Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number
Answers
The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).
We have an equation of line is
y(x) = mx + b --(1)
given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)
plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;
-2 = 2m +b ; 1 = -2m + b
The above equations can be written in matrix form as,
[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]
= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
AX = B
X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).
AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]
so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
let [ 17 -1 ; -1 6 ] = P
[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P
det P = 17×6 - 1 = 101
P⁻¹ = 1/101 [ 6 1 ; 1 17 ]
Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]
=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]
=> [ m ; b ] = [ -32/100 ; -39/100 ]
=> m = -32/100 , b = -39/100
then, y = mx + b
=> y = ( -32/100 )x + ( -39/100)
Hence, the required equation is
y = ( -32/100 )x + ( -39/100).
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Related Questions
The t distribution is a family of similar probability distributions, with each
individual distribution depending on a parameter known as the
Group of answer choices
degrees of freedom
sample size
standard deviation
population mean
Answers
The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.
How are the degrees of freedom determined?
When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom are frequently addressed in relation to different types of statistical hypothesis testing, like a chi-square.The number of independent bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. It is determined by subtracting the number of constraints from the sample size.Finding essential cutoff values for inferential statistical tests requires consideration of the degree of freedom. Degrees of freedom often (but not always) relate to sample size depending on the sort of study you conduct.Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.
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When a company sales x units of a product, its profits P can be determined
using the profit function
P(x) =
-2x² + 40x + 280
a) How many units must be sold to maximize profit?
b) What is the maximum profit?
Answers
(a) There are 10 units must be sold to maximize profit.
(b) The maximum profit is 480.
what is profit?
A profit is an income that is given to the owner in an efficient market production process in accounting. The owner's primary interest in the income-formation process of market production is profit, which is a measure of profitability. Different profit metrics are frequently employed.
Given:
A company sales x units of a product, its profits P can be determined
using the profit function P(x) = -2x² + 40x + 280 ..(1)
We have to find the maximum profit.
Differentiate equation (1) w.r.t x
P'(x) = -4x +40 ..(2)
-4x + 40 = 0
4x = 40
x = 10
Again differentiate equation (2) w.r.t x
P''(x) = -4 which is negative.
Hence, there are 10 units must be sold to maximize profit.
Now, to find the maximum profit.
Plug x = 10 in equation (1)
P(10) = -2(10)^2 + 40(10) + 280
= -200 + 400 + 280
P(10) = 480
Hence, the maximum profit is 480.
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write and find the general solution of the differential equation that models the verbal statement. evaluate the solution at the specified value of the independent variable. the rate of change of p is proportional to p. when t
Answers
When t = 3869, the rate of change of p is proportional to p.
What is differential equation?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.
Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.
The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.
Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.
When a closed-form expression is used, it is common for.
According to our question-
The revised equation is then
P=5000exp(-0.0513t)
Find P at t=5 now.
P=5000 exp(-0.0513×5)
P=5000 ×exp(-0.25647) (-0.25647)
P=5000 × 0.77378
P=3868.89.
P = 3869. Roughly
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Which expression is equivalent to 3√x^5y^?
Answers
The equivalent expression for the given expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression ∛x⁵y.
expression is equivalent to ∛x⁵y is
[tex](x^5y)^{\frac{1}{3} }[/tex]
= [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]
The equivalent expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
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Find the standard deviation for each data set. Use the standard deviations to compare the pair of data sets. fastest recorded speeds of various large wild cats (miles per hour): 70 45 25 45 35 35 40 40 25 fasted recorded speeds of various birds in flight (miles per hour): 216 103 96 56 63 35 50 32 55 25 25 20
The standard deviation of the large wild cats is ō=
The standard deviation of the birds in flight is ō=
The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate _____ from the mean than the fastest recorded speeds of birds in flight.
A. Less
b. more
Answers
(a) The standard deviation of the large wild cats is 25.5 (b) The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight . Option A
How to determine the standard deviation?We should understand that standard deviation looks at the amount of deviation from the means of the set of data.
(a) (70+45+25+45+35+35+40+40+25)÷9 = 40
mean is = 40
(x-m) =30+5+-15+5+-5+-5+0+0+-15)
(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9
Standard deviation = √650
Standard deviation = 25.5
(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776
Mean(m)=776/12=65
(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45
Now the square of the deviations from the mean is
(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12
=1452
Standard deviation = √1452=33
(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer: b. radius of the cone = 5; height of the cone = 12
Step-by-step explanation:
The volume of the cylinder is [tex]\pi (5^2)(4)=100\pi[/tex].
The only option that makes the same volume is option b. In this case, the volume is [tex]\frac{\pi}{3}(5^2)(12)=100\pi[/tex].
PLEASE HELP
Simplify the expression 4x³ × 2x³
3
A) 8x^6
B) 8x⁹
C)2x^6
D) 2x⁹
Answers
Answer:it isA
Step-by-step explanation:
Answer:
8x^6
Step-by-step explanation:
Add the exponents and multiply the numbers
6 3 points F L(2x-48) 32 W Using the diagram above find the value of x and use it to find the measures of all the missing angles. X = type your answer..... m/FOW= m/FLW= m/OLW= = type your answer... type your answer... type your answer.....
Answers
The value of x is 80
The measure of angle FOW, m ∠FOW, is 80°
The measure of angle FLW, m ∠FLW, is 112°
The measure of angle OLW, m ∠OLW, is = 68°
Calculating the measure of anglesFrom the question, we are to determine the measure of the missing angles
From the given diagram, we can write that
(2x - 48)° = x° + 32°
Solve for x
(2x - 48)° = x° + 32°
2x° - 48° = x° + 32°
Subtract x° from both sides of the equation
2x° - x° - 48° = x° - x° + 32°
x° - 48° = 32°
Add 48° to both sides of the equation
x° - 48° + 48° = 32° + 48°
x° = 32° + 48°
x° = 80°
Therefore,
x = 80
Calculating the m ∠FOW
m ∠FOW = x°
m ∠FOW = 80°
Calculating the m ∠FLW
m ∠FLW = (2x - 48)°
m ∠FLW = (2(80) - 48)°
m ∠FLW = (160 - 48)°
m ∠FLW = 112°
Calculating the m ∠OLW
m ∠OLW + m ∠FOW + m ∠OWL = 180° (Sum of angles in a triangle)
m ∠OLW + 80° + 32° = 180°
m ∠OLW + 112° = 180°
m ∠OLW = 180° - 112°
m ∠OLW = 68°
Hence, the measure of m ∠OLW is 68°
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The mortgage amount of a new home 170,000. The bank required a 8.6% down payment.
What was the original price before the down payment was made?
Answers
Answer: 15,507.44.
Step-by-step explanation: To find the original price of the home before the down payment was made, you need to use the following formula:
Original price = Mortgage amount / (1 - Down payment percentage)
Plugging in the values given in the question, you get:
Original price = $170,000 / (1 - 8.6%)
The original price of the home before the down payment was made is $<<170000/(1-.086)=185507.44>>185,507.44.
This means that the down payment amount was $185,507.44 - $170,000 = 185507.44-170000=15,507.44.
HELP PLEASE the question and answer choices are on the picture, please help it’s an emergency
Answers
Answer:
Its the 3rd one
Step-by-step explanation:
Find the volume of the composite solid (STEP BY STEP PLEASE) 15 POINTS
Answers
Answer: 226.19
Step-by-step explanation:
Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.
Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.
Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.
For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount. Type either a numerical value or the word no. Do not round the answer. Units are in parentheses, so do not convert your answer 2.6 (trillions of dollars) (millions of metric tons) 4.0 (trillions of dollars) (millions of metric tons) 7.1 (trillions of dollars) (millions of metric tons
Answers
For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount is 1300.715.
What is carbon dioxide ?
Our atmosphere contains carbon dioxide, an odorless and colorless gas. According to its chemical composition, CO2, it is made up of one carbon atom joined to two oxygen atoms. It is a waste product created both by burning fossil fuels and by human bodies.
Given regression eq.
[tex]$$\hat{y}=166.92+115.725$$[/tex]
* Given [tex]$x=2.6$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(2.6)+115.725 \\& \hat{y}=549.665\end{aligned}$$[/tex]
* Given [tex]$x=4.0$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(4.0)+115.725 \\& \hat{y}=783.325\end{aligned}$$[/tex]
* Given [tex]$x=7.1$[/tex]
[tex]$$\hat{y}=166.9(7.1)+115.725$$[/tex]
[tex]\hat{y}=1300.715[/tex]
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What is 7/2 with a denominator of 10
Answers
Answer: 35/10
Step-by-step explanation:
if you have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 by 5 35
2 by 5 10
The value of 7/2 with a denominator of 10 is 35/10
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
(we used the identity [tex](b-c)(b+c) = b^2 - c^2 )[/tex]
We actually rationalize just for the use of that later denominator or numerator
We have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 × 5 = 35
2 × 5 = 10
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Calculate the area, in square units, bounded by f(x) = 3x^3-3x^2-x+8 and g(x) = 2x^3 - 10x^2 + 29x + 8 over the interval [1, 5].
Answers
The area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8
over the interval [1, 5] is 164 square units.
What is meant by a function?Exactly one element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The domain and codomain of the function are, respectively, the sets X and Y as a whole.
The first presentation of the idea of function that is known about was developed by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were used to depict the desired relationship between two varying values. For example, time affects the position of a planet. Up to the 19th century, the functions that were taken into consideration were differentiable.
Given,
f(x)=3x³-3x²-x+8
g(x) = 2x³- 10x² + 29x + 8
And the interval is [1, 5].
By using area formula,
A=[tex]\int\limits^a_b {f(x)-g(x)} \, dx[/tex]
A=[tex]\int\limits^a_b[/tex](Upper function-Lower function)dx
A=[tex]\int\limits^3_1[/tex][g(x)-f(x)]dx+[tex]\int\limits^5_3[/tex][f(x)-g(x)]dx
A=[tex]\int\limits^3_1[/tex](-x³-7x²+30x)dx+[tex]\int\limits^5_3[/tex](x³+7x²-30x)dx
A= (118/3)+(374/3)
A=164 square units.
Therefore, the area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8
over the interval [1, 5] is 164 square units.
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Show that the set of numbers in the interval [0,1] having decimal expansions using only odd digits is closed. Describe this set by a Cantor set type construction.
Answers
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
What is Cantor set type construction?
The Cantor set is a collection of points situated on a single line segment that possesses a variety of odd characteristics.
By deleting the center third of a line segment and then repeating the process with the remaining shorter segments, the Cantor ternary set, the most popular construction, is created. The ternary construction was only briefly described by Cantor as an illustration of a more basic concept—that of a perfect set that isn't dense anywhere.
According to the given question:
The proportion (i.e., measure) of the unit interval that is left can be determined by subtracting the entire length as the Cantor set is defined as the set of points that are not excluded.
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
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3) Lourdes got a plant as a birthday gift. Her plant grows an average of 1 2/5 inches every month. How long will it take for the plant to grow a full 10 2/3
Answers
Answer:
7 13/21 months
Step-by-step explanation:
10 2/3 ÷ 1 2/5 =
= 32/3 ÷ 7/5
= 32/3 × 5/7
= 160/21
= 7 13/21
Answer: 7 13/21 months
We know the rate per month (1 2/5) and the end result (10 2/3).
X is the number of months, bc we don’t know how LONG it’s gonna take.
So 1 2/5 * x = 10 2/3
Now to solve this we have to first change the numbers to improper fractions. 1 2/5 becomes 7/5 and 10 2/3 becomes 32/3.
So now, 7/5 x = 32/3
To figure out what x is we have to isolate it. To do that when it’s connected to a fraction, we have to multiply both sides by the reciprocal of that fraction, which is 5/7. That cancels out the fraction.
So now, x = 160/21
Simplified that means x = 7 13/21
So it’s going to take the plant 7 13/21 months to grow a full 10 2/3.
This looks like a weird number, but my math looks right, so if I’m wrong correct me but hope this helps.
Prove that a polynomial function f of odd degree has at least one real root. Hint: it may help to consider first the case of a cubic f(x)=a0+a1x+a2x^2+a3x^3.
Answers
the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.
Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.
We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.
Now, consider the Discriminant of the polynomial, which is defined as the expression below:
Discriminant = b2 - 4ac
In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:
Discriminant = a2^2 - 4a0a3
Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.
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6x+6y=90 9x+2y=79 What pair of numbers solves the system?
Answers
Answer:
(7, 8)
Step-by-step explanation:
equation 1: [tex]6x+6y=90[/tex]
equation 2: [tex]9x+2y=79[/tex]
This system of equations can be solved for using the elimination method.
First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.
[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]
[tex]9x + 9y = 135[/tex]
Next, subtract this from the second equation.
[tex]9x+2y=79[/tex] ← eq. 2
[tex]\underline{- (9x+9y=135)}[/tex] ← modified eq. 1
[tex]0 - \, 7y \, = -56[/tex]
Then, solve for y by dividing by 7.
[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]
[tex]y=8[/tex]
So, the y-coordinate of the solution pair is 8.
Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.
[tex]6x+6y=90[/tex]
[tex]6x + 6(8) = 90[/tex]
↓ multiplying out 6 and 8
[tex]6x + 48 = 90[/tex]
↓ subtracting 48 from both sides
[tex]6x = 90 - 48[/tex]
[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]
[tex]x = 7[/tex]
So, the x-coordinate of the solution pair is 7.
Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].
(7, 8)
Answer:
(7, 8) is the required pair of numbers---------------------------
Given system6x + 6y = 90, 9x + 2y = 79.Solve it by substitutionFirst, simplify the first equation by dividing all terms by 6:
x + y = 15Then solve it for y:
y = 15 - xNow, substitute this into the second equation:
9x + 2(15 - x) = 799x + 30 - 2x = 797x = 79 - 307x = 49x = 7Finally, find the value of y:
y = 15 - 7y = 8The pair of numbers is (7, 8).
2. A gas in a flexible container with volume 8L has a temperature of 400 K. If the temperature of the gas changes to 200 K, what is the expected new volume of the gas?
A. 2 L
B. 4 L
C. 16 k
D. 32 L
Answers
The volume of the gas becomes 4L. Option B is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the ideal gas equation, we know that,
Volume is directly proportional to the temperature,
So,
V₁ / V₂ = T₁ / T₂
Where,
V₁ and T₁ are the initial pressure and temperature,
V₂ and T₂ are the final pressure and temperature.
Substitute the values,
8 / V₂ = 400 / 200
V₂ = 4
Thus, the volume of the gas becomes 4L. Option B is correct.
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592 x 43 in standard algorithm
Answers
Answer:
25456
Step-by-step explanation:
592 over 43
592
x 43
multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.
add a zero at the second row then,
multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.
if you aligned them properly, when you add them you should get 25456
I'll try to include a picture of my work, hopefully you can see it**
If i have 2 apples and i get 69 times that, than i give three-ninths of it to a friend, how much would i have left?
Answers
Answer:
92 apples remaining
Step-by-step explanation:
2 * 69 = 138 apples
138 * (3/9) =
138 * (1/3) =
138 * 1/3 =
138/3 = 46 apples
138 - 46 = 92 apples remaining
Answer:
you have 2 apples
then you got it 69 times= 2×69 = 138
then you give 3 ninths to a friend
138/9 = 15.33
you gave it 3 one-ninths = 3× 15.33 = 46
so must be left with 138-46 = 92
1. Assume there are 5 red balls, 6 blue balls, and 4 green balls. If the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable.
2. Give a recursive definition of the set of all even positive integers not divisible by 3.
Please write clearly so I can study from it! Try not to skip steps as much as you can.
Thank you!
Answers
There are 1307674368000 possible methods to remove each ball from the box one at a time.
what is probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. examination of events subject to probability.
given,
the quantity of balls inside a box ,
four red balls
6 balls in blue
four green balls
The variety of ways the balls can be taken out of the box one at a time must be determined.
Here,
Combination is possible because order is imperceptible;
mixture formula; nCr is equal to n!/r1(n-r)!
Here, There are 15 balls in the box overall (5 + 4 + 6 balls).
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
that is
There are 1307674368000 ways in which we can take the balls out of the box one at a time.
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Pls help its due today!!! 50 points!!!
Answers
Answer:
Step-by-step explanation:
Part 1: true
(-4, -1) and (0, 2)
m = 2+1/0+4
m = 3/4
(0, -3) and (4, 0)
m = 0+3/4+0
m = 3/4
Part 2: true
It intercepts at (0, -3)
Part 3:
I can't really see what slope it says but if it says -3/5, then its true, otherwise it's false.
(5, -1) and (0, 2)
m = 2+1/0-5
m = 3/-5
m = -3/5
Part 4: false
Graph A would have 2 and Graph C would have different intersecting points.
Determine which integer in the solution set will make the equation true
Answers
Answer:
2
Step-by-step explanation:
First, we must add 14 to both sides to put the variable and coefficient alone.
4s - 14 = -6
+14 +14
4s = 8
s = 2
During surgery, patient's circulatory system requires at least 50 milligrams of an anesthetic: The amount of anesthetic present hours after 70 milligrams of anesthetic administered given by the following T(t) 70(0.727)t (a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 30 minutes after the anesthetic is administered? (b) How long_ to the nearest minute can the operation last if the patient does not recelve additional anesthetic?
Answers
63 mg of anesthetic is present in the patient’s circulatory system.
The operation can last for 20 minutes.
During surgery, a patient’s circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present t hours after 70 mg of anesthetic is administered is given by the following,
T(t) = 70 × (0.727) ^t
Time = 1/3 hours
T (1/3) = 70 × (0.727) ^1/3
= 70 × ∛ 0.727
= 70 × 0.899176
= 62.94232
To the nearest mg: 63mg
Now,
63 = 70 × (0.727) ^t
63/70 = (0.727) ^t
0.9 = (0.727) ^t
Log0.9 = log (0.727) ^t
Log0.9 = t × log (0.727)
T = log0.9 / log0.727
T = 0.330461
T = 0.330461 hours
= 20 minutes
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a nail is measured with a ruler and its length is reported as 5.46 cm. select all the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
Answers
If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;
(b) The uncertainty is in the final digit of the measurement .
The Uncertainty of a number helps to estimates in comparison of experimental numbers .
it is given that , the reported length of the ruler is = 5.46 cm ;
we know that ,
the uncertainty In any number , is present in last digit only ,
the place value of the last digit in 5.46 is 0.01 .
So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm
Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .
The given question is incomplete , the complete question is
A nail is measured with a ruler and its length is reports as 5.46 cm.
Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,
(b) The uncertainty is in the final digit of the measurement ,
(c) All three digits shown in the measurement are known with certainty ,
(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm .
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what is the width of the frame?
Answers
(c) Solve by Completing the Square (Round answers to the nearest tenth)
x²+10 x+2=2 x+5
Answers
After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4 .
In the question ,
it is given that ,
the equation is x² + 10x + 2 = 2x + 5,
rewriting the equation ,
we get ,
x² + 8x - 3 = 0
adding 3 to both sides ,
we get ,
x² + 8x = 3 ,
For the method of completing the square ,
we take half of the second term's coefficient, and square it, then add it to both sides.
that is 8/2 = 4 .
the equation becomes ;
x² + 2*x*4 + 4² = 3 + 4²
(x + 4)² = 3 + 16
(x + 4)² = 19
taking root on both the sides ,
we get ,
x + 4 = ±√19
So , x = -4 + √19 or x = -4 - √19
Simplifying further ,
we get ,
x = 0.35889 or x = -8.35889
rounding to the nearest tenth we get
x = 0.4 or x = -8.4 .
Therefore , the solution of the given equation is x = 0.4 , x = -8.4 .
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Let X1,X2,...,Xn be a random sample of size n from a geometric distribution for which p is the probability of success.
(a) Use the method of moments to find a point estimate for p.
(b) Explain intuitively why your estimate makes good sense.
Answers
a) X1+X2 have distribution Bi(n1+n2, p)
b) P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).
b)
Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).
If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹
Thus,
P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
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Find the value of x in the figure
Please show all your work.
Answers
Answer:
x = 7/3.
Step-by-step explanation:
DE is parallel to BC and AD= DB and AD = EC.
So, AD/DB = (x+1)/(4x-6)
(x + 1)/(4x - 6) = 1
x + 1 = 4x - 6
1 + 6 = 4x - x
3x = 7
x = 7/3.