An observer on the top of a lighthouse observes the angles of depression of two ship at anchor to be 75 and 45 respectively. Find the distance between the two ships if the line joining them points to the base of the light house which is 100 meters high. (use tan 15 = 0.27) Answer should be 73 meter.

Answer:

443.1305

Step-by-step explanation:

1 mile=0.869 nautical miles

1 mph=0.869 knots

Average speed=Distance/time

Average speed=2172.5/5

=434.5

404.09=3487.5/hours

=8.6305

434.5+8.6305

=443.1305

Answer:

x=3

Step-by-step explanation:

To solve for x, we will follow the steps below:

First note that exterior angle =two  opposite interior angle

From the diagram below

(25x) ° + (57 + x)°   = (45x)°

25x° + 57° + x° = 45x°

next step is to collect the like term

45x° - 25 x°  - x°  =  57°

19x° = 57°

Divide both-side of the equation by 19

19x°/ 19 = 57° /19

On the left-hand side of the equation 19 will cancel out 19 leaving us with just x°  while on the right-hand side of the equation 57 will be divided by 19

x  =   3

Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

P starts at (-3,5)

Move to the right 2 units and you'll get to (-1,5). We add 2 to the x coordinate here.

Then shift the point up three units to get to (-1,8). We add 3 to the y coordinate.

Finally, reflect over the x axis to get the answer (-1, -8)

Note how the y coordinate flipped in sign but the x coordinate stays the same

Answer:

Step-by-step explanation:

eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go

Answer:

x= 3.8

y= -29.3

Step-by-step explanation:

Answer:jac ganko

Step-by-step explanation:

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

x=−0.23240812,−1.43425854

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

Answer:

Both spreads are best described by the standard deviation

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

there is no factor to convert one into the other.

moreover, 19 is prime and 9 is not, so no way.

Answer:

86.55 ft

Step-by-step explanation:

First find the perimeter for 3 sides of the rectangle that are solid

24+15+24 = 63

The we find the circumference for 1/2 of the circle

C = pi d

The diameter is 15 and pi = 3.14

But we only want 1/2

1/2 C = 1/2 pi d

        = 1/2 ( 3.14) * 15

       =23.55

Add the lengths together

23.55+63 =86.55 ft

Answer:

shape AREA= 35cm^2

Step-by-step explanation:

you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.

A=h/2(b1 + b2) for trapezoid

A=2/2((4+4)+4)

A=1*12

A=12cm^2

A=bh/2. for TRIANGLE

A=1/2((4+4)*5.75)

A=1/2(46)

A=23cm^2

shape AREA= triangle AREA + trapezoid AREA

shape AREA=12cm^2 + 23cm^2

shape AREA= 35cm^2

Answer:

9*((2-1)/9)

or

2 -1

9

2-9 =-7

9. 9

9× -7

9

=-7

2- 3

9. -3

=(1.22222222222)

or

11/9

or

1*(2/9)

Answer:

Not a triangle

Step-by-step explanation:

Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.

Answer:

3.6hours

Step-by-step explanation:

kevin-6hrs

so he gets 1/6 called in 1 minute

Anne-9 hrs

so she gets 1/9 called in 1 minute

together

1/6+1/9=5/18 called in one minute

so what about all which are 18/18

you get 3.6 hrs I guess

Answer:

a. 30 meters per second

b. -10 meters per second

Step-by-step explanation:

a. Average rate of change for the height from 0 to 6.6 secs can be calculated using the formula, [tex] m = \frac{H(b) - H(a)}{b - a} [/tex]

Thus,

Where,

[tex] a = 0, H(0) = 0 [/tex]

[tex] b = 6.6, H(6.6) = 198 [/tex]

Plug in the values into the formula:

[tex] m = \frac{198 - 0}{6.6 - 0} [/tex]

[tex] m = \frac{198}{6.6} [/tex]

[tex] m = 30 [/tex]

b. Average rate of change for the height from 8.8 to 13.2 secs = tex] m = \frac{H(b) - H(a)}{b - a} [/tex]

Where,

[tex] a = 8.8, H(8.8) = 44 [/tex]

[tex] b = 13.2, H(13.2) = 0 [/tex]

Plug in the values:

[tex] m = \frac{0 - 44}{13.2 - 8.8} [/tex]

[tex] m = \frac{-44}{4.4} [/tex]

[tex] m = -10 [/tex]

Answer:

n = 2

Step-by-step explanation:

Given

5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side

[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]

Since denominators are both 2 then equate numerators

n - 1 = 1 ( add 1 to both sides )

n = 2

Answer:

x = 60

Step-by-step explanation:

In a circle, the sum of the angles that meet at a point is 360 degrees. So now that we have the total, we can subtract all the given information in the picture. We have 84, 75, 68, and x + 73. Now let us set up and equation for this problem.

360 = 84 + 75 + 68 + x + 73

Now combine like terms.

360 = x + 300

Now subtract 300 on both sides.

x = 60

And this is the value of x.

Answer:

50 degrees

Step-by-step explanation:

84 + 75 + 68 = 227

227 - 360 = 133

133 - 73 = 50

The answer is 50 degrees.

Answer:

a=-5

Step-by-step explanation:

When you do this every time the slope will go down 2 and over 1 which is rise over run or slope. You can see the y coordinates go down 4 points and every time is should go down 2 so you will know that it would have gone down 2 times so a+2 should equal -3 so if we subtract 2 from both sides we would get a=-5 and that is our answer.

Answer:

a = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 2

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (a, 3)

m = [tex]\frac{3+1}{a+3}[/tex] = [tex]\frac{4}{a+3}[/tex] = - 2 ( multiply both sides by a + 3 )

- 2(a + 3) = 4 ( divide both sides by - 2 )

a + 3 = - 2 ( subtract 3 from both sides )

a = - 5

Answer:

59.0

Step-by-step explanation:

Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:

Opposite side to angle X = 6

Hypotenuse = 7

Therefore, we would apply the following trigonometric ratio formula to solve for m<X:

[tex] sin X = \frac{6}{7} [/tex]

[tex] sin X = 0.8571 [/tex]

[tex] X = sin^{-1}(0.8571) [/tex]

[tex] X = 58.99 [/tex]

[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)

Answer:

the probability that they find enough subjects for their​ study is 0.9515

Step-by-step explanation:

From the given information:

Let X be the random variable that follows a normal distribution.

Therefore:

X [tex]\sim[/tex]Binomial(n=733,p=0.04)

[tex]\mu = np[/tex]

[tex]\mu = 733*0.04[/tex]

[tex]\mu = 29.32[/tex]

[tex]\sigma = \sqrt{np(1-p)}[/tex]

[tex]\sigma = \sqrt{29.32(1-0.04)}[/tex]

[tex]\sigma = \sqrt{29.32(0.96)}[/tex]

[tex]\sigma = \sqrt{28.1472}[/tex]

[tex]\sigma = 5.305[/tex]

The probability of P(X ≥ 21) lies in the region between 20.5 and 21.5 by considering a discrete contribution of a continuous normal distribution. Eventually, X > 20.5

∴

P(X >20.5)= P(Z > z)

Using  standard normal z formula:

[tex]z = \dfrac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{20.5-29.32}{5.305}[/tex]

[tex]z = \dfrac{-8.82}{5.305}[/tex]

[tex]z = -1.662582[/tex]

z = -1.66

P(X >20.5)= P(Z > -1.66)

From the standard z tables ;

P(X >20.5)= 1 - 0.0485

P(X >20.5)= 0.9515

Answer:

Andy's house to Billy's hometown 15 ways

Andy's house to Willie's hometown 2 ways.

Step-by-step explanation:

Andy's house to Billy's hometown there are 3 roads. There 5 road from billy's hometown to Willie's house . In total there will be 15 ways to travel which is calculated by 3 * 5. For traveling to Willie's hometown there will be two ways. There are two roads that are built to get to Willie's house.

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Reasoning:

g(x) = 4*ln(x)

g(x) = 2*2ln(x)

g(x) = 2*f(x)

Whatever the output f(x) is, it is doubled to get g(x). Recall that y = f(x), so we're really doubling the y values to visually stretch it vertically by a factor of 2. In short, g(x) is twice as tall compared to f(x).

Answer:

C. g(x) stretches f(x) vertically by a factor of 2.

Step-by-step explanation:

a p e x

Answer:

h = 7 units

Step-by-step explanation:

Jessica made an error with the [tex]\frac{1}{2}[/tex] in that she multiplied A by it instead of dividing.

Given

A = [tex]\frac{1}{2}[/tex] bh

with A = 17.5 and b = 5, then

17.5 = [tex]\frac{1}{2}[/tex] × h × 5 ( multiply both sides by 2 to clear the fraction )

35 = 5h ( divide both sides by 5 )

h = 7

it is wrong .

Jessica's mistake:

A = 1/2bh

1/2A • b = h >she should multiply the area with 2 not 1/2 and divide the area by b rather than multiply by b

1/2 (17.5)(5) = h

43.75 = h

correct answer:

A = 1/2bh

2A/b=h

h=2(17.5)/5

h=7

Hey there!

The volume of a cone is always 1/3 of that of a cylinder with the same except dimensions. You multiply the base by the height and then divide by three!

This means that if the cylinder has a volume of 1200 meters cubed, you simply divide by three, giving you 400 meters cubed !

The answer is A. 400 m³.

Have a wonderful day! :D

Answer:900

Step-by-step explanation:A cylinder has more volume considering because of the space but a cone simply has less

Answer:

It is C

Step-by-step explanation:

42.60=43.00

587.70=588.00

27.99=28.00

Answer:

500[tex]\pi[/tex] or around 1570

Step-by-step explanation:

The formula for a volume of a cylinder is [tex]r^{2}h\pi[/tex]

The cylindrical garbage pain has a volume of 15700 cm².

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

The given cylindrical garbage has a radius(r) = 10 cm and a height(h) of

50 cm.

∴ The volume of the cylindrical garbage is = π(10)²×50 cm².

= 5000π cm².

= 15700 cm².

learn more about cylinders here :

https://brainly.com/question/16134180

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