Answer:
B= 21
Step-by-step explanation:
A^2 + B^2 = C^2
72^2 + B^2 = 75^2
Solve for B
B = 21
If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x)
A) 2x-3
B)3x-3
C)4x+1
D)2x-1
Answer:
C.
Step-by-step explanation:
Estimate the value of √2π / √5 .
Answer:
1.12099824328 or estimated is 1
Step-by-step explanation:
Give branliest if i was right!
The Land of Nod lies in the monsoon zone, and has just two seasons, Wet and Dry. The Wet season lasts for 1/3 of the year, and the Dry season for 2/3 of the year. During the Wet season, the probability that it is raining is 3/4; during the Dry season, the probability that it is raining is 1/6. (a) I visit the capital city, Oneirabad, on a random day of the year. What is the probability that it is raining when I arrive? (b) I visit Oneirabad on a random day, and it is raining when I arrive. Given this information, what is the probability that my visit is during the Wet season? (c) I visit Oneirabad on a random day, and it is raining when I arrive. Given this information, what is the probability that it will be raining when I return to Oneirabad in a year's time? (You may assume that in a year's time the season will be the same as today but, given the season, whether or not it is raining is independent of today's weather.)
Answer:
Step-by-step explanation:
(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.
Let A be the event that it is raining, and B be the event that it is the Wet season.
P(A) = P(A|B)P(B) + P(A|B')P(B')
Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.
The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.
Now we can calculate the probability that it is raining when you arrive:
P(A) = (3/4)(1/3) + (1/6)(2/3)
= 1/4 + 1/9
= 9/36 + 4/36
= 13/36
Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.
(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.
Let C be the event that your visit is during the Wet season.
P(C|A) = (P(A|C)P(C)) / P(A)
We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.
Now we can calculate the probability that your visit is during the Wet season:
P(C|A) = (3/4)(1/3) / (13/36)
= 1/4 / (13/36)
= 9/52
Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.
(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.
Let D be the event that it is raining when you return.
If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.
If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.
Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.
Let C' be the event that your visit is during the Dry season.
P(D) = P(D|C)P(C) + P(D|C')P(C')
Since P(C) = 1/3 and P(C') = 2/3, we can calculate:
P(D) = (3/4)(1/3) + (1/6)(2/3)
= 1/4 + 1/9
= 9/36 + 4/36
= 13/36
Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.
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9(42) - 9(4) = 9(30) - 9(___)
Answer: 8 (I might have gotten it wrong tho) could be -8 too btw.
Step-by-step explanation:
42x9=378 and 9x4=36. 9x30=270 so that would make the equation 378-36=270-9(_). Simplified a bit more would be 342=270-9(_). Now subtract 270 from both sides you get 72=9(_) so it would be 8. Sorry if I’m wrong tho.
Answer:
9(42) - 9(4) = 9(30) - 9(-8)
Step-by-step explanation:
9(42 - 4) = 9(38)
9[30 - (-8)] = 9(38) because of rules of subtracting integers is:
Two like signs become a positive sign
Example:
3+(+2) = 3 + 2 = 5
6−(−3) = 6 + 3 = 9
Two unlike signs become a negative sign
Example:
7+(−2) = 7 − 2 = 5
8−(+2) = 8 − 2 = 6
Jenny works mowing lawns and babysitting. She earns $8.80 an hour for mowing and $7.70 an hour for babysitting. How
much will she earn for 1 hour of mowing and 3 hours of babysitting?
Answer:
$31.90
Step-by-step explanation:
Hope it helps :)
Have a good day/night
Brainliest pls?
{(2,2),Is this a function?
Find the first and second derivatives of the function. (Factor your answer completely.)
g(u) = u(2u − 3)^3
g ' (u) = g'' (u) =
The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.
Given function: `g(u)
= u(2u - 3)^3`
To find the first derivative of the given function, we use the product rule of differentiation.`g(u)
= u(2u - 3)^3`
Differentiating both sides with respect to u, we get:
`g'(u)
= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`
Using the chain rule of differentiation, we have:
`g'(u)
= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`
Simplifying:
`g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`
To find the second derivative, we differentiate the obtained expression for
`g'(u)`:`g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`
Differentiating both sides with respect to u, we get:
`g''(u)
= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`
Using the product rule and chain rule of differentiation, we have:
`g''(u)
= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`
Simplifying:
`g''(u)
= 12(u - 1)(2u - 3)^2`.
The first derivative of the function `g(u)
= u(2u - 3)^3` is `g'(u)
= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)
= 12(u - 1)(2u - 3)^2`.
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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).
Using the product and chain ruleFirst, let's find the first derivative:
g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]
Using the chain rule, we can differentiate (2u - 3)³ and u as follows:
d(u)/du = 1
d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du
= 3(2u - 3)² * 2
Plugging these values back into the equation for g'(u), we have:
g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2
= (2u - 3)³ + 6u(2u - 3)²
Simplifying the expression, we have:
g'(u) = (2u - 3)³ + 6u(2u - 3)²
Now, let's find the second derivative:
g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]
Using the chain rule and product rule, we can differentiate each term:
d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du
= 3(2u - 3)² * 2
d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]
= 6(2u - 3)² + 6u * 2(2u - 3)
The Second derivativePlugging these values back into the equation for g''(u), we have:
g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)
= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)
= 12(2u - 3)² + 12u(2u - 3)
Simplifying the expression further, we have:
g''(u) = 12(2u - 3)² + 12u(2u - 3)
Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).
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what is 28.5 inches in height?
the directions on a sewing pattern say to cut an etrea 15% of fabric to account for error. chloe needs 0.75 yard of fabric to make a skirt, so she suts 0.1125 yard. did chloe cut the correct amount of fabric, why our why not?
The amount of fabric that Chloe cut is correct.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
The directions on a sewing pattern say to cut an extra 15% of fabric to account for an error.
and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard.
The amount of Fabric needed
0.75 x 1.15 = X
0.8625 = X
and, Chloe cut the fabric
= 0.8625 - 0.1125
= 0.75
Thus, the amount of fabric that Chloe cut is correct.
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0.60792 liters x ________ = 607.92 mL
0.60792 liters x 1000 = 607.92 mL
Multiplying the volume in liters by 1000 converts it to milliliters.
Dr. Nielsen evaluated Kris when he was 2-years-old and Dr. Perry evaluated him when he was 6-years-old. Both diagnosed him with an intellectual disability and ADHD. This is known as which type of reliability
The type of reliability being referred to in this scenario is inter-rater reliability. This means that multiple raters (in this case, Dr. Nielsen and Dr. Perry) are assessing the same individual and producing consistent results in their diagnoses.
The question is about the type of reliability when Dr. Nielsen evaluated Kris at 2-years-old and Dr. Perry evaluated him at 6-years-old, with both diagnosing him with an intellectual disability and ADHD.
The type of reliability in this scenario is known as inter-rater reliability. Inter-rater reliability refers to the consistency of measurements when different evaluators assess the same individual or situation. In this case, both Dr. Nielsen and Dr. Perry independently came to the same diagnosis, demonstrating a high level of inter-rater reliability.
Inter-rater reliability is an important aspect of psychological and diagnostic assessments as it provides confidence in the consistency of the evaluations conducted by different professionals. When multiple evaluators reach similar conclusions, it enhances the reliability and validity of the diagnoses made.
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Sebastian tiene una tarjeta de puntos para un cine.
Recibe 85 puntos de recompensa solo por registrarse.
Gana 2.5 puntos por cada visita al cine.
Necesita 115 puntos para una entrada de cine gratis.
Escribe y resuelve una ecuacion que se pueda usar para determinar vv, el numero de visitas que Sebastian debe hacer para ganar una entrada gratis al cine.
Por favor lo ocupo para ahora ayuda, por favor.
Sebastian has to make 12 visits in order to earn a free movie ticket.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Sebastian who has a points card for a cinema. He received 85 reward points just for signing up and will earn 2.5 points for each movie visit. He needs 115 points for a free movie ticket.
We can write the expression as -
115 = 85 + 2.5v
2.5v = 115 - 85
2.5v = 30
v = 30/2.5
v = 12
Therefore, Sebastian has to make 12 visits in order to earn a free movie ticket.
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[Question translated in english is as follows -
Sebastian has a points card for a cinema.
Receive 85 reward points just for signing up.
Earn 2.5 points for each movie visit.
You need 115 points for a free movie ticket.
Write and solve an equation that can be used to determine vv, the number of visits Sebastian must make to earn a free movie ticket.
Please I'll take it for now help please.]
Please answer and show work
Answer:
Answer and steps are in picture.
Rich Borne teaches Chemistry 101. Last week he gave his students a quiz. Their scores are listed below. 24 31 47 29 31 16 48 41 50 54 37 22 54 38 7 16
The quiz scores of Rich Borne's Chemistry 101 students are as follows: 24, 31, 47, 29, 31, 16, 48, 41, 50, 54, 37, 22, 54, 38, 7, and 16.the performance of Rich Borne's Chemistry 101 students on the quiz
To analyze this data, we can calculate various descriptive statistics such as the mean, median, mode, range, and standard deviation. The mean (average) score can be obtained by summing up all the scores and dividing by the total number of scores. The median represents the middle value when the scores are arranged in ascending order. The mode refers to the most frequently occurring score. The range is the difference between the highest and lowest scores, indicating the spread of the data. The standard deviation measures the variability or dispersion of the scores around the mean.
By calculating these descriptive statistics, we can gain insights into the performance of Rich Borne's Chemistry 101 students on the quiz and understand the central tendency and variability of their scores.
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Please help me!!! Thank you :DD
Answer:
x = 58°
Step-by-step explanation:
I need help with this problem please
Answer:
see picture... In simpler terms, take each point and count Ys down to the line (P=1) (don't count the line) then count that many down from the line.
Works the same with vertical lines except do Xs not Ys.
Step-by-step explanation: given P=1... orange line is the origin, don't forget to count it
coordinates of old shape
red (-2,7)
green (-6,8)
Blue (-6,6)
Black (-4,4)
NEW SHAPE
red (-2,-4)
green (-6,-5)
blue (-6,-3)
black (-4,-1)
Ezra is baking cookies his recipe uses 200 grams of sugar to make 48 cookies. He wants to know how many cookies he can make with 350 grams of sugar.
Part A which proportion can be used to find the number of cookies, y, Ezra can make with x grams of sugar?
A. y=0.24x
B. y=4.17x
C. y=48x
D. y =200x
Part B How many cookies can Ezra make with 350 grams of sugar? Enter the answer in the box
We are asked to find the proportion of sugar to number of cookies
Sugar = 200g
Number of cookies = 48
proportion of sugar to cookies = 200 : 48
how many cookies he can make with 350 grams of sugar?
let x = number of cookies
proportion of sugar to cookies = 350 : x
equate the proportions
200 : 48 = 350 : x
200/48 = 350/x
cross product
200 × x = 350 × 48
200x = 16800
x = 16800/200
x = 84 cookies
find the number of cookies, y, Ezra can make with x grams of sugar?
y = grams of sugar, x / number of cookies
y = 350/84
y = 4.17x
Therefore,
Ezra can make 84 cookies with 350 grams of sugar
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Select the correct answer. If x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
The correct answer is:
x + 12 ≤ 5 − y ≤ 2(x − 3)
Explanation:
From the given inequalities:
x + 12 ≤ 5 − y ... (1)
5 − y ≤ 2(x − 3) ... (2)
We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):
x + 7 ≤ -y ... (3)
-y ≤ 2(x - 8) ... (4)
Multiplying (3) by -1, we get:
y - 7 ≥ x ... (5)
Substituting this value of x in (4), we get:
y - 7 ≤ -2(7 - y)
y - 7 ≤ -14 + 2y
y ≤ 7
Substituting this value of y in (5), we get:
0 ≤ x + 7 ≤ 14
Subtracting 7 from all sides, we get:
-7 ≤ x ≤ 7
Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.
The volume of a spherical balloon is 950 cm. Find the radius of the
4
balloon. (Volume of a sphere
ZAR).
the radius of the spherical balloon is 8.53 cm.
The volume of a sphere of radius r is given by the formula (4/3)πr³ cm³.
Given that the volume of the spherical balloon is 950 cm³, we have:(4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5
Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Given that the volume of the spherical balloon is 950 cm³, we need to find the radius of the balloon.
To do this, we will use the formula for the volume of a sphere, which is given by (4/3)πr³ cm³, where r is the radius of the sphere. Using this formula, we can write:
4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:
r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Hence, the radius of the spherical balloon is 8.53 cm.
The radius of a spherical balloon was to be calculated based on the given volume of the balloon. The formula for the volume of a sphere was used which is (4/3)πr³.
On substituting the given volume and simplifying the obtained equation, we get the value of the radius of the spherical balloon. The final answer for the radius of the balloon was calculated to be 8.53 cm.
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Unit 3:
3. The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachel is at the 99th percentile in height for adult woman, then her height, in inches, is closest to
(A) 60
(B) 62
(C) 68
(D) 70
(E) 74
For the given Problem, The correct option giving Rachel's height in inches is (D) 70.
What does "z-score" mean?A z-score, also called standard score, can be used to measure- how much an observation or data point deviates from the mean of the distribution. By Subtracting the mean of the given distribution from the observation and after that dividing it by the standard deviation will give us the z-score for given observations.
Given:
Mean height (μ) = 65 inches
Standard deviation (σ) = 2 inches
Percentile (P) = 99%
The Z-score, commonly known as the standard score, helps in quantifying how much a data point deviates from the mean. It can be computers as:
\(Z = (X - \mu) / \sigma\)
where X is the value of the data point.
We can rearrange the equation to solve for X:
\(X = Z * \sigma + \mu\)
We may use a regular normal distribution table or a Z-table to obtain the Z-score corresponding to the 99th percentile. The Z-score for the 99th percentile is roughly 2.33.
\(X = 2.33 * 2 + 65\\\\X = 4.66 + 65\\\\X = 69.66\\\\{X}\;\approx70\; inches\)
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Choose the expression that represents a cubic expression. 19x4 18x3 − 16x2 − 12x 1 10x3 − 6x2 − 9x 12 −9x2 − 3x 4 4x 3
The expression "10x^3 - 6x^2 - 9x + 12" represents a cubic expression since it has a term with a variable raised to the power of 3 (x^3) and the highest power of the variable is 3.
A cubic expression is one that has a highest exponent of 3 on its variable. Out of the given expressions, the one that represents a cubic expression is 10x³ − 6x² − 9x + 12.
What is an expression? An expression is a combination of letters, digits, and symbols that represent a number or a quantity.
Expressions can be used to represent mathematical relationships between numbers, as well as the relationships between variables.
Cubic expressions A cubic expression is one that contains a single variable that has an exponent of 3.
The highest exponent of the variable is 3, and the expression will be in the form of ax³ + bx² + cx + d, where a, b, c, and d are constants.
For instance, 3x³ - 5x² + 2x + 1 is a cubic expression because the highest exponent of the variable x is 3.
This implies that the expression has a degree of 3.Choose the expression that represents a cubic expression Out of the given expressions, the one that represents a cubic expression is 10x³ − 6x² − 9x + 12.
This is because the highest exponent of the variable x is 3, which is the criteria for cubic expressions.
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A number is decreased by 40% to 525. what is the original amount?
Answer:
875
Step-by-step explanation:
lets assume the original amount X
the new amount = X - ( X × 40% )
525 = (60 × X) ÷ 100
X = ( 525 × 100 ) ÷ 60
X = 875
Answer:
The number is 875
Step-by-step explanation:
Step One:
Convert 40% to a decimal --> .40
Step Two
525 = n - .40n
(525 is equal to a number minus forty percent of a number )
Step Three
Isolate the variable by dividing each side by factors that don't contain the variable.
N = 875
What is the factored form of 1,458x ^3 - 2
Factorize
1,458x^3 - 2
2(729)x ^3-2 = 2 (729x ^3 -1)
Then use the next factoize form :
(ax ^3 - y^3) = (ax-y) (ax^2+axy + y^2)
where (a^3x ^3 - y^3) = (729x ^3 -1)
a^3 =729
a= 9
Using the form
(729x ^3 -1) = (9x-1) (9^2x^2+9x+1)
9^2 = 81
(9x-1) (9^2 x^2+9x+1) = (9x-1) (81 x^2+9x+1)
The whole exprresion is 2(9x-1) (81 x^2+9x+1)
The answer is the option A
acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. the abc electronics company has just manufactured 2100 write-rewrite cds, and 50 are defective. if 3 of these cds are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the entire batch will be accepted will be 9339
4000-90 = 3910 (non-defective) (non-defective)
If P(first not defective) = 3910/4000 and it is not changed (1 less to choose from and 1 less not defective)
P(second is not flawed if first is flawed) = 3909/3999 If the item is also not replaced (a total of 2 less to choose from and 2 less not defective)
P
(1st and 2nd are not defective, so the third is also not defective)) = 3908/3998
Simply multiply these three fractions to get the answer: 3910(3909>)(3908)) / (4000(3999)(3998)).
=9339
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6−2(8−x)=2x−10
l don't understand the question
Answer: x has infinite number of solutions
Step-by-step explanation:
6−2(8−x)=2x−10
6-16-2(-x)=2x-10
-10+2x=2x-10
2x-10=2x-10 ==> x has infinite number of solutions
I set z=t=0(x,y,z,t)
and I got a partial solution (0,1,0,0).
I solved two homogeneous matrices once for z=1
and t=0
, then for z=0
and t=1
and I got two solutions (1,1,1,0)
and (1,1,0,1).
Then, I got (0,1,0,0)+a∗(1,1,1,0)+b∗(1,1,0,1
)
Therefore, all possible results are (0,1,0,0),(1,0,1,0),(1,0,0,1),(0,1,1,1)
Would this be correct?
The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).
Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.
Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).
Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).
Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).
To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.
(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)
Expanding this expression, you get:
(0+a+b, 1+a+b, 0+a, 0+b)
Simplifying, you obtain the following set of solutions:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Therefore, the correct set of possible results would be:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.
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Can someone help me ASAP? It’s due today
The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
How to Identify Independent Events?Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
This is because each event does not depend on another one of the events being described.
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Find a positive number such that the sum of and is as small as possible. does this problem require optimization over an open interval or a closed interval? a. closed b. open
To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible.
To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible. So, we need to minimize the sum of and . Now, let's use calculus to find the minimum value of the sum.To find the minimum value, we have to find the derivative of the sum of and , i.e. f(x) with respect to x, which is given by f '(x) as shown below:
f '(x) = 1/x^2 - 1/(1-x)^2
We can see that this function is defined on the closed interval [0, 1]. The reason why we are using the closed interval is that x is a positive number, and both endpoints are included to ensure that we cover all positive numbers. Therefore, the problem requires optimization over a closed interval. This means that the minimum value exists and is achieved either at one of the endpoints of the interval or at a critical point in the interior of the interval.
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The graph of y = f(x) is the solid black graph below. Which function represents the dotted graph?
Answer:
y = -f(x - 5)
Step-by-step explanation:
the function of the dotted graph is f(x) shifted (or translated) 5 units to the right and then reflected across the x-axis.
shifting it to the right is happening by reducing every x value by 5 (so that we get for x the functional value of x-5).
and reflecting it across the x-axis simply means to flip the sign. everything that was originally above the x-axis is now with the same distance below the x-axis (and vice versa).
therefore, the new
y = -f(x - 5)
The perimeter of an airplane ticket is 36 centimeters. The area is 80 square centimeters. What are the dimensions of the ticket?
Answer:
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Step-by-step explanation:
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