If the player do not know exactly how many times the game will be repeated the maximum level of probability can be predicted through Nash equilibria.
The concept, Nash equilibrium in game theory where the optimal outcome is when there is no incentive for players to deviate from their initial strategy. The players have knowledge of their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player. Overall, an individual can receive no incremental benefit from changing actions, assuming that other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all. The Nash equilibrium is a decision making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy.
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please help!!
Given the function p(x) = 5x(x - 3)² Find p(3):
Answer:
The answer is 35.
Step-by-step explanation:
The given polynomial is p(x) = 5x² -4x + 2 we substitute x = 3 in the polynomial:
p(3) = 5(3)² -4(3) + 2 = 5×9 - 12 + 2 = 45 - 12 + 2 = 47 - 12 = 35
Hence, p(3) =35
Is Y =- 3x proportional?
Yes, y = -3x is proportional because the ratios are equivalent, the equation is proportional.
Describe proportion.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 used to indicate proportions. Using 2:5::4:8 as an example, 2/5 Equals 4/8 Here, the averages are 5 and 4 and the extremes are 2 and 8. A proportion is an equation that sets two ratios at the same value.
Given
y = -3x
Yes, Because the ratios are equivalent, the equation is proportional.
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What is f 0 in a function?
The expression f (0) in a function is used to represents the y-intercept on the graph of the function f (x).
The point where the graph cuts the y - axis is known as the y - intercept whereas the point where it cuts the x - axis is known as x - axis. The graph cuts y- axis when the value of x coordinate is 0.
The values which satisfies the equation is known as the zeros of the function. The graph of a function is the set of all points in the plane of the form (x f(x)).
The graph of f could similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.
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What is the example of unique number?
If there are no duplicate digits, then and only then, is a number considered to be unique. For instance, unique numbers include 20, 56, 9863, 145, etc., but non-unique numbers include 33, 121, 900, 1010, etc.
Which number is the most distinctive?Any two items that are the only ones of their kind are equally unique. Unique is defined as the only one like it. There is not a singular most. Each number is distinct because there is only one other one like it. For instance, if you subtract a three-digit number, like 345, from its reverse, 543, you get a difference of 198.
How can I locate the UN's special number?If the number An'obtained is subtracted from a number An made up of n consecutive digits in ascending order by reversing the digits of An, then the difference is always a constant. This constant is termed as the Unique number Un.
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What is the measure of
Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement.
∠ABD = 39°
What is meant by angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.Therefore, the correct option is c) 39°
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Sarah is going to invest in an account paying an interest rate of 5.3% compounded
quarterly. How much would Sarah need to invest, to the nearest dollar, for the value
of the account to reach $1,030 in 5 years?
The amount that Sarah need to invest for the value of the account to reach $1030 will be equal to $792.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently.
Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the details given in the question,
Rate, r = 5.3%
Time, t = 5 years
Amount = $1030
As per the formula of compound interest:
x × (1 + 5.3%/4)⁽⁵⁾⁽⁴⁾ = 1030
x × (1 + 53/4000)⁽⁵⁾⁽⁴⁾ = 1030
Now, calculate the product,
x × (1 + 53/4000)²⁰ = 1030
x × [(4000 + 53)/400]²⁰ = 1030
x = 1030/(4053/4000)²⁰
x = (1030 × 4000²⁰)/4053²⁰
x = 792.
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What fraction has the same value as 25% ?
Answer: 1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
We know that 25% is equal to the decimal 0.25. So, we can convert the decimal into a fraction
To do so, we need to write the fraction 0.25 x 100 / 100.
Solving the top part (100 x 0.25), we get 25/100.
Next, we need to simplify this fraction. The GCF (greatest common factor) of both numbers is 25, so we divide 25 by 25 and 100 by 25.
This leaves us with 1/4, and our answer.
Juan is trying to factor x² + 7x+3 and makes the following table.
- see picture-
Juan concludes that x² + 7x+3 cannot be factored using integers.
a. Is Juan correct?
b. Comment on Juan's strategy and improve it if possible.
a. Yes Juan is correct.
b. The given quadratic equation can be solve by using quadratic formula.
What is a quadratic equation?
A quadratic equation is a polynomial equation with a maximum degree of two. Where a ≠ 0, the equation is given by ax² + bx + c = 0.
Given equation is x² + 7x + 3.
The given equation can't factorized by using middle term or splitting method.
Factorization of quadratic equations can be done in different methods. They are:
Splitting the middle term
Using formula
Using Quadratic formula
Using algebraic identities
Assume that x² + 7x + 3 = 0
x = [-7 ± √(7² - 4 × 1 × 3)]/ 2 × 1
x = [-7 ± √37]/ 2
The factors of quadratic polynomial is ( x - [-7 ± √37]/ 2).
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Which of the following is equivalent to −2(5p − 2q)?
−10p + 4q
−10p − 2q
−7p + 4q
−7p − 4q
Please help me I’m so confused
Answer:
a) 81/500
b) 7/90
c) 3/11
Step-by-step explanation:
You want to write the fractions that correspond with the decimals ...
a) 0.162
b) 0.0777...
c) 0.272727...
Terminating decimalsThe fraction corresponding to a terminating decimal can be written based on how you pronounce the fraction.
a) 0.1620.162 = "one hundred sixty-two thousandths" = 162/1000
This can be reduced by removing a common factor of 2.
= 81/500
Repeating decimals
The fraction equivalent to a repeating decimal can be found by a multiply and subtract process. In general, this makes the denominator be a number that has as many 9s as the decimal has repeating digits.
b) 0.0777...This has one repeating digit, 7. This means we want to convert to a fraction by multiplying by 10 to the power of 1:
x = 0.0777...
10x = 0.7777...
Now, we can subtract the original number:
10x -x = 0.7777... -0.0777... = 0.7000...
Notice that the repeating digits cancel. Now we have ...
9x = 0.7 = 7/10
Dividing by 9 gives ...
x = 7/90
c) 0.272727...
Using the above method with 10 to the power of 2 (with a 2-digit repeat), we get ...
100x = 27.272727...
100x -x = 27.272727... -0.272727... = 27
99x = 27
x = 27/99 = 3/11
__
Additional comment
In general, the repeating part of a repeating decimal can be expressed over an equivalent number of 9s. For example, the 6-digit repeat 0.142857142857... is equivalent to 142857/999999. As it happens, this one reduces to 1/7.
If there are intervening digits, as in 0.4333... for example, then they can be treated as a terminating decimal, and the repeating part can be multiplied by an appropriate power of 10 to account for the shift from the decimal point:
0.4333... = 0.4 + 0.1 × 0.333...
= 4/10 + 1/10 × 3/9 = 4/10 + 1/30
= 12/30 +1/30 = 13/30
a triangle has sides of 12,36,37 is this a right triangle
The triangle has sides of 12, 36, and 37 and is not a right triangle.
What are Pythagoras's triples of the right triangle?
Pythagorean triples are defined as a² + b² = c², where a, b, and c are positive integers. These triples are denoted as (a,b,c). The perpendicular is a the base is b, and the hypotenuse is c of a right-angled triangle.
We have,
a triangle has sides of 12, 36, 37
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
(12)² + (36)² = (37)²
1440 = 1369
S0, LHS ≠ RHS
Hence, the triangle has sides of 12, 36, and 37 is not a right triangle.
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A, B, C and D are points on the circumference of a circle, and the center is O. AC is the diameter of the circle. AC and BD intersect at E.
Answer:
[tex]m\angle DAC=35^{\circ}[/tex]
Step-by-step explanation:
Arc [tex]BC=50^{\circ}[/tex] (inscribed angle theorem)
Arc [tex]AB=130^{\circ}[/tex] (semicircle)
[tex]m\angle ADB=65^{\circ}[/tex] (inscribed angle theorem)
[tex]m\angle DEA=80^{\circ}[/tex] (linear pair)
[tex]m\angle DAC=35^{\circ}[/tex] (angle sum of a triangle)
A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo. for every 12-foot leap of the kangaroo, the rabbit leaps 7 feet. how many leaps would the kangaroo have to make to catch up to the rabbit?
The kangaroo must take at least 23 leaps to catch up to the rabbit.
To catch up to the rabbit, the kangaroo must travel a total distance of 150 feet. For every 12-foot leap of the kangaroo, the rabbit leaps 7 feet, so the kangaroo must take one more leap than the rabbit in order to cover the same distance.
The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):
150 feet / 7 feet/leap = 21.43 leaps
Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.
However, since the number of leaps must be a whole number, the kangaroo must take at least 23 leaps to catch up to the rabbit.
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The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):
150 feet / 7 feet/leap = 21.43 leaps
Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.
How can you use transformations to verify that the triangles are similar?
Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another.
What are triangles?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a three-sided polygon that is also referred to as a trine on occasion (less frequently). There are three sides and three angles in every triangle, some of which may be equal.
Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You do this by twisting one form such that it is in alignment with the other. A rotation is the name given to such a change.
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when constructing an angle bisector, the compass must be used to make three arcs. do all three arcs need to have the same radius? explain.
When constructing an angle bisector, the compass should be used to make three arcs, but these arcs do not necessarily need to have the same radius.
To construct an angle bisector, you can follow these steps:
Place the compass on one of the angle's vertices, and draw an arc that intersects both sides of the angle.Without changing the compass width, draw a second arc that intersects the first arc and one of the sides of the angle.Without changing the compass width again, draw a third arc that intersects the second arc and the other side of the angle.The point where the third arc intersects the other side of the angle is the bisector of the angle.In step 1, the radius of the first arc can be any length, as long as it intersects both sides of the angle. The radius of the second and third arcs should be the same as the first arc because they are drawn using the same width setting on the compass. However, the radius of the second and third arcs does not need to be the same as the radius of the first arc. The important thing is that all three arcs are drawn using the same width setting on the compass so that they are all equidistant from the vertex of the angle.
The complete question is:-
When constructing an angle bisector, the compass must be used to make three arcs. Do all three arcs need to have the same radius? Explain.
- Yes, because then the marks are equidistant from each other.
- Yes, because you need the points of intersection of the angle and arcs to form a parallelogram.
- No; the second two arcs must have the same radius but it can be different from the first.
- No; any three radii will work.
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What is root function Short answer?
The Square root function is written in the form of f(x) = √x .
The Square Root function is defined as the function in which the parent function is written in the form of f(x) = √x .
and the inverse of the Square root function is square function , f(x) = x² .
The Domain and range of the root function is [0 , ∞) .
which means the range is the set of all positive real numbers and
hence in the square root function, result is always positive.
Some Examples of Root Functions are , √2 , √3 , √8 etc. .
Therefore , Square Root function is explained .
The given question is incomplete , the complete question is
What is the Square Root Function ?
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Consider the linear equation. 5x+6y=−15 Which point represents a solution to the equation?
The point that represents a solution to the linear equation 5x + 6y = -15 is (-1, -5 / 3)
How to solve linear equation ?Linear equation can be represented in different form such as standard form, general form, slope intercept form and point slope form.
Therefore, let's find the solution to the linear equation.
5x + 6y = -15
Let's put the equation in slope intercept form.
5x + 6y = -15
6y = -5x - 15
divide through by 6
y = - 5 / 6 x - 15 / 6
y = - 5 / 6 x - 5 / 2
Therefore, the slope of the equation is -5 / 6 and the y-intercept is - 5 / 2.
Using the equation we can find the solution of the equation.
We will substitute the value of x to get y value.
Hence,
y = - 5 / 6 x - 5 / 2
using (-1, -5 / 3)
y = - 5 / 6 (-1) - 5 /2
y = 5 / 6 - 5 / 2
y = - 5 / 3
Hence, the solution is (-1, -5 / 3)
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What is range in set?
In a list or collection of numbers, the range is the difference between the lowest and highest integers. Place all the numbers in order before attempting to determine the range.
what is range ?The statistics' range is the difference between the highest and lowest values for a specific data collection. The range could also be expressed as the difference between the highest and lowest observation. The sample interval is calculated as the greatest value less the smallest value. The sample range is a crucial measure of variability for continuous variables.
here
The x values for a function like f are contained in this collection (x).
The collection of numbers that the function assumes is known as its range.
Following the insertion of an x value, the function outputs this sequence of values.
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What should I Do here? I need steps pls......:)
Answer:
Step-by-step explanation:
Domain is constant since there are no value that x could be to make this not a possible answer
First f(x)=3x+5 y=3x+5 then y+5=3x so (y+5)/3
inverse is (x+5)/3
Then g(x)=x^2+6 y=x^2+6 then y-6=x^2 so then x= \sqrt{y-6}
inverse is \sqrt{y-6}
find the area of the region bounded by the given curves. y = 6x^2 ln x, y = 24 ln(x)
The area of the region bounded by the given curves is [tex]32lnx-\frac{58}{3}[/tex]
Given curves,
y = [tex]6x^{2} lnx[/tex]
y = 24lnx
We will find the intersection points of these two curves by equating and then solving.
The intersection of these two curves will be at x = 1,2.
The area under the curves,
A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]
To solve, concentrate on the unbounded (indefinite) integral:
a = [tex]\int\limits {(24lnx-6x^{2} lnx)} \, dx[/tex]
= [tex]-6\int\limits {(lnx)(x^{2} -4)} \, dx[/tex]
We will use integration by parts to solve this integration.
[tex]\int\limits {u} \, dv=vu-\int\limits{v} \, du[/tex]
Let us assume,
u = lnx and v = [tex]\frac{1}{3}x^{3} -4x[/tex]
Therefore,
[tex]du = \frac{1}{x}dx[/tex]
[tex]dv=x^{2}-4[/tex]
Putting the values,
a = [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - \int\limits{(\frac{1}{x} )(\frac{1}{3}x^{3}-4x)} \, dx ][/tex]
= [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - (\frac{1}{9}x^{3}-4x)][/tex]
= [tex]-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x[/tex]
Returning to the definite integral, now
A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]
= [tex][-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x]^{2} _{1}[/tex]
= [tex]-6ln2(\frac{8}{3}-8)+\frac{16}{3}-48-\frac{2}{3}+24[/tex]
= [tex]32lnx-\frac{58}{3}[/tex]
Hence, The area of the region bounded by the given curves is [tex]32lnx-\frac{58}{3}[/tex].
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. a model proposed for nba basketball supposes that when two teams with roughly the same record play each other, the number of points scored in a quarter by the home team minus the number scored by the visiting team is approximately a normal random variable with mean 1.5 and variance 6. in addition, the model supposes that the point differentials for the four quarters are independent. assume the model is correct. (a) what is the probability the home team wins? (b) what is the conditional probability that the home team wins, given that is is behind 5 points by the end of halftime. (c) what is the conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter
a) The probability the home team wins is of: 0.7291 = 72.91%.
b) The conditional probability that the home team wins, given that is is behind 5 points by the end of halftime is of: 0.3409 = 34.09%.
c) The conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter is of: 0.9015 = 90.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for each quarter are given as follows:
Mean: 1.5.Standard deviation: square root of 6 = 2.45.Hence for each case, the mean and the standard deviation are given as follows:
Entire game -> Four quarters -> [tex]\mu = 6, \sigma = 9.8[/tex]After halftime -> Two quarters -> [tex]\mu = 3, \sigma = 4.9[/tex]After the first quarter -> Three quarters -> [tex]\mu = 4.5, \sigma = 7.35[/tex]The probability of the home team winning is the probability of X being greater than zero for four quarters, hence it is one subtracted by the p-value of Z when X = 0, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (0 - 6)/9.8
Z = -0.61
Z = -0.61 has a p-value of 0.2709.
1 - 0.2709 = 0.7291 = 72.91%.
When the home team is down five points at the end of the halftime, the probability of winning is P(X > 5) for two quarters, hence one subtracted by the p-value of Z when X = 5 as follows:
Z = (5 - 3)/4.9
Z = 0.41
Z = 0.41 has a p-value of 0.6591.
Z = has a p-value of 0.6591.
1 - 0.6591 = 0.3409 = 34.09%.
When the home team is up five points at the end of the first quarter, the probability of winning is P(X > -5) for three quarters, hence one subtracted by the p-value of Z when X = -5.
Z = (-5 - 4.5)/7.35
Z = -1.29
Z = -1.29 has a p-value of 0.0985.
1 - 0.0985 = 0.9015 = 90.15%.
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Using the area model divide, true or false, 79/7 is equal to 11 R 1. True False
Answer: false
Step-by-step explanation:
does it make sense that the number of cats falling from the 5th floor would be greater than those of the 4th? why or why not?
No, it does not make sense that the probability of cats falling from the 5th floor would be greater than those of the 4th. The force of gravity is the same regardless of the floor, so the number of cats falling should be the same no matter what floor they start from.
The force of gravity is a constant force that is the same on all floors. This means that the same amount of force is acting on the cats, no matter which floor they start from. Therefore, the number of cats falling from the 5th floor should be the same as the number falling from the 4th floor. The number of cats falling from a higher floor may be greater if there are extra factors, such as wind, that could affect their fall, but the force of gravity does not change with the floor. Therefore, it does not make sense for the number of cats falling from the 5th floor to be greater than those of the 4th
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Is algebra from Islam?
Therefore , the algebra is derived from Islam word Arabic al‐jab used by its founder.
What is algebra?Mathematical branch known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics. Similar to how sentences illustrate the connections between particular words, in algebra,
Here,
The word algebra is derived from the Arabic word al‐jabr, which its creator, Muhammad ibn Mūsā al‐Khwārizmī, used in the title of his work.
Al-Jabr wa-l-muqbalah, which dates to the ninth century (The Science of Equations and Balancing).
Therefore , the algebra is derived from Islam word Arabic al‐jab used by its founder.
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A una exposición asisten menos de 100 personas y se recaudan más de 260€ con entradas de 2€ y de 4 €. ¿Cuántas entradas de cada tipo han podido ser vendidas?
Based on the graph, a solution for the system of inequalities is 70 and 30.
The number of 2 pounds tickets sold are 70 tickets.The number of 3 pounds tickets sold are 30 tickets.How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of 2 pounds tickets sold and number of 3 pounds tickets sold, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of 2 pounds tickets sold.Let the variable y represent the number of 3 pounds tickets sold.Since less than 100 people attend an exhibition, we have;
x + y < 100 ..........equation 1.
Additionally, more than €260 is raised with tickets of €2 and €4;
2x + 4y > 260 ..........equation 2.
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Hence, the required solution for the given system of linear inequalities is the point of intersection of the two (2) lines on the graph, which is given by the ordered pair (70, 30)
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Complete Question:
Less than 100 people attend an exhibition and more than €260 is raised with tickets of €2 and €4. How many tickets of each type could have been sold?
the number of unbroken charcoal briquets in a twenty-pound bag filled at the factory follows a normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. the company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5% of bags that have too few briquets. what is the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free? (a) 404 (c) 418 (e) 448 (b) 411 (d) 425
The minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free is b) 411.
A standard deviation (or σ) is a degree of the way dispersed the records is with regards to the mean. Low standard deviation approach records are clustered across the mean, and excessive widespread deviation suggests records are greater unfold out. The interval of filled bags is at confidence interval of 95%. At 95% confidence interval, Z=1.96 (from Z tables).But, Z= (x-mean)/SD => 1.96 = (x-450)/20 => x (upper limit)= 20*1.96+450489 bags. Lower limit or minimum number bags to avoid replace= 450-1.96*20 =411 bags.
Therefore, the correct option is b.
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What is the age limit for SSS?
Answer:
Step-by-step explanation: 62 is the limit
Write a rule for the reflection.
(x,y) = ( , )
The rule of the reflection of the triangle ABC to A'B'C' across the y-axis will be (x, y) to (-x, y).
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection will be given as,
Firstly, the rule for reflecting a point about the y-axis is;
While reflecting on the y-axis, we get the reflected points (x, y) by the coordinates (-x, y).
The standard of the impression of the triangle ABC to A'B'C' will be (x, y) to (- x, y).
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What is the vertex of the graph of the quadratic function y X² 6x 5?
We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when x = 3 and y = −4. That is the location of the vertex.
The coordinate of the vertex is (3 , −4)
given equation
y = [tex]x^{2}[/tex] - 6x + 5
= [tex](x - 3)^{2}[/tex] - 4
We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when x = 3 and y = −4. That is the location of the vertex.
The coordinate of the vertex is (3 , −4)
quadratic function :
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. The picture below shows three graphs, and they are all parabolas.
All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
You know that two points determine a line. This means that if you are given any two points in the plane, then there is one and only one line that contains both points. A similar statement can be made about points and quadratic functions.
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What is the value of log2 16 log 2 16?
We determine the value of log₂16 = 4 by using logarithm laws.
What is logarithm?
Logarithm is the alternative way of representing an exponent. The power at which a number is needed to raise to get the other values is termed as logarithm.
What does mean by log₂?It is called log base 2 or binary logarithm. It is the inverse of the power of function 2.
How do we calculate the value of log₂ 16?We stated before that log base 2 is an inverse expression of the power 2. let N is a real positive number and x is the number of exponents. Now, logarithm form of the exponent is written as log₂ N = x
2ˣ = N
We are given, log₂ 16
N= 16
log₂16 = x
2ˣ =16
we know that 2⁴ =16
hence, x= 4
hence, log₂ 16 = 4
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