You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing

Answers

Answer 1

Answer:

The distribution is  Poisson distribution

Step-by-step explanation:

From the question we are told that

   An expected number of fish was caught per hour is  1.5

The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution

   This because generally the  Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time


Related Questions

Jaclyn is one-fourth of a foot taller than John. John is 31/6 feet tall. How many feet tall is Jaclyn

Answers

Answer:

5 5/12

Step-by-step explanation:

31/6 feet + 1/4 foot

= 31/6 + 1/4

= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]

=  [ 124/24 ] + [ 6/24 ]

= (124 + 6) / 24

= 130 / 24

= 5 10/24

= 5 5/12

Hope this helps!  Tell me if I'm wrong!

Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room. If the bathroom measures 35 square feet, what is the area of the living room?\

Answers

25
Sfghhjjjjmmmmjjnmmmmmmm

Answer:

300 SF

Step-by-step explanation:

just took the test

A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.

a. Find the probability x = 2 cents.

b. Find the probability x = 6 cents.

c. Find the probability x = 10 cents.

d. Find the probability x = 11 cents.

e. Find the probability x = 15 cents.

f. Find the probability x = 20 cents.

g. Find the expected value of x.

Answers

Answer:

a. The probability x = 2 cents = 7/22

b. The probability x = 6 cents = 35/66

c. The probability x = 10 cents = 5/33

d. The probability x = 11 cents= 28/33

e. The probability x = 15 cents = 20/33

f. The probability x = 20 cents = 14/33

g. The expected value of x = 5.9

Step-by-step explanation:

This is a binomial probability distribution. The number of trials is known .

a. The probability x = 2 cents.

Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2

                                                    = 21 / 66 = 7/22

b. The probability x = 6 cents.

Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2

                                                    = 5*7 / 66 = 35/66

c. The probability x = 10 cents.

Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)

                                                    = 10/ 66 = 5/33

d. The probability x = 11 cents.

Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)

                                            = 8*7 / 66 = 56/66= 28/33

e. The probability x = 15 cents.

Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)

                                            = 8*5 / 66 = 40/66= 20/33

f. The probability x = 20 cents.

Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)

                                                = 28 / 66 = 14/33

g. The expected value of x.

E(X) = np

E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20

=2(59)/20= 5.9

Another trader would like to carry out a hypothesis test about stocks that offer dividends. Why is this hypothesis test right-tailed? Select the correct answer below: This is a right-tailed test because a direction is not specified. This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value. This is a right-tailed test because a direction is specified. The population parameter is less than the specified value. More information is needed.

Answers

Answer:

This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.

Step-by-step explanation:

The hypothesis testing technique is used to test an assumption regarding population parameter. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. A right tailed test is where the most of data is in the right side. This is one tailed test where the direction is specified.

STUCK Basic geometry A for senior year school

Answers

Answer:

(C) A reflection across a horizontal line and a horizontal translation

Step-by-step explanation:

We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.

Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.

Hope this helped!

Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

Answers

First find the critical points of f :

[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]

[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]

[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]

so the point (1, 0) is the only critical point, at which we have

[tex]f(1,0)=-7[/tex]

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]

Find the critical points of g :

[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]

[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]

[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]

where n is any integer. We get 4 critical points in the interval [0, 2π) at

[tex]t=0\implies f(10,0)=155[/tex]

[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]

[tex]t=\pi\implies f(-10,0)=235[/tex]

[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]

So f has a minimum of -7 and a maximum of 299.

Simplify to create an equivalent expression. 7n-(4n-3) a=3n+3 b=3n−3 c=11n+3 d=11n−3 I will rate you brainliest. :)

Answers

Answer:

3n +3

Step-by-step explanation:

7n-(4n-3)

Distribute the minus sign

7n -4n +3

3n +3

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

418 421 421 422 425 428 431 435 437
438 445 447 448 453 458 462 465
(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Note that it is plausible that the given sample observations were selected from a normal distribution and there are no outliers.

(___ , ___)



Does the interval suggest that 441 is a plausible value for true average degree of polymerization?

Yes or No


Does the interval suggest that 451 is a plausible value?

Yes or No

Answers

Answer:

Step-by-step explanation:

Form a set of values we get

n = 17

And with the help of a calculator

μ₀ = 438,47

σ  = 14,79

Normal Distribution is :  N ( 438,47 ; 14,79 )

c)

CI = 95 % means  α = 5 %    α/2 = 2,5 %    α/2 = 0,025

and as n < 30  we should use t-student distribution with n -1 degree of freedom  df = 16.  t score for 0,025 and 16 s from t-table 2,120

By definition:

CI = [  μ₀  ±  t α/2 ; n-1 * σ/√n ]

CI = [  μ₀  ± 2,120* 14,79/√17 ]

CI = [  μ₀  ±  7,60 ]

CI = [ 438,47 ± 7,60 ]

CI = [  430,87 ; 446,07 ]

95% confidence interval for true average degree of polymerization is  [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.

Given :

Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437,  438, 445, 447, 448, 453, 458, 462, 465 ]95% confidence interval.

The total number of values given is, n = 17

Mean, [tex]\mu_0=438.47[/tex]

Standard Deviation, [tex]\sigma = 14.79[/tex]

The normal distribution is given by: N (438.47 ; 14.79)

If Cl  is 95% then [tex]\alpha[/tex] is 5% and [tex]\alpha /2[/tex] is 2.5%

[tex]\alpha /2 = 0.025[/tex]

Now, use t-statistics distribution with (n-1) degree of freedom df = 16

So, the t score for 0.025 and 16 s from t-table 2.120.

[tex]\rm Cl = [\mu_0 \pm t_{\alpha /2};(n-1)\times \dfrac{\sigma}{\sqrt{n} }][/tex]

[tex]\rm Cl = [\mu_0 \pm 2.120\times \dfrac{14.79}{\sqrt{17} }][/tex]

[tex]\rm Cl = [\mu_0 \pm 7.60][/tex]

Cl = [430.87 ; 446.07]

Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.

No, the interval does not suggest that 451 is a plausible value.

For more information, refer to the link given below;

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I am performing a before and after evaluation on 30 students who have taken a keyboarding class. I want to see if the course improved their words per minute keyed.

Required:
a. State the Null and Alternate Hypothesis.
b. The statistic that I would use is:_________
c. What would my t critical be for this calculation at a 0.10 level of significance?
d. If my t calculated = 1.62, would I reject or fail to reject the null hypothesis?

Answers

Answer:

a)

H₀ : µd = 0  

H₁ : µd < 0  

b)

The test statistic is

tₙ₋₁ = α / s√n

c)

at 0.10 level of significance,

tₙ₋₁ , ₐ

t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311

d)

given that  T(critical) = 1.62

∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311

at 10% level of significance,

REJECT H₀

Since 1.62 > 1.311, we can reject the null hypothesis.

Translate and solve: 82 less than a is at least -82

Answers

Answer:

a≥0

Step-by-step explanation:

a-82≥-82

a≥-82+82

a≥0

The graph of g(x) = x – 8 is a transformation of the graph of f(x) = x. Which of
the following describes the transformation?
(A) translation 8 units down
(B) translation 8 units up
(C) translation 8 units right
(D) translation 8 units left

Answers

Technically the answer is both A and C, because you can see it as (x-8)^1, meaning 8 to the right, or just x-8, meaning 8 down.

Find a • b. a = 5i + 7j, b = -4i + 3j 1 41

Answers

Answer:

[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]

Step-by-step explanation:

[tex]\sf Plug \ in \ the \ values.[/tex]

[tex](5i+7j) \cdot (-4i+3j)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]

[tex]-20i^2 +15ij+-28ij +21j^2[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]-20i^2 -13ij+21j^2[/tex]

Given y(x) = f(x)g(x). Find the slope of the tangent line to y(x) at x = 7.​

Answers

Answer:

Step-by-step explanation:

Interesting problem.

At 6<x<8,

f(x) = x-7

at 5<x<8

g(x) = (15-x)/2

=>

y(x)

= f(x)*g(x)

= (x-7)(15-x)/2

= (x^2+22x-105)/2

differentiate y(x) with respect to x,

y'(x) = -x+11

at x = 7,

y'(7) = -(7) + 11 = 4

Solve Logarithm 5(2^x+4)=15. Round to the nearest thousandth. A.1.089 B.2.415 C.0.657 D.3.982

Answers

[tex]5(2^x+4)=15\\2^x+4=3\\2^x=-1\\x\in\emptyset[/tex]

Answer:

no solutions

Step-by-step explanation:

5(2^x+4)=15

Divide each side by 5

5/5(2^x+4)=15/5

(2^x+4)=3

Subtract 4 from each side

2^x = 3-4

2^x = -1

This cannot happen so there are no solutions

Draw the function
[tex]y = \tan(x) [/tex]
on the interval [-pi, pi]​

Answers

Answer:

The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.

Carl recorded the number of customers who visited his new store during the week:


Day Customers

Monday 17

Tuesday 13

Wednesday 14

Thursday 16


He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)


What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.

Answers

Answer:

The chi - square test can be [tex]\approx[/tex] 0.667

Step-by-step explanation:

From the given data :

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis: The number of customers does  follow  a uniform distribution

Alternative hypothesis: The number of customers does not  follow  a uniform distribution

We learnt that: Carl recorded the number of customers who visited his new store during the week:

Day              Customers

Monday               17

Tuesday              13

Wednesday         14

Thursday              16

The above given data was the observed value.

However, the question progress by stating that : He expected to have 15 customers each day.

Now; we can have an expected value for each customer  as:

                      Observed Value                   Expected Value

Day                 Customers                        

Monday                17                                          15

Tuesday               13                                          15

Wednesday          14                                          15

Thursday               16                                         15

The Chi square corresponding to each data can be determined by using the formula:

[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]

For Monday:

[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Tuesday :

[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Wednesday :

[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

For Thursday:

[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

                   Observed Value   Expected Value    chi - square

Day                 Customers                        

Monday                17                     15                       0.2666666667

Tuesday               13                     15                       0.2666666667

Wednesday          14                     15                       0.06666666667

Thursday               16                    15                       0.06666666667

Total :                                                                        0.6666666668

The chi - square test can be [tex]\approx[/tex] 0.667

At level of significance ∝ = 0.10

degree of freedom = n - 1

degree of freedom = 4 - 1

degree of freedom = 3

At ∝ = 0.10 and df = 3

The p - value for the chi - square test statistics is 0.880937

Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis

Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.

Answer:.67

Step-by-step explanation:

How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years? (which formula do I use? I am confused...txs)

Answers

Answer:

$3870

Step-by-step explanation:

Hello, the initial deposit is $1000.

After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)

= 1000 * 1.07

And we want to compound it so the second year we will get

[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]

And after n years, we will get

[tex]1000 * 1.07^n[/tex]

In that example, we want to know how much we will get after 20 years, so this is:

[tex]1000 * 1.07^{20}=3869.684462...[/tex]

Thank you.

When interest is compounded, it means that both the interest and the amount deposited will earn interest.

We are to determine the future value of $1000 with annual compounding.

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = amount deposited = $1000

R = interest rate = 7%

N = number of years = 20

$1000 x ( 1.07)^20 = $3,869.68

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This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!

Answers

Answer:

A Maybe

Step-by-step explanation:

Cogntive identification

Unable to answer mathematically or analytically

The Plan of the solid shape is shown by : (A)

What is the Meaning of solid shape?

A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.

A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.

solid shapes can take up space in the universe because they are more tangible and realistic.

In conclusion, the Plan of the solid shape is shown by : (A)

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I need help with the following question

Answers

Answer:

a. 2

b. x²+10x+26

c. x²+2x+2

Step-by-step explanation:

To find each value, you plug in the x value into the function and solve.

a. 2

f(2)=(2)²-2(2)+2                              [combine like terms]

f(2)=4-4+2

f(2)=2

---------------------------------------------------------------------------------------------------------

b. x²+10x+26

f(x+6)=(x+6)²-2(x+6)+2                  [use FOIL method and distributive property]

f(x+6)=x²+12x+36-2x-12+2            [combine like terms]

f(x+6)=x²+10x+26

---------------------------------------------------------------------------------------------------------

c. x²+2x+2

f(-x)=(-x)²-2(-x)+2                            [combine like terms]

f(-x)=x²+2x+2

This??? What is wrong with it?

Answers

Answer:

15.8 sq. in. of paper will be required.

Step-by-step explanation:

The problem is that a drinking cup does not have a cover, so only the lateral surface area counts.

I.e. We need only the first term.

A = pi r l = pi * 1.5 * sqrt(3^2+1.5^2)

= 15.81 sq. in.

10-
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
8-
(2,6)
-6
O x = 2
4
O x = 6
-2
-10 -3 -6 -22
2
4
B
8
10
X
O y = 2
O y = 6
(-34)
(814)
8
WO

Answers

Answer:

x = 2

Step-by-step explanation:

This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.

The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.

What is the Equation of line in Slope Intercept form?

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given is a line that passes through the points (-8, -4) and (8, -4).

This line is parallel to the X axis.

A line parallel to X axis has the equation y = b.

The y coordinate is -4 throughout the line.

So equation of the line is y = -4.

A line perpendicular to the given line will be parallel to Y axis.

Parallel lines to Y axis has the equation of the form x = a.

Line passes through the point (2, 6).

x coordinate will be 2 throughout.

So the equation of the perpendicular line is x = 2.

Hence the required equation is x = 2.

Learn more about Equations of Lines here :

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1. Why is money better than a bartering system?
A People might not have items to trade.
B It helps people to agree on the value of something.
C People might lose track of their money.
D Both A and B
E Both B and C

Answers

The correct answer is D. Both A and B

Explanation:

Bartering is an economic system in which products are directly exchanged for other products. For example, a pound of oranges is exchanged for a pound of rice. Due to this, in bartering, there is no money or elements such as coins or bills that represent the value of products or services. This system has both advantages and disadvantages in comparison to the use of money.

In terms of disadvantages, bartering implies individuals need products or services they can use to exchange, which might not be possible for all individuals as not all individuals might produce a product or have a product other are interested in. Also, in bartering the value of products varies, for example, a pound of blueberries can be equal to a pound of rice, three pounds of rice, or even half pound of rice, as values change according to the situation of those participating in the exchange. This means, in bartering the value fluctuates and it is more difficult to agree on the value of something, which does not occur if money is used as each product has a defined price which might just vary slightly. According to this, options A and B are advantages of money over bartering.

A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.

Answers

Answer:

a. False

b. True

c. False

d. False

e.True

f. True

Step-by-step explanation:

The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.

idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast

Graph -8x-y=8

Answers

Answer:

(-1,0) and (0,-8)

Step-by-step explanation:

Hey there!

Well first we’ll graph -8x - y = 8,

Look at the image below

By lookig at the image below we can tell the 2 points are at,

(-1,0) and (0,-8)

Hope this helps :)

Someone please help me ASAP

Answers

Answer:

x > -7/3

Step-by-step explanation:

-3x+8 < 15

Subtract 8 from each side

-3x+8-8 < 15-8

-3x < 7

Divide by 3 remembering to flip the inequality

-3x/-3 > 7/-3

x > -7/3

Answer:

[tex]x <-\frac{7}{3}[/tex]

Determine the Perimeter of the shape #1.

Answers

Answer:

56.8

Step-by-step explanation:

7.1*8=56.8

-8 + (-15)
Evaluate this expression ​

Answers

Answer:

-23

Step-by-step explanation:

-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.


What is the midline equation of the function h(x) = -4 cos(5x - 9) - 7?

Answers

Answer: Midline equation: y = -7

Step-by-step explanation: This function is a sinusoidal function of the form:

y = a.cos(b(x+c))+d

Midline is a horizontal line where the function oscillates above and below.

In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,

Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]

Answer:

y=-7

Step-by-step explanation:

What is the mulitplicative rate of change for the exponential function f(x) = 2 (5over2) to the negative x power ?

Answers

Answer:

  2/5

Step-by-step explanation:

  f(x) = 2(5/2)^-x = 2(2/5)^x

The multiplicative rate of change is the base of the positive exponent, 2/5.

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Answers

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Answer:

[tex] BD = c*sin(A) [/tex]

[tex] BD = c*cos(B) [/tex]

[tex] BD = b*tan(A) [/tex]

Step-by-step explanation:

∆ABD is a right triangle.

Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.

SOH => sin(θ) = opposite/hypotenuse

CAH => Cos(θ) = adjacent/hypotenuse

TOA = tan(θ) = opposite/adjacent

Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:

Let BD = x

AB = c

AD = b

=>The sine ratio for the length of line segment BD = x, using SOH.

θ = A

Opposite = DB = x

hypotenuse = AB = c

[tex] sin(A) = \frac{x}{c} [/tex]

Make x the subject of formula.

[tex] c*sin(A) = x [/tex]

[tex] BD = x = c*sin(A) [/tex]

=>The Cosine ratio for the length of line segment BD = x, using CAH

θ = B

Adjacent = DB = x

hypotenuse = AB = c

[tex] cos(B) = \frac{x}{c} [/tex]

Make x the subject of formula.

[tex] c*cos(B) = x [/tex]

[tex] BD = x = c*cos(B) [/tex]

=>The Tangent ratio for the length of line segment BD = x, using TOA

θ = A

Adjacent = DB = x

hypotenuse = AD = b

[tex] tan(A) = \frac{x}{b} [/tex]

Make x the subject of formula.

[tex] b*tan(A) = x [/tex]

[tex] BD = x = b*tan(A) [/tex]

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