A light house operator is 34m above sea level. He spots a sailboat in the distance. The angle of depression of the sighting is 10. How far is the boat from the base of the lighthouse?

Final answer:

To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).

Explanation:

To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:

y = x - 2

Now substitute this expression for y into the first equation:

x - 2 = 2x^2 - 8x + 5

Now we have a quadratic equation. Rearrange it into standard form:

2x^2 - 9x + 7 = 0

Next, factor the quadratic equation:

(2x - 1)(x - 7) = 0

Set each factor equal to zero and solve for x:

2x - 1 = 0, x - 7 = 0

x = 1/2, x = 7

Now substitute these values of x back into either of the original equations to find the corresponding values of y:

For x = 1/2: y = 1/2 - 2 = -3/2

For x = 7: y = 7 - 2 = 5

So the solutions to the system of equations are (1/2, -3/2) and (7, 5).

Answer: the height of the melted candies in the pot is 12.2 mm

Step-by-step explanation:

The formula for determining the volume of a square base pyramid is expressed as

Volume = area of base × height

Area of the square base = 12² = 144 mm²

Volume of each pyramid = 15 × 144 = 2160 mm³

The volume of 100 pyramid shaped chocolate candies is

2160 × 100 = 216000 mm³

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that

216000 = 3.14 × 75² × h

17662.5h = 216000

h = 216000/17662.5

h = 12.2 mm

Answer:

The height of the melted candies in the pot is 4.07mm

Step-by-step explanation:

H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07

Answer:

(a) [tex]P(X < 12)=0.26[/tex]

(b) [tex]P(X=2)=0.15[/tex]

Step-by-step explanation:

Question a

This is a Poisson distribution. The average/mean, μ = 14

So, probability that fewer than 12 field mice are found on a given acre is:

[tex]P(X < 12) = e^{-14}(\frac{14^{0}}{0!} +\frac{14^{1}}{1!} + \frac{14^{2}}{2!} + \frac{14^{3}}{3!} +\frac{14^{4}}{4!} + \frac{14^{5}}{5!} +\frac{14^{6}}{6!}+\frac{14^{7}}{7!}+\frac{14^{8}}{8!} +\frac{14^{9}}{9!}+\frac{14^{10}}{10!}+\frac{14^{11}}{11!})\\ \\P(X < 12) = e^{-14}(1+14+98+457.33+1600.67+4481.87+10457.69+20915.38+36601.91+56936.31+79710.83+101450.15)\\\\P(X < 12) = 8.315*10^{-7}(312725.1248)=0.26 \\\\P(X < 12)=0.26[/tex]

Question b

This is a Binomial distribution with:

Probability of success, p = 0.26

n = 3

[tex]P(X=2)= (3C2)p^{2}(1-p)=\frac{3!}{2!(3-2)!}*(0.26^{2})*(1-0.26)\\ \\P(X=2)=3(0.0676)(0.74)=0.15\\\\P(X=2)=0.15[/tex]

Final answer:

To find the probability that fewer than 12 field mice are found on a given acre and on 2 of the next 3 acres inspected, use the cumulative distribution function (CDF) of the Poisson distribution and the binomial distribution.

Explanation:

To find the probability that fewer than 12 field mice are found on a given acre, we need to use the cumulative distribution function (CDF) of the Poisson distribution. The average number of field mice per acre is 14, so the parameter of the Poisson distribution is also 14.

(a) To find the probability that fewer than 12 field mice are found on a given acre, we calculate P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11), where X is the number of field mice found on a given acre

(b) To find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected, we calculate P(X < 12) for each acre and use the binomial distribution to determine the probability of 2 successes out of 3 trials.

Answer:

the answer is d

Step-by-step explanation:

Answer:

(1,-3)

Step-by-step explanation:

the x-axis for A is positive and the y-axis is negative. point A's X value is 1 because it is 1 point away from the origin and the value of the Y is 3 units away from the origin and it has to be negative.

Answer:

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2

Step-by-step explanation:

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2

(16)^1/4 = (2^4)^1/4

4 cancels 4

2^1 = 2

Answer:

Step-by-step explanation:

The answer is the first one.

[tex]16^{\frac{1}{4}}[/tex]  simplifies down to

[tex](2^4)^{\frac{1}{4}}[/tex]  The power to power rule is that you multiply the exponents together:

[tex]2^{\frac{4}{4}}[/tex]  which is [tex]2^1[/tex]  which is 2

I'm assuming that you are also working with radicals (since radicals and exponents are inverses of each other).  The way to write this is as a radical and simplify it is:

[tex]16^{\frac{1}{4}[/tex]  as a radical is

[tex]\sqrt[4]{16^1}[/tex]

To simplify, try to write the radicand (the number under the square root) so it's a number with a power that matches the index (the number in the "arm" of the radical sign.  Our index is a 4).  

16 is the same as 2⁴:

[tex]\sqrt[4]{2^4}[/tex]

The power on the 2 is a 4, which is the same as the index.  When the power matches the index, you pull out the base as a single number:

[tex]\sqrt[4]{2^4}=2[/tex]

Answer:

Answer in explanation

Step-by-step explanation:

The two laws are mathematical laws which are used in navigating problems which involves triangles. While the Pythagorean theorem is used primarily and exclusively for right angled triangle, the cosine rule is used for any type of triangle.

So, why is the cosine rule a stronger statement? The reason is not far fetched. As said earlier, the cosine rule can be used to resolve any triangle type while the Pythagorean theorem only works for right angled triangle. In fact, we can say the Pythagorean theorem is a special case of cosine rule. The reason why the expression is different is that, for the expression, cos 90 is zero, which thus makes our expression bend towards the Pythagorean expression view.

The explanation regarding the law of cosines is the stronger statement if compared with the Pythagorean theorem is explained below.

The Pythagorean theorem is used when there is the right-angled triangle, while on the other hand, the cosine rule is used for any type of triangle. Here the Pythagorean theorem should be considered for the special case of cosine rule. Due to this the cosine law should be stronger if we compared it with the Pythagorean theorem.

Learn more about cosine here;https://brainly.com/question/16299322

Answer:

B. 1 1/7

Step-by-step explanation:

-9 2/7-(-10 3/7)

=-9 2/7+10 3/7

=1 1/7

Therefore, B. 1 1/7

Answer:

The answer is B

Step-by-step explanation:

B. 1 1/7

Answer: the account that earned compound interest has the greater balance at the end of four years.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 1000

R = 4%

T = 4 years

I = (1000 × 4 × 4)/100 = 160

Total amount earned is

1000 + 160 = $1160

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,.

A = 1000(1+0.04/1)^1 × 4

A = 1000(1.04)^4

A = $1170

Answer:

5000 + x = 23600  

Step-by-step explanation:

a car that cost = 23600

down payment = 5000

So he needs to pay: 23600 - 5000 = 18600 more to get the car

Let x represent the amount he needs to pay more, an equation for his situation:

5000 + x = 23600  

Answer:

40/13

The decimal form is going to be 3.076

Answer:

Tara bought a total of 160 treats.

Step-by-step explanation:

We are given the following in the question:

Number of boxes of dog treats = 3

Number of treats in each dog box = 40

Total number of treats in dog box =

[tex]40 \times 3 = 120[/tex]

Number of boxes of cat treats = 2

Number of treats in each cat box = 20

Total number of treats in cat box =

[tex]20\times 2 = 40[/tex]

Total number of treats Tara brought =

Total number of treats in dog box + Total number of treats in cat box

[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]

Thus, Tara bought a total of 160 treats.

Answer:

The first zero after decimal point and 4 only

Step-by-step explanation:

Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.

Answer:

b = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

period = [tex]\frac{2\pi }{b}[/tex], that is

b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]

Answer:

f(x) = 4cos(8/3)x - 3.

The missing space is 8/3.

Step-by-step explanation:

The general form is  f(x) = Acosfx + B    where A = the amplitude, f = frequency and B is the vertical shift..

Here A is given as  4,  B is - 3 and the frequency f = 2 π / period  =

2π / (3π/4)

= 8/3.

So the answer is f(x) = 4cos(8/3)x - 3.

Answer:

Option C, SAS Postulate

Step-by-step explanation:

I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.

Answer:  Option C, SAS Postulate

Answer:

A. I Only.

Step-by-step explanation:

To begin, we must first be clear that it is the median and that it is the arithmetic mean:

Median is the middle value of a sequence of ordered numbers, for example:

{4,4,4,4,4}, the median is 4 despite being the same numbers.

Now the arithmetic mean is the average value of the samples and is independent of the amplitudes of the intervals.

Then let's analyze each of our options:

I. At least one of the homes was sold for more than $ 165,000.

We know through the flushed:

X1 + X2 +. . . + X7 + (X8 = $130,000) + X9 +. . . + X15 = 15 ∗ 150,000 = $ 2,250,000

Now we will assume the lowest possible value from X1 to X8 = $ 130,000 and from X9 to X15 = X, which is what we want to calculate. That is to say:

X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 130 and X9 = X10 = X11 = X12 = X13 = X14 = X15 = X,

knowing that the total value must be the average of 15, which is equal to $ 2250000 , we have the following equation:

8 ∗ $ 130,000 + 7X = $ 2,250,000

Rearranging:

X = ($ 2,250,000 $ - $ 1,040,000) / 7

X = $ 172,857

Therefore the first statement is true, because at least one house was sold at $ 172,857 which is more than $ 165,000

Evaluating the second option

II. At least one of the homes was sold for more than $ 130,0000 and less than $ 150,000

As the example of the median in the previous case you could have 8 houses that were sold for $ 130,000 or less, therefore here it loses validity, statement II is false.

Evaluating the third option

III. At least one of the homes was sold for less than $ 130,000.

We know that the eighth house sold for $ 130,000, but houses 1 to 7 may also have been sold for that same price. The statement III is false.

Therefore the answer is A. I Only.

What is the volume of a cylinder, in cubic m, with a height of 5m and a base diameter of 20m? Round to the nearest tenths place.

Answer: 1570.8

The volume of a cylinder with a height of 5m and a base diameter of 20m is approximately 1,570.8 cubic meters when rounded to the nearest tenths place.

To find the volume of a cylinder with a height of 5m and a base diameter of 20m, we will use the formula for the volume of a cylinder: V = πr²h , where V is volume, r is the radius of the base, and h is the height of the cylinder. The radius is half of the diameter, so for a diameter of 20m, the radius is 10m. Substituting these values into the formula gives us V = (π × 10² × 5), which we can calculate as V = 3.1416 × 100 × 5 = 1,570.8 cubic meters, rounded to the nearest tenths place.

Answer:

105 miles

Step-by-step explanation:

The question seeks to know the number of miles traveled by Tiera given that she received a certain amount of money in payment.

The total amount of money she received is $147. She receives $7 for every 5 miles traveled. The number of 5 miles traveled is calculated as 147/7 = 21

This means she traveled 5 miles 21 times.

Thus, the total number of miles she had traveled would be 21 * 5 = 105 miles in total

Answer:

A because the linesnever cross.

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

Answer:

8pi feet per second

Or, 25.1 feet per second (3 sf)

Step-by-step explanation:

C = 2pi×r

dC/dr = 2pi

dC/dt = dC/dr × dr/dt

= 2pi × 4 = 8pi feet per second

dC/dt = 25.1327412287

Answer:

Explanation:

The question is incomplete. The complete question is:

A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.

If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?

The probability that the first jelly bean will be green is the number of green jelly beans divided by the total number of jelly beans:

After chosing the first green jelly bean, there will be 13 jelly beans, from which 6 are red. Thus, the probability that the second jelly bean will be red is:

The probability of the joint events is the product of the two consecutive events:

The probability that the first jelly bean will be green and the second will be red is 12/91.

We start by determining the total number of jelly beans in the bag, which is:

6 red + 4 green + 4 blue = 14 jelly beans.

Step 1: Probability of the first jelly bean being green

The probability of drawing a green jelly bean first is the number of green jelly beans divided by the total number of jelly beans:

P(Green first) = 4/14 = 2/7.

Step 2: Probability of the second jelly bean being red

Once the first green jelly bean is chosen, there are now 13 jelly beans left in the bag, with 6 being red:

P(Red second | Green first) = 6/13.

Step 3: Combined probability

The combined probability of both events happening (first green, then red) is given by multiplying their individual probabilities:

P(Green first and Red second) = (2/7) * (6/13) = 12/91.

Thus, the combined probability is 12/91.

Complete question: A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?

Answer: kg*m^2 / s^3

​

Answer:

Answer: kg*m^2 / s^3

Step-by-step explanation:

Answer:

P =  x³ − 9x² + 36x − 54

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−3i is a zero, then 3+3i is also a zero.

P = (x − 3) (x − (3−3i)) (x − (3+3i))

P = (x − 3) (x − 3 + 3i) (x − 3 − 3i)

P = (x − 3) ((x − 3)² − (3i)²)

P = (x − 3) ((x − 3)² + 9)

P =  (x − 3)³ + 9 (x − 3)

P =  x³ − 9x² + 27x − 27 + 9x − 27

P =  x³ − 9x² + 36x − 54

Answer:

x = 2

y = 2 +  t

z = -20 -20t

Step-by-step explanation:

First, we are going to find the equation for this parabola. We replace x = 2 in the equation of the paraboloid, thus:

[tex]z = 6-x-x^{2} -5y^{2}[/tex]

if x = 2, then

[tex]z = 6-(2)-2^{2}-5y^{2}[/tex]

[tex]z = -5y^{2}[/tex]

Now, we calculate the tangent line to this parabola at the point (2,2,-20)

The parametrization of the parabola is:

x = 2

y = t  

[tex]z = -5t^{2}[/tex]  since [tex]z = -5y^{2}[/tex]

We calculate the derivative

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10t[/tex]

we evaluate the derivative in t=2, since at the point (2,2,-20) y = 2 and y = t

Thus:

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10(2)= -20[/tex]

Then, the director vector for the tangent line is (0,1,-20)

and the parametric equation for this line is:

x = 2

y = 2 +  t

z = -20 -20t

The parametric equation of the tangent line is [tex]L(t)=(2,2+t,-20-20t)[/tex]

The equation of Paraboloid is,

                 [tex]z =6-x-x^{2} -5y^{2}[/tex]

Equation of parabola when [tex]x = 2[/tex] is,

       [tex]z=6-2-2^{2} -5y^{2} \\\\z=-5y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(2,t,-5t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-10t)[/tex]

We get, the point [tex](2, 2, -20)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-20)[/tex]

The tangent line to this parabola at the point (2, 2, −20) will be,

     [tex]L(t)=(2,2,-20)+t(0,1,-20)\\\\L(t)=(2,2+t,-20-20t)[/tex]

Learn more about the Parametric equation here:

https://brainly.com/question/21845570

Answer:

D

Step-by-step explanation:

Answer:

12cm

Step-by-step explanation:

The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.

For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.

Radius of the Sphere=3cm

Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]

[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]

The Cone of same radius must be 12cm tall.

In a cyclic quadrilateral ( a quadrilateral that is inscribed in a circle),

opposite angles add up to 180 degrees. So you can form an equation and solve for x, and thus angle E.

Therefore:

(-2 + 6x) + (7x - 13) = 180

13x - 15 = 180

13x = 195

x = 15

So angle E = 5x

                 = 5 (15)

                 = 75 degrees

Answer:

3.5x + 15 ≥ 55

Step-by-step explanation:

I think the question below contains the missing information.

Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?

My answer:

Let x is the number of times he visits = 3.5x

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

We know the total points must be at least 55 for a free movie ticket.  This can be expressed as:

3.5x + 15 ≥ 55

Answer:

The answer to the question is

The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is  (-∞, 4)

Step-by-step explanation:

To apply look for the interval, we divide the ordinary differential equation by (t-4) to

y'' + [tex]\frac{3t}{t-4}[/tex] y' + [tex]\frac{4}{t-4}[/tex]y = [tex]\frac{2}{t-4}[/tex]

Using theorem 3.2.1 we have p(t) =  [tex]\frac{3t}{t-4}[/tex], q(t) =  [tex]\frac{4}{t-4}[/tex], g(t) = [tex]\frac{2}{t-4}[/tex]

Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.

The existence and uniqueness theorems for ODEs determine that the longest interval where the initial value problem has a unique and twice-differentiable solution is (0, 4), avoiding discontinuities at t=0 and t=4.

The initial value problem provided is a second-order linear ordinary differential equation (ODE) of the form:

t(t-4)y"+3ty'+4y=2, with initial conditions y(3)=0 and y'(3)=-1.

To determine the longest interval in which the solution is guaranteed to be unique and twice-differentiable, we need to consider the existence and uniqueness theorems for ODE's, which are predicated on the functions of the equation being continuous over the interval considered. Here, the coefficients of y" and y' are t(t-4) and 3t respectively. The problematic points occur where the coefficient of y" is zero because it will make the equation not well-defined, which occurs at t=0 and t=4. Therefore, the longest interval around the initial condition t=3 that avoids these points is (0, 4). Within this interval, the coefficients are continuous, and hence, the conditions for the existence and uniqueness of the solution are satisfied.

Answer:

(96π + 160) cm2

Step-by-step explanation: