122. Density Function of Y Let X = N(0, 1). Calculate the density function of Y = √|X|.
Answers
The density function of Y, denoted as \(f_Y\)(y), is given by \(f_Y\)(y) = 2y × φ(y²), where φ(y) is the standard normal density function.
To find the density function of Y = √|X|, we need to calculate the cumulative distribution function (CDF) of Y and then differentiate it to obtain the density function.
Start with the CDF of Y:
\(f_Y\)(y) = P(Y ≤ y) = P(√|X| ≤ y)
Since X is normally distributed with mean 0 and variance 1, we know that X follows a standard normal distribution.
We can rewrite the CDF of Y in terms of X:
\(f_Y\)(y) = P(-y ≤ √|X| ≤ y) = P(X ≤ y²) - P(X ≤ -y²)
Using the standard normal distribution table, we can find the probabilities:
\(f_Y\)(y) = Φ(y²) - Φ(-y²)
Differentiating the CDF with respect to y, we obtain the density function of Y:
\(f_Y\)(y) = d/dy[\(f_Y\)(y)] = d/dy[Φ(y²) - Φ(-y²)]
Simplifying the derivative, we get:
\(f_Y\)(y) = 2y × φ(y²)
where φ(y) is the standard normal density function.
Thus, the density function of Y is \(f_Y\)(y) = 2y × φ(y²), where φ(y) is the standard normal density function.
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Related Questions
during an accident, skid marks may result from sudden breaking. the formula approximates a vehicle's speed, s, in miles per hour given the length d in feet of the skid marks. if skid marks on dry concrete are 54 feet long, how fast was the car traveling when the brakes were applied?
Answers
The car was travelling with the speed of 183.5 mph when the brakes were applied.
The pace at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed. M/s is the SI unit of speed. We will learn more about the speed formula and its uses in this section.
Let's continue and investigate the speed formula in this part in more detail. Speed can be expressed in a variety of ways, including m/s, km/hr, miles/hr, etc. [LT-1] is the dimensional formula for speed. A body's speed may be defined as how quickly it is going. The equation for a given body's speed may be written as,
Speed = Distance ÷ Time
We have the equation,
\(s=\frac{\sqrt{d} }{0.04}\)
we have the value of d as 54
putting the value pf d in the equation we get,
\(s=\frac{\sqrt{54} }{0.04}\)
s = 7.34/0.04
s = 183.5 mph
So the car was travelling with the speed of 183.5 mph when the brakes were applied.
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Complete question:
The speed that a vehicle was traveling, s, in miles per hour, when the brakes were first applied, can be estimated using the formula
\(s=\frac{\sqrt{d} }{0.04}\) where d is the length of the vehicle's skid marks, in feet.
if skid marks on dry concrete are 54 feet long, how fast was the car traveling when the brakes were applied?
A circular feild has a diameter of 32 meters. A farmer wants to build a fence around the edge of the feild. Each metre of fence will cost £15. 95
Work out the total cost of the fence
Answers
The total cost of the fence is £1603.87.
Given,
The diameter of a circular field = 32 meters.
The cost of each meter of fence = £15.95
We are to find the total cost of the fence.In a circle, the perimeter is given by;
Perimeter = π × diameter
The radius of a circle is the half of the diameter.
Thus, the radius of the circular field can be obtained as follows;
Radius, r = diameter/2r
= 32/2
= 16m
Hence, the circumference of the circular field
= 2 × π × r
= 2 × π × 16
= 100.53 m
Now we can obtain the total cost of the fence as follows;
Total cost = cost per meter of fence × perimeter
= £15.95 × 100.53
= £1603.87
Therefore, the total cost of the fence is £1603.87.
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What fractional part of the bar is blue? ill mark brainliest!
Group of answer choices
1/6
2/6 or 1/3
3/6 or 1/2
4/6 or 2/3
Answers
Answer:
3/6 or 1/2
Step-by-step explanation:
⇒ out of 6 blocks 3 are shaded so, it will be 3/6
⇒ out of 6 blocks 3 are shaded (3 is half of 6) so, it will be 1/2
Answer:
Answer: 3/6 or 1/2
Step-by-step explanation:
Basically there are six bars and we are to find the fractional part of the blue bars. The fractional part of the blue bars is 3/6 or 1/2.
Select the expression equivalent to(6x + 5)-(4x – 6).
Answers
6. A company ordering parts
$20 per part. Which equation represents the cost c(in dollars) of ordering p parts?
F. c= 25 + 20p
G. c= 20 + 25p
1. p= 20 + 25c
H. p= 25+ 200
8. Which property is illustrated by the statement?
Answers
p=20+25c because it i did this on paper so i got what it equals to
How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers probability?
Answers
The total number of possible 7-place license plates are 67600000.
Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible
Let's solve the given problem:
The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.
Combination of letters: As there are no restrictions given in the question, so the first letter can be any alphabet out of the 26 alphabets (A, B, C, D, ......... Z). So the first place for the letter can be filled in ²⁶C₁ ways that are 26 ways. Also for the second place, as the letters can repeat so it can be filled in ²⁶C₁ ways too which are 26 ways. Therefore, the possible ways in which the place for two letters can be filled is 26 × 26 ways = 676 ways.Combination of numbers: As there are no restrictions given in the question so the first number can be any of the numbers out of the 10 numbers (10, 1, 2, 3, ....... 9). So the first number can be filled in ¹⁰C₁ = 10 ways. Similarly, as the numbers can repeat so the 2nd, 3rd, 4th and 5th numbers can be filled in ¹⁰C₁ ways that all the other places can be filled in 10 ways each. Therefore the total number of ways in which the place for 5 numbers can be filled is 10 × 10 × 10 × 10 × 10 ways = 100000 ways.Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled
= 676 × 100000
= 67600000 ways
Hence the total number of possible 7-place license plates are 67600000.
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An animal shelter conducts an annual fundraising drive. The animal shelter must raise at least enough money to cover their annual rental of $2,500 and weekly expenses of $450. So far, the shelter has received a one-time donation of $125 and pledged donations of $680 per week. Which inequality can be used to find w, the number of weeks it can take for the shelter to meet the goal?
Answers
The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10
To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.
Let's break down the expenses and donations:
Expenses:
Annual rental = $2,500
Weekly expenses = $450
Donations:
One-time donation = $125
Pledged donations per week = $680
Let w represent the number of weeks it takes for the shelter to meet its goal.
Total expenses for w weeks = Annual rental + Weekly expenses * w
Total expenses = $2,500 + $450w
Total donations for w weeks = One-time donation + Pledged donations per week * w
Total donations = $125 + $680w
To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:
Total donations ≥ Total expenses
$125 + $680w ≥ $2,500 + $450w
Simplifying the inequality, we have:
$230w ≥ $2,375
Dividing both sides of the inequality by 230, we get:
w ≥ $2,375 / $230
Rounding the result to the nearest whole number, we have:
w ≥ 10
Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:
w ≥ 10
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You plan to purchase a house for 12.5 million baht, using a 30-year mortgage. You will make a down payment of 15 percent of the purchase price and you will not pay off the mortgage early. Ignore taxes in your analysis. Your bank offers you the following two options for payment.
Option 1: Mortgage rate of 7.25 percent and zero points.
Option 2: Mortgage rate of 6.75 percent and 4 points.
You would choose option ------- (1 or 2) because the Net Present Value of choosing option 2 is------ . (The answer can be negative. Do not round intermediate calculations and round your answer to two decimal places, e.g., 32.16.)
Answers
Option 2 has a lower NPV and thus should be chosen as it results in less total payment and better savings. Hence, you would choose option 2 as the Net Present Value of choosing option 2 is -9,903,615.48.
Given:
Purchase price = 12.5 million baht
Down payment = 15%30-year mortgage
We have to calculate the option which is best for us.
Option 1: Mortgage rate = 7.25%
Option 2:Mortgage rate = 6.75%
(a) Monthly Payment of Option 1:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12
= 360
i = 7.25%/12
= 0.006042857
Yearly Interest Paid = i * 10,625,000
= 64,515.48 baht
Monthly Interest Paid = 64,515.48 / 12
= 5,376.29 baht
EMI =\([P x R x (1+R)^n] / [(1+R)^n-1]\)
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI = \([10,625,000 x 0.006042857 x (1+0.006042857)^360] / [(1+0.006042857)^360-1]\)
EMI = 69,677.31 baht
(b) Monthly Payment of Option 2:
Loan Amount = 12.5 * (100-15)%
= 10,625,000 baht
n = 30 * 12 = 360
i = 6.75%/12 = 0.005625
Yearly Interest Paid = i * 10,625,000
= 59,765.63 baht
Monthly Interest Paid = 59,765.63 / 12
= 4,980.47 baht
Point cost = 4% of Loan Amount
= 10,625,000 x 4/100
= 425,000 baht
Loan Amount after Deducting Points = 10,625,000 - 425,000
= 10,200,000 baht
EMI = \([P x R x (1+R)^n] / [(1+R)^n-1]\)
where P = Loan Amount, R= Interest Rate per month, n= total number of payments.
EMI =\([10,200,000 x 0.005625 x (1+0.005625)^360] / [(1+0.005625)^360-1]\)
EMI = 66,128.92 baht
(c) We have to calculate the NPV of the payments to decide which option is better.
We use the formula to calculate NPV:-
NPV = - \([B + (PMT / i) * (1 - (1 + i)^-n)] / ((1 + i)^t)\)
Where B = amount borrowed, PMT = monthly payment, i = interest rate, n = total number of payments, t = year.
NPV =\(- [10625000 + (69677.31 / 0.006042857) * (1 - (1 + 0.006042857)^-360)] / ((1 + 0.006042857)^30)\)
= -9,892,571.85 baht
NPV = \(- [10200000 + (66128.92 / 0.005625) * (1 - (1 + 0.005625)^-360)] / ((1 + 0.005625)^30)\)
= -9,903,615.48 baht
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student chosen randomly from the class passed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
12
2
4
3
Answers
Answer:
20/27
Step-by-step explanation:
What is the slope of the line that passes through the points (-6, -10) and (3,-13)? Write your answer in simplest form.
Answers
We must use slope formula* to solve this.
\(\frac{-13 - (-10)}{3 - (-6)}\\\\\frac{-3}{9} = -\frac{1}{3}\)
m** = \(-\frac{1}{3}\)
*Slope Formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
**m is the symbol for slope.
At the surface of the ocean, the water pressure on the submarine is the same as the air pressure above the water—about 15 lb/in.2. Below the surface, the water pressure increases by about 9 lb/in.2 for every 20 ft of descent. What are the x and y values?
Answers
The x and y values represent the depth of descent and the corresponding increase in water pressure, respectively, along the linear relationship described by the equation.
To find the x and y values, we can set up a linear equation that represents the relationship between the depth of descent and the increase in water pressure.
Let's denote the depth of descent as x (in feet) and the increase in water pressure as y (in lb/in²).
We know that for every 20 ft of descent, the water pressure increases by 9 lb/in². This gives us a slope of 9/20 (change in y/change in x).
So, the slope (m) of the linear equation is 9/20.
Now, we need to find the y-intercept, which represents the water pressure at the surface of the ocean (0 ft descent). We know that at the surface, the water pressure is 15 lb/in².
Therefore, the y-intercept (b) is 15.
Putting it all together, the linear equation that represents the relationship between depth of descent (x) and increases in water pressure (y) is:
y = (9/20)x + 15.
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1. Assume random samples from normal populations with known variance (or standard deviation) were drawn. Find confidence intervals for the true population mean given the sample mean, population variance/standard deviation, and the confidence/alpha level.
a. N = 28, M = 14, 2 = 6, confidence level = 95%
b. N = 65, M= 190, =12, = 0.01
2. Now, suppose the population variance is not known, and the variance/standard deviation values given in the previous question are actually sample statistics. Find the confidence intervals using the t-distribution.
3. How do the results from question 2 compare to the results from question 1? (Respond in the form of a sentence.)
Answers
To find confidence intervals for the true population mean given the sample mean, population variance/standard deviation, and the confidence/alpha level.
1(a). Confidence Interval ≈ (11.79, 16.21)
1(b). Confidence Interval ≈ (186.67, 193.33)
1a. To find the confidence interval for the true population mean when the population variance or standard deviation is known, we can use the formula:
Confidence Interval = Sample Mean ± (Z * (Population Standard Deviation / √(Sample Size)))
Given N = 28, M = 14, σ = 6, and a confidence level of 95%, we need to find the critical value Z corresponding to the confidence level. For a 95% confidence level, Z is approximately 1.96.
Substituting the values into the formula:
Confidence Interval = 14 ± (1.96 * (6 / √28))
Calculating the confidence interval:
Confidence Interval = 14 ± (1.96 * 1.131)
Confidence Interval ≈ (11.79, 16.21)
1b. Similarly, for N = 65, M = 190, σ = 12, and α = 0.01, we find the critical value Z corresponding to a 99% confidence level. Z is approximately 2.33 for a 99% confidence level.
Confidence Interval = 190 ± (2.33 * (12 / √65))
Calculating the confidence interval:
Confidence Interval = 190 ± (2.33 * 1.491)
Confidence Interval ≈ (186.67, 193.33)
2.When the population variance is not known and sample statistics are used, we need to use the t-distribution instead of the standard normal distribution. The formula for the confidence interval remains the same, but we replace the critical value Z with the critical value t, which depends on the degrees of freedom (df) based on the sample size.
3.The results from question 2 using the t-distribution will generally yield wider confidence intervals compared to those from question 1 using the standard normal distribution. This is because the t-distribution has fatter tails than the standard normal distribution, accounting for the additional uncertainty when estimating the population mean with limited sample information. Therefore, the confidence intervals obtained using the t-distribution provide a more conservative estimate of the true population mean.
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2x(x + y) + 2(x2 + 3xy)
Answers
Answer:
4x² + 8xy
Step-by-step explanation:
Given
2x(x + y) + 2(x² + 3xy) ← distribute both parenthesis
= 2x² + 2xy + 2x² + 6xy ← collect like terms
= 4x² + 8xy
Asymptote (horizontal) of f(x)=2(3)^-x
Answers
The Value of the horizontal asymptote is 0
What is horizontal asymptote?
The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute \(x=\)±∞. We can also find the vertical asymptote.
now we are given a function
\(f(x)=2(3)^{-x}\)
Now substitute x=±∞ in the equation, as the x in denominator we get
f(x)= 0
This is the value of the horizontal asymptote
Hence the value of horizontal asymptote comes out to be 0
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My girl friends face
whats 7x7
Answers
Answer: Why is the basic math question is here? But the answer is 49, don’t put the basic expression next time!
Step-by-step explanation:
Answer: this is 2 grade stuff but ok... 49
A pharmaceutical company wants to determine if its new medicine helps heal bruises more quickly than not treating the bruise. What type of study would be best suited to make this determination?(a) Survey(b) Simulation(c) Experimental(d) Observational.
Answers
The best type of study to make this determination would be an Experimental study. (C)
In an experimental study, the researcher manipulates one or more variables and measures the effect on another variable. In this case, the variable being manipulated is the new medicine, and the variable being measured is the healing time of the bruise.
By comparing the healing time of bruises treated with the new medicine to those not treated, the pharmaceutical company can determine if their new medicine is effective.
An experimental study (C) is the best choice for this type of research because it allows the researcher to control for other variables that may affect the outcome, such as the severity of the bruise or the age of the patient. This control helps to ensure that any differences in healing time are due to the new medicine and not other factors.
A survey would not be appropriate because it would not allow for the manipulation of variables or the control of other factors.
A simulation would also not be appropriate because it would not involve actual patients or real bruises. An observational study would not be appropriate because it would not allow for the manipulation of variables or the control of other factors.
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Given ABCD is a parallelogram, prove AB CD and BC & AD.
Answers
Does anyone know the correct choice for this question? If its correct ill mark you as the best answer choice!
Answers
Answer:
A
Step-by-step explanation:
The slope is positive. Also, using the rise/run method, I found that the slope is 3. The b is 4 because the line crosses the y axis at 4.
Answer:
A) go to desmos.graphingcal for future help with graph questions.
Step-by-step explanation:
go to desmos online graphing cal and enter you points
enter the following:
f(x)=3x+4
(-1,1)
(0,4)
(1,7)
money is invested in a saving account at 12% simple interest.after one year there is $1680 in the account. how much was originally invested?
Answers
Step-by-step explanation:
check the pic. I just sent
the answer is $1500
The originally invested price will be;
⇒ $1,500
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Money is invested in a saving account at 12% simple interest.
And, After one year there is $1680 in the account.
Now,
Let the original invested amount = x
So, We can formulate;
⇒ x + 12% of x = 1680
⇒ x + 12x/100 = 1680
⇒ 112x = 1680 × 100
⇒ 112x = 1,68,000
⇒ x = 1,68,000/112
⇒ x = $1,500
Thus, The original invested amount = $1,500
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Find the Nth term of this number sequnce
7,10,13,16
Answers
\(\text{It is an arithmetic series.}\\\\\text{First term,}~ a = 7\\\\\text{Common difference,}~ d=10 -7 = 3\\\\\text{Nth term} = a + (n -1) d\\\\~~~~~~~~~~~~~=7+(n-1)3\\\\~~~~~~~~~~~~~=7+3n-3\\\\~~~~~~~~~~~~~=4+3n\)
What's the volume of a sphere with a radius of one.
Answers
Answer:
Step-by-step explanation:
Givens
r = 1
V = ?
pi = 3.14
Formula
V = 4/3 * pi * r^3
Solution
V = 4/3 * 3.14 * 1^3
V = 4.1867 m^3
find the area of the figure.
Answers
Answer:
The are is 136 cm.
Step-by-step explanation:
12 * 8 = 96cm
8 * 4 = 32cm
96 + 32 = 128cm
8 - 4 = 4 / 2 = 2
4 * 2 = 8
128 + 8 = 136cm
plz mark as brainliest if correct!
Answer:
Step-by-step explanation:
12-4=8
area=8×8+(8+4)/2 ×4
=64+6×4
=64+24
=88 cm²
an independent research was made asking people about their bank deposits. using the data in the table, calculate the deposit sample mean and deposit sample standard deviation
Answers
To calculate the deposit sample mean, we need to add up all the bank deposits and divide by the number of respondents. From the table, the total bank deposits is $45,000 and there are 10 respondents. So the deposit sample mean is:
Deposit sample mean = Total bank deposits / Number of respondents
Deposit sample mean = $45,000 / 10
Deposit sample mean = $4,500
To calculate the deposit sample standard deviation, we need to first find the differences between each respondent's bank deposit and the sample mean. We then square these differences, add them up, divide by the number of respondents minus one (known as the degrees of freedom), and then take the square root. Here are the steps:
Step 1: Find the differences between each respondent's bank deposit and the sample mean:
Respondent 1: $3,000 - $4,500 = -$1,500
Respondent 2: $5,000 - $4,500 = $500
Respondent 3: $4,500 - $4,500 = $0
Respondent 4: $6,000 - $4,500 = $1,500
Respondent 5: $3,500 - $4,500 = -$1,000
Respondent 6: $5,500 - $4,500 = $1,000
Respondent 7: $6,500 - $4,500 = $2,000
Respondent 8: $4,000 - $4,500 = -$500
Respondent 9: $4,500 - $4,500 = $0
Respondent 10: $4,500 - $4,500 = $0
Step 2: Square each difference:
Respondent 1: (-$1,500)^2 = $2,250,000
Respondent 2: $500^2 = $250,000
Respondent 3: $0^2 = $0
Respondent 4: $1,500^2 = $2,250,000
Respondent 5: (-$1,000)^2 = $1,000,000
Respondent 6: $1,000^2 = $1,000,000
Respondent 7: $2,000^2 = $4,000,000
Respondent 8: (-$500)^2 = $250,000
Respondent 9: $0^2 = $0
Respondent 10: $0^2 = $0
Step 3: Add up the squared differences:
$2,250,000 + $250,000 + $0 + $2,250,000 + $1,000,000 + $1,000,000 + $4,000,000 + $250,000 + $0 + $0 = $11,000,000
Step 4: Divide by the degrees of freedom (number of respondents minus one):
$11,000,000 / 9 = $1,222,222.22
Step 5: Take the square root:
Deposit sample standard deviation = √$1,222,222.22 = $1,105.54
Therefore, the deposit sample mean is $4,500 and the deposit sample standard deviation is $1,105.54.
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why is paying back along with a nominal interest rate of 13.62% if the interest is compounded quarterly, how much greater is white effective interest rate than his nominal interest rate
Answers
The required white effective interest rate is 0.71% more than his nominal interest rate.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent
So
Difference in interest = 14.33%-13.62%
=0.71%
Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.
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HELP Solve: p – 23 = 23 A. p = 24 B. p = 46 C. p = 52 D. p = 44
Answers
Answer:
B. p=46
Step-by-step explanation:
46
- 23
23
Answer:
B
Step-by-step explanation:
how many are 7 raised to 3 ???
Answers
Answer:
343
Step-by-step explanation:
7^3 =
7*7*7
343
Roberto' employer offer a liding paid vacation. When he tarted work, he wa given three paid day of vacation. For each ix-month period he tay at the job, hi vacation i increaed by two day. Let x repreent the number of 6-month period worked and y repreent the total number of paid vacation day. Write an equation that mode the relationhip between thee two variable
Answers
An equation that mode the relationship between thee two variable is y=2x+3 .
Let x represent the number of 6-month period worked
Let y represent the total number of paid vacation day
According to the question,
When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.
Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19
An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).
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An automatic dog feeder contains 30 cups of food and dispenses 2 cups of dog food each day. What expression can the dog owner use to express the amount of food left in the feeder after d days?
Answers
9514 1404 393
Answer:
30 -2d
Step-by-step explanation:
The total amount used in d days is 2d (cups). The amount remaining is the initial amount (30 cups) less the amount used. A suitable expression is ...
30 - 2d
. Given that O is the centre of the following circle, find the values of the unknowns.
Answers
Given:
Radius of circle is 13 cm
Height of triangle is 5 cm
To find:
Value of 'a' and 'b'
Steps:
To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,
A² + B² = C²
\(a^{2} + 5^{2} = 13^{2}\)
\(a^{2} + 25 = 169\)
\(a^{2} = 169 - 25\)
\(a^{2} = 144\)
\(\sqrt{a^{2}}=\sqrt{144}\)
\(a = 12\)
Now to find the value of 'b', i will use law of cosine,
\(c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }\)
\(12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38\)
Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively
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find the measure of the missing angles
Answers
Answer:
b=80
c=80
Step-by-step explanation:
the angle opposite to the 100 degree angle is congruent to it
same goes for b and c
so far we have 2 angles that measure 100 degrees 100+100=200
the sum of the 4 angles is 360
360-200=160
160/2=80=b=c
because of where 100 is you can make a line where b and c are. a straight line is 180 so you subtract from 100 to get 80