The vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩ is ⟨-4+t, -4+4t⟩.
To find a vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩, we need to first find the direction vector of the line we want to create. Since the line we want is perpendicular to ⟨1+4t,4-t⟩, its direction vector should be orthogonal to ⟨1, -1/4⟩ which is the direction vector of ⟨1+4t,4-t⟩.
So, we can find a direction vector for the line we want by taking the dot product of the direction vector of ⟨1+4t,4-t⟩ and any vector that is orthogonal to ⟨1, -1/4⟩. A convenient choice for an orthogonal vector is ⟨1, 4⟩ since their dot product is 1 * 1 + (-1/4) * 4 = 0.
Thus, a direction vector for the line we want is ⟨1, 4⟩. Now we can use the point (-4,-4) and the direction vector ⟨1, 4⟩ to find a vector parametric equation for the line we want:
x = -4 + t
y = -4 + 4t
So the vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩ is ⟨-4+t, -4+4t⟩.
Learn more about :
vector : brainly.com/question/31343602
#SPJ11
in problems 1–8, classify the equation as separable, linear, exact, or none of these. notice that some equations may have more than one classification. 1. 1x2 y x4 cos x2 dx - x3 dy = 0
The given equation dy/dx - (1/x)y = (xcosx)/x³ is linear with y as the dependent variable.
Given differential equation is (x²y+x⁴ cosx)dx -x³dy = 0
The given equation can indeed be classified as linear with y as the dependent variable.
A linear equation with respect to the dependent variable y is of the form:
dy/dx + P(x)y = Q(x),
where P(x) and Q(x) are functions of x. In this case, we have:
(x²y + x⁴cosx)dx - x³dy = 0.
By rearranging the terms, we can write it as:
x²ydx - x³dy + x⁴cosxdx = 0.
Now, we can rewrite the equation in the form:
dy/dx + (-x²/x³)y = x⁴cosx/x³.
Simplifying further, we get:
dy/dx - (1/x)y = (xcosx)/x³.
As you can see, the equation is in the form of a linear equation with respect to y. The coefficient of y, (-1/x), is a function of x, while the right-hand side (RHS) is also a function of x. Therefore, the given equation is linear with y as the dependent variable.
Learn more about Differential equation here
https://brainly.com/question/31492438
#SPJ4
What is the probability that a man and a woman who are dating both like in-n-out the best? assuming their burger tastes are independent
There is a 4% chance that both the man and the woman like In-N-Out the best if we assume that their burger tastes are independent and which the probability of liking In-N-Out the best is around 20%.
Let a man and a woman who are dating have independent burger tastes then the probability which both of them like In-N-Out the best can be calculated as follows,
We can let that the probability that the man likes In-N-Out the best is p1 and the probability that the woman likes In-N-Out the best is [tex]p_2[/tex]
So, the probability that both of them like In-N-Out the best can be calculated as the product of their individual probabilities:
P(both like In-N-Out) = P(man likes In-N-Out) × P(woman likes In-N-Out) [tex]= p_1 × p_2[/tex] of them like In-N-Out the best.
Let's the probability that any person likes In-N-Out the best is around 20% (which is roughly the percentage of people who ranked In-N-Out as their favorite burger chain in the Harris Poll).
Then the probability that both the man and the woman like In-N-Out the best can be calculated as:
P(both like In-N-Out) = 0.2 × 0.2 = 0.04
Hence, there is a 4% chance that both the man and the woman like In-N-Out the best if we assume that their burger tastes are independent and which the probability of liking In-N-Out the best is around 20%.
Learn more about probability here,
https://brainly.com/question/31895831
#SPJ4
Correct question is "What is the probability that a man and a woman who are dating both like in-n-out the best? assuming their burger tastes are independent."
Simplify the expression and then put your answer in scientific notation. (8. 2 x 107 7 ) - (4. 1 x 106 6 )
The expression in the scientific notation will be 7.79 × [tex]10^{7}[/tex] .
Simplifying 8.2 × [tex]10^{7}[/tex] - 4.1 × [tex]10^{6}[/tex]
To simplify the equation power should be same
To convert to decrease power the decimal will move to the right
It can be written as
8.2 × [tex]10^{7}[/tex] = 82.0 × [tex]10^{6}[/tex]
Now solving the equation
82.0 × [tex]10^{6}[/tex] - 4.1 × [tex]10^{6}[/tex]
= 77.9 × [tex]10^{6}[/tex]
To convert the equation into scientific notation
The decimal should be after one significant figure
To convert to increase power the decimal will move to the left
It can be written as
7.79 × [tex]10^{7}[/tex]
Simplifying the equation will give 7.79 × [tex]10^{7}[/tex] .
To know more about scientific notation click here :
https://brainly.com/question/18073768
#SPJ4
Consider vector field F on R3 and non-intersecting curves (t) and c(t) over te [0, 1] with 7(0) = 2(0) and 7(1) = c(1). Suppose we have that Só F.dő = S. F. dē. Then what is the value of F. dr where ris given by: Sõ(t) for 0
Given a vector field F on R3 and non-intersecting curves s(t) and c(t) over t ∈ [0, 1] with s(0) = c(0) and s(1) = c(1), if we have ∮s F · d = ∮c F · d, then the value of F · dr where r is given by s(t) for t ∈ [0, 1] is the same as the value of F · dr where r is given by c(t) for t ∈ [0, 1].
The given equation, ∮s F · d = ∮c F · d, is a statement of the conservative nature of the vector field F. It means that the line integral of F around a closed curve is zero, which implies that F is a conservative vector field.
Since s(t) and c(t) are non-intersecting curves with the same endpoints, they form a closed loop. By the conservative property of F, the line integral of F along both curves will be equal.
The value of F · dr where r is given by s(t) for t ∈ [0, 1] is the line integral of F along the curve s(t). Since s(t) and c(t) form a closed loop, we can apply the equation ∮s F · d = ∮c F · d to conclude that the value of F · dr along s(t) is the same as the value of F · dr along c(t). Thus, we can evaluate F · dr by choosing either curve and applying the line integral formula.
To learn more about conservative vector field click here: brainly.com/question/24332269
#SPJ11
Determine the following probability Meeting at least one person with the flu in twelve random encounters on campus when the infection rate is 4% (4 in 100 people have the hu) The probability is____.
The probability of meeting at least one person with the flu in twelve random encounters on campus when the infection rate is 4% is 0.391 or approximately 39.1%.
To determine the probability of meeting at least one person with the flu in twelve random encounters on campus when the infection rate is 4%, we can use the binomial distribution formula:
P(X ≥ 1) = 1 - P(X = 0)
where X is the number of people with the flu in twelve random encounters, and P(X = 0) is the probability of meeting zero people with the flu.
The probability of meeting zero people with the flu in one random encounter is:
P(X = 0) = (96/100)^1 * (4/100)^0 = 0.96
where 96/100 represents the probability of not meeting someone with the flu, and 4/100 represents the probability of meeting someone with the flu.
Therefore, the probability of meeting at least one person with the flu in twelve random encounters is:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - 0.96^12
P(X ≥ 1) = 0.391
Therefore, the probability of meeting at least one person with the flu in twelve random encounters on campus when the infection rate is 4% is 0.391 or approximately 39.1%.
To know more about probability visit:-
https://brainly.com/question/29255928
#SPJ11
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 990(0.95)
The exponential function y = 990(0.95) represents exponential decay with a 5% decrease per unit increase in x.
The given exponential function is y = 990(0.95). To determine whether it represents growth or decay, we need to examine the base of the exponent, which is 0.95 in this case.
When the base of an exponential function is between 0 and 1, such as 0.95, it represents exponential decay. This means that as x increases, the corresponding y-values decrease exponentially.
To calculate the percentage rate of decrease, we can compare the base (0.95) to 1. A decrease from 1 to 0.95 represents a difference of 0.05. To convert this difference into a percentage, we multiply by 100.
Percentage rate of decrease = 0.05 * 100 = 5%
Therefore, the given exponential function y = 990(0.95) represents exponential decay with a rate of 5% decrease per unit increase in x. This implies that for each unit increase in x, the y-value will decrease by 5% of its previous value.
It's important to note that the rate of decrease remains constant throughout the function. As x increases, the value of y will continue to decrease by 5% with each unit increase.
For more question on exponential visit:
https://brainly.com/question/2456547
#SPJ11
If S = {a,b,c) with P(a) = 2P(b) = 4P(c), find P(a).
The probability of event a, P(a), is 4/7 for the given sample set.
To find P(a), we need to use the given information about the probabilities and the fact that the total probability of all outcomes in a sample space S is equal to 1. We have:
S = {a, b, c}
P(a) = 2P(b) = 4P(c)
First, we can express P(b) and P(c) in terms of P(a):
P(b) = P(a) / 2
P(c) = P(a) / 4
Now we use the fact that the sum of probabilities of all outcomes in S equals 1:
P(a) + P(b) + P(c) = 1
Substitute P(b) and P(c) with their expressions in terms of P(a):
P(a) + (P(a) / 2) + (P(a) / 4) = 1
To solve for P(a), combine the terms:
P(a) * (1 + 1/2 + 1/4) = 1
P(a) * (4/4 + 2/4 + 1/4) = 1
P(a) * (7/4) = 1
Now, divide both sides by (7/4) to isolate P(a):
P(a) = 1 / (7/4)
P(a) = 4/7
So, the probability of event a, P(a), is 4/7.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ11
A student randomly selected 65 vehicles in the student parking lot and noted the color of each. She found that 9 were black, 10 were blue, 13 were brown, 7 were green, 12 were red, and 14 were a variety of other colors. What is P(not blue)?
Answer:
p(not blue) = 11/13 = 0.8461538462 = approx 0.85 = approx 85%
Step-by-step explanation:
65-10 = 55 are not blue, so 55 out of 65 cars are not blue.
p(not blue) = 55/65 = 11/13 = 0.8461538462 = approx 0.85 = approx 85%
Find the cos of angle c and tangent of angle c round answer up two decimal places
The cosine of angle C is 7/25 and using tangent, the value of C is 73.7°
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sinθ = opp/ hyp
cos θ = adj/ hyp
tan θ = opp/adj
The value of cosine of C is
cos C = adj/hyp
= 7/25
therefore the value of cos C is 7/25
to find the value of C
Tan C = 24/7
TanC = 3.43
C = tan^-1 ( 3.43)
C = 73.7°
Therefore the value of C is 73.7°
learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
what is the slope of the line tangent to the polar curve r = 2θ2 when θ = π
The slope of the line tangent to the polar curve r = 2θ² when θ = π is 4π.
How we find the slope of the line tangent?To find the slope of the line tangent to the polar curve r = 2θ² at θ = π, we need to find the derivative of r with respect to θ, and then evaluate it at θ = π.
Differentiating r = 2θ² with respect to θ, we get:
dr/dθ = 4θ
Evaluating this expression at θ = π, we get:
dr/dθ = 4π
This is the slope of the tangent line to the polar curve r = 2θ² at the point where θ = π.
Learn more about Tangent line
brainly.com/question/31179315
#SPJ11
Find the point at which the line with parametric equations I = 1+ 21, y = 4t and z = 2 - 3t intersects the plane 2 + 2y – z + 1 = 0.Previous question
The point of intersection is (17/9, -4/9, 29/9). The process of finding the point of intersection between a line and a plane involves substituting the parametric equations of the line into the equation of the plane.
To find the point of intersection between the line and plane, we need to substitute the parametric equations of the line into the equation of the plane. This gives us:
2 + 2(4t) - (2 - 3t) + 1 = 0
Simplifying, we get:
9t + 1 = 0
Therefore, t = -1/9. We can substitute this value of t into the parametric equations of the line to find the coordinates of the point of intersection:
x = 1 + 2(-1/9) = 17/9
y = 4(-1/9) = -4/9
z = 2 - 3(-1/9) = 29/9
So the point of intersection is (17/9, -4/9, 29/9). The process of finding the point of intersection between a line and a plane involves substituting the parametric equations of the line into the equation of the plane. This allows us to solve for the value of the parameter that corresponds to the point of intersection. Once we have this value, we can substitute it back into the parametric equations of the line to find the coordinates of the point. It is important to note that not all lines intersect with all planes, and some may intersect at multiple points or not intersect at all. Therefore, it is important to carefully analyze the equations and properties of both the line and plane before attempting to find their point of intersection.
To know more about parametric equations visit :
https://brainly.com/question/30286426
#SPJ11
the formula for calculating the two-tailed critical value of r, the sample correlation coefficient, is:
Answer:
rcritical = tα/2 sq(t2α/2+n−2)
Step-by-step explanation:
find the general solution of the given differential equation. y'' − y' − 2y = −6t 4t2
The general solution of the given differential equation is y(t) = [tex]c_1 e^{2t} + c_2 e^{-t} -2t^2 + 6t -5[/tex]
We first solve the associated homogeneous equation y'' − y' − 2y = −8t + 4t² to find the general solution of the given differential equation y'' − y' − 2y = 0.
The characteristic equation is r² - r - 2 = 0, which factors as (r - 2)(r + 1) = 0. Therefore, the roots are r = 2 and r = -1.
The general solution of the associated homogeneous equation is y_h(t) = [tex]c_1 e^{2t} + c_2 e^{-t}[/tex], where c_1 and c_2 are constants.
To find a particular solution of the given non-homogeneous equation, we use the method of undetermined coefficients. Since the right-hand side of the equation is a polynomial of degree 2, we assume a particular solution of the form y_p(t) = At² + Bt + C. Substituting this into the differential equation, we get:
2A - 2A t - 2At² - B - 2Bt - 2C = -8t + 4t²
2A -B -2C - (2A + 2B)t -2At²= -8t + 4t²
Equating coefficients of like terms, we get:
2A -B -2C = 0
- (2A + 2B) = -8
-2A = 4
Therefore, A = -2, B = 6, and C = -5. Thus, a particular solution of the given non-homogeneous equation is y_p(t) = -2t² + 6t -5.
The general solution of the given differential equation is the sum of the general solution of the associated homogeneous equation and a particular solution of the non-homogeneous equation. Therefore, the general solution is:
y(t) = y_h(t) + y_p(t)
= [tex]c_1 e^{2t} + c_2 e^{-t} -2t^2 + 6t -5[/tex]
where c_1 and c_2 are constants.
Learn more about Differential equation here
https://brainly.com/question/31230406
#SPJ4
When a group of individuals selects a particular consumer-submitted entry, it is called a:SamplePremiumContestSweepstake
A contest is a type of promotional marketing strategy that requires participants to submit their entries based on specific criteria or requirements. The correct answer to your question is "contest."
A long answer to your question is that when a group of individuals selects a particular consumer-submitted entry, it is called a contest.
The entries are then judged by a panel or group of individuals who select the best or most appropriate entry.
The winner of the contest may receive a prize or premium, such as cash, gift cards, or products.
Unlike a sweepstake, which randomly selects a winner, a contest is based on merit or creativity and involves a selection process.
Therefore, the correct answer to your question is "contest."
Know more about the contest here:
https://brainly.com/question/9698922
#SPJ11
someone please help me!!
Answer:
See below
Step-by-step explanation:
Slope-intercept form of an equation of line:
[tex]y = mx + c[/tex] —— eq(i)
Where:
c = y-intercept
= y-value for which the corresponding x-value is 0
= [tex]-1[/tex] (From the provided table)
m = slope
= [tex]\frac{rise}{run}[/tex]
= [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex] —- eq(ii)
Choose any two sets of coordinates and then substitute in eq(ii). I chose:
[tex](3, 8)[/tex] as [tex](x_{1}, y_{1})[/tex]
[tex](4, 11)[/tex] as [tex](x_{2}, y_{2})[/tex]
= [tex]\frac{11 - 8}{4 - 3}[/tex]
= [tex]\frac{3}{1}[/tex]
∴ m = [tex]3[/tex]
Substituting the values of c and m in eq(i):
[tex]y = (3)x + (-1)[/tex]
∴ Equation for the function
[tex]y = 3x - 1[/tex]
Find the appropriate values of n1 and n2 (assume n1equalsn2) needed to estimate (mu1minusmu2) with each of the following. a. A sampling error equal to 3.6 with 95% confidence. From prior experience it is known that sigma1almost equals13 and sigma2almost equals22. b. A sampling error equal to 6 with 99% confidence. The range of each population is 60. c. A 90% confidence interval of width 1.3.
To estimate (mu1 - mu2) with a sampling error of 3.6 and 95% confidence, n1 and n2 should be determined based on the known standard deviations (sigma1 = 13, sigma2 = 22), to estimate (mu1 - mu2) with a sampling error of 6 and 99% confidence, n1 and n2 should be determined based on the range of each population (60 and to achieve a 90% confidence interval of width 1.3, the appropriate values of n1 and n2 need to be calculated.
a) To estimate (mu1 - mu2) with a sampling error of 3.6 and 95% confidence, we can use the formula:
\[ n = \left(\frac{{Z * \sqrt{{\sigma_1^2 + \sigma_2^2}}}}{{E}}\right)^2 \]
where Z is the Z-score corresponding to the desired confidence level (95% corresponds to Z = 1.96), sigma1 and sigma2 are the known standard deviations (sigma1 = 13, sigma2 = 22), and E is the desired sampling error (E = 3.6).
By plugging in the values, we get:
\[ n = \left(\frac{{1.96 * \sqrt{{13^2 + 22^2}}}}{{3.6}}\right)^2 \]
Simplifying this expression will give us the appropriate value for n1 and n2.
b) To estimate (mu1 - mu2) with a sampling error of 6 and 99% confidence, we can use the formula:
\[ n = \left(\frac{{Z * R}}{{2 * E}}\right)^2 \]
where Z is the Z-score corresponding to the desired confidence level (99% corresponds to Z = 2.58), R is the range of each population (R = 60), and E is the desired sampling error (E = 6).
By substituting the values, we get:
\[ n = \left(\frac{{2.58 * 60}}{{2 * 6}}\right)^2 \]
Simplifying this expression will give us the appropriate value for n1 and n2.
c) To achieve a 90% confidence interval of width 1.3, we can use the formula:
\[ n = \left(\frac{{Z * \sigma}}{{E}}\right)^2 \]
where Z is the Z-score corresponding to the desired confidence level (90% corresponds to Z = 1.645), sigma is the unknown standard deviation, and E is the desired interval width (E = 1.3).
Since the standard deviation (sigma) is unknown, we don't have enough information to calculate the appropriate values for n1 and n2.
Learn more about sampling error here:
brainly.com/question/15375591
#SPJ11
in the book the giver, birth mothers are allowed to have only 3 babies. when they have twins one of released. how can the problem be solved in a different way
One possible solution could be to allow birth mothers to have as many children as they want, but enforce strict population control measures on the entire community to ensure resources are not depleted.
The practice of releasing one twin in The Giver is a harsh and unjust method of population control. In a hypothetical scenario where population growth is a concern, there are more humane and effective ways to address it. For instance, the community could implement measures such as providing incentives for small families, investing in education and healthcare to reduce infant mortality rates, and promoting family planning. Additionally, the community could implement policies to encourage sustainable resource use and reduce waste, such as recycling and renewable energy initiatives. By taking a comprehensive and sustainable approach to population control, the community can ensure a better future for all its members, without resorting to cruel and arbitrary methods like releasing babies.
Learn more about resources here: brainly.com/question/14289367
#SPJ11
Problem 3. A shoe store sells a new type of basketball shoe. The table shows the pairs sold s over time f
(in weeks).
Week (t)
Pairs sold (s)
1
5
32
3.1 Write a function that models the pairs sold s over time t.
Model:
5
48
3.2 Estimate the number of pairs of shoes sold after 6 weeks.
ANSWER:
7
58
65
3.1 The function that models the pairs sold (s) over time (t) is:
[tex]s(t) = -3t^2 + 6t + 2.[/tex]
3.2 The estimated number of pairs of shoes sold after 6 weeks is -70.
3.1 To write a function that models the pairs sold (s) over time (t), we can use the given data points to find the pattern or relationship between the weeks (t) and the pairs sold (s).
From the table:
Week (t) Pairs sold (s)
1 5
3 2
5 48
By observing the data, we can see that the pairs sold (s) increases by a certain amount after each week. Let's calculate the difference between consecutive pairs sold:
Difference between pairs sold at week 3 and week 1: 2 - 5 = -3
Difference between pairs sold at week 5 and week 3: 48 - 2 = 46
We notice that the difference is not constant, which suggests a nonlinear relationship. To model this, we can use a quadratic function.
Let's assume the function is of the form s(t) = at^2 + bt + c, where a, b, and c are constants to be determined.
Substituting the given data point (t, s) = (1, 5) into the function, we get:
[tex]5 = a(1)^2 + b(1) + c[/tex]
5 = a + b + c (Equation 1)
Substituting the data point (t, s) = (3, 2) into the function, we get:
[tex]2 = a(3)^2 + b(3) + c[/tex]
2 = 9a + 3b + c (Equation 2)
Substituting the data point (t, s) = (5, 48) into the function, we get:
[tex]48 = a(5)^2 + b(5) + c[/tex]
48 = 25a + 5b + c (Equation 3)
Now we have a system of three equations (Equations 1, 2, and 3) that we can solve to find the values of a, b, and c.
Solving the system of equations, we find:
a = -3
b = 6
c = 2
Therefore, the function that models the pairs sold (s) over time (t) is:
[tex]s(t) = -3t^2 + 6t + 2.[/tex]
3.2 To estimate the number of pairs of shoes sold after 6 weeks, we can substitute t = 6 into the function [tex]s(t) = -3t^2 + 6t + 2.[/tex]
[tex]s(6) = -3(6)^2 + 6(6) + 2[/tex]
s(6) = -3(36) + 36 + 2
s(6) = -108 + 36 + 2
s(6) = -70
Therefore, the estimated number of pairs of shoes sold after 6 weeks is -70.
for such more question on number
https://brainly.com/question/15858152
#SPJ11
PLEASE HELP ME, THIS HAS TO BE DONE BY TODAY!!!
You toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then use it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."
2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.
3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."
4. How many outcomes are in the event "Toss a tails, spin yellow"?
5. What is the probability of tossing tails and spinning yellow?
Answer and Explanation:
1. The left column should be labeled coin toss because we can see that there are two outcomes from a coin toss: heads or tails.
We know that the right column should be labeled spinner because it has three outcomes (red, yellow, or blue) for every previous outcome.
2. We can label the top box of the left column as H (for Heads) and the lower box as T (for Tails). Then, we can label the top, middle, and bottom boxes in the right column as R, Y, and B, respectively (for Red, Yellow, Blue).
3. Next to each box on the right, label the two events that lead to that outcome. For example, "HR" means that you tossed a heads, then spun a red.
4. There is only 1 outcome in the event "toss a tails, spin a yellow" because there is only one way (out of two ways) to toss a tails, and from there, there is only one way to spin a yellow (out of three ways).
5. The probability of tossing tails, then spinning a yellow is:
[tex]\dfrac{1}{2} \cdot \dfrac{1}{3} = \boxed{\dfrac{1}{6}}[/tex]
Please please help please please
Answer:
G(9, -5)
Step-by-step explanation:
Point G is not shown in the figure, but I assume point G is on the bottom side of the square, directly below point F.
We are told each side of the square is 8 units long.
Starting at point E, to get to point G, go 8 units right and 8 units down.
Start at E(1, 3).
Then go 8 units right to point F(9, 3).
Now go 8 units down to point G(9, -5).
33% of the population has 20/20 vision. if 70 individuals are selected at random from the population, what is the mean number who will have 20/20 vision?
The mean number of individuals with 20/20 vision is 23.
To find the mean number of individuals with 20/20 vision, we can use the formula for the expected value of a binomial distribution. In this case, the probability of an individual having 20/20 vision is p = 0.33, and the number of trials (i.e. individuals selected) is n = 70.
The formula for the expected value of a binomial distribution is:
E(X) = np
Substituting in our values, we get:
E(X) = 70 x 0.33
E(X) = 23.1
So, the mean number of individuals with 20/20 vision out of 70 selected at random from the population is approximately 23.1. However, since we can't have a fraction of a person, we should round our answer to the nearest whole number.
Therefore, the mean number of individuals with 20/20 vision is 23.
Learn more about individuals here:
https://brainly.com/question/30167465
#SPJ11
find a matrix p that orthogonally diagonalizes a, and determine p − 1ap. a=[4 1 1 4]
The matrix P that orthogonally diagonalizes A is obtained by finding the eigenvalues and eigenvectors of A, normalizing the eigenvectors, and using them as columns of P.
First, we find the eigenvalues and eigenvectors of A:
|4-λ 1| (4-λ)(λ-1) - 1 = 0 → λ1 = 5, λ2 = 3
|1 4-λ|
For λ1 = 5, we get the eigenvector (1,1)/√2, and for λ2 = 3, we get the eigenvector (1,-1)/√2.
Thus, P = [ (1/√2) (1/√2); (1/√2) (-1/√2) ].
Then, P^-1AP = D, where D is the diagonal matrix of the eigenvalues of A.
P^-1 = P^T (since P is orthogonal), so we have:
P^-1AP = P^TAP = [ (1/√2) (1/√2); (1/√2) (-1/√2) ] [ 4 1; 1 4 ] [ (1/√2) (1/√2); (1/√2) (-1/√2) ] = [ 5 0; 0 3 ]
Therefore, the matrix P that orthogonally diagonalizes A is [ (1/√2) (1/√2); (1/√2) (-1/√2) ], and P^-1AP = [ 5 0; 0 3 ].
Learn more about Eigenvalues here: brainly.com/question/31650198
#SPJ11
find the taylor series for f(x) centered at the given value of a. f(x) = 10 x - 4 x^3 text(, ) a=-2
The taylor series for f(x) centered at the given value of a. f(x) = 10 x - 4 x^3 text(, ) a=-2 is:
f(x) = -56 + 34(x+2) + 12(x+2)^2 - 4(x+2)^3/3 + ...
The Taylor series for f(x) centered at a=-2 is:
f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)*(x-a)^3/3! + ...
Plugging in the given function and the value of a:
f(-2) = 10(-2) - 4(-2)^3 = -56
f'(-2) = 10 - 4(3)(-2)^2 = 34
f''(-2) = -4(6)(-2) = 48
f'''(-2) = -4(6) = -24
Thus, the Taylor series for f(x) centered at a=-2 is:
f(x) = -56 + 34(x+2) + 24(x+2)^2/2! - 24(x+2)^3/3! + ...
Simplifying:
Therefore the final equation is:
f(x) = -56 + 34(x+2) + 12(x+2)^2 - 4(x+2)^3/3 + ...
Learn more about Taylor series here:-brainly.com/question/29733106
#SPJ11
12 A quantity of 20c and 50c coins has a total value of $54. There are twice as many 20c coins as 50c coins. How many 20c coins are there?
120
Step-by-step explanation:
turning $54 to cents
$1= 100c
$54=54×100= 5400
calling the number of 20c coins a and 50c coins b
20a + 50b= 5400 ...equ(1)
since there are twice as many 20c coins as 50c coins
a=2b ...equ(2)
substituting a=2b in equ(1)
20(2b) + 50b = 5400
40b + 50b = 5400
90b = 5400
dividing both sides by 90
b= 60
to get the number of 20c coins I'm substituting b=60 in equ(2)
a= 2×60
a=120
therefore the number of 20c coins is 120
Please Help Me On This one! Tsym! if you do I really do appreciate help!
Answer:
15
Step-by-step explanation:
Since the angles are complementary, that means that when the angles are added together, they are equal to 90*. With this information, we can make the equation: x + (3x + 30) = 90
From this we can add like terms and get 4x + 30 = 90
After this, subtract 30 from both sides: 4x = 60
Divide both sides by 4
x = 15
(Ignore the degree sign in my picture, sorry!)
5x2-17/2x+3/2=0 please help
Answer:
x= 3/2
x= 1/5
Step-by-step explanation:
find the measures of the angles of the triangle whose vertices are a = ( − 2,0), b = (2,1), and c = (1, − 2).
So the triangle has three equal angles of 60 degrees.
To find the measures of the angles of the triangle with vertices at (-2,0), (2,1), and (1,-2), we can use trigonometry.
Let's use the following notation:
a = (-2,0)
b = (2,1)
c = (1,-2)
First, we need to find the coordinates of the midpoint of line segment AB, which is the length of the hypotenuse of the triangle.
Using the Pythagorean theorem, we have:
[tex]c^2 = a^2 + b^2\\1^2 + (-2)^2 = 2^2 + 1^2[/tex]
25 = 4 + 1
23 = 3
So the length of the hypotenuse is 3 units.
Next, we need to find the coordinates of the midpoint of line segment BC, which is the length of one of the legs of the triangle.
Again, using the Pythagorean theorem, we have:
[tex]b^2 = a^2 + c^2\\1^2 + (-2)^2 = 2^2 + 1^2[/tex]
25 = 4 + 1
23 = 3
So the length of the leg of the triangle is 3 units.
Now, we can use the law of cosines to find the measures of the angles of the triangle.
Let's denote the angle between lines AB and BC as alpha, the angle between lines AB and AC as beta, and the angle between lines BC and AC as gamma.
Using the law of cosines, we have:
[tex]cos(alpha) = (b^2 + c^2 - a^2) / (2bc)\\cos(beta) = (a^2 + c^2 - b^2) / (2ac)\\cos(gamma) = (a^2 + b^2 - c^2) / (2ab)[/tex]
We know that:
a = (-2,0)
b = (2,1)
c = (1,-2)
So we can substitute these values into the above equations:
[tex]cos(alpha) = (2^2 + (-2)^2 - (-2)^2) / (2(-2)1) = (2 + (-2) + 2) / (2(-2)1) = 4 / 3\\cos(beta) = ((-2)^2 + 2^2 - (-2)^2) / (2(-2)2) = (-2 + 4 + 2) / (2(-2)2) = -1\\cos(gamma) = (2^2 + 1^2 - 1^2) / (2(1)(-2)) = 2 + (-1) + (-1) / (2(1)(-2)) = 1[/tex]
Now we can substitute these values into the Pythagorean theorem to find the length of the legs of the triangle:
sin(alpha) = length of leg 1 / (2bc)
sin(beta) = length of leg 2 / (2ac)
sin(gamma) = length of leg 2 / (2ab)
We know that:
a = (-2,0)
b = (2,1)
c = (1,-2)
So we can substitute these values into the above equations:
sin(alpha) = √(8) / (2(-2)1)
= √(8) / √(3)
= √(2)
sin(beta) = √(5) / (2(1)2)
= √(5) / √(3)
= √(2)
sin(gamma) = √(5) / (2(1)(-2))
= √(5) / 1
= √(5)
Therefore, the measures of the angles of the triangle are:
alpha = 60 degrees
beta = 60 degrees
gamma = 60 degrees
So the triangle has three equal angles of 60 degrees.
Learn more about triangle visit: brainly.com/question/28470545
#SPJ4
pls hurry. 2. Which step is the first incorrect step in the solution shown below?
Answer:
step 1
Step-by-step explanation:
Step 1: they accidentally changed the 20 in the original prob to 2.
Answer:
step 1
Step-by-step explanation:
they wrote 2x+6=3x+2 but they wrote 2 instead of 20
it should have been 2x+6=3x+20
Solve the system of equations. − 5 � + 2 � = 9 � = 7 � −5x+2y=9 y=7x
if we want to estimate with a 95.i., a standard deviation of 4, and a margin of error m=1.347, what should the sample size be?
The sample size should be 41.
We can use the formula for the margin of error for a population standard deviation:
m = z*sigma/sqrt(n)
where z is the z-score corresponding to the desired level of confidence, sigma is the population standard deviation, and n is the sample size.
Plugging in the given values, we have:
1.347 = z*4/sqrt(n)
Solving for n, we get:
n = (z*sigma/m)^2
At a 95% confidence level, the z-score is approximately 1.96. Plugging in the values, we get:
n = (1.96*4/1.347)^2
n = 40.28
Rounding up to the nearest whole number, the sample size should be 41.
Learn more about sample size here
https://brainly.com/question/30647570
#SPJ11