184.6

Therefore, loan amount = $1184.6

The outstanding amount at the end of one year, which is 12 months, is shown in the table as $84.18

After one year of payments, the amount need to be paid to interest:

= Loan amount - Outstanding amount after 12 months

= 1184.6 - 84.18

= $1100.425

Thus, after one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

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Answer:

72 games in total

Step-by-step explanation:

hope this helps :)

Answer:

y = -3x + 10

Step-by-step explanation:

We write The slope-intercept equation of a line D Like this

D : y = mx+b    (where m is the slope and p is the y-intercept)

__________________________

According to the given information:

The slope = -3

Then ,the equation of our line is : y = -3x + p

Now we need to find p:

Since The point (4, -2) lie on the line

then

-2 = -3(4) + p

then

-2 = -12 + p

then

p = 12 - 2 = 10

Conclusion:

y = -3x + 10

The equation that can be used to find the measure of angle GFE is given by: Option B: cos−1(11.9/14.5) = θ

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

The missing information, not present in this question are:

Since for the triangle GFE, if we look from the angle ∠GFE, the sides given are hypotenuse FG and the base FE.

Thus, we can use cosine ratio, and then its inverse to find the value of angle θ.

Thus, we get:

[tex]\cos(\theta) = \dfrac{|FE|}{|FG|} = \dfrac{11.9}{14.5} \\\\\theta = \cos^{-1}\left(\dfrac{11.9}{14.5}\right)\\\\[/tex]

Thus, the equation that can be used to find the measure of angle GFE is given by: Option B: cos−1(11.9/14.5) = θ

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Answer:

option B

Step-by-step explanation:

Answer:

the second option

Step-by-step explanation:

Answer:

1 2 3

Step-by-step explanation: 1 times 18, 2 times 9, 3 times 6

Answer:

24 pages per hour :)

Step-by-step explanation:

We need to divide to solve :)

144/6 = 24

Have an amazing day!!

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Answer:

Jessiah has 14 pencils

Miles has 28 pencils

Grace has 8 pencils

Step-by-step explanation:

I'm going to assume that you mean Jessaih instead of Jessia because otherwise it would be impossible to solve

Let the # of Jessaih's pencils equal j, # of Grace's pencils equal g, # of Miles' pencils equal m,

j=g+6

m=2j

So m=2(g+6) or 2g+12

Therefore, g+g+6+2g+12, or 4g+18=50, so g = 8

j=8+6, which is 14

m = 2(14), which is 28

Answer: 6, 6, 15, 6, 15, 12, 3 , 15, 1

Step-by-step explanation: I have shown in the file two ways to calculate HCF. That's the answer from 1-9 above.

An example with number 6.

36= 12×3

24=12×2

60=12×5
HCF is 12. The highest number that can divide them all

Answer:

r = 4.5 ft

Step-by-step explanation:

Circumference of circle = πd

πd = 9π ft

d = 9π ÷ π

d = 9 ft

Radius = d ÷ 2

            = 9 ÷ 2

            = 4.5 ft

In order to calculate efficiency

Option A

528 ÷ 24 = 22 mi/gal

Option B

690 ÷ 30 = 23 mi/gal

Option C

840 ÷ 42 = 20 mi/gal

Option B, gives the best fuel efficiency because the car can travel further using 1 gallons of fuel than others.

As you can see, the area of the scarf is equal to the area of the rectangle minus the area of the 2 semi-circles (which form a circle)

Now, we calculate the area of the rectangle : 28 x 15 = 420 in2

The diameter of the circle is 15in -> The radius = 15 : 2 = 7.5in.

We now find the area of the 2 semi-circles : 7.5 x 7.5 x 3.14 = 176.625 in2

So, the area of the scarf is : 420 - 176.625 = 243.375 in2

The picture isin't clear can you write it

Answer:

5

Step-by-step explanation:

half of 10 is 50 on tenth of 50 is 5

Answer:

115

Step-by-step explanation:

B) <2≅<6

When a transversal crosses over 2 parallel lines there are certain statements that can be made, such as the fact that corresponding angles are congruent.

Defining a Corresponding Angle

Corresponding angles are angles that have the same relative position with different vertices. For example, if 2 angles are both in the bottom left of an intersection of 2 lines, they are corresponding. Since both angle 2 and 6 are in the top right, they are corresponding.

Proving the Lines are Parallel

Since corresponding angles are congruent when a transversal crosses parallel lines, any statement that proves corresponding angles are congruent would prove the lines are parallel. This means that <2≅<6 must prove that l║m.

Process of Elimination

Additionally, we can prove that B is correct by proving that the other answers are incorrect.

A) Angle 2 and 3 are vertical angles. This has nothing to do with parallel lines and cannot be used to prove that l║m.

C) Angle 7 and 8 are a linear pair, and, once again, this has nothing to do with whether or not l and m are parallel.

D) If l and m were parallel, then angles 3 and 5 would sum to 180 degrees. this is because if l║m, then <3 and <5 would be same side interior angles. Same side interior angles always sum to 180. So, this statement would actually disprove l║m.