State the correct polar coordinate for the graph shown. It is not the option selected.
Answers
Answer:
Solution : Option D
Step-by-step explanation:
Let's start by listing two cases made possible when r is positive, in ( r, θ ). Remember that in polar coordinates a point is expressed in an ordered pair, where r is the distance from the pole (in this case 9, as it lies on the 9th circle) and theta is the directed angle from the positive x - axis.
( 9, θ ) here theta will be the angle to the terminal side with respect to the positive x - axis. This angle will be 60 degrees more than 90, or 90 + 60 = 150 degrees
( 9, θ ) and here theta will be the remaining degrees, or 360 - 150 = 210 degrees. Right away your solution will be (9, 210°)
Related Questions
The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?
Answers
Answer:
125π ft²
Step-by-step explanation:
1/4π(30)² - 1/4π(20)² = 125π
in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio
Answers
Answer:
common ratio = 2
Step-by-step explanation:
T6 = ar^5
T3 = ar²
T6 = 8 x T³
ar^5 = 8 x ar²
ar^5/ar² = 8
r³ = 8
r = ³√8
r = 2
if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged
Answers
Answer:
35%
Step-by-step explanation:
[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]
[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]
Answer:
35%
Step-by-step explanation:
I REALLY HOPE I HELPED
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
What is the radius of the circle whose center is the
origin and that passes through the point (5,12)?
Answers
Answer:
13 units
Step-by-step explanation:
Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.
Plug in the values and solve for r:
(5 - 0)² + (12 - 0)² = r²
25 + 144 = r²
169 = r²
13 = r
A Prefeitura da Cidade Feliz doou um
terreno para a Comunidade Viver Bem
discutir projetos que deveriam ser
implantados no local. Após um planejamento
participativo, ficou acertado que 45% da área
total desse terreno serão destinados a uma
creche;
3%,
para banheiros públicos e 12%
para uma academia de ginástica comunitária.
A sobra da área, que é de 960m² será
utilizada para uma pequena praça com
parque de lazer. Qual é a área total ocupada
pela creche, banheiros públicos e academia
de ginástica comunitária?
Answers
Aqui temos a seguinte divisao de terreno:
creche + banheiros + academia = 45% + 3% + 12% = 60%
O que sobra: Fazendo a conta, 100 - 60 = 40, restará 40%
No enunciado informa que sobraram 960m².
Logo concluimos que 40% = 960m²
Sendo assim, regra de 3:
m² %
960 -------- 40
X -------- 60
40X = 960 . 60
X = 57600/40
X = 1440
Logo 1440m² é destinado para: creche, banheiros públicos e academia
de ginástica comunitária.
O terreno tem um total de 1440 + 960 = 2400m²
para cada espaço - novamente diversas regra de 3:
→ creche = 45%
m² %
2400 -------- 100
X -------- 45
X = 108000/100 = 1080
→ banheiros públicos = 3%
m² %
2400 -------- 100
X -------- 3
X = 7200/100 = 72
→ academia de ginástica comunitária = 12%
m² %
2400 -------- 100
X -------- 12
X = 28800/100 = 288
provando:
60% = 1440m² (visto acima)
creche - 1080
banheiros - 72
academia - 288
1080 + 72 + 288 = 1440 (60%)
which expression is equivalent to x^-5/3
Answers
Answer:
B
Step-by-step explanation:
Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.
The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.
What is 5 over 30= 3 over c
Answers
Answer:
c=18
Step-by-step explanation:
5/30=3/c
1/6=3/18
1✖️3=3
6✖️3=18
Answer gets BRAINLIEST If q varies inversely as r, and g = 10 when r = 2.5, find the equation that connects a
and r.
Answers
Answer:
D.
Step-by-step explanation:
In direct variations, we would have:
[tex]q=kr[/tex]
Where k is some constant.
Since this is indirect variation, instead of that, we would have:
[tex]q=\frac{k}{r}[/tex]
To determine the equation, find k by putting in the values for q and r:
[tex]10=\frac{k}{2.5}\\k=2.5(10)=25[/tex]
Now plug this back into the variation:
[tex]q=\frac{25}{r}[/tex]
The answer is D.
Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765
Answers
Answer:
(i) 0.32 (ii) 0.85
(iii) 0.3412 (iv) 0.20
(v) 0.29 (vi) 0.12
Step-by-step explanation:
The data provided is as follows:
Race Smoker (S) Nonsmoker (N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
(i)
Compute the value of P (S) as follows:
[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]
P (S) = 0.32.
(ii)
Compute the value of P (W) as follows:
[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]
P (W) = 0.85.
(iii)
Compute the value of P (S|W) as follows:
[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]
P (S|W) = 0.3412.
(iv)
Compute the value of P (S|B) as follows:
[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]
P (S|W) = 0.20.
(v)
Compute the value of P (S∩W) as follows:
[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]
P (S∩W) = 0.29.
(vi)
Compute the value of P (N∩B) as follows:
[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]
P (S∩W) = 0.12.
A researcher examines typing speed before a typing class begins, halfway through the class, and after the class is over. 4. Identify the number of levels: 5. Identify the type of design: 6. Identify the dependent variable:
Answers
Answer:
Number of levels = 2
Type of design = Repeated measure
Dependent variable = Typing Speed
Step-by-step explanation:
The number of levels in an experiment simply refers to the number of experimental conditions in which participants are subjected to. In the scenario above, the number of levels is 2. Which are ; Halfway through the class and After the class is over.
The type of designed employed is REPEATED MEASURE, this is because the participants all took part in each experimental condition.
The dependent variable is TYPING SPEED, which is the variable which is measured with respect to the independent variable. Hence the observed value depends on period that is (halfway through the class or after the class is over).
(x-2) is a factor of x^2-3x^2+kx+14. The value of k is?
Answers
Answer:
k = 5
Step-by-step explanation:
I will assume that your polynomial is
x^2 - 3x^2 + kx + 14
If x - a is a factor of this polynomial, then a is a root.
Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:
2 / 1 -3 k 14
2 -2 2k - 4
-------------------------------------
1 -1 (k - 2) 2k - 10
If 2 is a root (if x - 2 is a factor), then the remainder must be zero.
Setting 2k - 10 = to zero, we get k = 5.
The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14
If 5x + 2 =12x- 5, then x = ?
Answers
Answer:
x = 1
Step-by-step explanation:
First, move all the variables to one side by subtracting 5x on both sides:
5x + 2 = 12x - 5
2 = 7x - 5
Add 5 to both sides:
7 = 7x
1 = x
Answer:
x=1
Step-by-step explanation:
5x + 2 =12x- 5
Subtract 5x from each side
5x-5x + 2 =12x-5x- 5
2 = 7x-5
Add 5 to each side
2+5 = 7x-5+5
7 = 7x
Divide each side by 7
7/7 = 7x/7
1 =x
* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.
Answers
Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answers
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.
Answers
Answer:
D. The z scores are numbers without units of measurement.
Step-by-step explanation:
Z-scores are without units, or are pure numbers.
What is the sign of -1.69+(-1.69)
Answers
Answer: Negative sign
Adding two negative values results in another negative value.
-1.69 + (-1.69) = -3.38
It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.
The sign is negative as the value of -1.69 + (-1.69) is -3.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-1.69 + (-1.69)
= -1.69 - 1.69
= -3.38
This means,
The sign is negative.
Thus,
The value of -1.69 + (-1.69) is -3.38.
Learn more about expressions here:
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What is the perimeter of the image attached?? (PLEASE HELP I WILL MARK BRAINLIEST)
Answers
Answer:
[tex] Perimeter = 3x + 3 [/tex]
Step-by-step explanation:
Perimeter of the given triangle in the figure is the sum of all three sides.
The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].
Therefore,
[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]
Simplify,
[tex] Perimeter = x + x - 3 + x + 6 [/tex]
Collect like terms
[tex] Perimeter = x + x + x - 3 + 6 [/tex]
[tex] Perimeter = 3x + 3 [/tex]
Select the graph that correctly represents f(x) = –(x + 1)^2 – 3.
Answers
Answer:
Hey there!
The third graph, with a maximum at (-1, -3) is the correct choice.
Let me know if this helps :)
Answer:
see below
Step-by-step explanation:
f(x) = –(x + 1)^2 – 3
We know that this is a parabola in the form
y = a( x-h)^2 +k
where ( h,k) is the vertex
y = -1( x- -1)^2 + -3
a is negative so the parabola opens downward
( -1,-3) is the vertex
At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?
Answers
Answer:
£32 in total for the top and two trousers
Step-by-step explanation:
The price for a top In the "cloth for you" shop= £10
The price for a bermuda trouser In the "cloth for you" shop= £12
There is a 20% discount on tops
The price If I bought one top and would trouser will be
(10-(0.2*10)) for the top
2(12) for the trouser
Total= (10-(0.2*10))+ 2(12)
Total = 10-2+24
Total = £32
So I spent £32 in total for the top and two trousers
what number should replace the question mark
Answers
Answer: The missing number is 5.
Step-by-step explanation:
In the table we can only have numbers between 1 and 9,
The pattern that i see is:
We have sets of 3 numbers.
"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"
Goin from right to left we have:
9 - 6 = 3
6 - 2 = 4
4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)
4 - 4 = 0 (we can not use zero, so we use the next number, 9)
3 - 3 = 0 (same as above)
? - 1 = 4
? = 4 + 1 = 5
The missing number is 5.
Given the function f ( x ) = 2 x + 8 , evaluate and simplify the expressions below. See special instructions on how to enter your answers.
Answers
Answer:
[tex]f(a) = 2a + 8[/tex]
[tex]f(x + h) = 2x + 2h + 8[/tex]
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x + 8[/tex]
Required
[tex]f(a)[/tex]
[tex]f(x + h)[/tex]
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
Solving for f(a)
Substitute a for x in the given parameter
[tex]f(x) = 2x + 8[/tex] becomes
[tex]f(a) = 2a + 8[/tex]
Solving for f(x+h)
Substitute x + h for x in the given parameter
[tex]f(x + h) = 2(x + h) + 8[/tex]
Open Bracket
[tex]f(x + h) = 2x + 2h + 8[/tex]
Solving for [tex]\frac{f(x + h) - f(x)}{h}[/tex]
Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)
[tex]\frac{f(x + h) - f(x)}{h}[/tex] becomes
[tex]\frac{2x + 2h + 8 - (2x + 8)}{h}[/tex]
Open Bracket
[tex]\frac{2x + 2h + 8 - 2x - 8}{h}[/tex]
Collect Like Terms
[tex]\frac{2x - 2x+ 2h + 8 - 8}{h}[/tex]
Evaluate the numerator
[tex]\frac{2h}{h}[/tex]
[tex]2[/tex]
Hence;
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
Frank and Gregory leave Centreville traveling in opposite directions on a straight road. Gregory drives 22 miles per hour faster than Frank. After 2.25 hours, they are 216 miles apart. Find Frank's speed and Gregory's speed.
Answers
Answer:
Frank speed = 37mi/hGregory speed = 59mi/hrStep-by-step explanation:
Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,
Speed = Distance/Time
Total time travelled by them = 2.25hours
Total distance = 216 hours
Total speed = x+y = x+22+x
Substituting this parameters into the formula given to get x we will have;
x+22+x = 216/2.25
2x+22 = 96
2x = 96-22
2x = 74
x = 74/2
x = 37
Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour
A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?
a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)
Answers
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:
The interval for 95% will be given as,
Pr(X) = μ ± 2σ
Pr(X) = 200 ± 2(40)
Pr(X) = 200 ± 80
Pr(X) = (200 - 80, 200 + 80)
Pr(X) = (120, 280)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
More about the normal distribution link is given below.
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Apply the distributive property to factor out the greatest common factor. 18d+12 =18d+12=18, d, plus, 12, equals
Answers
Answer:
[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]
Step-by-step explanation:
18d + 12
The greatest common factor is 6, So we need to factor out 6
=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]
Answer:
6(3d+2)
Step-by-step explanation:
6 is the gcd of the two terms.
In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\
Answers
Answer: i don’t kno I’m 6 years old
Step-by-step explanation:
A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician
Answers
Answer:
[tex]Probability = \frac{3}{7}[/tex]
Step-by-step explanation:
Given
Electrician = 6
Mechanic = 8
Required
Determine the probability of selecting an electrician
First, we need the total number of employees;
[tex]Total = n(Electrician) + n(Mechanic)[/tex]
[tex]Total = 6 + 8[/tex]
[tex]Total = 14[/tex]
Next, is to determine the required probability using the following formula;
[tex]Probability = \frac{n(Electrician)}{Total}[/tex]
[tex]Probability = \frac{6}{14}[/tex]
Divide numerator and denominator by 2
[tex]Probability = \frac{3}{7}[/tex]
Hence, the probability of selecting an electrician is 3/7
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answers
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
1.Find the value of x in the equation below
3^(2x+1)÷3^(3x-4)×3^(6-7x)=27x
2.Solve the equation 2^(x+y)=8 and 3^(x-y)=1 simultaneously
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
Question 1.
[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]
Question2.
[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]
So, it gives (by adding the two equations) 2x = 3
[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x
Answers
Answer:
[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]
Step-by-step explanation:
Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:
1) [tex]t = 2-x[/tex] Given
2) [tex]y = 5\cdot x +11[/tex] Given
3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties
4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property
5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property
6) [tex]y = -5\cdot (-x)+11[/tex] [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]
7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property
8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse
9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties
10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property
11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]
12) [tex]y = (-5)\cdot t +21[/tex] By 1)
13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result
14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition
15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition
16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property
17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property
18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?
Answers
Answer:
The answer and explanation are below
Step-by-step explanation:
i followed the data that was given in the question.
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
a.) please refer to the attachment for the scatter diagram. Y was plotted against X.
b. The equation is given as:
Y = b₁ + b₀X
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²
b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)
= 1375-1309.5/275-225
= 65.5/50
= 1.31
b₀ = 87.3/5 - 1.31(15/5)
= 87.3/5 - 1.31x3
= 13.53
the regression line is
Y = 13.53 + 1.31X
please refer to the attachment for the diagram for the regression line.
c. we are required to find r.
r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
inserting these values:
r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29
= 65.5/106.69
= 0.6139
Coefficient of determination = r²
r = 0.6139
r² = 0.3769 = 37.69%
Therefore 37.69% variation in y is explained by variation in x and the least square model.
