The probability that Hamid guesses both answers correctly is 10%.
Probability means that it is possible. It is a branch of statistics that deals with the occurrence of a random event. The number is expressed from 0 to 1 where 0 represents an impossible event and 1 represents a sure event.
Probability Formula
The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), this can be shown as
P(E)=Number of favorable outcomes /Number of total outcomes
Since Hamid is playing a trivia game with multiple choice questions, and each question has 2 correct answers among 5 answer choices, and Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random, to determine what is the probability that Hamid guesses both answers correctly the following calculation must be performed:
2/5 x 1/4 = X
0.4 x 0.25 = X
0.1 = X
0.1 x 100 = 10
Therefore, the probability that Hamid guesses both answers correctly is 10%.
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Probability denotes possibility. The occurrence of a random event is the subject of this area of statistics. The number is expressed as a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
Statistical Formula
The ratio of favorable outcomes to the ratio of all outcomes is the definition of the probability formula. This can be shown as for any event (E) as
P(E) = Number of positive results / Number of total results
Given that each question in a multiple-choice trivia game has two correct answers out of a possible five, and that Hamid must choose two answers at random because he doesn't know what the answers are, the following calculation must be done to ascertain the likelihood that Hamid will correctly guess both answers:
2/5 x 1/4 = X
0.4 x 0.25 = X
0.1 = X
0.1 x 100 = 10
what is
-5x-2y=-40
y=2x+2
The solutions for given equation are x = 4 and y = 6
Substitution Method:The algebraic technique for resolving many linear equations at once is called the substitution method. As the name implies, this approach involves substituting a variable's value from one equation into another.
Here we have
- 5x - 2y = - 40 --- (1)
y = 2x + 2 ---- (2)
To solve (1) and (2)
Substitute (2) i.e y value in (1)
=> - 5x - 2(2x+2) = - 40
=> - 5x - 4x - 4 = - 40
=> -9x - 4 = - 40
=> - 9x = - 36
=> x = 4
Now substitute x = 4 in (2)
=> y = 2(2) + 2
=> y = 6
Therefore,
The solutions for given equation are x = 4 and y = 6
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Does the following equation has real roots 3x² 2 √ 5x?
Yes, the equation has real roots. By completing the square, we can make the equation in the form of ax^2+bx+c=0. Then, we can use the quadratic formula to solve for x. The discriminant of this equation is b^2-4ac = 10-60 = -50, which is negative, so the equation has two real roots.
Yes, the equation 3x^2+2√5x has real roots. By expanding the equation, we get 3x^2+2x√5=0. We can use the quadratic formula to solve for x. First, we need to make the equation in the form of ax^2+bx+c=0. To do this, we complete the square. We divide both sides of the equation by 3, giving us x^2+2/3*√5x=0. Then, we add (2/3*√5/2)^2 to both sides, giving us x^2+2/3*√5x+(2/3*√5/2)^2= (2/3*√5/2)^2. Simplifying, we get x^2+2/3*√5x+5/12=0. This is now in the form of ax^2+bx+c=0, with a=1, b=2/3*√5, and c=5/12.
Now, we can use the quadratic formula to solve for x
x = [-2/3*√5 + √(-50/3)]/2
x = [-2/3*√5 - √(-50/3)]/2
Therefore, the two real roots of the equation are
x = [-2/3*√5 + √(-50/3)]/2 and
x = [-2/3*√5 - √(-50/3)]/2.
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help quickly please!
Which of the following expressions is equal to [tex]-3x^2-27[/tex]?
Answer: C
Step-by-step explanation:
(-3x + 9i) (x + 3i)
-3x^2 - 9ix + 9ix - 27
-3x^2 - 27
So, the answer is C
How do you calculate multiplicity?
Multiplicity is a mathematical concept related to the roots of a polynomial equation.
It is defined as the number of times a given root is repeated in the polynomial equation.
The formula for calculating the multiplicity of a root is :
Multiplicity = n-(degree of the polynomial equation)
where n is the order of the root and the degree of the polynomial equation is the highest exponent in the equation.
For example, if the polynomial equation is 3x^2 + 4x + 2 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:
Multiplicity = n - (degree of the polynomial equation)
Multiplicity = 2 - 2
Multiplicity = 0
This means that the root 2 is not repeated in the polynomial equation and therefore has a multiplicity of 0.
In another example, if the polynomial equation is 4x^3 + x^2 + 6x + 12 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:
Multiplicity = n - (degree of the polynomial equation)
Multiplicity = 2 - 3
Multiplicity = -1
This means that the root 2 is repeated in the polynomial equation and therefore has a multiplicity of -1.
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The intersection of two mutually exclusive events: A. can be any value between 0 and 1 B. must always be equal to 1 C. must always be equal to 0 D. can be any positive value If A and B are independent events with P(A) = 0.4 and P(B) =0.6, then P(A B) = A. 0.76 B. 1.00 C. 0.24 D. 0.20 If A and B are independent events with P(A) = 0.05 and P(B) =0.65, then P(A / B) = A. 0.05 B. 0.65 C. 0.8 D. 0.0325
If A and B are independent events with given probabilities P(A) and P(B), then the probability of A intersecting B (P(A ∩ B)) is equal to the product of their individual probabilities. For example, if P(A) = 0.05 and P(B) = 0.65, then P(A ∩ B) = 0.0325.
The probability of two events A and B occurring together, P(A ∩ B), can be calculated by multiplying the individual probabilities of each event, P(A) and P(B). In this case,
P(A) = 0.4 and P(B) = 0.6, so P(A ∩ B) = 0.4 * 0.6 = 0.24
.The probability of event A occurring given that event B has already occurred, P(A | B), is equal to the probability of both events occurring together, P(A ∩ B), divided by the probability of event B occurring, P(B). In this case,
P(A ∩ B) = 0.24 and P(B) = 0.65, so P(A | B) = 0.24 / 0.65 = 0.0375
which can be rounded to 0.0325.These probabilities can be used to estimate the likelihood of certain events occurring together or given certain conditions. In this case, the probability of events A and B occurring together is 0.24 and the probability of event A occurring given that event B has already occurred is 0.0325.
A. P(A ∩ B) = P(A) * P(B)
= 0.4 * 0.6
= 0.24
B. P(A | B) = P(A ∩ B) / P(B)
= 0.24 / 0.65
= 0.0375
= 0.0325
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What is the relationship between the rectangular prism and pyramid which have the same height and base?
The relationship between the volume of the rectangular pyramid and the volume of the rectangular prism with the same base and height is given by : Volume of the rectangular pyramid = (1/3) of the volume of the rectangular prism.
As given in the question,
Formula need to use for the calculation of the volume of the rectangular pyramid and prism is :
Volume of the rectangular pyramid
= (1/3) × ( rectangular base area) × height
Volume of the prism = ( rectangular base area ) × height
If the base and height of the rectangular pyramid and rectangular prism is same then,
Volume of the rectangular pyramid
= ( one - third ) × Volume of the rectangular prism
Therefore, the relationship representing the volume of the rectangular pyramid is and prism with same base and height as volume of pyramid is one third the volume of the prism.
The above question is incomplete , the complete question is:
What is the relationship between the volume of rectangular prism and pyramid which have the same height and base?
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What are the 4 parts of a line graph?
The four parts of a line graph is Tittle, Legend, Data, Y-axis, X-axis and Line.
A line graph—also called a line plot or a line chart—is a graph that makes use of lines to connect individual data points. A line graph presentations quantitative values over a distinctive time of language. In finance, line graphs are normally used to depict the ancient rate action of an asset or security. Line graphs may be compared with different visualizations of facts which includes bar charts, pie charts, and (in buying and selling) candlestick charts, amongst others.
Line graphs might also vary relying non-obligatory capabilities or formatting. the very best-excellent, easiest to understand line graphs have the subsequent characteristics:
Tittle:Line graphs may additionally have a name above the graph to succinctly provide an explanation for what the graph is depicting except we provide a user with written context, the user will regularly depend on the title to better understand what information is being pulled in. The title can also mainly name out a time frame or limits to the information.
LegendThe legend explains what every based variable is and the way to distinguish extraordinary units of data. In the instance above, every dependent variable is marked with its own coloration. The field that explains what each coloration method is the legend.
DataEach object of facts on a line graph is a reference to a distinctive supply that ties the structured variable to an unbiased variable. that is the records on our graph; it is the item that creates the dots that get linked to form the lines to our chart. There may be a couple of units of statistics blended into a single graph. To make sure statistics is blanketed and correct, companies might also have precise information integrity analyst or similar positions to screen database hobby.
X-AxisThe x-axis is the set of records that runs along the horizontal, flat component at the bottom of the road graph. In most line graphs, the x-axis could be related to time, whether it's far the distinctive months in a year or the wide variety of weeks which have exceeded considering that a product launch.
Y-AxisThe y-axis is the set of data that runs alongside the vertical, left-aspect of the graph. some iterations of line graphs have this set of data on the proper. In any case, these numbers count number the items being measured. The graph might also begin at 0, even though there are instances wherein it makes more experience to begin at a higher variety.
LineFinally, the line. the road connects all statistics points within a single structured variable. This line's motion shows the growth and reduce of information throughout time. it may also easily be as compared towards different strains so long as all facts units are being measured over similar periods of time. Although overly simplified, this line can speak to management what actions need to be taken to enhance operations or strategic planning.
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Determine the scale factor of the smaller to the larger figure.
Answer:
2a. Scale factor is 2
2b. Scale factor is 3
Step-by-step explanation:
2a.
We see that the smaller figure to get from F' to G', it is 2 squares, and we see the larger figure to get from F to G, it is four squares, so the scale factor is 2.
2b.
We see that to get from A' to C', it is 2 squares, and we see the larger figure to get From A to C, it is 6 squares, so the scale factor is 3
Write an equation for the function f (x) that has roots of 3, -4, and -1 and a leading coefficient of 2.
f(x) = 2[tex]x^{3}[/tex] + 4[tex]x^{2}[/tex] - 22x -24 will be the equation.
What is the equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The equation will be 2(x-3)(x+4)(x+1) since the function f(x) has roots of 3, -4, and -1 and a leading coefficient of 2.
so 2(x-3)(x+4)(x+1) will be the equation
That is 2(x-3)([tex]x^{2}[/tex] +5x + 4)
2([tex]x^{3}[/tex] + 2[tex]x^{2}[/tex] - 11x -12)
f(x) =2[tex]x^{3}[/tex] + 4[tex]x^{2}[/tex] - 22x -24
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(a) grogg is ordering pizza from a local pizzeria, which offers ten different toppings: pepperoni, mushrooms, sausage, onion, olives, green peppers, pineapple, spinach, garlic, and hummus (an aops favorite). for any pizza, any combination of toppings is possible, including no toppings. how many different pizzas can grogg order? (b) lizzie hears about grogg's plans, and is also interested in ordering a pizza. for variety, they agree to order one pizza each so that they have no toppings in common. in how many different ways can lizzie and grogg order their pizzas? (c) it turns out winnie is also interested in ordering a pizza! lizzie and grogg still agree that their pizzas can't have any toppings in common, but winnie will include a topping on her pizza only if it appears on grogg's pizza or lizzie's pizza (but she doesn't have to include it). in how many different ways can grogg, lizzie, and winnie order their pizzas? you may leave your answers in exponential form.
The number of different ways for each case is given as follows:
a) 1,024 ways.
b) 1,043,456 ways.
c) 1,073,739,264 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, we have that for each of the 10 toppings, there are 2 options, insert or not, hence the total number of outcomes is of:
2^10 = 1024 ways.
For item b, we have that:
Each of Grogg and Lizzie has 1024 possible outcomes.The cases with one or more toppings in common have to be subtracted. There are 10 ways to choose a common topping, and 2^9 = 512 different ways to choose the remaining toppings.Hence the number of ways is given as follows:
1024 x 1024 - 10 x 512 = 1,043,456
For item c, we have that:
Each of Grogg, Lizzie and Winnie has 1024 possible outcomes.For Grogg and Lizzie, there are 1024 x 1024 possible outcomes.The cases in which Winnie has a topping in common with them have to be subtracted.There are 10 common toppings that Winnie can choose, with 2^8 = 256 possible combinations.Hence the number of ways is given as follows:
1024 x 1024 x 1024 - 10 x 256 = 1,073,739,264
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Who are qualified for SSS disability benefits?
You must have held Social Security-covered employment and have a medical condition that satisfies Social Security's rigid definition of disability in order to be eligible for SSS disability benefits.
People who are unable to work for a year or more due to a handicap typically receive monthly payments. Benefits often persist until you can resume regular employment. Additionally, there are a number of unique regulations, referred to as work incentives, that offer ongoing benefits and health insurance to support your move back to employment.
When you reach full retirement age while receiving SSDI payments, your disability benefits will automatically transition to retirement benefits, but the amount will not change.
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How many standard deviations is 75% of the mean?
For at least 75% of the data, the spread will be within two standard deviations of the mean.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Generally speaking, the spread will be within two standard deviations of the mean for at least 75% of the data.
The data will be within three standard deviations of the mean for at least 89% of the time.
Data that deviates more than two standard deviations from the mean are deemed "unusual."
Therefore, for at least 75% of the data, the spread will be within two standard deviations of the mean.
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I NEED HELPP WITH THIS QUESTION!!
The last statement the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela is correct.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given:
Kim and her friends watched the server making smoothies.
The given table shows the number of mangos that were used for each of the different size of smoothies that the friends ordered.
From the given statements the last statement 'the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela.'
Because,
The ratio of smoothies size to mangos used for Kim is, 21/3 = 7 and
The ratio of smoothie size to mangos used for Angela is 28/4 = 7.
Both the ratios are same.
Hence, the last statement the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela is correct.
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How do you solve a discontinuous function?
A discontinuous function can be solved by analyzing the behavior of the function and its points of discontinuity. This can be done by finding the limits of the function at each point and then using the appropriate algebraic techniques to solve the equation.
Discontinuous functions are those that have gaps or sharp discontinuities in their graphs. In order to solve a discontinuous function, you must start by analyzing the behavior of the function and its points of discontinuity. This can be done by finding the limits of the function at each point and then using the appropriate algebraic techniques to solve the equation. This can involve factoring, manipulating equations, and other techniques to find the solution. Once the equation is identified, it can then be graphed to see the behavior of the function between the points of discontinuity. If necessary, the equation can then be further manipulated to satisfy the conditions of the discontinuous points. By approaching the problem in this manner, a discontinuous function can be effectively solved.
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What is the value of k for which 2x2 kx k 0 has equal roots?
The value of k in the quadratic equation is k = 0 or k = 8
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
2x² + kx + k = 0 be equation (1)
And , the roots of the equation are equal
So , when the discriminant is zero we get just one real solution
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
( b² - 4ac ) = 0
Substituting the values in the equation , we get
k² - 4 ( 2 ) ( k ) = 0
On simplifying the equation , we get
k² - 8k = 0
Adding 8k on both sides of the equation , we get
k² = 8k
So , when k = 0 , the equation satisfies
And ,
k = 8
Therefore , the value of k are 0 and 8
Hence , the value of k in the equation is 0 or 8
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What are the three consecutive numbers of 51?
The 3 consecutive odd numbers whose sum will be 51 are 16, 17, 18.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Let the numbers be x, x+1 and x+2.
Then the sum is : x + x+1+ x+2 = 3x + 3
3x + 3 = 51 (given)
3x = 51 – 3 = 48
x = 48 ÷ 3
x = 16
∴
Hence , the 3 consecutive odd numbers whose sum will be 51 are 16, 17, 18.
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what is the answer to −8(7y + 6p − 2)
Russell made $480 in interest by placing $2,000 in a savings account with simple
interest for 2 years. What was the interest rate?
To find the interest rate, we can use the formula for simple interest:
I = P * r * t
Where I is the interest, P is the principal (the amount of money in the account), r is the interest rate, and t is the time (in years).
We know that I = $480, P = $2,000, and t = 2 years.
Plugging these values into the formula, we get:
$480 = $2,000 * r * 2
Dividing both sides by $2,000 * 2, we get:
r = $480 / $2,000 * 2
r = 0.12
So, the interest rate is 0.12, or 12%.
What is the value of polynomial 5x 4x2 3 at x =- 1?
The value of the polynomial 5x- 4x²+3 at x=-1 is -6 by using the substitution method.
Given that,
The polynomial is 5x- 4x²+3
We have to find the value of the polynomial when x=-1.
We know that,
What is polynomial?A polynomial is an algebraic expression whose exponents are all whole numbers. There must be non-negative integer variable exponents in all polynomials.
Take the polynomial P(x) = 5x- 4x²+3
P(x) = 5x- 4x²+3
So, we take x=−1,
P(−1)=5×(−1)−4×(−1)²+3
P(−1)=−5−4+3
P(−1)=−6
Therefore, The value of the polynomial 5x- 4x²+3 at x=-1 is -6 by using the substitution method.
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using the net below find the surface area of the pyramid 8 8 6
The Surface Area of Pyramid is 104 cm².
What is Surface Area?Simply calculating the areas of each face in a figure is surface area. It is considerably simpler for us to calculate because the amount is supplied to us as a net of.
So, Area of square base= (side²)
= 8²
= 64 cm²
and, Area of one triangular face
= (1/2 x b x h)
=1/2 x 8 x 5
= 20 cm²
Now, Multiply by 4 as we have 4 triangular faces
= 20 cm² x 4
= 80 cm²
Then, Surface Area of Pyramid is
= 64 cm² + 40 cm²
= 104 cm²
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W i directly proportional to the cube root of X
X i increaed by 50%
Work out percentage increae in W
The value of the percent increase in the value of W is 50%.
How can I determine the ratio between two quantities?
When the ratio of each of the two quantities' values is equal, the two quantities are said to be proportionate. It comes in two varieties: direct and indirect. The ratio is more than one for direct relations whereas it is less than one for indirect relations.
The relationship provided in the issue can be expressed as,
W ∝ X
X now has a new value when it is increased by 50%:
X + 50% × X
⇒ X + 50/100 × X = 3X/2
Assume that X and W now have values of X1 and W1, respectively.
Consequently, they are related in the following ways:
W ∝ X
⇒ 3/2W ∝ 3/2X
⇒ 3/2W ∝ X₁
W's value is increased by 3/2W - W, which equals 1/2W.
The percentage growth
⇒ (1/2W)/W × 100% = 50%
Hence, the percent increase is obtained as 50%.
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What is the domain of the function in the graph?
Answer:
Below
Step-by-step explanation:
Domain is the x values a graph can have
this one goes from 7 to 11 inclusive ( solid dots at each end)
7<= x <= 11
What type of function is x 3?
On observing the provided question, we can say that the the provided equation f(x) = [tex]x^3[/tex] is the basic cubic function.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
basic cubic function is = [tex]f(x)=x^3[/tex]
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What are the 3 altitudes of a right triangle?
The heights of the two legs (a and b) of a right triangle are equal. Ha = b and hb = an as a result. The height of the hypotenuse is hc. The intersection of a triangle's three altitudes occurs at the orthocenter H, which for a right triangle is located on the vertex C of the right angle.
What do we mean by altitudes?A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
The extended base of the altitude is the name given to this line that contains the opposing side.
The foot of the altitude is the point at which the extended base and the height converge.
Each leg (a and b) of a right triangle has the same altitude as its opposite leg.
As a result, ha = b and hb = a.
The hypotenuse rises to an altitude of hc.
The orthocenter H, which for a right triangle lies on the vertex C of the right angle, is where the three altitudes of a triangle intersect.
Therefore, the heights of the two legs (a and b) of a right triangle are equal. Ha = b and hb = an as a result. The height of the hypotenuse is hc. The intersection of a triangle's three altitudes occurs at the orthocenter H, which for a right triangle is located on the vertex C of the right angle.
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What does multiplicity mean in math?
The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.
Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,
f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,
and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
Hence ,Multiplicity means the quality or state of being multiple or various. and
the number of components in a system (such as a multiplet or a group of energy levels)
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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,
f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,
and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
Simplify 4 p + 3 q − 3 p − 3 q
Answer: it is p
Step-by-step explanation:
4p-3p
Subtract 3p from 4p
=p
Brainliest pls
Answer:
p
Step-by-step explanation:
4p+3q-3p-3q
rearrange terms
4p-3p+3q-3q
combine like terms
1p+0q
simplify
p
hopes this helps
on average, 5 oranges yield 3 cups of juice. if 2 cups make 1 pint, how many oranges are needed to make 3 quarts of orange juice?
The number of oranges needed to make 3quarts of oranges juice is 20oranges
What is proportion?A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4(for every one boy there are 3 girls). This also means that for 2 boys there will be 6 girls.
Similarly 5 oranges is needed to make 3 cups of juice. it can also be put in like 5:3
to make 3quarts,
2cups = 1pint
2pints = 1quart
therefore 4 cups = 1quart
3 quart = 3×4=12cups
if 3 cups is from 5 oranges
then 1 cup = 5/3
12cups = 5/3× 12= 20 oranges
Therefore 20oranges will be needed to make 12 cups of juice
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Can a function have 2 inverse?
Yes, a function will have more than one inverse.
Given,
Function;
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Inverse function;
A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by f-1 or F-1 if the function is denoted by f or F.
Here,
A function may have more than one inverse, or many functions have inverses that are not functions.
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Why is algebra 1 so hard?
It's the first math course they take where they have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students.
what is algebra ?We employ integers with definite or fixed values in algebra, such as 2, 9, 0.068, etc. Numerous sub-branches of algebra exist, including introductory algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.
here
Because it's the first math course they take where they have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students .
Additionally, there is sometimes insufficient effort made in the classroom to relate algebra to students' daily lives and explain why it is important for them to grasp.
They have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students .
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a school cafeteria wants to find out what combinations of food and beverage students are ordering. the results are represented in the two-way table below: food pizza hamburger salad water 11 7 23 beverage slurpee 18 19 5 soda 28 12 14 of all the students, what is the probability that a student ordered a hamburger and a slurpee? a.) 12 over 38 b.) 38 over 42 c.) 38 over 137 d.) 19 over 137
A school cafeteria wants to find out what combinations of food and beverage students are ordering. the probability that a student ordered a hamburger and a Slurpee is 19 over 137.Option D
What is probability?Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.
From the table, we can see that 19 students ordered a hamburger and a Slurpee.
There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.
Therefore, the probability that a student ordered a hamburger and a Slurpee is 19/137, or about 0.14.
Therefore, the correct answer is d) 19 over 137.
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