The quadratic equation x² - 9 has two real roots.
The quadratic equation x² + 3 · x - 10 has two real roots.
The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.
How to determine if complex conjugate root theorem is applicable to quadratic equation
According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:
b² + 4 · a · c < 0
Now we proceed to check each quadratic equations:
Case 1: (a = 1, b = 0, c = - 9)
D = 0² - 4 · 1 · (- 9)
D = 36
The equation has no complex conjugate roots.
Case 2: (a = 1, b = 3, c = - 10)
D = 3² - 4 · 1 · (- 10)
D = 9 + 40
D = 49
The equation has no complex conjugate roots.
The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:
18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0
Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)
D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²
D = - 28
The equation has a real root and two complex conjugate roots.
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I need Help on this pls
Answer:(2,6)
Step-by-step explanation: 4/1 is going rise/run. your rise would be 4 and your run would be 1. 4/1 is up 4 to the right 1. another point would be (0,-2). you are still gonne do the same thing as rise over run just go negavtive. -4/1 which is down 4 to the left 1.
g suppose we roll 20 fair six-sided dice. what is the probability that the minimum of the dice is 1?
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
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Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
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*Thabiso's parents opened an investment account when he was born, in which they deposit R5 000. They intend to withdraw the money on his 18th birthday. If the account earns 8% p.a. for the first 10 years and 6% p.a. for the next 6 years and 10% p.a. for the final 2 years, all compounded, how much money will Thabiso receive?
Convert 20 feet per minute to yards per hour.
400 yards/hour
3600 yards/hour
60 yards/hour
6.3 yards/hour
20 feet per minute is equal to 400 yards/hour
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
For 1 minute 20 feet
For 60 minutes , 60*20=1200 feet
1 hour = 60 minutes
Thus, we have 1200 feet per hour
3 feet = 1 yard
So, 1200 feet = 1200/3 yrads = 400 yards
Thus, 20 feet per minute is equal to 400 yards/hour
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Please helppppp fastttttt
Answer:
C is the answer
Step-by-step explanation:
Regina is shopping for clothes, and she sees that T-shirts are marked at $10 each and sweatshirts are marked at $14 each. She wants to buy at least 5 items while spending under $60.
Which graph represents the number of T-shirts and sweatshirts Regina can buy to meet her goal?
Answer: She can buy 2 sweatshirts and 3 T-Shirts or 1 sweatshirt and 4 T-Shirts
Step-by-step explanation:
the roots of a polynomial are values that make the polynomial equal ___.
The roots of a polynomial are values that make the polynomial equal zero.
In mathematics, a polynomial is an expression containing indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.A polynomial is a mathematical expression involving a summation of powers in one or more variables multiplied by coefficients. A polynomial function is made of terms called monomials; If the expression has exactly two monomials it’s called a binomial.Read more about polynomials:
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4. 678 es un número racional o irracional.
-103 es un número racional o irracional
Los números racionales son números que se pueden expresar en la forma a/b donde a y b son números enteros y b ≠ 0.
Los números racionales también se conocen como números fraccionarios. En los números racionales de la forma a/b, el número a representa el cuantificador y b es el denominador del número racional.
Qué pasa si el valor de b = 0?
Si un número fraccionario o racional tiene un denominador de 0, como 1/0; 2/0; 10/0; y otros, entonces el número fraccionario o racional no está definido.
Los números racionales también se pueden reclasificar en números enteros, números enteros, números naturales y otros grupos de números que forman parte de los números racionales.
Ejemplo de número racionalAlgunos ejemplos de números racionales como 1/2, 2/3, 5/7, 12/7 y otros.
En los números racionales también hay varias operaciones simples como la suma, la resta, la multiplicación, la división y otras operaciones numéricas.
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withω=seiφ,wheres≥0andφ∈r,solvetheequationzn =ωincwhere n is a natural number. how many solutions are there?
For an nth root, there are n solutions of the equation z^n = ω.
To find these solutions, we use the polar form of z = r * e^(iθ). Substituting into the equation, we get:
r^n * e^(iθn) = s * e^iφ
Comparing the magnitude of both sides, we have:
r^n = s
Comparing the phase of both sides, we have:
nθ = φ + 2πk (where k is an integer)
So, we can set:
r = s^(1/n)
θ = (φ + 2πk) / n
Therefore, the n solutions are:
z = s^(1/n) * e^(i(φ + 2πk) / n)
for k = 0, 1, 2, ..., n-1.
--The question is not readable, answering to the question below--
"With ω = se^iφ, where s ≥ 0 and φ ∈ r , solve the equation z^n = ω in C where n is a natural number. How many solutions are there?"
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what is 17.9 divided by 7?
The Answer is 2.557 when 17.9 is divided by 7
HELP! what is 1 + 1 please help
Answer:
1 + 1 = 2.
Step-by-step explanation:
Answer NOBODY KNOWS THAT
Step-by-step explanation: MATHMATIONS HAVE BEEN TRYING TO FIND THAT OUT FOR YEARS AND YOU THINK YOU'LL FIND IT ON BRAINLY THE EQUATION IS FAR TO COMPLEX FOR HUMAN MINDS THE ONLY WAY YOU'LL GET THE ANSWER IS IF YOU ASKED GOD HIMSELF: but i think 1 + 1 = 2
let x be an ordered set. if y is a proper subset of x that is convex in x, does it follow that y is an interval or a ray in x?
No, it does not follow that y is an interval or a ray in x. A convex subset of an ordered set is a set that contains all the points between any two points in the set.
This means that a convex subset of an ordered set could be a collection of points, it could be an interval, or it could be a ray. A proper subset of an ordered set is any subset except the entire set, so a proper subset of an ordered set could be any of these possibilities.
Therefore, while a proper subset of an ordered set that is convex in that set must be a collection of points, an interval, or a ray, it does not necessarily have to be one of those three options.
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ABCD i a trapezium AD and BC are parallel
work the length of ad
work the lenght of bc
The length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.
AB = 10 cm and BC = 18 cm and angle ADB = 56 degrees.
A: Length of BD:
Using the law of sines, BD can be calculated as:
BD = 10 * sin(56) = 8.62 cm (approx)
B: Length of CD:
Using the Pythagorean theorem, AD can be calculated as:
AD = sqrt(BD^2 + AB^2 - 2 * BD * AB * cos(56)) = 12.92 cm (approx)
And then, CD can be calculated as:
CD = AD - BD = 12.92 cm - 8.62 cm = 4.30 cm (approx)
So, the length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.
"
Complete question
ABCD is a trapezium AD and BC are parallel
where AB = 10cm and BC = 18cm and angle ADB = 56degree
Find
A: work out the length of BD
B: work out the length of CD
"
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Question
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(4, 10), B(14, 15); 3 to 2
The coordinates of point P along the directed line segment AB is (10, 13).
What is the midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
The line AB.
P is the point between the line AB.
Now,
A = (4, 10) = (a, b) and B = (14, 15) = (c, d)
m : n = 3 : 2
So,
P = (x, y)
The coordinates is given by:
x = (mc + na) / (m + n)
y = (md + nb) / (m + n)
So,
x = (42 + 8) / 5
x = 10
y = (45 + 20) / 5
y = 13
Now,
P = (10, 13)
Thus,
The coordinates of point P is (10, 13).
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toru rode his bike from his house to the library, to the park, and then back home. toru realized that his route made an isosceles triangle, and that the library was the exact same distance from both his house and the park. what is the measure of the angle at the library?
The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
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The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
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For f(x) = 2x - 3x², evaluate f(-3).
A. -33
B. 33
C. -21
D. 6
[tex]\huge\begin{array}{ccc}f(-3)=-33\to\boxed{A.}\end{array}[/tex]
Value of the function.
We have the function:
[tex]f(x)=2x-3x^2[/tex]
We need
[tex]f(-3)=?[/tex]
Substitute [tex]x=-3[/tex] to [tex]f(x)[/tex]:
[tex]f(-3)=2\cdot(-3)-3\cdot(-3)^2=-6-3\cdot9=-6-27=-33\to\boxed{A.}[/tex]
what is the answer to b²-17b-38
Answer:
Step-by-step explanation:
I hope this helps you
Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed.
(a) Prove that the kth-order statistic, Y(k), has Beta distribution with α = k and β = n−k+ 1.
(b) What is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer?
(c) Find the joint density of the middle two of Y(1),Y(2),··· ,Y(n) when n is an even integer.
a) k/6 = 1 → k=6 is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer
b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16
a) if distribution
f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere
for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then
P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1
then integrated between
y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1
∫∫f (y1, y2) dy1*dy2 = ∫∫k(1 − y2) dy1*dy2 = k ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)- (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)
then
k/6 = 1 → k=6
b)
P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p
then
p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =
6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)= 9/16
therefore
P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16
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Lashonda is a software saleswoman. Her base salary is $1800 and she makes an additional $70 for every copy of English is Fun she sells.
solve the equation and the Total pay if Lashonda sells 28 copies
The equation which represents total pay P and number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
From the question, we were given the following parameters
P = total pay
N = copies sold
P = 1800 +70N
replace N with 28
P=1800 + 70(28)
P=1800 + 1960
P= 3760 is her total pay selling 28 copies
Hence The equation which represents total pay P and a number of copies sold N is P =1800 + 70N and the total pay for 28 copies sells will be $3760
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Marcu and hi dad were going camping. When they went into the garage to get their tent they noticed it wa ripped. Marcu' dad aid he could fix the tent. He would buy ome new material to cover the one rectangle ide that ripped
Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.
What is meant by rectangular?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides. Answer. Rectangles and rectangular prisms differ primarily in that rectangles exist in two dimensions whereas rectangular prisms exist in three dimensions. Unlike a rectangle, which only has width and length, a rectangular prism has three dimensions: width, height, and length. A quadrilateral with all of its angles equal, or right angles, is a rectangle. In addition to having all equal angles, a square also has all equal sides.He needs 55 to completely cover the tent's one rectangular side with the rip. 55
Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.
3 rectangular sides = 165
2 triangular sides = 24
165 + 24 = 189
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Find out the length of segment GF?
The length of segment GF in the triangle is 8 inches
How to Find out the length of segment GF?From the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following ratio
3 : 6 = 4 : GF
So, we have
GF = 6/3 * 4
Evaluate
GF = 8 inches
Hence, the length is 8 inches
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How are the average rate of change and the instantaneous rate of change related for ƒ(x) = 2x + 5?
The average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5. The solution has been obtained by using the concept of rate of change.
What is rate of change?
The pace at which one quantity changes in relation to another is described by the rate of change function. Simply expressed, the amount of change in one item is divided by the same amount of change in another to determine the rate of change. The relationship between how one quantity changes in relation to a change in another quantity is provided by the rate of change formula.
The average rate of change is:
[tex]r_{avg} =\frac{f(b)-f(a)}{b-a}[/tex], on interval [a,b]
Here, we are given ƒ(x) = 2x + 5
So,
[tex]r_{avg} =\frac{(2b+5)-(2a+5)}{b-a}[/tex]
[tex]r_{avg} =\frac{2b-2a}{b-a}[/tex]
[tex]r_{avg} =2[/tex]
The slope of f assessed at a single point, such as f′(c), where c is a predetermined point, is the definition of the instantaneous rate of change.
So, for ƒ(x) = 2x + 5,
f′(c) = 2
Therefore, instantaneous rate of change is 2.
Hence, the average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5.
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which equation justifies why 27 1 3 is equivalent to the cube root of 27?
The equation that justifies why[tex]27^{(1/3)}[/tex] is equivalent to the cube root of 27 is:[tex]27^{(1/3)} = (27^{1)^{(1/3)}} = 27^{(1/3)}[/tex]
The definition of cube rootThe cube root symbol is represented by the number "3". In the square root case, only the root symbol—also known as a radical—was employed. Therefore, the cube root of different numbers can be symbolically represented as follows: 5 divided by its cube = 3. 11 has a cube root of 311 and so on.
What does a cube of 3 inches mean?The cube root of three is the same as the number 1.442224957031. The cube root of three has the radical representations 33 and 31/3. " denotes the square root.
The cube root formula aids in computing the cube root of any given number that is represented by the symbol in radical form. It can be determined by first determining the number's prime factorization and then using the cube root formula. Assume that x is any number such that it equals y, y, and y.
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The cost of 10 ounces of cheese is 99 cents. What is the price of 10 pounds of cheese in dollars?
160 ounces or 10 pounds of cheese is $ 15 and 84 cents.
What is Unitary method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Direct Variation
When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.
Indirect Variation
A change in one quantity will directly affect a change in another, known as a direct variation. A rise in the quantity of goods, for instance, will result in higher costs.
We can say 1 pound = 16 ounces
10 pounds = 10 * 16 = 160 ounces
10 ounces of cheese is 99 cents
1 ounce of chess is 99/10 cents
160 ounces of cheese is 99*160/10 = 1584 cents = $ 15 and 84 cents.
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The internal revenue service estimates that 8% of all taxpayers filling out long forms make mistakes. Suppose that a random sample of 10,000 forms is selected. What is the approximate probability that more than 800 forms have mistakes? 11. A survey conducted by the harris polling organization discovered that 63% of all americans are overweight. Suppose that a number of randomly selected americans are weighed. (a) find the probability that the fourth person weighed is the first person to be overweight? (b) find the probability that it takes more than 4 people to observe the first overweight person. (c) find the mean and variance of the number of americans that would have to be weighed in order to find the first person who was overweight
The answer to this question requires the use of the Poisson distribution and the cumulative distribution function.
(a) We are asked to find the probability that the fourth person weighed is the first person to be overweight. Since 63% of Americans are overweight, this means that the probability of a randomly selected American being overweight is 0.63. The probability of the first overweight person being the fourth person weighed is given by P(X=3) where X is the number of overweight people in the first 4 people weighed. Using the binomial distribution formula, we have:
[tex]P(X=3) = (4 choose 3) * (0.63)^3 * (0.37)^1\\\\ = 4 * (0.63)^3 * (0.37)[/tex]
(b) We are asked to find the probability that it takes more than 4 people to observe the first overweight person. This is equivalent to finding the probability that none of the first 4 people weighed are overweight. Using the complement rule, we have:
[tex]P(X=0) = 1 - P(X > 0)\\\\ = 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4)]\\\\ = 1 - [ (4 choose 1) * (0.63)^1 * (0.37)^3 + (4 choose 2) * (0.63)^2 * (0.37)^2 + P(X=3) ][/tex]
(c) The expected value (mean) of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. In this case, n=4 and p=0.63. Thus, the mean number of overweight people in 4 trials is 4 * 0.63 = 2.52. The variance of a binomial distribution is given by σ^2 = np(1-p), so in this case the variance is 4 * 0.63 * 0.37 = 1.41. The standard deviation is the square root of the variance, so the standard deviation is approximately [tex]\sqrt{(1.41) } = 1.19[/tex]. This means that the number of overweight people in 4 trials is expected to be around 2.52, with a standard deviation of 1.19.
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If f(x) = 4x2 - 3x + 2, evaluate f(-1).
State the domain of the function f(x) = (x+3)/(x-1).
Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form.
1. f(-1) = 9
2. the domain of the function f(x) = (x+3)/(x-1) is: x ∈ R {1} or x ∈ R {- 1}
3. y = 3x + 2
4. y = 2/3x + 1
What is slope-intercept form?The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. When the slope of the line being studied is known, and the provided point is also the y-intercept, the slope-intercept formula, y = mx + b, is utilized (0, b). b stands in for the y value of the y-intercept point in the formula.
1.
Given f(x) = 4x² - 3x + 2
f(-1) = 4(-1)² - 3(-1) + 2
f(-1) = 4 + 3 + 2
f(-1) = 9
2.
f(x) = x + 3/ x - 1
x - 1 ≠ 0
x ≠ 1
therefore, x ∈ R {1} or x ∈ R {- 1}
3.
Two points (1, 1) and (2, 4)
(x₁, y₁) = (1,1)
(x₂, y₂) = (2, 4)
Two points form an equation:
y - y₁ = {(y₂ - y₁) / (x₂ - x₁)} (x - x₁)
y - 1 = {(4 - 1) / (2 - 1)} (x - 1)
3x - y = 2
x/ (2/3) + y / (-2) = 1
intercept form: x/a + y/b = 1
y = 3x + 2
this is slope intercept form.
4.
given slope (m) = 2/3
y - intercept (c) = 1
y = mx + c
y = 2/3x + 1
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A mechatronic aembly i ubjected to a final functional tet. Suppoe that defect occur at random in thee aemblie, and that defect occur according to a Poion ditribution with parameter λ= 0. 2. (a) What i the probability that an aembly will have exactly one defect? (b) What i the probability that an aembly will have one or more defect? (c) Suppoe that you improve the proce o that the occurrence rate of defect i cut in half to λ=0. 1. What effect doe thi have on the probability that an aembly will have one or more defect? \
(a) The probability that an assembly will have exactly one defect is 0.2.
This can be calculated using the Poisson distribution formula, which states that the probability of a given number of events (in this case, defects) occurring in a given interval is equal to the mean number of events (in this case, defects) multiplied by the exponential of the mean number of events (in this case, defects).
And multiplied by the exponential of the mean number of events (in this case, defects) multiplied by the exponential of the mean number of events (in this case, defects) divided by the factorial of the given number of events (in this case, defects). Thus, the probability of an assembly having exactly one defect is 0.2.
(b) The probability of an assembly having one or more defects is 1 - 0.2 = 0.8. This can be calculated using the same formula as in (a).
(c) By reducing the occurrence rate of defects to λ = 0.1, the probability of an assembly having one or more defects is reduced to 1 - 0.1 = 0.9. This can be calculated using the same formula as in (a).
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Correct question:
A mechatronic assembly is subjected to a final functional test. Suppose that a defect occurs at random in the assemblies, and that defect occurs according to a Poisson distribution with parameter λ= 0. 2. (a) What i the probability that an assembly will have exactly one defect? (b) What i the probability that an assembly will have one or more defects? (c) Suppose that you improve the process o that the occurrence rate of defects i cut in half to λ=0. 1. What effect doe this have on the probability that an assembly will have one or more defects? \
4x -3Expand and simplify 2(x+7) + 3(x+ 1)
Step-by-step explanation:
Expanding and simplifying 2(x + 7) + 3(x + 1):
2(x + 7) = 2x + 14
3(x + 1) = 3x + 3
Adding the two expressions:
2x + 14 + 3x + 3 = 5x + 17
So 2(x + 7) + 3(x + 1) = 5x + 17.
[tex] \sf2(x + 7) + 3(x + 1) \\ \sf2x + 14 + 3x + 3 \\ \sf5x + 17[/tex]
Factor this equation
81a^2+5b^2
Answer:
The equation 81a^2 + 5b^2 cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares. Factoring a sum of squares means writing it as the product of two binomials, each of which is the square root of one of the terms. Since 81 and 5 are not perfect squares, the equation 81a^2 + 5b^2 cannot be written as the product of two binomials.
The equation [tex]81a^2 + 5b^2[/tex] cannot be written as the product of two binomials.
An equation is defined as an expression that shows the relationship between two or more numbers and variables.
Given equation as [tex]81a^2 + 5b^2[/tex]
Since we know that Factoring a sum of squares means writing it as the product of two binomials, each of that is the square root of one of the terms.
Hence, 81 and 5 are not perfect squares.
The given equation [tex]81a^2 + 5b^2[/tex] cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares.
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Carlos wants to buy himself a medium drink and a popcorn for each of his 3 cousins. If the medium drink cost $1. 50, what is the most he can pay for each popcorn if he only has $12. Inequality: solution:
If the medium drink cost $1. 50, the inequality that represents the cost of a popcorn is x ≤ 3.5. Hence, the most he can pay for each popcorn is $3.5.
To translate a word problem into an inequality:
Assign the unknowns to variablesCombine the like termsIsolate the target variableRemember that addition/subtraction will not change the inequality. However, when applying multiplication or division with a negative number, flip the inequality sign.In this problem, let:
x = the cost of 1 popcorn
Three popcorns means = 3x
The cost of a medium drink = 1.5
The amount he need to pay for a medium drink and 3 popcorn:
amount = 1.5 + 3x
However, he only has 12 dollars. Hence,
1.5 + 3x ≤ 12
Subtract both sides by 1.5
3x ≤ 12 - 1.5
3x ≤ 10.5
Divide both sides by 3
x ≤ 10.5/3
x ≤ 3.5
Hence, the maximum price of a popcorn is $3.5
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