The statement is true , that the given sample follows binomial distribution.
If a random variable has two alternative outcomes (success or failure), it has a binomial distribution.
Each draw must be separate from the ones that came before it.
There is a set number of drawn components.
We randomly select 15 students, and since the sample size of 15 is less than 10% of the total population, we can assume that each draw is independent.
Because X has a binomial distribution, success is determined by whether the student is left-handed (failure is determined by whether the student is not left-handed).
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for success or failure as the possible outcomes of an experiment.
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If f(x)=x+7 and g(x)=1/x-13}, what is the domain of (f g)(x) ?
{x l x ≠6}
{x l x ≠-6}
{x l x ≠ 13}
{x l x ≠ 13}
domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)
What is domain of function?Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.
Given: f(x) = x+7
g(x) = 1/(x-13)
First we need to find (f.g)(x) i.e multiplication of f(x) and g(x)
(f.g)(x) = (x+7) ×1/(x-13) = [tex]\frac{x+7}{x-13}[/tex]
Domain of function is values of x over which function is defined
For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.
So, x - 13 ≠ 0
Adding 13 on both sides, we get
x ≠ 13
So domain of (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}
Hence, option (c) is correct answer.
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Twenty five out of 40 student athletes received over 3.0 gpa or better this semester. What percent of student athletes received under a 3.0 gpa?
A. 37.5
B. 35.7
C. 50
D. 39.5
Answer: A. 37.5%
Step-by-step explanation:
Technically, you can't even solve this, because you don't know how many athletes got exactly a 3.0 GPA.
Ignoring this major oversight, let's just say that no one received a 3.0 GPA. In that case, there would be 40 - 25 = 15 athletes who received a sub-3.0 GPA.
Therefore, the percentage of student athletes who received a sub-3.0 GPA is 15/40 = 3/8 = 37.5%.
Write an equation of the line that passes through the given points.
(−7,0),(−7,5)
Answer:
x= -7
Step-by-step explanation:
the 2 x values are the same so it is an undefined slope so we set this equation x=-7
hopes this helps please mark brainliest
Match the statement with the property it illustrates.
1. ∠ B=∠aD
2. If FO=N N, then RS=1 E E
3. If m ∠A=m∠B and m∠A=m∠C, then m∠A=m ∠ C F
4. If MN=DP and OP=OP, then MN=OK C
5. m<1-m<1 B
6. If m ∠3=m<4, then m∠4=m∠ 3. A
A. Meflexive Proprivy of Tquality
B. Bymenetre Pruperty of Hlquality
Q. Transitive Properiy of Elqualiry
ix. Reflexives Property of Congruence
F. Symmetric Property of Congruence.
f. Transitive Property of Congruence
Name the property that the statement illustrates.
7. If m ∠ 1=m ∠2, then m∠ 1-m ∠ 3=m∠2-m ∠ 3.
8. If K L=P Q, then 2, K L=2 . PQ.
9. If m ∠ A=m ∠ C, then m∠ A+m ∠D=m ∠ C+m ∠D.
10. If x y=5, then xy/3=5/3.
11. If m∠ 2=90° and m∠3=m∠2+44°, then m∠ 3=90°+44°.
12. In the diagram at the right, M is the midpoint of EF. Complete the argument to show that E M=1/2 EF.
E M =M F Definition of ?
E M+M F =E F ? ? Postulate
E M+E M =E F ? Property of Equality
2 . E M =E F Distributive property
E M =1/2 E F ? Property of Equality
13. In the diagram, m∠1+m ∠ 2=98°, and m ∠ 1=42°. Complete the argument to show that m∠2=56°.
m ∠1+m ∠ 2 =98° Given
m ∠1 =42° Given
42°+m∠2 =98° -?
m∠2 =56° ?
Value of AB = 9 units by using property of equality according to given equation.
What is a line?
In pure mathematics, a line is associate infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas. The word line might also see a line section in existence, that has 2 points to denote its ends.
Main body:
Question 12
According to question,
AB +BC = 12
BC= 3
therefore,
AB + 3 = 12
AB = 9 -------( by using property of equality)
Hence value of AB = 9 units.
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on 3 of 10
Which of the numbers below are whole numbers? Check all that apply.
A. 99.6
B. 4538
C. 0.716
1
☐D. 6
E. 207.69
F. 773
let f(x)=8x and g(x)=8^x+5 +1 which transformations are needed to transform the graph of f(x) to the graph of g(x)
Select each correct answer.
vertical translation 1 unit up
horizontal translation 1 unit left
vertical translation 5 units up
horizontal translation 5 units night.
horizontal translation 5 units left
vertical translation 1 unit down
Transformation involves changing the form of a function. The transformations are:
vertical translation 1 unit up .
horizontal translation 5 units left.
The functions are given as:
f(x) = 8x
g(x) = [tex]8^{x+5}[/tex] + 1
Start by translating the function 5 units left.
The rule of this translation is:
f'(x) = f(x+5)
So, we have:
f'(x) = 8(x+5)
Next, translate the function 1 unit up
The rule of this translation is:
f"(x) = f'(x) + 1
∴ f"(x) = 8(x+5) + 1
Rewrite as:
g(x) = 8(x+5) + 1
Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left
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Transformation involves changing the form of a function. The transformations are:
Vertical translation 1 unit up Horizontal translation 5 units leftWhat are transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
The functions are given as:
f(x) = 8x
g(x) = + 1
Start by translating the function 5 units left.
The rule of this translation is:
f'(x) = f(x+5)
So, we have:
f'(x) = 8(x+5)
Next, translate the function 1 unit up
The rule of this translation is:
f"(x) = f'(x) + 1
∴ f"(x) = 8(x+5) + 1
Rewrite as:
g(x) = 8(x+5) + 1
Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left
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A certain lottery requires players to select 6 different numbers, in any order, from 1 to 53 inclusive. How many different sets of 6 numbers can be chosen?
221643611 ways of 6 numbers can be chosen
What is Combination?An arrangement of objects where the order in which the objects are selected does not matter.
Given,
A certain lottery requires players to select 6 different numbers in any order, from 1 to 53 inclusive.
We need to find different sets of 6 numbers can be chosen
Total=53
Numbers=6
The first number can be any of the 53 numbers
The second number can be any of the 53 numbers
The third number can be any of the 53 numbers
The fourth number can be any of the 53 numbers
And so on
Hence, number of selections is:
53×53×53×53×53×53
53⁶
221643611 ways
Hence, 221643611 ways of 6 numbers can be chosen
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5. In ΔA B C, if A C ≅ C B, m ∠A=3 x+18, m ∠ B=7 x- 58 , and m ∠C=2 x-8, find the measure of each angle.
x=____
m∠ A= ___
m∠ B= ___
m∠ C=___
[tex]AC \cong BC \implies \angle A \cong \angle B \\ \\ \therefore m\angle A=m\angle B \implies 3x+18=7x-58 \\ \\ \implies 18=4x-58 \\ \\ 76=4x \\ \\ \boxed{x=19} \\ \\ m\angle A=3(19)+18 \implies \boxed{m\angle A=75^{\circ}} \\ \\ m\angle A=m\angle B \implies \boxed{m\angle B=75^{\circ}} \\ \\ m\angle C=180^{\circ}-m\angle A-m\angle B \implies \boxed{m\angle C=30^{\circ}}[/tex]
Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth.
The temperature in Austin is 33.5 ◦F and rising at a rate of 2.5 ◦F per hour. The temperature in San Antonio is 37.5 ◦F and rising at a rate of 1.5 ◦F per hour. Write an inequality that shows how long the temperature in Austin will remain colder than that in San Antonio.
The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours
How to determine the inequality and the intervals ?From the question, we have the following parameters that can be used in our computation:
Austin
Initial temperature = 33.5 degrees Fahrenheit
Rate of increment = 2.5 degrees Fahrenheit
San Antonio
Initial temperature = 37.5 degrees Fahrenheit
Rate of increment = 1.5 degrees Fahrenheit
The above parameters mean that
Current temperature = Initial temperature + Rate of increment x Number of hours
Austin: A(t) = 33.5 + 2.5t
an Antonio: B(t) = 37.5 + 1.5t
When Austin is colder than San Antonio, we have
Substitute the known values in the above equation, so, we have the following representation
33.5 + 2.5t < 37.5 + 1.5t
Divide both sides by 1
t < 4
Hence, the interval is less than 4 hours
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In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005. President Hoover's 1931 salary is equivalent to what amount in 2005?
According to the given consumer price index, President Hoover's 1931 salary is equivalent to what amount in 2005 is $962,250
Consumer price index:
In math, the concept of consumer price index (CPI) is significant in the analysis of inflation.
The general form of CPI of current years is computed as
=> (GDP of current period / GDP of base period) x 100.
Given,
In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005.
Here we need to find the President Hoover's 1931 salary is equivalent to what amount in 2005.
Here we have the values of
=> CPI = 15.2 in 1931,
=> salary 75000;
=> CPI = 195 in 2005,
Then the salary is calculated as,
=> 75000 x (195/15.2)
=> 75000 x 12.83
=> 962250
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help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.
Expressing the probability as a decimal rounded to 4 decimal places the value of p ( z < 0.74 ) is 0.7704.
Given :
for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.
Standard normal distribution :
The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
From z - score table :
the test statistic follows the standard normal distribution N(0,1).
the probability p = 0.7704
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in the multiplication example shown different letters represent different digits find the value of a and of b
You forgot the question
Class records at a particular college indicate that a student selected at random has probability 0.67 of passing French 101. For the student who passes French 101, the probability is 0.88 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102?
The probability that a student passes both the tests is 0.5896.
What is conditional probability?The conditional probability deals with dependent events. In order to evaluate it, Bayes' theorem is applied which can be written as P(B|A) = P(A ∩ B)/P(A), where B|A denotes the event of occurring B when A has already happened and A ∩ B denotes the occurring of both events simultaneously.
The given problem can be solved as follows,
Suppose A be the event a student passes French 101 and B be the event that he passes French 102.
Then, as per the question the probabilities are given as,
P(A) = 0.67,
And, P(B|A) = 0.88.
Suppose, A ∩ B be the event a student passes both tests.
Apply Bayes' theorem to obtain,
P(B|A) = P(A ∩ B)/P(A)
Substitute the corresponding values in the above expression.
0.88 = P(A ∩ B)/0.67
=> P(A ∩ B) = 0.88 × 0.67
=> P(A ∩ B) = 0.5896
Hence, the probability that a student selected at random will pass both French 101 and French 102 is 0.5896.
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A sequence of positive numbers is defined by
given that a1=2
find a2 and a3 leaving your answer in a surd form
The values of a2 and a3 that satisfy the sequence [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex]
What is a sequence?
A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4 etc. denote the terms of a sequence, then 1,2,3,4 denotes the position of the term.
the rule of the sequence is [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] when n = 1
[tex]a_{2}[/tex] = [tex]\sqrt{a_{1} ^{2} + 3 }[/tex] but [tex]a_{1}[/tex] = 2
[tex]a_{2}[/tex] = [tex]\sqrt{(2) ^{2} + 3 }[/tex]
[tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
when n = 2
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex] but [tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{(\sqrt{7}) ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{7 + 3}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{10}[/tex]
In conclusion [tex]a_{2}[/tex] and [tex]a_{3}[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex] respectively.
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one effective way to protect my bank account is to suspend my account logon if i fail to provide the correct password in 44 trials.False
Phishing is when a hacker impersonating a reliable entity sends you a phony email in the hopes that you will voluntarily divulge your personal information.
What is phishing?Phishing is a type of social engineering in which an attacker sends a false (for example, spoofed, phony, or other deceptive) communication with the goal of tricking a person into providing the attacker with vital information[1] or to install harmful software, such as ransomware, on the victim's infrastructure.
Phishing attacks are becoming more and more sophisticated, and they frequently transparently mirror the site that is being attacked, allowing the attacker to see everything the victim does there and to get past any further security measures with them.
[] According to the FBI's Internet Crime Complaint Center, which tracks more phishing incidents than any other type of computer crime combined, phishing attacks will be by far the most common type of hacker attack through 2020. []
For the first time, the term "phishing" was employed.
Hence, Phishing is when a hacker impersonating a reliable entity sends you a phony email in the hopes that you will voluntarily divulge your personal information.
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An unbiased die is tossed. Find the probability that the number
obtained is
(c) Greater than 6
(a) An event number (b) Less than 4
Step-by-step explanation:
greater than 6=0 cause no number on a dice is greater than six
an even number=1/2
less than 4=1/2
Use long division to rewrite the following rational expression.
Answer:
—4—
_x+1_/4x+3
-(4x+4)
———–––
-1
#4x+3/x+1=4-1/x+1
100 POINTS!!!! solve for x 2/3= x-1/5
Answer:
Below
Step-by-step explanation:
2/3 = x-15 Just add 15 to both sides to get
15 2/3 = x
Solving
The product of 5 and the difference
between a number and 7 is 75. What is
the number?
The number whose product of 5 and the difference between a number and 7 is 75 is, 22.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given statement is The product of 5 and the difference
between a number and 7 is 75.
Let, The unknown number be 'n'.
∴ 5(n - 7) = 75.
Now, 5 will move from the numerator to the denominator.
n - 7 = 75/5.
n - 7 = 15.
Now, we'll move the constant to the other side such that the variable and the constants are on different sides for our further calculation.
n = 15 + 7.
n = 22.
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4. Draw a coordinate grid from -10 to 10 on both axes. Using table of the same grid.
(i) y=x-4
(ii) y=2 x-4
(iii) y=3 x-4
The linear functions for this problem are graphed on the image given at the end of the answer.
How to graph the linear functions?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing by how much y changes when x is increased by one.y is the intercept, representing the value of y of the function when it's graph crosses the y-axis.Hence the functions in this problem are graphed as follows:
y = x - 4: when x = 0, y = -4, when x increases by one, y increases by one.y = 2x - 4: when x = 0, y = -4, when x increases by one, y increases by two.y = 3x - 4: when x = 0, y = -4, when x increases by one, y increases by three.More can be learned about linear functions at https://brainly.com/question/24808124
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4. Using the statistics in the following report generated for Community Hospital, calculate (round to two decimal places) the percentage of occupancy for the month of December. Remember to calculate the Total for Patient Care Units (IPSD, Bed Count and Percent of Occupancy).
The percentage of occupancy for the month of December is 86.5%.
What is percentage?
Percentage is a fundamental concept in mathematics that describes a portion or proportion of a whole number. It is expressed as a fraction or ratio of two numbers and is typically represented with a percent symbol (%). This concept is frequently used in business, finance, and other fields to compare and analyze data. For example, a company might use a percentage to track the success of a marketing campaign or to compare the amount of sales between two different stores. Percentage can also be used to calculate discounts, taxes, and other types of fees.
Given: Community Hospital December, 20XX
PCU Inpatient Service Days Bed Count Percentage of Occupancy
⇒ Med/Surg 1876, 70 = (1,876 x 100)/ (70 x 31)
= 187,600/ 2,170 = 86.45 = 86.5%
⇒ ICU 300, 10 (300 x 100)/ (10 x 31)
= 30,000/ 310 = 96.77 = 96.8%
⇒ CCU 240, 8 (240 x 100)/ (8 x 31)
= 24,000/ 248 = 96.77 = 96.8%
⇒ Rehabilitation 300, 12 (300 x 100)/ (12 x 31)
= 30,000/372 = 80.6%
⇒ Burn 75, 5 (75 x 100)/ (5 x 31)
= 7,500/ 155 = 48.38 = 48.4%
⇒ Psychiatry 200, 15 (200 x 100)/(15 x 31)
= 20,000/465 = 43.0%
⇒ Pediatric 870, 30 (870 x 100)/ (30 x 31)
= 87,000/ 930 = 93.5%
⇒ Total for patient care 3861, 150 (3,861 x 100)/ (150 x 31)
= 386,100/ 4,650 = 83.0%
⇒ Nursery 280, 10 (280 x 100)/ (910 x 31)
= 28,000/ 310 = 90.3%
For example, Med/Surg has 1,876 inpatient service days and 70 beds in the month of December (31 days). The percentage of occupancy is therefore the inpatient service days multiplied by 100 and divided by the product of the number of beds (70) and the number of days (31) to get 86.5%
⇒ (1,876 x 100)/ (70 x 31)
= 187,600/ 2,170 = 86.45 = 86.5%
Hence, the percentage is 86.5%.
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For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean and compare the result to the expected percentage of a normal distribution.
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
What is the standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The given data is:
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
Now find the mean of the given data would be
Mean = sum of all points/n
= 491/10
= 49.1
Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
Standard deviation(s) = 29.31988
Considering one standard deviation from the mean, the lower and upper limits are given by the following
[49.1-29.31988, 49.1+29.31988}
=[19.78012, 78.41988]
We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.
Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.
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Simplify and state the restrictions on the domain:
Answer:
Step-by-step explanation:
First factor the left expression to get
Then cancel out .[tex]\frac{(x+3)(x+2)}{(x+4)(x+2)}*\frac{x+4}{2x}\\ \\\frac{(x+3)}{2x}[/tex]
The x+2 cancel's as well as the x+4's.
We know these things about a polynomial function, f(x): it has exactly one relative maximum and one relative minimum, it has exactly three zeros, and it has a known factor of (x - 4). Sketch a graph of f(x) given this information.
A graph with three zeros, one of which is at x = 4, will resemble the one below.
Describe the polynomial function?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.
Minimum and Maximum?
The extrema of a function are known as its maximum and minimum. The highest and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The largest value of the function under the full range is referred to as the absolute maxima, while the least value is referred to as the absolute minima.
If the function has three zeros with one relative maximum and one relative minimum, it could be a cubic equation.
If it has a factor of x - 4, the graph crosses the x-axis at (4,0).
Your graph might look like the one below.
It has three zeros, one of which is at x = 4, and a local maximum and minimum.
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find the x- and y- intercepts
Answer:
(8, 0) and (0, 4)
Step-by-step explanation:
x-intercepts occur when y = 0, so just find the row in the table when y is 0, and then put the coordinates from that row into a ordered pair:
(8, 0)
y-intercepts occur when x = 0, so just find the row in the table when x is 0, and then put the coordinates from that row into a ordered pair:
(0, 4)
Suppose an investigator has data on the amount of shelf space x devoted to display of a particular product and sales revenue y for that product. The investigator may wish to fit a model for which the true regression line passes through (0, 0). The appropriate model is Y ¼ b1x + e. Assume that (x1, y1), . . ., (xn, yn) are observed pairs generated from this model, and derive the least squares estimator of b1. [Hint: Write the sum of squared deviations as a function of b1, a trial value, and use calculus to find the minimizing value of b1.]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex]
What is the line of regression?
A regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.
Here given that,
Suppose an investigator has data on the amount of shelf space [tex]x[/tex] devoted to display of a particular product and sales revenue [tex]y[/tex] for that product.
The investigator may wish to fit a model for which the true regression line passes through [tex](0, 0)[/tex]. The appropriate model is [tex]Y=\beta x+E[/tex]
Assume that[tex](x_1, y_1), . . ., (x_n, y_n)[/tex] are observed pairs generated from this model, and derive the least squares estimator of [tex]b_1[/tex].
Here, our motive is to minimize the function
[tex]f(b_1)=[/tex][tex]\sum_{i=1}^{n}(y_i-b_1x_i)^2[/tex]
Now,
[tex]f`(b_1)=0\\\\f`(b_1)=2\sum{i=1}^{n}(y_i-b_1x_i).(-x_i)\\\\[/tex]
So, the least square estimate [tex]b_1[/tex] is
[tex]\sum_{i=1}^{n}x_iy_i=b_1\sum_{i=1}^{n}x_i^2[/tex]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex].
To know more about the line of regression
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A surveyor is 980 feet from the base of the world's tallest fountain at Fountain Hills, Arizona. The angle of elevation to the top of the column of water is 29.7 degrees. His angle measuring device is at the same level as the base of the fountain. Find the height of the column of water to the nearest 10 feet.
To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.
We can then use the tangent function to find the height of the column of water as follows:
tan(29.7°) = opposite/adjacent
opposite = tan(29.7°) * adjacent
opposite = tan(29.7°) * 980 feet
opposite = 0.56 * 980 feet
opposite = 548.8 feet
Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.
What is the sum of the matrices shown below?
3
6 0
9
5 -2
+
6
0
-8 4
=
Answer:
Option 2
Step-by-step explanation:
[tex]\begin{bmatrix} 3+6 & 9+0 \\ 5-8 & -2+4 \end{bmatrix}=\begin{bmatrix} 9 & 9 \\ -3 & 2 \end{bmatrix}[/tex]
Answer:
(b)
Step-by-step explanation:
You want the sum of the given matrices.
Matrix sumThe sum of two matrices is the matrix of the sums of corresponding terms.
Here, we observe that we can choose the correct answer by finding the bottom right term. The sum of bottom right terms is -2+4 = 2. The only answer choice with that value at bottom right is the second answer choice.
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Additional comment
You need to know how to work the problem, but you don't actually need to work the whole problem in order to make the correct answer choice. (This is often the case with multiple choice questions, so it pays to look before you leap.)