The outcomes listed must be independent is false about probability distributions.
In probability theory, statistics, and the theory of stochastic processes, independence is a key concept. Informally speaking, two occurrences are independent, statistically independent, or stochastically independent if their occurrence has no bearing on either their chances or probability of occurring. Similarly to this, two random variables are independent if the probability distribution of either one is unaffected by the realization of the other.
It is important to distinguish between two definitions of independence when working with collections of more than two occurrences. Informally, mutual independence of events refers to each event being independent of any combination of other events in the collection, whereas pairwise independence of events refers to any two events in the collection being independent of each other.
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How do I find the value of a + b + c?
The expression of (a + b + c) is equivalent to 16.5.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given are two circles intersecting at each others centers at D and E.
We can write the area of the common region as -
[A] = 4 x {(θ/180) x (πr²/2) - (1/2)r²sinθcosθ}
Now, we can write θ as -
cos(θ) = (3/6) = 1/2
θ = 60°
[A] = 4 x {(60/180) x (π(6)²/2) - (1/2)(6)²sin(60)cos(60)}
[A] = 4 x {(1/3 x 36π/2 - (1/2) x 36 x [tex]\sqrt{\frac{3}{2} }[/tex] x 1/2}
[A] = 4 x {6π - 9 [tex]\sqrt{\frac{3}{2} }[/tex] }
[A] = 24π + (- 9 [tex]\sqrt{\frac{3}{2} }[/tex])
So, on comparing, with the expression below -
aπ + b[tex]\sqrt{c}[/tex]
We get -
a = 24
b = - 9
c = 3/2
So, we get -
a + b + c
24 - 9 + 3/2
24 - 9 + 1.5
24 - 7.5
16.5
Therefore, the expression of (a + b + c) is equivalent to 16.5.
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In a network of 39 computers, 4 have a copy of a particularly critical file to sustain an organization's regular operations. Suppose that 8 computers at random fail. What is the probability that all 4 computers with the critical file fail in this incident? (Round to four decimal places.)
What is the area of the triangle with vertices at A(2, 2), B(4, 5) and C(7, 5)? Express your
answer as a decimal to the nearest tenth.
Answer:
Therefore, the area of the triangle with vertices at A(2, 2), B(4, 5), and C(7, 5) is approximately 4.5, to the nearest tenth.
Step-by-step explanation:
To find the area of a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can use the Shoelace Theorem.
The Shoelace Theorem states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) is given by the following formula:
A = 1/2 * |(x1y2 + x2y3 + ... + xn-1yn + xny1) - (y1x2 + y2x3 + ... + yn-1xn + ynx1)|
To apply the Shoelace Theorem to a triangle with vertices at A(2, 2), B(4, 5), and C(7, 5), you can plug in the coordinates of these vertices into the formula:
A = 1/2 * |(25 + 45 + 72) - (24 + 57 + 52)|
= 1/2 * |(10 + 20 + 14) - (8 + 35 + 10)|
= 1/2 * |44 - 53|
= 1/2 * |-9|
= 1/2 * 9
= 4.5
Use the model to help you find 1/(8/12)
1/(8/12)=___
Answer:
3/2 or 1.5 or 1 1/2 in mix number
The question is in the picture
Answer:
-6/6 or -1
Step-by-step explanation:
To find the equation of the line (or the slope, assuming that's what equation means, ) we need to write the formula Y1-Y2/X1-X2
So, we need to fill in the numbers, which gives us the fraction -6-0/-2-(-8)
When we solve for the numerator (-6-0), we get -6.
When we solve for the denominator (-2 - {-8}), we get 6.
So, we have -6/6, which, when simplified, is -1.
(If the problem is not asking for slope when it says equation, then sorry!)
Find the equation perpendicular to y=-2x+10 through (10,7)
Answer:
y = [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x + 10 ← is in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (10, 7 ) into the partial equation
7 = 5 + c ⇒ c = 7 - 5 = 2
y = [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line
Rewrite the expression as a single logarithm
Please help will give brainlist only if correct!
The correct option is (d) i.e. log [ √x × (x-1)^3 / ∛ (x+1)^2 ] is as the single logarithm.
What is logarithm?
Logarithm is a mathematical operation which is used to determine the exponential power of a number. It is the inverse operation of exponentiation. Logarithm is commonly used in calculus, algebra, and other areas of mathematics. It can also be used to solve problems involving exponents, roots, and powers. Logarithm is denoted by the symbol log, and is read as "log to the base". The base is the number which the logarithm is taken to. For example, log2 10 is the logarithm to the base 2 of 10. This is equivalent to saying "2 to the power of what equals 10?" The answer is that 2 raised to the power of 3 (2^3) would equal 10.
Given, log x / 2 + 3 [ log(x-1) - 2/9 log(x+1) ]
= log √x + 3 log(x-1) - 2/3 log (x+1) {∵ log x^a = a log x }
= log √x + log (x-1)^3 - log (x+1)^2/3
= log √x + log [(x-1)^3 / (x+1)^2/3] {∵ log a - log b = log a/b }
= log [√x × (x-1)^3 / (x+1)^2/3 ]
= log [ √x × (x-1)^3 / ∛ (x+1)^2 ]
Hence, (d) is the correct option.
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You are packing books into a box. The box can hold at most 10 books. The function y=5.2x represent the weight y (in pounds) of x books
Is 52 the range?
Is 45 the range?
Is 15 the domain?
Is the domain discrete or continuous?
Answer:
52 is range
Step-by-step explanation:
Range is the 'y' values the function can have
from 0 to 10 books would give a range of 0 - 52
Domain is the x-values 0, 1,2,3,4,56,7,8,9,10
discrete, because you cannot have anything but the whole numbers listed for the values of 'x'
Answer:
The domain is the input. It is the number of books. You can have 0-10 books. These would be the domains.
The range is the outputs. The outputs can be from 0 to 52 pounds.
The domain is discrete. The domain is the number of books. We cannot have half or a book or 3/4 of a book. So this will be discrete. The number of books can only be whole numbers up to 10.
Step-by-step explanation:
Damian works after school. Each day he earns a set amount, plus an hourly wage. The function f(x)=12 x+10 models the amount he earns each day for working x hours. How much does Damian earn on Friday if he works for 2.75 hours?
$=________
The amount earned by Damian on Friday, if The function f(x) = 12 x + 10, and he works for 2.75 hours, is $43.
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function f(x) = 12 x + 10, where x is working hours,
Calculate the amount by putting the value of x = 2.75 in the function as shown below,
f(x) = 12 × 2.75 + 10
f(x) = 33 + 10
f(x) = $43
Thus, the amount earned is $43.
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Let T(n) denote the nth term of a sequence t. if T(1) = 3, and T(n+1) = T(n) +5 for n>1, what are the first four terms of the sequence
Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9
What is the first four terms of the sequence?First term, T(1) = 3
nth term, T(n+1) = T(n) +5 for n>1
Second term, T2 = T(n) +5
= 2 + 5
= 7
Third term, T3 = T(n) +5
= 3 + 5
= 8
Fourth term, T3 = T(n) +5
= 4 + 5
= 9
Therefore, the first four terms of the sequence are 3, 7, 8, 9
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Which of the following choices can be considered binomial random variables? Choose all answers that apply: A Roll a fair die 5 times and let X = the number of rolls that land showing a "4". B Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6). Roll 5 fair dice at once and let Y = the number of dice that land showing a "4"
The following are binomial random variable,
A)A Roll a fair die 5 times and X = the number of rolls that land showing a "4", is a binomial random variable.
B) Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6), is a binomial random variable.
C) Roll 5 fair dice at once and let Y = the number of dice that land showing a "4" , is a binomial random variable.
A random binomial variable should satisfy the following conditions:
1. The number of trials are defined or fixed.
2. Each trial is independent of others.
3. The probability of success is same in all trials.
4. There should be only two outcomes in each trial.
Lets we evaluate the options based on the above conditions:
(A) Rolling fair dice 5 times have 5 trials, each rolling is independent, probability of 4 is 1/6 in all cases and the dice will either land 4 or will not land 4. So, X will have values from 0 to 5, 0 when dice doesn't land 4 even once in 5 rolls and 5 when dice land 4 in all rolls. This variable satisfies the condition to be a random binomial variable. So, X is a random binomial variable.
(B)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice with even number to all 5 dices with even number. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Z is a random binomial variable as it satisfies all the conditions.
(C)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice land with 4 to all 5 dices land with 4. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Y is a random binomial variable as it satisfies all the conditions.
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What is the discontinuity and zero of the function f of x equals x squared plus 5 times x minus 6 all over quantity x plus 6 end quantity question mark
a
Discontinuity at (−6, −7), zero at (−1, 0)
b
Discontinuity at (6, 5), zero at (−1, 0)
c
Discontinuity at (−6, −7), zero at (1, 0)
d
Discontinuity at (6, 5), zero at (1, 0)
The discontinuity of our given function is at point (-6, -7).
The zero of our given function is, (1, 0).
What is discontinuity and zero of the function?
A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.
The x-intercept(s) of the function's graph represent the real zero of the function.
Consider the given function,
[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]
We know that a function is discontinuous, when its denominator is equal to zero.
To find the discontinuity for our given function, we will equate denominator to 0 as:
x + 6 = 0
x = -6
Now simplify the given function.
[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]
Take y = x - 1
Since the denominator term is cancelled out, so our give function has a removable discontinuity.
Now, we will find value of y by substituting x = -6
⇒ y = -6 - 1
y = -7
Therefore, the discontinuity of our given function is at point (-6, -7).
Now, we will find zero of our given function by substituting f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:
⇒ 0 = x - 1
x - 1 = 0
x = 1
Therefore, the zero of our given function is, (1, 0).
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Mariah has a total of $15,000 invested in two accounts. The total amount of interest she earns from the accounts in the first year is $1540. If one account pays 8% per year and the other pays 12% per year, how much did she invest in each account?
The amount invested in the account that earns 8% interest is $6500
The amount invested in the account that earns 12% interest is $8500
How much did she invest in each account?a + b = $15,000 equation 1
0.08a + 0.12b = $1540 equation 2
Where:
a = amount invested in the account that earns 8% interest
b = amount invested in the account that earns 12% interest
The elimination method would be used to determine the required values:
Multiply equation 1 by 0.08
0.08a + 0.08b = 1200 equation 3
Subtract equation 3 from equation 2
0.04b = 340
Divide both sides of the equation by 0.04
b = 340 / 0.04
b = $8500
a + 8500 = 15,000
a = $15,000 - $8,500
a = $6500
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Does meditation cure insomnia? Researchers randomly divided 400 people into two equal-sized groups. One group meditated daily for 30 minutes, the other group attended a 2-hour information session on insomnia.
At the beginning of the study, the average difference between the number of minutes slept between the two groups was about 0. After the study, the average difference was about 32 minutes, and the meditation group had a higher average number of minutes slept.
To test whether an average difference of 32 minutes could be attributed to chance, a statistics student decided to conduct a randomization test. She wrote the number of minutes slept by each subject in the study on an index card. She shuffled the cards together very well, and then dealt them into two equal-sized groups, representing those who meditated and those who attended the information session.
Which of the following best describes the outcome of the randomization test.
O The average difference between the two values on the two stacks of cards is expected to be about 0 minutes.
O If meditation is effective, the average difference between the values on the two stacks of cards is expected to be more than 32 minutes.
O The average difference between the two values on the two stacks of cards is expected to be about 32 minutes.
1. The average difference between the two values on the two stacks of cards is expected to be about 0 minutes best describes the outcome of the randomization test.
This randomization test was conducted to test whether the average difference of 32 minutes between the two groups could be attributed to chance. The test essentially involved shuffling the index cards containing the minutes slept by each subject and then dealing them into two equal-sized groups.
This process allows for a fair comparison between the two groups and ensures that any differences in the average minutes slept are due to chance. Since the cards are shuffled randomly, the average difference between the two stacks of cards is expected to be about 0 minutes.
If meditation is effective, then the difference between the values on the two stacks of cards would be expected to be more than 32 minutes.
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Reese is taller than Gage. If r represents Reeses's height and g represents Gage's height, write an inequality that shows the relationship between thier heights
The inequality that shows the relationship between thier heights is g < r or r > g
How to determine the inequality that shows the relationship between thier heightsFrom the question, we have the following parameters that can be used in our computation:
Reese is taller than Gage.
Also, from the question; we have
Reeses's height = r
Gage's height = g
Because Reese is taller than Gage, then it means that
The value of r is greater than the value of g
So, we have the following inequality expression
r > g
Also, we have
g < r
Hence, the inequality is g < r
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The graph of the linear function passes through points (2, 44) and (5, 80). What is the equation of the function? PLEASE HELP!! I WILL MARK BRAINLIEST!!!
Answer:
y=12x+20
Step-by-step explanation:
Your question and a graph of picture are different. So I just considered your question.
m= (80-44)/(5-2) = 36/3=12
(y- y_1)=m(x-x_1)
(y-44)= 12(x-2)
y-44=12x-24
y= 12x-24+44
y=12x+20
To start dividing 126 by 23, Miranda used the estimate 120÷20 = 6. How could you tell six is too high?
Answer:
the product of 6 and 23 is more than 126
Step-by-step explanation:
You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.
Trial dividendWhen the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.
__
Additional comment
Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.
Given
G(t) = 9 − 5t,
write
G(−5 + h) − G(−5)
in simplest form.
The value of the function G(-5 + h) - G(-5) in the simplest form -5h.
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given function is,
G(t) = 9 - 5t (1)
To find the value of expression G(-5 + h) - G(-5),
First, find the value of G(-5 +h) by substituting t = -5+h in equation (1),
G(-5 + h) = 9 - 5(-5 + h)
= 9 +25 -5h
= 34 - 5h
The value of G(-5)
G(-5) = 9 - 5(-5)
= 9 + 25
= 34
The required value,
G(-5 + h) - G(-5) = 34 - 5h - 34 = -5h.
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Zendaya's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=7.6x+60y=7.6x+60, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the xx-value when y=100y=100?
For the quiz score of 100, the time will be equal to 5.26 hours.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.
The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.
Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.
At the score of the quiz of 100, the value of x will be calculated as,
y = 7.6x+60
100 = 7.6x + 60
40 = 7.6x
x = 40 / 7.6
x = 5.26 hours
The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.
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You give a test to 100 students and determine the median of the scores. After grading the test you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points each. The median of the new score distribution will be (less than, greater than or the same as) that of the original score distribution?
Answer:
R'>R
Step-by-step explanation:
To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.
We know the range is defined by R
R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.
Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5. So, our range also becomes
R = X(n) + 5 - X(1)
So, R'>R. Hence, the range of the new score will be greater than that of the original score distribution.
If four vertices of a regular octagon are chosen at random then the probability that the quadrilateral formed by them is a rectangle is
A.1/8
B.2/21
C.1/32
D.1/35
The correct answer is option D. 1/35. To count the number of rectangles that can be formed, we need to consider the two cases where the diagonals of the rectangle are parallel to the sides of the octagon, and where the diagonals are perpendicular to the sides of the octagon.
In the first case, there are four choices for which side the diagonals are parallel to, and once that side is chosen, there are two choices for which pair of vertices lie on that side. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.
In the second case, there are four choices for which vertex the diagonals intersect, and once that vertex is chosen, there are two choices for which pair of vertices lie on the same side of the intersection point as the chosen vertex. Therefore, there are $4 \cdot 2 = 8$ rectangles of this type.
Altogether, there are $8 + 8 = 16$ rectangles. Therefore, the probability that the quadrilateral formed by the four vertices is a rectangle is
$\frac{16}{70} = \frac{16}{{8 \choose 4}}= \frac{1}{{8 \choose 4}/16}
= \frac{1}{{8 \choose 4}/2^4}
= \frac{1}{{8 \choose 4}/2^4}
= \boxed{\text{(D) } 1/35}$.
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Question
Solve the equation.
−2w=−9
w=
w=9/2 =4,5
Step-by-step:
:)
Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly, and requiring monthly payments. At this time, interest rates on 15-year loans have dropped to 2.1% APR, compounded monthly, and you wish to refinance what you still owe with a new loan at this new rate. (a) How much (in dollars) will you be refinancing? Round your answer to the nearest dollar. (b) How much (in dollars) will your new monthly payment be after refinancing? Round your answer to the nearest cent.
Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly,
a) You will be refinancing $122536.
b) New monthly payment be after refinancing is
$794.1858 or 79 418.58 cents.
We have given that
Initial loan amount = $ 130,750
Number of year of loan = 30 year
Nomber of month of loan "n" = 30x12= 360
Annual interest rate = 6.6%
monthly rate "r" = 6.6% /12 =
monthly payment on the loan is
PMT= loan× r / [1 - (1+r)⁻ⁿ]
= $ 130750 X 12/(1 - (1+ 6.6%/12)⁻³⁶⁰)
= $719,125/(1- (1+0.0055) ⁻³⁶⁰
= $835.046
Monthly payment, $835.046 on initial loan.
Now after 5 years refinishing is done . So, amount and remaining balance is for 30-5 = 25 years and 25×12 = 300 months . The present value of unpaid monthly payment is
= PMT× ( (1 - (1+r)⁻ⁿ)/r)
= $835.046( 1 - (1+6.6%/12)⁻³⁰⁰/ 6.6%/12]
= $835.046× 196.74179
= $122536
Hence, amount refinanced is $122536.
b) New monthly payment will be on loan =$122536
Annual rate = 2.1%
monthly rate, r' = 2.1%/12
Number of years for refinancing = 15 years
Number of months , n' = 15× 12 = 180
Using the formula new monthly payment is
PMT = new loan× r'/ [1 - (1+r')⁻ⁿ´ ]
= $122536× 2.1%/12[ 1 - (1+2.1%/12)⁻¹⁸⁰]
= $214.43826/0.2700104
= $794.1858
Hence, new monthly payment is $794.1858.
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In the article, Attitudes About Marijuana and Political Views (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970's.
To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were
In the hypothesis test about cannabis use by conservatives and liberals, the test statistic was z = -4.27, with a corresponding p-value of about 0.00001.
Which conclusion is most appropriate in the context of this situation?
The data do not support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.
The data support the claim that the proportion of conservatives who smoke cannabis is no different that the proportion for liberals.
The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.
The z-test statistic is used to test the claim that the proportions of the two populations differ. A normal test statistic, the z-test statistic can also be used to measure the proportion of a single population.
Let's say that:
p1: Liberal voters' proportion of the population who smoked cannabis, p. 2:
Conservative voters' proportion of the population who smoked cannabis The null hypothesis is H 0:
The alternative hypothesis is H 0: p 1 = p 2.
p 1 p 2 P-value = 0.00001 The P-value is less than the significance level of 1%. The null hypothesis is rejected at the 1% significance level.
We can conclude that conservative voters had a lower percentage of voters who regularly smoked cannabis.
What is theory trying?Two distinct hypotheses are tested by all analysts using a random population sample: the alternative hypothesis and the null hypothesis. Typically, the null hypothesis is a hypothesis that all population parameters are equal; For instance, a null hypothesis might assert that the population mean return is zero.
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Solve the equation b/16 = -4 for b
-64
-4
4
64
Answer: -64
Step-by-step explanation:
To solve this equation, you need to isolate the b term on one side of the equation. You can do this by dividing both sides of the equation by 16. This will give you:
b/16 = (-4)
You can then divide both sides of the equation by -4 to get:
b/16 = -4
b/16 * -4 = -4 * -4
b = -64
Therefore, the solution to the equation is b = -64.
Solve for x -13x<65 simplify
The value of x in the inequality, -13x < 65, is simplified as, x > 5.
How to Solve an Inequality?Any inequality given can be solved by find the value of the variable in the inequality, which will make it a true statement. To do this, isolate the given variable to make it stand alone on one side.
Given the inequality, -13x < 65, solve as shown below:
-13x < 65 [given]
Divide both sides by -13:
-13x/-13 < 65/-13
x > -65/13 {the sign changes from < to > because we divided both sides by a negative quantity]
x > 5
The value of x is simplified as x > 5.
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100 points for this one
Answer:
C) x < - 11 or x > 8---------------------------------------
First, solve the inequality:
|2x + 3| > 192x + 3 > 19 or 2x + 3 < - 192x > 16 or 2x < - 22x > 8 or x < - 11This is option C (you have chosen it correctly).
Now, graph it:
Mark points - 11 and 8 on the number line with open circle, then shade to the left from point - 11 and to the right from point 8.Answer:
x < -11 or x > 8
Step-by-step explanation:
Given absolute value inequality:
[tex]|2x+3| > 19[/tex]
[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]
Apply the absolute rule:
[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex] [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]
To graph the solution:
Place open circles at -11 and 8.Shade to the left of the open circle at -11.Shade to the right of the open circle at 8.(20points) Let A be a symmetric positive define matrix with Cholesky decomposition A = LLT = RTR. Prove that the lower triangular matrix L(or that the upper triangular matrix R) in the factorization is unique.
In the factorization, the bottom triangular matrix L is the only one.
What is Cholesky decomposition?The exponent of a number indicates how many times it has been multiplied by itself.
Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.
Given that A is a positively defined symmetric matrix with a Cholesky decomposition,
A = L[tex]L^{T}[/tex] = [tex]R^{T} R[/tex]
Let A be our positive define symmetric matrix,
suppose A has Cholesky decomposition,
A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,
thus (A x ,x) = (Lx, Lx) = (Lx, Lx)
pick x = eₓ the last coordinate vector,
then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²
Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,
The Kth entry is currently the last row.
given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)
so the last row of L₁, L₂ be the same,
we reduce our A to new (n - 1)x(n - 1) submatrix,
which will likewise be true, and then repeat the process to discover each row's unique value.
Thus, the inductive process shows that L1 = L2.
As a result, the factorization's bottom triangular matrix L is exclusive.
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Can you please help me
Answer:
the first option
Step-by-step explanation:
in an "and" statement both parts need to be true, so that the overall condition is true.
is x = 6 a valid solution ?
no, it violates both, x <= -8 and x <= 4
is a value between -8 and 4 a valid solution like x = -2 ?
no, it violates x <= -8, even though it is true for x <= 4.
only values that are smaller or equal to -8 (like -9) are true for both.
and therefore the first answer option is correct.
on monday therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Therease should take her 7th dose on Friday at 9:00AM
What is time ?
Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.
The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.
If Theresa took her first dose at 9:00 AM on Monday,
Simply add 12 hours every time up to the 7th dose,
First dose ----> 9:00 AM on Monday,
Second dose ----> 9:00 PM on Monday,
Third dose ----> 9:00 AM on Tuesday,
Fourth dose ----> 9:00 PM on Tuesday,
Fifth dose ----> 9:00 AM on Thursday,
Sixth dose ----> 9:00 PM on Thursday,
Seventh dose ----> 9:00 AM on Friday,
Hence, Theresa should take her 7th dose at 9:00 AM on Friday.
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