Suppose I go on a fishing trip where I visit 4 lakes, lakes L1, L2, L3, and L4. Let C1 be the event that I catch a fish from lake L1. Let C2 be the event that I catch a fish from lake L2. Let
C3
be the event that I catch a fish from lake L3. Let
C4
be the event that I catch a fish from lake L4. I am a poor fisherman, so I am happy if I catch at least one fish. The lakes are far enough apart so that whether I catch a fish in any lake is independent from catching a fish in any other lake. There is a
.3
probability that C1 happens, a .4 probability that C2 happens, a .2 probability that C3 happens and a
.2
probability that C4 happens a. What is the probability I catch fish in all 4 lakes? b. What is the probability I do not catch any fish at all? c. What is the probability that I catch at least one fish? (I am happy.) d. What is the probability that I catch fish in Lake L1 and lake L2? e. What is the probability that I catch fish in lake L1 or lake L2? f. What is the probability that I catch fish in exactly one lake? Add any comments below.

Answers

Answer 1

The required probabilities of catching or not catching a fish is given by,

Catching fish in all 4 lakes = 0.0048

Not catching any fish at all = 0.2688

Catching at least one fish  = 0.7312

Catching fish in Lake L1 and lake L2 = 0.12

Catching fish in lake L1 or lake L2 = 0.58

Catching fish in exactly one lake = 1.1

Probability of catching fish in all 4 lakes,

Simply multiply the probabilities of catching fish in each lake,

since the events are independent,

P(C1 and C2 and C3 and C4)

= P(C1) x P(C2) x P(C3) x P(C4)

= 0.3 x 0.4 x 0.2 x 0.2

= 0.0048

= 0.48%

Probability of not catching any fish at all,

Probability of the complement of the event of catching at least one fish.

Happy if we catch at least one fish, the probability of not catching any fish is the probability that is not happy,

P(not happy)

= P(not C1 and not C2 and not C3 and not C4)

= (1 - P(C1)) x (1 - P(C2)) x (1 - P(C3)) x (1 - P(C4))

= 0.7 x 0.6 x 0.8 x 0.8

= 0.2688

= 26.88%

Probability of catching at least one fish,

Probability of the complement of the event of not catching any fish and subtract it from 1,

P(at least one fish)

= 1 - P(not happy)

= 1 - 0.2688

= 0.7312

= 73.12%

Probability of catching fish in Lake L1 and lake L2,

Simply multiply the probabilities of catching fish in each lake,

P(C1 and C2)

= P(C1) x P(C2)

= 0.3 x 0.4

= 0.12

= 12%

Probability of catching fish in lake L1 or lake L2,

Add the probabilities of catching fish in each lake,

And then subtract the probability of catching fish in both lakes to avoid double counting,

P(C1 or C2)

= P(C1) + P(C2) - P(C1 and C2)

= 0.3 + 0.4 - 0.12

= 0.58

= 58%

Probability of catching fish in exactly one lake can be broken down into four mutually exclusive events,

Catching fish in L1 only, catching fish in L2 only, catching fish in L3 only, or catching fish in L4 only.

Probabilities of each of these events is,

P(C1 or C2 or C3 or C4)

= P(C1) +  P(C2) + P(C3) + P(C4)

=  0.3 + 0.4 + 0.2 + 0.2

= 1.1

Learn more about probability here

brainly.com/question/31171507

#SPJ4


Related Questions

! 100 POINTS !
What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated. ​

Brainliest, ratings and thanks are promised if a helpful answer is received.

Answers

Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

6TH GRADE MATH, WRITE THE EQUATION FOR THIS GRAPH IN THE FORM OF Y=MX+B, TYSM

Answers

Answer:

m = 0

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (1,2)

We see the y stay the same and the x increase by 1, so the slope is

m = 0/1 = 0

So, the slope is 0

We have a circular plate of radius a
. The temperature distribution, u(rho,ϕ)
, has boundary conditions u(a,ϕ)=T1
when 0<ϕ<π
and T2
when π<ϕ<2π
. The steady state temperature distribution satisfies the Laplace equation.
I have used separation of variables to reduce the equation to two ODE's which I solved to find the general solution to be u(rho,ϕ)=∑Cλexp(λϕ)ϕλ
The question then asks us to find the Fourier series for u(a,ϕ)
. I did this by finding the series for the two boundary conditions which resulted in: u(a,ϕ)=(T1−T2)2+∑((−1m)−1)(T2−T1)sin(mϕ)πm
(Noted that I am not 100% sure this is correct)
The final part of the question, and the source of my problem, asks us to find an expression for u(rho,ϕ)
as an infinite series using the previous answer. I do not understand how to form a general solution using this - I cannot see how the Fourier series is of any relevance to a general solution as it doesnt appear to help us find Cλ
or λ
itself. Any help would be much appreciated!

Answers

the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.

The Fourier series approach that you have used helps in finding the solution to the boundary value problem, i.e., finding u(a,ϕ) for the given boundary conditions. However, to find a general solution to the Laplace equation, we need to use the superposition principle, which states that the sum of any two solutions to the Laplace equation is also a solution.

Therefore, we can use the previously obtained Fourier series solution for u(a,ϕ) as a building block to construct the general solution. We know that the Laplace equation has radial symmetry, which means that the temperature distribution is only a function of radius (rho) and not of angle (ϕ). Hence, we can write the general solution as:

u(rho,ϕ) = f(rho) + u(a,ϕ)

where f(rho) is the radial component of the solution and u(a,ϕ) is the previously obtained Fourier series solution.

To find f(rho), we need to solve the radial ODE using the boundary conditions at rho=0 and rho=a. Once we have obtained f(rho), we can add it to u(a,ϕ) to get the general solution.

Therefore, the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.

To know more about Fourier series solution  click here:

brainly.com/question/29672996

#SPJ4

the c on the left has blank1 - word answer please type your answer to submit electron geometry and a bond angle of

Answers

The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.

Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.

The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.

The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.

Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:

CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees

CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees

To know more about electron geometry:

https://brainly.com/question/7558603

#SPJ4

_____The given question is incomplete, the complete question is given below:

Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI

When conducting a survey, which of the following is the most important reason to use a random sample? Correct. Random selection ensures that the sample is unbiased on average, so that the results of the study can be generalized to the population.

Answers

Random sampling is crucial when surveying as it ensures that the sample selected is representative of the population.

By randomly selecting participants from the population, the sample is likely to be unbiased on average, which means that the results of the study can be generalized to the entire population. Without random sampling, the results of the study may be skewed or biased towards a certain group, which can lead to incorrect conclusions and poor decision-making. Therefore, it is essential to use random sampling when surveying to obtain accurate and reliable results.

Find out more about Random selection

at brainly.com/question/30135122

#SPJ4

please help asap!!!!!!!

Answers

To remove the y-term in  the given linear equation in two Variable multiply the equation by 4 then add these two equations.

What is linear equation in two Variable;

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.

According to given question;

5X+8y=5   ……..eqn 1.

3x-2y=3    ………eqn 2.

Multiply by 4 in the eqn 2.

We get

12x-8y=12 ……..eqn 3 .

When we add eqn 1 and eqn 3 we get ;

17x =17

X =1

To Know  more about linear equation in two Variable visit:

https://brainly.com/question/31143114

#SPJ1

After eliminating the y-term in the given equations i.e 5x+8y=5 and

3x-2y=3, The solution to the system of equations is x = 1, y = 0.

What is elimination method?

The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.

To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:

12x - 8y = 12

Now, you can add this equation to the first equation:

5x + 12x + 0y = 5 + 12

Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:

17x = 17

Solving for x gives you x = 1.

Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:

5(1) + 8y = 5

Simplifying this equation gives you:

8y = 0

Solving for y gives you y = 0.

To know more about linear equations visit:

https://brainly.com/question/13738061

#SPJ1

The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?

Answers

The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.

Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.

The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.

Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.

The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:

6.8x + 4.2(35 - x) (35 - x)

When we simplify, we get:

6.8x + 147 - 4.2x

2.6x + 147

The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:

35(5.31) = 185.85

When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:

2.6x + 147 = 185.85

Subtractiοn οf 147 frοm bοth sides yields:

2.6x = 38.85

When we divide by 2.6, we get:

x ≈ 14.94

Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.

To know more pοunds visit:

https://brainly.com/question/29145297

#SPJ1

Participant A did 120 jumping jacks in 10 minutes. Participant B did 140 jumping jacks in 14 minutes. Which participant had the greater jumping jack rate?​

Answers

Answer:  Participant A

Step-by-step explanation:

if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute

Raul's favorite gummy bear colors are yellow and red. He bought a package of gummy bears that only had his favorite colors. When he counted the gummy bears, he had 20 red and 23 yellow. What is the ratio of red gummy bears to yellow gummy bears?

Question 2 options:

23/20

23/43

20/23

20/43

Answers

The ratio between the number of red gummy bears to the number of yellow gummy bears is of:

20/23.

How to obtain the ratio?

The ratio between the number of red gummy bears and the number of yellow gummy bears is obtained applying the proportions in the context of the problem.

To obtain the ratio between two amounts A and B, you need to divide the first amount by the second amount. The result of this division will give you the ratio of the two amounts.

The amounts for this problem are given as follows:

Amount A: 20 red gummy bears.Amount B: 23 yellow gummy bears.

Hence the ratio between these two amounts is given as follows:

20/23.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

PLEASE HELP!
whoever answers right get brainliest!!!

Answers

Answer:

FIRST ONE "Deb sold vases for two years, neither sold nor bought the next year and then sold bases for two more years"

Step-by-step explanation:

Notice the number of bases in debs collection is DECREASING as the years passes for the first and third period. This is she is selling her vases but in the middle the number is the same (two point in the same horizontal line) this means she neither sold nor bought any vase in that period.

Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
92 19 41 24 75 53 70 3 67 64 9

Answers

Step-by-step explanation:

To find the range, we need to subtract the smallest value from the largest value in the dataset:

Range = Largest value - Smallest value

Range = 92 - 3

Range = 89

To find the variance and standard deviation, we need to calculate the mean first:

Mean = (Sum of all values) / (Number of values)

Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11

Mean = 45.09 (rounded to two decimal places)

Next, we need to calculate the variance:

Variance = (Sum of squared differences from the mean) / (Number of values - 1)

Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)

Variance = 1071.45 (rounded to two decimal places)

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = Square root of variance

Standard deviation = Square root of 1071.45

Standard deviation = 32.74 (rounded to two decimal places)

The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.

Find the probability of landing on yellow, the probability of the complement, and the sum of the event and the complement. Type your answers without any spaces.​

Answers

The probability of landing on yellow is 0.2, probability of component is 0.8, and sum of event and complement is 1.

On assuming that the pie is evenly divided into 5 parts,

So, the probability of landing on yellow is = 1/5 = 0.2,

The complement of landing on yellow is the probability of not landing on yellow, which is the probability of landing on any of the other 4 parts of the pie.

So, the probability of the complement is = 4/5 = 0.8,

The sum of the event (landing on yellow) and the complement (not landing on yellow) is equal to the probability of the entire sample space, which is 1.

⇒ P(Yellow) + P(Not Yellow) = 1

⇒ 0.2 + 0.8 = 1

So, the sum of the event and the complement is 1 or 100%.

Learn more about Probability here

https://brainly.com/question/16551257

#SPJ4

The given question is incomplete, the complete question is

A circular pie is divided in 5 parts , Green , Yellow, Blue Black and Red.

Find the probability of landing on yellow, the probability of complement, and the sum of the event and the complement.

The Stamp-M-Out Company manufactures rubber stamps. An inspector finds that there are 10 defective stamps in a sample of 700. a) What is the probability that a randomly selected stamp will be defective?

b) According to Stamp-M-Out Company quality control standards no more than 3.5% of stamps produced may be defective. Does Stamp-M-Out Company need to adjust its manufacturing process to meet this standard?

Answers

A defective stamp is likely to be chosen at random 1.4% of the time, or about 0.014 times. The observed percentage probability  faulty stamps is below the 3.5% maximum permitted rate,

How can I figure out probability?

Name an event from one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favorable outcomes from the total number of possibilities that are feasible.

P(faulty) = quantity of defective stamps divided by total quantity of stamps

P(defective) = 10/700.

0.014 P(defective)

Consequently, there is a 1.4% chance (or about 0.014) that a randomly chosen stamp will be flawed.

B-The observed percentage of flawed stamps is:

10 / 700 0.5 – 0.014

Divide this rate by 100 to get the percentage:

0.014 x 100 approximately 1.4%

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

What is the measure of angle ABC?

Answers

the awnser is 60 because it cant be any other awnsers because they are to wide or to small

tapas and paella that originated in what country

Answers

Answer: Spain

Tapas and Paella are from Spain, they serves as an appetizers

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.08°C and 1.68°C.

Answers

The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

What are the four types of probability?

Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.

The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.

To solve this problem, we must use the z-score formula to standardise the values:

z = (x - μ) / σ

where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.

The lower bound is -0.08°C:

z1 = (-0.08 - 0) / 1.00 = -0.08

1.68°C is the upper bound:

z2 = (1.68 - 0) / 1.00 = 1.68

We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.

The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:

P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854

As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.

To know more about probability visit:

https://brainly.com/question/30719832

#SPJ1

Use the slope and y-intercept to identify the equation of this line.

Answers

The equation of the line is y = -2x. The correct option is the last option y = -2x

Writing the equation of the line in the given graph

From the question, we are to write the equation of the line in the given graph using the slope and y-intercept from the graph

First, we will determine the slope of the graph

The slope of the graph calculated from the formula

Slope = Change in y / Change in x

Slope = (y₂ - y₁) / (x₂ - x₁)

Picking the points (-1, 2) and (0, 0)

Slope = (0 - 2) / (0 - (-1))

Slope = -2/(0 + 1)

Slope = -2/1

Thus,

Slope = -2

From the graph, the y-intercept of the graph is 0

Then,

From the slope-intercept form of the equation of a line,

y = mx + c

Where m is the slope

and c is the y-intercepts

The equation of the line is

y = -2x + 0

y = -2x

Hence, the equation is y = -2x

Learn more on Writing the equation of a line here: https://brainly.com/question/25722412

#SPJ1

which of the following assumptions must be true in order for this to be the correct sampling distribution

Answers

Since means cannot be smaller than 0, the sampling distribution of the mean is always right skewed.

No matter the sample size, the form of the sampling distribution of means is always the same as the population distribution.

We require two assumptions in order to apply the sampling distribution model to sample proportions: The selected values must be independent of one another, according to the independence assumption. The Sample Size Assumption demands that the sample size, n, be sufficiently large.

While doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.

To know more about sampling distribution, click the below link

https://brainly.com/question/29375938

#SPJ4

the actual question is :

Which of the following is true about the sampling distribution of the mean?

a. It is an observed distribution of scores

b. It is a hypothetical distribution

c. It will tend to be normally distributed with a

standard deviation equal to the population

standard deviation

d. The mean will be estimated by the standard

error

e. Both (a) and (b)

State whether the triangles could be proven congruent as SSS or SAS Theorem.

Answers

Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.

What do you mean by congruent triangles?

Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.

The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.

Here in the question,

It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.

Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.

Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.

To know more about congruent triangles, visit:

https://brainly.com/question/29639035

#SPJ1

NEED HELP ASAP 10 PONTS!!! please help me find the area and the perimeter!!!! i beg you at this point.

Answers

Answer: Area = 113.14 ft sq. Perimeter =

Step-by-step explanation:

break down the figure and solve area and perimeter for each

triangle = A = 1/2bh

A = 1/2 (8) (6)

A = 24 ft sq.

square = A = LW

A = (8) (8)

A = 64 ft sq

semi circle = A = 1/2 TT r^2

A = 1/2 (3.14) (4)^2

A = 1/2 (3.14) (16)

A = approximately 25.14 ft sq

rounded to hundredths

total AREA = 24 + 64 + 25.14 = 113.14

now we can find perimeter by breaking down the figures again

triangle

we know one leg is 6 ft and the other is 8 ft

we need to find the hypoteneuse using Pythagorean theorem.

a^2 + b^2 = c^2

6^2 = 8^2 = c^2

36 + 64 = c^2

100 = c^2

√100 = √c^2

10 ft = c

square

given two sides are 8ft and 8ft

semi circle - P is the same as circumference

P = ( 1/2 ) 2 π r

P = (1/2) (2) (3.14) (4)

P = 12.56

total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft

i attached a print screen showing my breakdowns

Explain the Pythagorean identity in terms of the unit circle.

Answers

The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

can someone help?

solve for x, using the secant lines
10cm, 7cm, 7cm. round to the nearest tenth

Answers

x = 4.9

Solution:

We can use the intersecting chords formula:

[tex]\text{(segment piece) x (segment piece) = (segment piece) x (segment piece)}[/tex]

[tex]7\times7 = 10x[/tex]

[tex]49 = 10x[/tex]

Divide each side by 10

[tex]49\div10=10x\div10[/tex]

[tex]4.9 = x[/tex]

Therefore, x = 4.9.

A human head can be approximated as a sphere with a circumference of 60
centimeters. What is the approximate volume of a human head, rounded to the nearest 1,000
cubic centimeters?(GEOMETRY HELP)

Answers

The approximate volume of a human head is 4000 cubic centimeter.

What is the approximate volume of a human head?

A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

The circumference of a sphere is given by the formula:

C = 2πr

Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:

60 cm = 2πr

Solve for r

r = 60/2π

r = 30/π

The volume of a sphere is given by the formula:

V = (4/3)πr³.

Substituting the value we found for r, we get:

V = (4/3) × π × ( 30/π )³

V = (4/3) × π × ( 30/π )³

V = 3647.566 cm³

V = 4000 cm³

Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.

Learn more about volume of sphere here: https://brainly.com/question/27933834

#SPJ1

solve the quadratic equation 9×^2-15×-6=0​

Answers

Answer:

To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:

x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)

Simplifying this expression gives:

x = (15 ± sqrt(225 + 216)) / 18

x = (15 ± sqrt(441)) / 18

x = (15 ± 21) / 18

So the two solutions to the quadratic equation are:

x = (15 + 21) / 18 = 2

x = (15 - 21) / 18 = -1/3

Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.

Earnings per Share, Price-Earnings Ratio, Dividend Yield

The following information was taken from the financial statements of Zeil Inc. for December 31 of the current fiscal year:

Common stock, $25 par value (no change during the year) $3,500,000
Preferred $10 stock, $100 par (no change during the year) 2,000,000
The net income was $424,000 and the declared dividends on the common stock were $35,000 for the current year. The market price of the common stock is $11.20 per share.

For the common stock, determine (a) the earnings per share, (b) the price-earnings ratio, (c) the dividends per share, and (d) the dividend yield. If required, round your answers to two decimal places.

a. Earnings per Share $fill in the blank 1

b. Price-Earnings Ratio fill in the blank 2

c. Dividends per Share $fill in the blank 3

d. Dividend Yield fill in the blank 4
%

Answers

Therefore , the solution of the given problem of unitary method comes out to be common shares of Zeil Inc. is 2.23%.

An unitary method is what?

This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.

Here,

Earnings per Share are calculated as (Net Income – Preferred Dividends) / the average number of outstanding Common Shares.

=>  Market price per share / earnings per share is the Price-Earnings Ratio.

=> Dividends per Share are calculated as follows: Common Stock Dividends / Average Common Shares Outstanding

=>  Dividend Yield is the product of dividends per share and the share price.

=>  (Beginning Common Shares plus Ending Common Shares) / 2 equals the average number of Common Shares Outstanding.

=>  Starting common shares equals ending common shares, which is

=>  $3,500,000 / $25, or 140,000.

(a) The earnings per share are ($424,000 - $0) / 140,000, which equals $3.03.

The ordinary stock price of Zeil Inc.

(b) The price-earnings ratio for Zeil Inc.'s common shares is 11.20 divided by 3.03, or 3.69.

(c) Dividends per Share: $35,000./140,000. = $0.25

Therefore, $0.25 in dividends are paid per unit of Zeil Inc. common stock.

(d) Dividend Yield: $0.25 divided by $11.20 equals 0.0223, or 2.23%.

The common shares of Zeil Inc. is 2.23%.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

After y - 4x = 12 is put in slope-intercept form, what is the slope?
-4
-1/4
-3
4

Answers

Given: y-4x=12

Add 4x to both sides:

y=4x+12

The function is now in y=mx+b form. The slope is 4.

find the area of a circle with a circumference of 50.24 50.24start color #11accd, 50, point, 24, end color #11accd units.

Answers

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Solving for the radius, we have:

r = C/(2π) = 50.24/(2π) ≈ 8

So the radius of the circle is approximately 8 units.

The formula for the area of a circle is A = πr^2, so we have:

A = π(8)^2 = 64π ≈ 201.06

Therefore, the area of the circle is approximately 201.06 square units.

Given the equation x² + 4x + y²-2y = 20: (HINT: Type in the equation is the desmos calculator and get the answers from the graph.)
What is the radius of the circle?
What is the center of the circle?

Answers

Answer:    

The radius of the circle is 3.

The center of the circle is (-2, 1).

Step-by-step explanation:

   Rewrite the equation in standard form:

   We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.

x² + 4x + y²-2y = 20

(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1

(x + 2)² + (y - 1)² = 25

   Identify the center and radius:

   Now that we have the equation in standard form, we can identify the center and radius of the circle.

The center is the point (-2, 1), which we can read directly from the equation.

The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.

Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.

the function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0. g

Answers

The required value of the function  (f + g)(x) for given f(x) and g(x) as ( 3 / √x )  - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Function f(x) is equals to,

( 3 / √x )  - ( 2 / x³ ) for all x > 0

Function g(x) is equals to,

g(x) = √(5x - 7)

To get the value of (f + g)(x),

Substitute the value of f(x) and g(x) and  add the functions f(x) and g(x) together,

Sum of f(x) and g(x) is equals to,

(f + g)(x)

= f(x) + g(x)

= ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7)

Therefore, value of the function (f + g)(x) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Learn more about function here

brainly.com/question/12827129

#SPJ4

The above question is incomplete, the complete question is:

The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).

3x + y = 6
Y + 2 = x

Answers

Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Other Questions
aaron has lost control of his finances and has been getting calls from debt collectors. his first step should be to The _____ approach treats laws as being actively constructed by judges as serving social policy goals, whereas ____ treats laws as evolved to reflect the principles found in nature. explain three ways that show how your personal online profile or post could negatively influence a prospective employers view of you during the recruitment process At periodic time intervals, ____ technology downloads updated, personalized information on your screen. 93. Electricity Usage The graph showsthe daily megawatts of electricity usedon a record-breaking summer day inSacramento, California.(a) Is this the graph of a function?(b) What is the domain?(c) Estimate the number of megawattsused at 8 A.M.(d) At what time was the most electric-ity used? the least electricity?(e) Call this function f. What is f(12)?Interpret this answer.(f) During what time intervals is usageincreasing? decreasing? _'s diamond model Theory of National Competitiveness sought to explain the factors that lead a country to have a competitive advantage over other countries in a certain product or products? a.Adam Smith b.David Ricardo c.Michael Porte. A girl walks from her home to a friends home 3 blocks north. She then walks 2 blocks east to the post office. 1 block north to the library, and one block east to the park. From the park, she walks 2 blocks west to the movie theater. After the movie, she walks 4 blocks south to the pet store. What is the girls displacement from her starting point to the pet store? Where is the location of the pet store in relation to her home? Calculate the distance she walked in blocks. What does it mean if you and your partner have the same moon sign? an american politician and attorney who is the 49th and current vice president of the us. she is the first female and first african american vp, who is she? how many legs does it take to make 109657 spiders Describe the evolution of the Auschwitz concentration camps in 3-5 sentences if a media company wants information on consumers' television viewing habits, it can purchase reports compiled by commercial research firms such as nielsen. this is an example of Commercial agriculture in dry climates relies heavily on irrigation. Which of the following best explains an environmental concern that results from irrigation in arid regions?The high use of water for agriculture increases the price of water for people in urban areas.The soil will have increased salinity, leading to soil erosion and reduced nutrients in the soil for plant health.The increased production that results from irrigation of the crop will lead to decreases in crop prices as the total crop harvested will be higher.The plants grown in this dry region will start to adapt to use less water, but the period to maturity will increase. Why does Twain call the apprentice an undeserving reptile Find the inverse of the function Which of the following sequence is used by the attacker, in the Directory Traversal Attacks to access restricted directories outside of the web server root directory. Select one/...//.....//../ When electrons flow along the electron transport chains of mitochondria, which of the changes occurs? The correct answer is (B) the pH of the matrix increases. As electrons are passed along the electron transport chains, protons are actively transported from the mitochondrial matrix into the intermembrane space. true or false there is a risk that a company will differentiate its products or services in ways that the customer does not value. we are too late . The train. _________ (leaving) Determine the total amount of money that was utilized on fuel in June 2022