The workload of the resource is 20.5 units.
To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.
For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:
Workload = (10*2 + 8*1 + 5*3) / 2
= 41 / 2
= 20.5 units
Therefore, the workload of the resource is 20.5 units.
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Complete question
What are the flow unit types that the resource is serving?
write and equation to state the following: a varies jointly with b and the square root of c and inversely with the cube of d.
The equation that expresses the joint variation of a with b and the square root of c, and the inverse variation of a with the cube of d is:
[tex]a = k * \frac{(b * \sqrt{c})}{d^3}[/tex]
In mathematics, A variation equation is an equation that describes how one variable (the dependent variable) changes with respect to changes in one or more other variables (the independent variables). There are several types of variation equations, including direct variation, inverse variation, joint variation, and combined variation.
Now let's consider the given question:
It is given that,
a varies jointly with b and the square root of c, means
[tex]a \propto b[/tex] and [tex]a\propto \sqrt{c}[/tex].
It is also given,
a varies inversely with the cube of d, means
[tex]a \propto \frac{1}{d^3}[/tex]
Then by combining those, we can write
[tex]a \propto \frac{(b * \sqrt{c})}{d^3}[/tex]
The equation that expresses the joint variation of a with b and the square root of c, and the inverse variation of a with the cube of d is:
[tex]a = k * \frac{(b * \sqrt{c})}{d^3}[/tex]
Where k is the constant of proportionality. This equation states that as b and the square root of c increase, and as d decreases, the value of a increases proportionally. The constant of proportionality k depends on the specific values of a, b, c, d, and the units of measurement being used.
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There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability P_i, i, .., N. Hence, P_1 + P_2 +... + P_N = 1. Let T denote the number of coupons one needs to select to obtain at least one of each type. Compute P(T > n).
If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.
Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:
P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)
By the principle of inclusion-exclusion, we can write:
P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.
This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.
In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.
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When a tuba is played, the player makes a buzzing sound and blows into one end of a tube that has an effective length of 3.50 m. The other end of the tube is open. If the speed of sound in air is 343 m/s, what is the lowest frequency the tuba can produce?Please show all work and formulas to receive credit for best answer
The lowest frequency the tuba can produce is approximately 49 Hz.
The lowest frequency produced by the tuba is called its fundamental frequency, which corresponds to the longest wavelength that can fit in the tube. The wavelength of a sound wave is related to its frequency and the speed of sound by the equation
wavelength = speed of sound / frequency
In this case, the effective length of the tube is equal to half of the wavelength of the fundamental frequency (because the tube is open at one end and closed at the other), so we can write
wavelength = 2 × effective length = 7.00 m
Solving for the frequency using the above equation, we get
frequency = speed of sound / wavelength = 343 m/s / 7.00 m ≈ 49 Hz
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5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)
Answer:
Player Efficiency Rating (PER)
Step-by-step explanation:
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.
PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.
PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.
On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.
Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.
Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.
So, correct option is D.
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find the probability of not spinning red on either spin. (not red on the first spin and not red on the second spin.)
The probability of not spinning red on either spin (not red on the first spin and not red on the second spin) is 1/12
The probability of an event is a number that indicates how likely the event is to do. It's expressed as a number in the range from 0 and 1, or, using chance memorandum, in the range from 0 to 100. The more likely it's that the event will do, the advanced its probability. The probability of an insolvable event is 0; that of an event that's certain to do is 1.
It is know to us that Probability (Red) = 3/6 = 1/2
also Probability (Blue) = 2/6 = 1/3
and Probability (CYAN) = 1/6, therefore,
a) Probability ( CYAN then red) = 1/6 x 1/2 = 1/12
b) Probability ( CYAN then Blue) = 1/6 x 1/3 = 1/18
c) Probability ( no Cyan on 2 spins) = (1/2+1/3) x (1/2+1/3) = 5/6 x 5/6 = 25/36
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Complete question:
The spinner below is spun twice. If the spinner lands on a border, that spin does not count and spin again. It is equally likely that the spinner will land in each of the six sectors.
REDREDREDBLUEBLUECYAN
For each question below, enter your response as a reduced fraction.
a) Find the probability of spinning cyan on the first spin and red on the second spin.
b) Find the probability of spinning cyan on the first spin and blue on the second spin.
c) Find the probability of NOT spinning cyan on either spin. (Not cyan on the first spin and not cyan on the second spin.)
Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long would you have to wait for 1/7 of it to disappear?
You would have to wait ___ years for 1/7 of the radium to disappear.
Accοrding tο the half-life fοrmula, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
What is Expοnential Decay ?Expοnential decay is a mathematical prοcess in which a quantity decreases οver time in a manner prοpοrtiοnal tο its current value. This means that the rate οf decay is prοpοrtiοnal tο the amοunt οf the substance remaining, and as the amοunt οf the substance decreases, the rate οf decay alsο decreases. The fοrmula fοr expοnential decay is οften written as:
N(t) = N₀ *[tex]e^{(-kt)[/tex]
where N(t) is the amοunt οf substance remaining at time t, N₀ is the initial amοunt οf the substance, k is the decay cοnstant, and e is the base οf the natural lοgarithm.
The half-life οf radium is apprοximately 1590 years, which means that after 1590 years, half οf the οriginal radium will have decayed. Therefοre, we can use the half-life fοrmula tο find the amοunt οf time it wοuld take fοr 1/7 οf the radium tο decay:
N = N₀[tex]* (1/2)^{(t/t1/2)[/tex]
where N is the final amοunt (1/7 οf the οriginal amοunt), N0 is the initial amοunt, t is the time elapsed, and t1/2 is the half-life.
We can rearrange this fοrmula tο sοlve fοr t:
t = t1/2 * lοg2(N₀/N)
t = 1590 years * lοg2(7)
t ≈ 4975 years
Therefοre, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
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Imagine that there is an urn containing 5 blue chips and 5 red chips where chips are of equal dimensions and all chips in the urn at a time are equally likely to be selected. Let
X
denote the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement. (a) (10 points) Compute the probability that
X=3
The probability that X = 3 is 1/12.
To compute the probability that X = 3, we need to consider all possible ways of drawing three chips and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
10C3 = (10!)/(3!7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter.
Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
5C3 = (5!)/(3!2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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The probability that X which denotes the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement is 1/12.
To calculate the probability that X = 3, the first step is to consider all the possible ways in which three chips can be drawn and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
¹⁰C₃ = (10!)/(3!)(7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter. Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
⁵C₃ = (5!)/(3!)(2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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ABC ~ DFE , solve for X please help
Step-by-step explanation:
x+2 is to 4 as 28 is to 7
(x+2) / 4 = 28 / 7 <====solve for 'x'
x+2 = 16
x = 14
Thomas bought 120 whistles, 168 yo-yos and 192 tops . He packed an equal amount of items in each bag.
a) What is the maximum number of bag that he can get?
Answer:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
Prime factorizing the three numbers:
120 = 2^3 x 3 x 5
168 = 2^3 x 3 x 7
192 = 2^6 x 3
The GCD is the product of the common prime factors with the lowest exponents, which is 2^3 x 3 = 24.
So, Thomas can pack the items into 24 bags, each containing an equal number of whistles, yo-yos, and tops.
Answer:
Step-by-step explanation:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
We can start by finding the prime factorization of each number:
120 = 2^3 × 3 × 5
168 = 2^3 × 3 × 7
192 = 2^6 × 3
Then we can find the GCD by taking the product of the smallest power of each common prime factor:
GCD = 2^3 × 3 = 24
Therefore, Thomas can pack a maximum of 24 bags.
Please answer these correctly asap
Answer:
Step-by-step explanation:
13. [tex]\frac{4}{20}*100= 20[/tex]%
14. [tex]\frac{2}{25}*100=8[/tex]%
15. [tex]\frac{35}{50}*100=70[/tex]%
16. [tex]\frac{150}{200} *100=75[/tex]%
17. [tex]\frac{4}{100}*x=56\\ 56*\frac{100}{4}=1400\\[/tex]days
Mar 10, 11:04:59 PM
What is the slope of the line that passes through the points (9, 2) and
(9, 27)? Write your answer in simplest form.
Answer: There is no slope.
Step-by-step explanation:
First, we use the slope-intercept form to find out the slope. The slope-intercept form formula is : m = y2 - y1 / x2 - x1.
m = (27 - 2) / (9 - 9)
m = 25 / 0
m = undefined
This isn't a positive, nor negative slope, rather a slope called "undefined". (Think of every slope as a hill for your skateboard, if it's easier to remember.) And since the x is 0, x is stagnant, making the y and number that doesn't move from the x-coordinates. So, The entered points belong to a vertical line. There is no slope.
Hope this helps.
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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What is the value of 2 x² - 4 y when x = -4 and y = 16?
Answer:
-32
Step-by-step explanation:
2x ^ 2 - 4
2(-4) ^ 2 - 4(16)
32 - 64
-32
Mr. wings class collected empty soda, cans for recycling project. each of the 20 students had to collect 40 cans. Each can has a mass of 15 grams. How many kilograms of cans did the class collect to recycle?
A 0.6 kg.
B 12 kg
C 12,000 kg
D 12,000,000 kg
Step-by-step explanation:
40 cans/student X 20 students X 15 gram/can = 12 000 gm = 12 kg
which of the following represents the percentage of students who have disabilities in both reading and math?
The percentage of students who have disabilities in both reading and math is 20%.
The percentage of students who have disabilities in both reading and math refers to the proportion of students who are identified as having a disability in both reading and math. This means that these students require additional support and accommodations to help them succeed academically. Among the total number of students, 20% of them have disabilities in both reading and math.
Students with disabilities in reading and math may struggle with comprehension, fluency, or other aspects of these subjects. They may require specialized instruction, such as one-on-one tutoring, assistive technology, or modifications to classroom materials or assessments, in order to fully participate in the curriculum.
It is important for schools and educators to identify students who have disabilities in both reading and math early on and provide them with the necessary support and accommodations to help them succeed. This can help to ensure that these students are able to access high-quality education and achieve their full potential, despite their disabilities.
The complete question is
Which of the following represents the percentage of students who have disabilities in both reading and math?
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Jacobil and her friends are making a large homemade circular pizza. Jacobi cut her piece of pizza and it formed a sector with a radius of 9 Inches and a central angle measuring 75°. If the other 5 friends
equally share the remaining portion of the pizza, what is the approximate area of pizza each person receives? Use 3.14 for and round your answer to the nearest hundredth.
Jacobi get area of pizza is 52.987 in²
5 friends getting equally share each one area of pizza is 40.27 in²
Area of sectorAny point in a plane that is a certain distance away from another point forms a circle. The fixed point is known as the center of the circle and the fixed distance is known as the radius of the circle.
The formula for calculating a circle's sector's area is (∅/360°) ×π×r²
Jacobi get area of pizza =(75/360°) × π×9²=52.987in²
5 friends getting pizza with each central angle measuring=360°-75°/5
=57°
5 friends getting each one area of pizza = (57/360°) × π×9²
40.27in².
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SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
Graph the equation y = 3/2x -2
Graph these twο pοints (0, -2) & (4/3, 0) and yοu have yοur slοpe graphed fοr the equatiοn y = 3/2x -2.
What is an equatiοn?
An equatiοn is a mathematical statement containing two algebraic expressiοns flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressiοns is equal.
All fοrmulas have LHS = RHS (left side = right side).
Yοu can sοlve equatiοns tο determine the values οf unknοwn variables that represent unknοwn quantities.
If a statement does not have an equals sign, it is not an equatiοn. A mathematical statement called an equatiοn cοntains the symbοl "equal tο" between twο expressiοns οf equal value.
Tο find the x-intercept, substitute y = 0 and sοlve fοr x. Tο find the y-intercept, substitute x = 0 and sοlve fοr y.
y = 3/2(0) -2
y = -2
⇒ (0, -2)
And for x
0 = 3/2x -2
2 = 3/2x
x = 4/3
(4/3, 0)
Now graph these two points and you have your slope graphed
Hence, The graph of the equation is given below.
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I need help with this
By answering the presented question, we may conclude that As a result, the slope equation for the line perpendicular to y = 1/4 and passing through (-6,9) is x = -6.
what is slope?Slope is the slope of the regression of a curve or a line in mathematics. It serves as a measure of the way the como of a formula varies once the x-value alters. The slope of a line is commonly symbolised by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) have been any 2 things on the line. A line's slopes might be favorable, zero, zero, or unknown. A positive slope signifies that the line ascends to left to right, even though a negative slope indicates that now the line drops from left to right.
We must first determine the slope of a line perpendicular to the line y = 1/4 in order to derive its equation.
Because y = 1/4 is a horizontal line, its slope is zero. The slope of a line perpendicular to this line is the inverse of the slope of y = 1/4.
The negative reciprocal of 0 is undefined, although the perpendicular line can be considered a vertical line. The equation of a vertical line going through the point (-6,9) is x = -6.
As a result, the equation for the line perpendicular to y = 1/4 and passing through (-6,9) is x = -6.
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The equation of a perpendicular line passing through a point (x1, y1) may be expressed in the form: if the slope-intercept form of the equation of the original line is [tex]y = mx + b[/tex] , where m is the slope and b is the y-intercept, then Thus, option A is correct.
What is the equation for perpendicular line?The given equation is [tex]y = 7 - 11x[/tex] .
In order to determine the equation of the line perpendicular to this one, we must first determine its slope. Given that x has a -11 coefficients, the slope of the given line is -11.
The slope of the line we are looking for will be 1/11, which is the negative reciprocal of -11 because it is perpendicular to the line we are looking for.
Using the point-slope form of a line's equation, we can determine the equation of the line passing through (-6,-9) and having a slope of 1/11:
[tex]y - (-9) = (1/11)(x - (-6))[/tex]
Simplifying this equation gives:
[tex]y + 9 = (1/11)(x + 6)[/tex]
Multiplying both sides by 11 gives:
[tex]11y + 99 = x + 6[/tex]
Subtracting 6 from both sides gives:
[tex]x = 11y + 93[/tex]
Therefore, the answer is A. [tex]x = -9[/tex] .
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
Directions: Find the prime factors of the polynomials.
1. 2a2 - 2b2
2. 6x2 - 6y2
3. 4x2 - 4
4. ax2 - ay2
5. cm2 - cn2
6. st2 - s
7. 2x2 - 18
8. 2x2 - 32
9. 3x2 - 27y2
10. 18m2 - 8
11. 12a2 - 27b2
12. 63c2 - 7
13. x3 - 4x
14. y3 - 25y
15. z3 - z
16. 4c3 - 49c
17. 9db2 - d
18. 4a3 - ab2
19. 4a2 - 36
20. x4 - 1
21. 3x2+ 6x
22. 4r2 - 4r - 48
23. x3 - 7x2 + 10x
24. 4x2 -6 x - 8
25. 16x2 - x2 v 4
The prime factors of the given polynomial are 1. 2(a + b)(a - b), 2. 6(x + y)(x - y).
What is factoring?A mathematical equation is factored when it is divided into smaller parts, or factors, that may be multiplied together to create the original expression. Mathematicians can benefit from factoring for a variety of reasons. It can aid in the simplification of complicated phrases, making them simpler to use and comprehend. By dividing an expression into its component parts and making each factor equal to zero, it may also be used to solve equations. In algebra, factoring is crucial for solving quadratic equations, locating polynomial roots, and factoring huge integers.
The given expressions is 2a² - 2b².
Factor out 2 and using the difference of squares identity we have:
2(a² - b²) = 2(a + b)(a - b)
2. 6x² - 6y²
6(x² - y²) = 6(x + y)(x - y)
Hence, the prime factors of the given polynomial are 1. 2(a + b)(a - b), 2. 6(x + y)(x - y).
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From the given graph, how many students worked at least 10 hours per week?
Answer:
39.
Step-by-step explanation:
From the group of 10-14 hours worked per week, 8 students.
From the group of 15-19 hours worked per week, 4 students.
From the group of 20-24 hours worked per week, 12 students.
From the group of 25-29 hours worked per week, 8 students.
From the group of 30-34 hours worked per week, 4 students.
And finally, from the group of 35+ hours worked per week, 3 students.
So, 8+4+12+8+4+3 = 39 students.
If A B C are three matric such that AB=AC such that A=C then A is
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
Let
X 1
,…,X n
be i.i.d. random variables with the inverse Gaussian distribution whose pdf is given by
f(x∣μ,λ)=( 2πx 3
λ
) 1/2
exp[− 2μ 2
x
λ(x−μ) 2
],0
Find a sufficient statistic for
(μ,λ)
A sufficient statistic for the parameters (μ, λ) is T(X) = (T1(X), T2(X)) where T1(X) = Σ Xi^(-1) and T2(X) = Π Xi.
To find a sufficient statistic for (μ,λ), we can use the factorization theorem which states that a statistic T(X) is sufficient for a parameter θ if and only if the joint probability distribution of X can be factorized as follows
f(x∣θ) = g[T(x)∣θ]h(x)
where g and h are non-negative functions that do not depend on θ.
Using the given probability density function, we have
f(x∣μ,λ) = (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−λ(x-μ)^2/(2μ^2 x)]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−(λ/2μ^2) x + (λμ/μ^2) x^(-1)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [x^(-3/2) exp(−λ/2μ^2 x)]
Let's define two functions as follows
T1(X) = Σ Xi^(-1)
T2(X) = Π Xi
Then, we can write the joint pdf of X as follows
f(x1, x2, ..., xn | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2) exp(−λ/2μ^2 xi)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2)] [exp(−λ/2μ^2 Σ xi)]
Notice that the term [Π xi^(-3/2)] does not depend on (μ, λ), and can be factored out. Therefore, the joint pdf can be rewritten as
f(x1, x2, ..., xn | μ, λ) = [Π xi^(-3/2)] [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)]
= g(T1(X), T2(X) | μ, λ) h(X)
where g(T1(X), T2(X) | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)] and h(X) = [Π xi^(-3/2)].
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The given question is incomplete, the complete question is:
Let X1,…,Xn be i.i.d. random variables with the inverse Gaussian distribution having pdf is given by f(x∣μ,λ)= (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ] 0 <x <∞, Find a sufficient statistic for
(μ,λ)
Danielle is saving money to buy a new computer game. She needs to save at least 45 dollars to buy the
game. She has saved 11 dollars so far. Let n represent the number of dollars she still needs to save in order to buy the game. Which number sentence best describes this situation?
Answer choices:
A. 11 + n ≥ 45
B. 11 + n ≤ 45
C. 11n ≥ 45
D. 11n ≤ 45
Answer:
Step-by-step explanation:
A
Please see attached picture.
Need help answering.
In the given graph, the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
To find the equation of the quadratic function, we start by using the vertex form:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:
[tex]y = a(x - 4)^2 - 2[/tex]
Next, we use the other two points to find two additional equations:
[tex]6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))[/tex]
Simplifying these equations, we get:
[tex]6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\[/tex]
So the equation of the quadratic function is:
[tex]y = (1/2)(x - 4)^2 - 2[/tex]
Now, we can answer the questions:
The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:
[tex]y = (1/2)(0 - 4)^2 - 2 = 6[/tex]
So the y-intercept is (0,6).
To find the x-intercepts, we set y = 0 in the equation:
[tex]0 = (1/2)(x - 4)^2 - 2[/tex]
Simplifying, we get:
[tex](x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6[/tex]
So the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
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for a given sample size, when we increase the probability of a type i error, the probability of a type ii error
Increasing the probability of a type I error generally leads to a decrease in the probability of a type II error, and vice versa.
What is type 1 and type II error?If your data have statistical significance, this suggests that even if the null hypothesis is correct, they are extremely improbable to occur. You would then reject your null hypothesis in this situation. Yet occasionally, this may be a Type I mistake.
If your results are not statistically significant, the null hypothesis is likely to be correct and they have a high probability of occurring. As a result, your null hypothesis is not rejected. Yet occasionally, this may be a Type II mistake.
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Which is not a good way to protect yourself from fraud? O A. Keeping your personal information private B. Shredding or locking up your important documents OC. Using encrypted websites when entering bank account information D. Sharing your passwords with others