Multiply the following 2 polynomials
(9 + 2x)(9 - 2x)
find the eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector . the larger eigenvalue has associated unit eigenvector .
The eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector is Ax = λx.
Symmetric matrix:
In algebra, symmetric matrix a square matrix that remains unaltered when its transpose is calculated.
Given,
Here we need to find the the eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector and the larger eigenvalue has associated unit eigenvector.
Here the eigenvector is a vector that is associated with a set of linear equations.
And in the eigenvector of a matrix is also known as a latent vector, proper vector, or characteristic vector.
Therefore, those are defined in the reference of a square matrix.
So, the smaller eigenvalue has associated unit eigenvector is Ax is λx.
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Use the appropriate normal distribution to approximate the resulting binomial distributions. A fair coin is tossed 130 times. What is the probability of obtaining between 56 and 73 tails, inclusive?.
The probability of obtaining between 56 and 73 tails, inclusive will be approximately 0.8561.
To approximate the resulting binomial distribution, we will use the normal distribution as an approximation when certain conditions are met.
The number of trials, n, is large n = 130.
The probability of success, p, is not too close to 0 or 1
Then the coin is fair, so p = 0.5.
We have to calculate the probability of obtaining between 56 and 73 tails, inclusive.
Mean (μ) = n x p = 130 x 0.5 = 65
Standard Deviation (σ) = √(np (1 - p))
(σ) = √(130 x 0.5 x 0.5) ≈ 5.7
Using a standard normal distribution, we can determine the z-scores corresponding to 56 and 73 tails:
z1 = (56 - μ) / σ ≈ (56 - 65) / 5.7
≈ -1.58
z2 = (73 - μ) / σ ≈ (73 - 65) / 5.7
≈ 1.40
P(56 ≤ x ≤ 73) ≈ P(-1.58 ≤ z ≤ 1.40)
Now we can determine these probabilities and subtract them.
P(-1.58 ≤ z ≤ 1.40) ≈ 0.9155 - 0.0594
P(-1.58 ≤ z ≤ 1.40) ≈ 0.8561
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While playing a game with her friends, Ellen scores 12 points less than twice the lowest score. She scored 98. What was the lowest score in the game?
I need HELP! I dont understand and need help!
algebra 2 please HELP
Answer:
[tex]y = 3.48(1.32)^{x}[/tex]
Step-by-step explanation:
8 = ab^3
42 = ab^9
b = 1.32
[tex]\frac{8}{(1.32)^{3} } =\frac{a(1.32)^{3} }{(1.32)^{3} }[/tex]
a = 3.48
Answer:
[tex]y = 3.48(1.32)^{x}[/tex]
ms. wilson's science test scores are normally distributed with a mean score of 84 (μ) and a standard deviation of 3 (σ). using the empirical rule, about 99.7% of the scores lie between which two values?
Using the empirical rule, about 99.7% of the scores lie between 75 to 93
In this question, we have been given ms. wilson's science test scores are normally distributed with a mean score of 84 (μ) and a standard deviation of 3 (σ).
We know that the empirical rule predicts that 99.7% within the first three standard deviations (µ ± 3σ).
An empirical rule is also known as 68-95-99.7 rule.
We find the interval (µ ± 3σ)
The upper value would be,
µ + 3σ
= 84 + 3(3)
= 84 + 9
= 93
and the lower value would be,
µ - 3σ
= 84 - 3(3)
= 84 - 9
= 75
Therefore, about 99.7% of the scores lie between (75, 93)
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please help solve! cannot find answer and i’m trying to work on math
Answer: 19/21>8/9
Step-by-step explanation:
common denominator is 63
19*3=57 so thats 57/63
8*7=56 so thats 56/63
Need some help, explain.
Answer:
hope this will help you
9^2/9^-4 using a single positive exponent
Answer:
9⁶
Step-by-step explanation:
[tex]\dfrac{9^2}{9^{-4}} = 9^2 9^{4} = 9 ^ {(2 + 4)} = 9^6[/tex]
Reciprocal of a number raised to exponent is the same as the number raised to the negative of the original exponent
So
[tex]\dfrac{1}{9^{-4}} \text{ becomes } 9^4[/tex]
Consider the equation xy = 0 In this equation, variables are multiplied and the result is Can the equation be true neither variable is equal to ? Can the equation be true only one variable is equal to 0If so, which one needs to be equal to Can the equation be true if both variables are equal to ? What process could you use to solve equations of the form (x + a)(x + b) = 0 In this case there are only two factors (values being multiplied ) that are being set equal to How would you solve the equation if there were more than two factors ? Explain
Answer: 1+1
Step-by-step explanation:
I not giving
5а – 2 = 8
6
a = [?]
Answer:
5a=8+2
5a=10/:5
a=2
it is okay?
suppose a random variable has population standard deviation 29.5. what is the margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53?
The margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53 is 7.94.
Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.
MOE = z x (SD / √n)
where MOE = margin of error
z = found by using a z-score table
SD = sample standard deviation = 29.5
n = sample size = 53
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.975, z = 1.96
Plug in the values to the formula and solve for the margin of error.
MOE = z x (SD / √n)
MOE = 1.96 x (29.5/√53)
MOE = 7.94
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Which of the equations is NOT equivalent to 6x = 20? Select all that apply. 6x ÷ 6 = 20 ÷ 6 6x ÷ 6 = 20 ÷ 20 6x + 5 = 20 + 5 6x − 1 = 20 − 1 6x × 6 = 20 × 20
These three expressions
6x ÷ 6 = 20 ÷ 6
6x + 5 = 20 + 5
6x − 1 = 20 − 1
will be equal to the given expression.
What is Expression ?Operators, constants, and variables all come together to form an expression. A value can be produced by an expression using one or more operands and zero or more operators.
We have to check which equation will be equal to 6x = 20
6x ÷ 6 = 20 ÷ 6
After Multiplying both sides by 6.
We get, 6x = 20
6x ÷ 6 = 20 ÷ 20
After simplifying we get,
x = 1
Multiplying both sides by 6
6x = 6, Hence it doesn't satisfy.
6x + 5 = 20 + 5
Subtract 5 both sides of the equation
We get, 6x = 20
6x − 1 = 20 − 1
Adding 1 both sides of the equation,
We get, 6x = 20
6x × 6 = 20 × 20
After simplifying, we get
36x = 400
Hence, only
6x ÷ 6 = 20 ÷ 6
6x + 5 = 20 + 5
6x − 1 = 20 − 1
will be equal to the given expression.
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PLEASE HELP ME WITH THIS PROBLEM!!!!!!
Answer:
720
Step-by-step explanation:
100/5 = 20, so 20 tires made in 1 hour and 20 x 36 would be 720 so answer is 720
(7x³ + x² + x) divided by (x² + 1)
Answer:
Q=7x+1, R=-6x-1
Step-by-step explanation:
7x + 1
----‐----------------------------
x² + 1 | 7x^3 + x^2 + x
-) 7x^3 +7x
---‐---‐----------------------------
x^2 -6x
-) x^2 +1
--------------------
-6x-1
what are all of the equivalent ratios to 4.5
Answer:
The two equivalent ratios of 4:5 are 8:10 and 12:15.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
catalina multiplied 842 and 3 and got 3326.how did she check to see if her answer is reasonable?
Answer: Take 3326 and divide by 3
Step-by-step explanation: This will check to see if her answer is correct or not. If 3326 is divided by 3 and gets 842 then her answer is correct!
If you can please give me a Brainliest, I only need 2 more to become an Ace, thank you!
3326 ÷ 3 = 1108.666667
Step-by-step explanation:Question: 842 x 3 = 3326?Check:
Take the answer 3326, and divide it by 3, and we should get 842:
3326 ÷ 3 = 1108.666667
It does not equal 842.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Using your answer from the previous question, state the value of ‘w’ if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
Answer:
16.5
Step-by-step explanation:
hence the answer is 16.5 feet
HELP ME PLEASE!!! it’s for algebra and i really need to get this awnser right!! please literally anyone help me
Answer:
Below
Step-by-step explanation:
Start with point (3,5) slope (5/3) form:
(y-5) = 5/3 (x-3) expand
y-5 = 5/3 x -5 re-arrange by adding 5 to both sides
y = 5/3 x done!
A synthetic fiber used in manufacturing carpet has tensile that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. (a) Find the probability that a random sample of n = 6 fiber specimens will have a sample mean tensile strength that exceeds 75.75 psi. 75.75 - р X- р M P[X > 75.75] = P o In o Tn 75.75 – 75.5 P[X > 75.75] = P2> 3.5 va = P[Z > 0.175] = 1-0(0.175) = 0.4325 BC (b) How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 to n = 49?
The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
Given that,
The tensile strength of a synthetic fiber used to make carpet is regularly distributed, with a mean of 75.5 psi and a standard deviation of 3.5 psi. We have to determine probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi.
We know that,
The Z score is used to determine how far the raw score deviates from the mean, either above or below.
z = (score - mean) / (standard deviation ÷ √sample)
Mean 75.5 psi and standard deviation 3.5 psi. n = 6.
For > 75.75:
z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17
P(z>0.17) = 1-P(z<0.17)
= 1-0.5675
= 43.25%
Therefore, The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
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A restaurant is offering a dinner special that includes one starter and one entree. The choices are listed below. How many possible dinner special combinations are there?
Starter: breadsticks, soup, salad
Entree: beef, fish, chicken, shrimp, pork
The total number of possible dinner combinations are 15
What are Combinations?
The number of ways of selecting r objects from n unlike objects is calculated by combination. The formula for combination is
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the total number of dinner combinations be = T
Now ,
The values of Starters is represented in set = A
The values of Entree is represented in set = B
The values of Set A = { bread sticks , soup , salad }
The values of Set B = { beef , fish , chicken , shrimp , pork }
Now , the total combinations of possible selection of Starters = ³C₁
The total combinations of possible selection of Entree = ⁵C₁
So , the total number of dinner combinations T = total combinations of possible selection of Starters x total combinations of selection of Entree
And , the equation is
The total number of dinner combinations T = ³C₁ x ⁵C₁
The total number of dinner combinations T = 3 x 5
The total number of dinner combinations T = 15
Therefore , the value of T is 15
Hence , The total number of possible dinner combinations are 15
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# 3 Mia has $50 on a gift card to her favorite
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card.
+
The equation to represent the relationship between n, the number of times she visits the coffee shop, and b, the total balance on her gift card is b = - 3.75n + 50
How to represent a situation with equation?Mia has $50 on a gift card to her favourite coffee shop. Each time she visits the coffee shop she spends $3.75 on her favourite drink.
The equation to represent the relationship between n, the number of times she visits the coffee shop, and b, the total balance on her gift card can be represented as follows:
Therefore,
n = number of times she visit the coffee shopb = total balance on her gift cardHence, the equation is as follows;
b = - 3.75n + 50
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please answer this question
The correct equation is Option A which states that x+16 = 70. The reason for this is opposite angles (or vertical angles) in parallel lines are congruent.
What are opposite angles?When two lines intersect they form a pair of opposite or vertical angles. In this case, the vertical angles are:
70° ≅ t
p ≅ s
q ≅ (x +16)°
r ≅ u
Given that lines AB and CD are parallel, and that both cut through lines EF, that means q ≅ 70°
Hence,
∡ ApE = 70° = ∡DrF
If we need to find x
Since DrF (x+16) °= 70°
x = 54°
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Where does the graph of y = -3x - 18 intersect with the x axis?
A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defectives ones are identified. Denote by N1the number o tsis mad un the first defectiv is identified and by N2 ihe number of additional tests until the second defective is identified. Find the joint probability mass function of N1 and N
The joint probability mass function of N1 and N2 for the given transistors is 1/15.
Explain the term selection without replacement?The total number of things available for the initial selection is one extra than the number of units available for such second option when items are chosen without replacement. Due to the fact that one object has been chosen and not returned to the pool.For the stated question-
Six transistors total.2 transistors are faulty in total.Four non-defective transistors are present.N1: The number of tests conducted before the first flaw is found = 2/6.
N2: The number of tests that must be performed before the second problem is found = 1/5.
If N1 = 1 and N2 = 1, then
P(N1 = 1; N2 = 1) = 2/6 x 1/5
P(N1 = 1; N2 = 1) = 2/30
P(N1 = 1; N2 = 1) = 1/15
Thus, joint probability mass function of N1 and N2 for the given transistors is 1/15.
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the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) estimate how long it takes the population to double.
As the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year and according to that it will take 63.36 years to double the population.
A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.
According to the question:
We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.
A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.
P(t) = [tex](1.011)^{t}[/tex]
⇒ [tex]7.1[/tex] × [tex]2 = 7.1 (1.011^{t}[/tex]
⇒ [tex]\frac{7.1 * 2}{7.1} = 1.011^{t}[/tex]
⇒ [tex]1.011^{t}[/tex] = 2
Now let us solve for t using logarithm.
[tex]ln(2) = ln(1.011)^{t}[/tex]
⇒ ln(2) = t . ln(1.011)
⇒ 0.6931471805599 = t × 0.0109399400383
⇒ t = 0.0109399400383/ 0.6931471805599
⇒ t = 63.3593217
⇒ t ≈ 63.36
Therefore, it will take 63.36 years the population to be double.
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Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model f(t)=89−17log10(t+1),0≤t≤24 where t is the time in months.
(a) What is the average score on the original exam? (b) What was the average score after one year? (c) After how many months would it take for it to predict that the average dropped to 82? (Assume that the the model could continue past two years, if necessary)
Answer:
Step-by-step explanation:
Classify each pair of numbered angles.
Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
[Linear pair ] [ vertical ] [ adjacent ] [none of these ]
Based on the image given above, the angles that are numbered can be classified as:
∠1 and ∠2: vertical angles
∠3 and ∠4: adjacent angles
What are Adjacent Angles?Angles that share the same vertex and also the same side, are said to be angles that lie next to each other which are called adjacent angles.
For example, the angles in the image given that are numbered as 3 and 4, share the same vertex and a common side. Therefore, they are adjacent angles.
What are Vertical Angles?If two angles are formed to lie directly opposite to each other when two lines intersect at a point, the angles share a common point but do not share a common side. These set of angles are called vertical angles.
For example, in the image given, angles 1 and 2 are vertical angles.
Therefore, the angles would be classified as:
Angles 1 and 2: vertical angles
Angles 3 and 4: adjacent angles
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Answer:
3 and 4 are adjacent angles, and 1 and 2 are vertical angles.
Step-by-step explanation:
vertical angles are across from each other while adjacent is next to each other. the other person's explanation is better than mine though. :')
a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.
The side length of the original cube for the given measurements and condition is equal to 8.6ft.
As given in the question,
Let 'x' be the side of the original cube.
Volume of original cube = x³
As given 8ft thick slice is cut from the top of the cube.
Volume of the thick slice = 8x²
Volume of the resulting rectangular box = 44
⇒ x³ - 8x² = 44
⇒ x³ - 8x² -44 =0
Plot the graph of the function.
Graph is attached.
From the graph approximate value of side length 'x' = 8.6 ft.
Therefore, the side length of the original cube is equal to 8.6ft.
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Is -2/3 greater then 1 2/4
Answer: No
Step-by-step explanation:
Because 1 2/4 = 6/4 = 3/2 or 1.5
When the other one is a negative fraction which is very obviously that 1 2/4 is greater than -2/3
Answer: 1 2/4 is greater than -2/3
Step-by-step explanation: A positive number is always greater than a negative number, even when dealing with fractions