A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the lighthouse.

Answer:

Option (2)

Step-by-step explanation:

In the two triangles ΔWVZ and ΔYXZ,

If the sides WV and XY are parallel and the segments WY and VX are the transverse.

∠X ≅ ∠V [Alternate angles]

∠W ≅ ∠Y [Alternate angles]

Therefore, ΔWVZ ~ ΔYXZ [By AA postulate of the similarity]

Option (2) will be the answer.

Answer:

3,200 ft²

Step-by-step explanation:

first you want to convert the sides from inches to feet so 20* 4= 80, and 10* 4= 40 then you multiply the sides to get the area which is 80*40= 3,200 ft²

Answer:

[tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]

Step-by-step explanation:

Solution:-

- We are given a logistic growth model of the fish population cultured. The logistic growth of fish population is modeled by the following equation:

                         [tex]P ( t ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^t}[/tex]

Where,        c: the constant to be evaluated.

- We are given the initial conditions for the model where at t = 0. The initial population was given to be:

t = 0 ,              Po = 160

                       N ( carrying capacity ) = 9100

- After a year, t = 1. The population was tripled from the initial value. That is P ( 1 ) = Po*3 = 160*3 = 480.

- We will use the given logistic model and set P ( 1 ) = 480 and determine the constant ( c ) as follows:

                           [tex]P ( 1 ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^*^1} = 480\\\\c = 480* [ 1 + 55.875e^-^ 1^.^1^3^5^0^6]\\\\c = 9100.024[/tex]

- The complete model can be written as:

                            [tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]

Answer:

There are 455 different  handfuls of 12 jellybeans possible

Step-by-step explanation:

From the given information;

we are told that there exist 50 kinds of jellybean for each of these colors (red, orange, green, yellow)

Also the jellybeans of each color are identical.  

i.e Let say y represent the color of the jellybean.

Then y₁ = y₂ = y₃ = y₄ corresponds to each of these colors (red, orange, green, yellow)

The objective is to determine how many different handfuls of 12 jellybeans are possible?

So;

y₁ + y₂ + y₃ + y₄ = 12

Therefore; the number of different  handfuls of 12 jellybean possible can be computed by using the formula:

[tex]C(r+k-1,r) = \dfrac{(r+k-1)!}{r! (k-1)!}[/tex]

where;

r =12 jellybeans

k = 4  types of colors

[tex]C(12+4-1,4) = \dfrac{(12+4-1)!}{12! (4-1)!}[/tex]

[tex]C(15,4) = \dfrac{15!}{12! (3)!}[/tex]

[tex]C(15,4) = \dfrac{15\times 14 \times 13 \times 12!}{12! (3)!}[/tex]

[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3!}[/tex]

[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3 \times 2 \times 1}[/tex]

[tex]C(15,4) =5\times 7 \times 13[/tex]

[tex]C(15,4) =455[/tex]

There are 455 different  handfuls of 12 jellybeans possible  

There are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans that are possible.

Probability is termed as the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen. The probability formula is determined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.

Given information are:

There are exist of [tex]50[/tex] kinds of jellybean of different colors i.e. red, orange, green, yellow.

The jellybeans of each color are identical.

i.e Let say [tex]y[/tex] represent the color of the jellybean.

Then [tex]y_1=y_2=y_3=y_4[/tex] corresponds to each of these colors (red, orange, green, yellow)

So,

[tex]y_1+y_2+y_3+y_4=12[/tex]

Therefore, the number of different handfuls of [tex]12[/tex] jellybean possible can be computed by using the formula:

[tex]C\left ( r+k-1,r \right )=\frac{\left (r+k-1 \right )!}{r!\left ( k-1 \right )!}[/tex]

where,

[tex]r=12[/tex] jellybeans

[tex]k=4[/tex] types of colors

[tex]C\left ( 12+4-1,4 \right )=\frac{\left (12+4-1 \right )!}{12!\left ( 4-1 \right )!} \\ C(15,4)=\frac{15!}{12!(3)!} \\ C\left ( 15,4 \right )=\frac{15\times 14\times 13\times 12!}{12!(3!)} \\ C(15,4)=\frac{15\times 14\times 13}{3!} \\ C(15,4)=\frac{15\times 14\times 13}{3\times2\times1} \\ C(15,4)=5\times7\times13 \\ C(15,4)=455[/tex]

So, the possibility are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans.

Learn more about the topic Probability: https://brainly.com/question/26571971

Answer:

The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.

Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.

Hope this helps!

Answer

Step-by-step explanation:

Given,

r = 10

Let's create an equation,

[tex]3r = 10 + 5s[/tex]

plugging the value of r

[tex]3 \times 10 = 10 + 5s[/tex]

Multiply the numbers

[tex]30 = 10 + 5s[/tex]

Move 5s to L.H.S and change its sign

Similarly, Move 30 to R.H.S and change its sign.

[tex] - 5s = 10 - 30[/tex]

Calculate

[tex] - 5s = - 20[/tex]

The difference sign ( - ) should be cancelled on both sides

[tex]5s = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5s}{2} = \frac{20}{5} [/tex]

Calculate

[tex]s = 4[/tex]

The value of s is 4.

Hope this helps..

Best regards!!

Answer:

A. 4 (on edgenuity)

Step-by-step explanation:

Answer:

B. [tex] -3x [/tex]

Step-by-step explanation:

In algebra, a term could be a single negative or positive number (constant), a variable or a variable with a coefficient. It could also be 2 variables multiplied together.

The algebraic expression [tex] -3x - 7(x + 4) [/tex] , can be expanded and expressed as:

[tex] -3x - 7(x) -7(+4) [/tex]

[tex] -3x - 7x - 28 [/tex]

The three terms are: [tex]-3x, - 7x, -28[/tex]

Therefore, from the given answer choices, the term that is a term in the expression, [tex] -3x - 7(x + 4) [/tex] , is B. [tex] -3x [/tex]

Answer:

A horizontal cross-section is obtained when the plane that passes through the solid object is parallel to its base. On the other hand, a vertical cross section is found when the intersecting plane is perpendicular to the base of the solid. These are known as a parallel cross-section and perpendicular cross section.

Step-by-step explanation:

=========================================

Work Shown:

1.5/3 = 31.5/x

1.5x = 3*31.5  cross multiply

1.5x = 94.5

x = 94.5/1.5  dividing both sides by 1.5

x = 63

-----------

An alternative equation to solve is

1.5/31.5 = 3/x

1.5x = 31.5*3

1.5x = 94.5

The remainder of the steps are the same as in the previous section above.

Answer:

b=7

Step-by-step explanation:

Answer:

b must equal 7 and a second solution to the system must be located at the point (2, 5).

Step-by-step explanation:

i got it right on the test

Answer:

  B A C D

Step-by-step explanation:

Your calculator can tell you the values of these expressions. In the order given, they are ...

We hope you have no trouble recognizing that swapping the first two expressions will put them all in increasing order.

-3 3/10 -(-7/20) = -2.95

5/-1.6 = -3.125

5 6/15 +(-2 4/5) = 2.6

-4.5×-2.3 = 10.35

Answer:

[tex]\large \boxed{\sf \ \ -3x^3-x^2+x+18 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex](f-g)(x)=f(x)-g(x)=x^2-3x+9-(3x^3+2x^2-4x-9)\\\\=x^2-3x+9-3x^3-2x^2+4x+9\\\\=\boxed{-3x^3-x^2+x+18}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]\boxed{x<20}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} x<10[/tex]

Multiply both sides by 2.

[tex]x<20[/tex]

Answer:

x = 1.

Step-by-step explanation:

x + y + z = 5

2x - y - z = -2

3x = 3

x = 1

Hope this helps!

Answer:The vertex, or turning point, is at (1, 4). From the graph, you can see that f(x) ≤ 4. Answer. The domain is all real numbers, and the range is all real numbers f(x) such that f(x) ≤ 4.

Step-by-step explanation:

I really hope this helped! :)

Answer:

14.3 km

Step-by-step explanation:

Using the paths shown, we would need to add the path length from Belmont to Yardley and Yardley to Oxford. When we add 8.5 and 5.8, we get 14.3 km.

Hence,

the distance from Belmont to Oxford is 14.3 km.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

-1.96

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 500 defective tablets is under test. 20 tablets found to be defective so the null hypothesis is accepted as less than 6% of tablets are defective.

Answer:

6. 156.6 cm

7. 687.7’

Step-by-step explanation:

45 cm and 150 cm are the legs of one triangle.

The longest side is the hypotenuse.

Apply Pythagorean theorem, since the two triangles are right triangles.

a² + b² = c²

a and b are the legs, c is the hypotenuse.

45² + 150² = c²

24525 = c²

√24525 = c

c = 156.604597634...

c ≈ 156.6

Brain hang-glided from a 520’ high cliff. He landed 450’ away from the base of the cliff. Create a right triangle and apply Pythagorean theorem. The distance he travelled is the hypotenuse of the triangle. The 520’ and 450’ are the legs.

a² + b² = c²

450² + 520² = c²

c² = 472900

c = √472900

c = 687.677249878...

c ≈ 687.7

Answer: 6) =approx 156.60 cm

7) =approx 687.68'

Step-by-step explanation:

6.  Let the shortest side of the triangle is AB=45 cm ( ∡A=90° so ABCD  is a rectangle). The middle side AD=150 cm.  The longest side is BD

The length of BD can be calculated using Phitagore theorem  because triangle BAD ia right angle.

BD=sqrt(AD²+AB²)=sqrt(2025+22500)=approx 156.60 cm

7. So we can create the model of the situation described in this problem.

The model is right-angle triangle ABC  with side AB=520'  ,side AC=450', right angle is A. So we have to find the length of side BC .

BC is hypotenuse of triangle ABC. We can find it  using Phitagore theorem again.

BC=sqrt(AC²+AB²)=sqrt(450²+520²)=sqrt(472900)=approx 687.68'

Answer:

The total profit when 240 members are enrolled is:

3,587,212.8 cents

Step-by-step explanation:

First of all, the total profit function is gotten by integrating the marginal profit function.

Integrate thus:

Total Profit = P(x) = [-0.0008x^4 ÷ 4] + [0.35x^3 ÷ 3] + [45.5x^2 ÷ 2]

P(x) = 0.0002x^4 + 0.1167x^3 + 22.75x^2

Next, substitute 240 for x, in the total profit function.

P(x) = 0.0002[240]^4 + 0.1167[240]^3 + 22.75[240]^2

P(x) = 663552 + 1613260.8 + 1310400

P(x) = 3,587,212.8 cents

Equivalent to $35,872.128

Answer:

A. (1, -2)

Step-by-step explanation:

We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].

Let's start with A, -2 being y and 1 being x.

[tex]-2 < - |1|[/tex]

The absolute value of 1 is 1, and negating that gets us -1.

[tex]-2 < -1[/tex]

Indeed, -2 is less than -1! So A is a solution to the inequality.

Let's test the rest of them, just in case.

For B:

[tex]-1 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]-1<-1[/tex]

-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.

Let's try C.

[tex]0 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]0 < -1[/tex]

0 is GREATER than -1, so that is not a solution to the inequality.

Hope this helped!

Answer:

3057.6 cm³

Step-by-step explanation:

You have a cylinder and a rectangular prism.  Solve for the area of each separately.

Cylinder

The formula for volume of a cylinder is V = πr²h.  The radius is 7, and the height is 7.

V = πr²h

V = π(7)²(7)

V = π(49)(7)

V = 343π

V = 1077.57 cm³

Rectangular Prism

The formula for volume of a rectangular prism is V = lwh.  The length is 20, the width is 11, and the height is 9.

V = lwh

V = (20)(11)(9)

V = (220)(9)

V = 1980 cm³

Add the areas of the two shapes.

1077.57 cm³ + 1980 cm³ = 3057.57 cm³

Round to the nearest tenth.

3057.57 cm³ ≈ 3057.6 cm³

Answer:

Step-by-step explanation:

cos^-1(6/13)=62.5136°

sin(2*62.5136°)=0.8189

cos(2*62.5136°)=-0.5740

Answer:

83,403

Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.

Hope this helps!

Answer:

A road with a pitch of 1 in 8 is steeper.

Step-by-step explanation:

Let us convert these to the same units so that we can better compare them.

[tex]\frac{1}{8} = 0.125[/tex]

0.125=12.5 %

As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.

Answer:

1 is 1.

2 is 2.

3 is 3. (this is not a joke, keep going)

4 is -1/3.

5 is -1/2.

6 is -1/4.

7 is -5/3.

8 is -4/15, if you meant that the points are (8,10) and (-7,14). You might have typed wrong.

9 is -1/4.

10 is 1/3. Take a look at it. It goes up by 1 and it goes over 3. 1 divided by 3 is 1/3.

11 is 1. It rises 2 and goes across by 2. 2 divided by 2 is 1.

12 is -3/4, because it goes down 3 and over 4.

13 is -3/2. Do you see why?

14 is 1. It's super easy, since it only goes up 1 and over 1.

15 is easy. You have to figure this one out, but I'll give you a hint. It goes down by 3 .

Answer:  

[tex]1)\quad f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]

2) D: x = [0, 24]

3) R: y = [0, 384]

4) see graph

Step-by-step explanation:

Eric's regular wage is $12 per hour for all hours less than 9 hours.

The minimum number of hours Eric can work each day is 0.

f(x) = 12x    for   0 ≤ x < 9

Eric's overtime wage is $18 per hour for 9 hours and greater.

The maximum number of hours Eric can work each day is 24 (because there are only 24 hours in a day).

f(x) = 18(x - 8) + 12(8)

    = 18x - 144 + 96

    = 18x - 48           for 9 ≤ x ≤ 24

The daily wage where x represents the number of hours worked can be displayed in function format as follows:

[tex]f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]

2) Domain represents the x-values (number of hours Eric can work).

The minimum hours he can work in one day is 0 and the maximum he can work in one day is 24.

D:  0 ≤ x ≤ 24        →        D: x = [0, 24]

3) Range represents the y-values (wage Eric will earn).

Eric's wage depends on the number of hours he works. Use the Domain (given above) to find the wage.

The minimum hours he can work in one day is 0.

f(x) = 12x

f(0) = 12(0)

     =  0

The maximum hours he can work in one day is 24 (although unlikely, it is theoretically possible).

f(x) = 18x - 48

f(24) = 18(24) - 48

       = 432 - 48

       = 384

D:  0 ≤ y ≤ 384        →        D: x = [0, 384]

4) see graph.

Notice that there is an open dot at x = 9 for f(x) = 12x

and a closed dot at x = 9 for f(x) = 18x - 48

Answer: 3. 0.287

Step-by-step explanation:

Let p be the true proportion of BB fans who favor that song.

As per given, Sample size for survey of Beach Boys fans = 394

Number of Beach Boys fans said that California girls was their fav song = 113

Then, the sample proportion of BB fans who favor that song: [tex]\hat{p}=\dfrac{113}{394}[/tex]

[tex]=0.286802030457\approx0.287[/tex]

Since sample proportion is the best estimate for the true proportion.

Hence, a point estimate for the true proportion of BB fans who favor that song is 0.287.

So, the correct option is 3. 0.287 .

Answer:

Step-by-step explanation:

From 6 to 9 is 3 units, the horizontal distance between C and D.  From 4 to 5 is 1 unit, the vertical distance between C and D.

Using the Pythagorean Theorem (or the closely related distance formula), we find the distance between C and D as follows:

distance between C and D:   sqrt(3^2 + 1^2) = sqrt(10)

Answer:

Sum of money = $600

Step-by-step explanation:

X = sum of money

Simple interest means that its the same percentage of interest for a given number of years.

The interest per annum is 5% for 3 years, so 5% x 3 = 15%

15% = 0.15 (as a decimal)

Now, we can put this into an equation:

0.15x = 90

x = 90 / 0.15

x = 600.

sum of money invested = $600