Using the Poisson Approximation the probability are:
a) 0.6321
b) 0.3679
c) 0.2642
The Poisson distribution is utilized to compute the likelihood of a particular amount of occurrences happening over a set period. The Poisson approximation will be used to answer the given question, and it is a form of a probability distribution that can be used to approximate the probability of particular events that occur infrequently, and it is suitable for both continuous and discrete variables.
a) The probability of having at least one student with the same birthday as Brad using the Poisson Approximation.
Let the number of other students with the same birthday as Brad be represented by x. Here, x is a discrete variable with a Poisson distribution that follows a Poisson distribution with an average of λ, which is equal to 1:
λ = average number of students having the same birthday as Brad = 1.
Using the Poisson distribution formula, the probability of having at least one student with the same birthday as Brad is given by:
P(X >= 1) = 1 - P(X = 0)
= 1 - e ^ (-λ)P(X = 0)
= (e^(-λ))(λ^0) / 0!
= e^(-λ)
= e^(-1)
= 0.3679
Therefore, the probability of having at least one student with the same birthday as Brad is:
P(X >= 1) = 1 - P(X = 0)
= 1 - 0.3679
= 0.6321
b) The probability of having exactly one student with the same birthday as Brad using Poisson Approximation
P(X = 1) = (e^(-λ))(λ^1) / 1!
= e^(-1)(1) / 1!
= e^(-1)
= 0.3679
Therefore, the probability of having exactly one student with the same birthday as Brad is:
P(X = 1)
= e^(-1)
= 0.3679
c) The probability of having at least two students with the same birthday as Brad using Poisson Approximation
P(X >= 2) = 1 - P(X < 2)
= 1 - [P(X = 0) + P(X = 1)]
= 1 - [e^(-λ)(λ^0) / 0! + e^(-λ)(λ^1) / 1!]
= 1 - [e^(-1) + e^(-1)(1) / 1!]
= 1 - [e^(-1) + e^(-1)]
= 1 - 2e^(-1)
= 0.2642
Compare the Poisson Approximation (a) Probability with the exact probability- At least one student with the same birthday as BradExact probability: 1 - (364/365)^180 = 0.4406
Poisson Approximation Probability: 0.6321
The exact probability is 0.4406, which is less than the Poisson approximation probability, which is 0.6321.
This result indicates that the Poisson approximation formula overestimates the likelihood of having at least one student with the same birthday as Brad.
(b) Exactly one student with the same birthday as BradExact probability: (364/365)^179(1/365) = 0.3775
Poisson Approximation Probability: 0.3679
The exact probability is 0.3775, which is quite similar to the Poisson approximation probability, which is 0.3679.
This result indicates that the Poisson approximation formula provides a reasonably precise estimate of the likelihood of having exactly one student with the same birthday as Brad.
(c) At least two students with the same birthday as BradExact probability: 1 - [1 + 364/365 + ... + (364!/347!)/365^34] = 0.1827
Poisson Approximation Probability: 0.2642
The exact probability is 0.1827, which is less than the Poisson approximation probability, which is 0.2642.
This result indicates that the Poisson approximation formula overestimates the likelihood of having at least two students with the same birthday as Brad.
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The perimeter of a rectangle is 3.5 times the length. The width is 2.5 cm less than the length. What is the width?
It is 7.5
the steps are in the photo
camilia saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal
I need help! I need the graph drawn and the steps to how I got the answer but I don’t know it! Please help me!
Answer:
25 computers per hour
Step-by-step explanation:
look ate the point 2 hours corresponding to 50 computers
50/2 = 25/1 or 25 computers per hour
Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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Victor spent $61 on some sandpaper for his model
cars. He bought 2 packages of the smallest-grain
sandpaper and spent the rest on the largest-grain
sandpaper. How many packages of the largest-
grain sandpaper did he buy?
Size of
Grain (cm)
0.003
0.011
0.001
Cost per
Package (S)
13
7
20
Answer:
3 packages
Step-by-step explanation:
61 - 20 * 2 (small grain sandpaper) = $21 remain. The largest grain costs $7, so 21/7 = 3 packages of the largest grain sandpaper was bought.
Hope this helped!
Solve the inequality 12≥ 73x + 2
10/73 is the value of x in inequality.
What does the word "inequality" mean?
In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.
However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.
the inequality 12≥ 73x + 2
= 12 - 2 ≥ 73x
= 10 ≥ 73x
= 10/73 ≥ x
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A triangle can have sides with the following measures: 1, 1, 2
True
False
Answer: false
Step-by-step explanation:
Q4 NEED HELP PLEASE HELP
Answer:
D. The electrician charges $23 per hour.
Step-by-step explanation:
C(h)= 23h+30 is in the form y=mx +b
$30 is the initial fee (b)
$23 is the amount charged per hour (h)
let x1 and x2 be two independent random variables both with mean 10 and variance 5. let y 2x1 x2 3 2. find the mean and the variance of y.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
what is variable ?A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.
given
To get the mean and variance of y, we can apply the characteristics of expected value and variance:
We can start by determining the expected value of y:
E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]
By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.
Next, we may determine y's variance:
Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4
Var(x1)
Var(x2) + 9
Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.
As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.
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The area of a rectangle is x2 – 6x +8. Find its possible length and breadth:
Answer:
Step-by-step explanation:
To find the possible length and breadth of the rectangle, we need to factor the given expression:
x^2 - 6x + 8 = (x - 4)(x - 2)
Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).
For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:
Length = x - 4
Breadth = x - 2
Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:
Length = x - 2
Breadth = x - 4
So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.
Answer:(x-4) and (x-2)
Step-by-step explanation:
a cylindrical glass is half full of lemonade. the ratio of lemon juice to water in the lemonade is $1:11$. if the glass is $6$ inches tall and has a diameter of $2$ inches, what is the volume of lemon juice in the glass? express your answer as a decimal to the nearest hundredth.
The volume of lemon juice in the glass is 0.38 cubic inches.
Explanation:
Given,
Let the volume of the lemonade in the glass be V cubic inches
Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches
Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches
The volume of the cylindrical glass is given by:
[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]
Here,
Radius r = 1 inch
Height h = 6 inches
[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]
Since the glass is half full of lemonade, the volume of lemonade in the glass is:
[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]
The volume of lemon juice in the lemonade is given by:
[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]
Therefore
[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches
Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).
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9) A survey asked 915 people how many times per week they dine out at a restaurant. Th results are presented in the following table. Number of Times Frequency 134 273 249 127 72 30 24 Total915 Consider the 915 people to be a population. Let X be the number of times per week a person dines out for a person sampled at random from this population. Compute the standard deviation A) 2.1 в) 1.5 C 1.9 D) 2.2 10) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p 15, p 0.4, P(12) A) 0.0016 B) 0.0634 C 0 4000 D) 0.0000
The correct option is B) 0.0634.
1) Standard deviationThe table is shown as below:Number of Times Frequency 1 34 2 73 3 249 4 127 5 72 6 30 7 24 Total 915The given population contains 915 people. Let X be the number of times per week a person dines out for a person sampled at random from this population.The population standard deviation is given by the formula below:$$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$where N is the population size, X is the value of the individual element of the population, μ is the mean value of the population. $$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$$$= \sqrt{\frac{\sum X^2 - 2X\mu + \mu^2}{N}}$$We need to compute the variance first.$$\sigma^2 = \frac{\sum X^2 - 2X\mu + \mu^2}{N}$$$$= \frac{(1^2 \cdot 34 + 2^2 \cdot 73 + 3^2 \cdot 249 + 4^2 \cdot 127 + 5^2 \cdot 72 + 6^2 \cdot 30 + 7^2 \cdot 24) - 2\cdot 3.176 \cdot (34 + 2\cdot 73 + 3\cdot 249 + 4\cdot 127 + 5\cdot 72 + 6\cdot 30 + 7\cdot 24) + 3.176^2 \cdot 915}{915}$$$$= 3.5689$$Therefore, the population standard deviation is given by:$\sigma = \sqrt{3.5689} = 1.8911\approx 1.9$Hence, the correct option is C) 1.92) The probability of a binomial experiment can be calculated by the formula below:$${\rm P}(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$$where n is the number of trials, k is the number of successes, p is the probability of success for each trial, and $1-p$ is the probability of failure for each trial.Here, n = 15 and p = 0.4.We need to find the probability of getting 12 successes out of 15 trials. Hence, k = 12.Using the formula above, we get$${\rm P}(X=12) = \binom{15}{12}0.4^{12}0.6^{3}$$$$= \frac{15 \times 14 \times 13}{3 \times 2 \times 1} \cdot 0.4^{12} \cdot 0.6^{3}$$$$= 0.0633605376$$Hence, the correct option is B) 0.0634.
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The segment of a circle of radius 14 cm has an angle of 135° at the centre. Calculate its perimeter.
Answer: 61
Step-by-step explanation:
explination in image
A ball is thrown straight up into the air. The x-axis shows the time, in seconds, and the y-axis shows the height of the ball, in feet, at any time (x)
Based on the information in the graph, it can be inferred that the false sentence is: The ball landed 11 feet from the person (option C).
How to identify the false option?To identify the false option we must read all the options and check them with the information in the graph:
The first option is true because the highest point the ball reaches is between 11 and 12 feet high.The second option is true because the person drops the ball about 5 feet above the ground.The third option is false because the graph does not show the displacement of the ball with respect to the person who throws it. It only shows your height and the time elapsed in the launch.The fourth option is true because the ball falls between 0.7 and 1.45 seconds.According to the above, the correct answer to this question would be option C because the sentence is false with respect to the information in the graph.
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Find The surface area of the composite figure
Answer: It should be 470 cm^2
Step-by-step explanation:
The null hypothesis is rejected whenever:A. past studies prove it wrong. B. there is a low probability that the obtained results could be due to random error.C. the independent variable fails to have an effect on the dependent variable.D. the researcher is convinced that the variable is ineffective in causing changes in behavior.
The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.
What is the null hypothesis?The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.
A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.
Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.
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The selling price of a table is ₹ 5400.If the shopkeeper makes a profit of 20%, find the cost
price of the table?
Sure! I can help you with that.
First, we should calculate the profit made by the shopkeeper. To calculate the profit, we will multiply the selling price of the table with 20%, which is 20% of 5400, or 1080.
Next, we should subtract the profit from the selling price to find the cost price of the table.
The cost price of the table = 5400 - 1080
The cost price of the table = 4320
Therefore, the cost price of the table is ₹ 4320.
Simplify the product: (4x-3) (3x+1)
O A. x-2
OB. 12x²-3
O C. 12x-5x-3
OD. 12x³-9x² +4x-3
Answer:
[tex]\large\boxed{\mathtt{C) \ 12x^{2}-5x-3}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to multiply 2 Binomials.}[/tex]
[tex]\textsf{We should use the FOIL Method.}[/tex]
[tex]\large\underline{\textsf{FOIL Broken Down;}}[/tex]
[tex]\textsf{F - Fronts}[/tex]
[tex]\textsf{O - Outers}[/tex]
[tex]\textsf{I - Inners}[/tex]
[tex]\textsf{L - Last}[/tex]
[tex]\large\underline{\textsf{For Example.}}[/tex]
[tex]\mathtt{(2x+2y)(3x+3y)}[/tex]
[tex]\mathtt{(F) \ 2x \times 3x = 6x^{2}}[/tex]
[tex]\mathtt{(O) \ 2x \times 3y = 6xy}[/tex]
[tex]\mathtt{(I) \ 2y \times 3x = 6xy}[/tex]
[tex]\mathtt{(L) \ 2y \times 3y = 6y^{2}}[/tex]
[tex]\textsf{Let's use the FOIL Method for our problem.}[/tex]
[tex]\large\underline{\textsf{FOIL;}}[/tex]
[tex]\mathtt{(4x-3)(3x+1)}[/tex]
[tex]\mathtt{(F) \ 4x \times 3x = 12x^{2}}[/tex]
[tex]\mathtt{(O) \ 4x \times 1 = 4x}[/tex]
[tex]\mathtt{(I) \ -3 \times 3x = -9x}[/tex]
[tex]\mathtt{(L) \ -3 \times 1 = -3}[/tex]
[tex]\large\underline{\textsf{We should have;}}[/tex]
[tex]\mathtt{12x^{2}+4x-9x-3}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms;}}[/tex]
[tex]\large\boxed{\mathtt{C) \ 12x^{2}-5x-3}}[/tex]
solve the following questions based on the information provided: i. six students a, b, c, d, e and f participated in a self-evaluation test of quants and data interpretation (d.i.). ii. the total marks of a in quants was just above c and in d.i. just above f. iii. b was just above c in d.i. but he scored less than d in quants. iv. f got more marks than d and e in d.i. but did not perform as well in quants as in d.i. as compared to d and e. v. no one is in between c and d in quant and c and a in d.i. 16.who got the highest marks in d.i.? a b c data inadequate 17.which of the following students has scored the least in d.i.? only d only e only d or e none of these 18.who was just below d in quants? b e c data inadequate 19.which of the given statements is not necessary to answer the questions? (ii) (iii) (iv) all are necessary
For all the following questions all the statements are required, It is possible to determine that c was just below d in quants based on the given information. Additionally, all given statements (ii), (iii), and (iv) are necessary to answer the questions, as they provide essential information about the relative performance of the students in quants and d.
The given statements which are not necessary to answer the questions are:
To answer this question, we need to find out who got the highest marks in d.i. According to statement (iv), F got more marks than D and E in d.i. Therefore, we can conclude that F got the highest marks in d.i. To answer this question, we need to find out who scored the least in d.i. However, the information provided does not tell us the score of any student in d.i., except that F got the highest marks. Therefore, we cannot determine which student scored the least in d.i. To answer this question, we need to find out who was just below D in quants. According to statement (v), no one is in between C and D in quants, which means that D got the highest marks in quants among the students listed. According to statement (ii), A's marks in quants were just above C's. Therefore, E must have been just below D in quants. To answer this question, we need to identify the statement that is not necessary to answer the questions. Statements (ii) and (iv) provide information about who got more marks in d.i. than certain other students, which is necessary to answer question 16. Statement (v) provides information about the order of marks in quants, which is necessary to answer question 18. Therefore, the statement that is not necessary to answer the questions is statement (iii), which only provides information about B's marks in quants relative to D and in d.i. relative to C. This information is not required to answer any of the questions.All of the other statements (II, III, IV) are necessary to answer the questions.
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3. What is the value of x?
x + 5
X
05
02.5
07.5
O 10
x-2
x + 1
(1 point)
The value of x is equal to; A. 5.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
x/(x + 5) = (x - 2)/(x + 1)
By cross-multiplying, we have the following:
x(x + 1) = (x - 2)(x + 5)
x² + x = x² + 5x - 2x - 10
By rearranging and collecting like-terms, the value of x is given by:
2x - 10 = 0
2x = 10
x = 10/2
x = 5.
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A baseball team sells snacks at their games to raise money. At their last game, they made 6/7 as much money as they made at their first game. Did they make more money at their first or last game? Explain how you know?
The first game brought in more money than the last game.
What is Fraction?Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.
According to question:
The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.
Therefore, the first game brought in more money than the last game.
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a quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. step 2 of 2 : suppose a sample of 1015 1015 floppy disks is drawn. of these disks, 904 904 were not defective. using the data, construct the 95% 95 % confidence interval for the population proportion of disks which are defective. round your answers to three decimal places.
Therefore, the 95% confidence interval for the population proportion of disks that are defective is (0.8357, 0.9475). This means that there is a 95% probability that the true population proportion of disks that are defective is between 0.8357 and 0.9475.
The quality-conscious disk manufacturer can use a 95% confidence interval to estimate the fraction of defective disks made by the company. The 95% confidence interval is calculated using the sample data to construct an interval estimate of the population proportion.
Using the given data, the sample proportion of disks that are not defective is 904/1015 = 0.8915.
The 95% confidence interval for the population proportion of disks that are defective is then given by:
Lower limit = 0.8915 – (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 – (1.96 x 0.0285)
= 0.8915 – 0.0558
= 0.8357
Upper limit = 0.8915 + (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 + (1.96 x 0.0285)
= 0.8915 + 0.0558
= 0.9475
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HELPPPP HURRY PLSS………………..
Answer:
C is your answer
Step-by-step explanation:
in my opinion, i think it would be the mode.
what is 2 1/2 + x = 3 1/2. Please answer it quick
Answer:
x=1
Step-by-step explanation:
2.5+x=3.5
3.5-2.5=x
1=x
x=1
Solve 2log 12 (-8x)=6
The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .
What are logarithmic properties ?
Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:
Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]
This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.
Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]
This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.
Power property:[tex]logb(x^y) = ylogb(x)[/tex]
This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.
Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]
This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.
Solving the given logarithmic equation :
The equation can be solved by using logarithmic properties and basic algebraic manipulation.
We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:
[tex]log12((-8x)^2) = log12(64x^2)[/tex]
Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:
[tex]12^{2log12(64x^2)} = 12^6[/tex]
Simplifying the left side, we get:
[tex]64x^2 = 12^6 / 12^2[/tex]
[tex]64x^2 = 144[/tex]
Dividing both sides by 64, we get:
[tex]x^2 = 144/64[/tex]
[tex]x^2 = 9/4[/tex]
Taking the square root of both sides, we get:
[tex]x=\pm 3/2[/tex]
However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.
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1/1 point (graded) Compute X(), the matrix of predicted rankings UVT given the initial values for U() and V (0). 2 1 (Enter your answer as a matrix, e.g., type [[2,1],[1,0],[3,-1]] for a 3 x 2 matrix 1 0 Note the square brackets, and 3 -1 commas as separators. ) [[24,12,6], [0,0,0], (12,6,3], [24 ✓ 24 12 6 0 0 0 12 6 3 24 12 6
The matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].
The matrix of predicted rankings UVT can be calculated using the formula UVT = UV.The provided initial values for U() and V(0) are as follows:U() = [[2,1],[1,0],[3,-1]]V(0) = [[24,12,6],[0,0,0],[12,6,3]]Using the above values, the matrix of predicted rankings UVT can be computed as follows:UVT = UVU = [[2,1],[1,0],[3,-1]]V = [[24,12,6],[0,0,0],[12,6,3]]UVT = [[2,1],[1,0],[3,-1]] x [[24,12,6],[0,0,0],[12,6,3]]= [[48,24,12],[0,0,0],[24,12,6]]Therefore, the matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].
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Shanika bought 1 Notebook and 5 pencils at a cost of $10.00. Jules paid $14.90 for 1 Notebook and 12 pencils. How much did Jules pay for 1 pencil if both pay the similar prices?
ANSWER
Jules paid $0.70 for one pencil
STEPS
Cost of One Pencil.
Let's assume the cost of one notebook be x and one pencil be y.
According to the given information,
Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,
1x + 5y = 10 --- equation 1
Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,
1x + 12y = 14.9 --- equation 2
We need to find the cost of one pencil, i.e., y.
We can solve the above equations simultaneously to find the value of y.
Multiplying equation 1 by 12 and equation 2 by 5, we get:
12x + 60y = 120 --- equation 3
5x + 60y = 74.5 --- equation 4
Subtracting equation 4 from equation 3, we get:
7x = 45.5
x = 6.5
Substituting the value of x in equation 1, we get:
1(6.5) + 5y = 10
5y = 3.5
y = 0.7
Therefore, Jules paid $0.70 for one pencil.
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Answer:
Jules pay:
$0.7
Step-by-step explanation:
1n + 5p = 10 Eq. 1
1n + 12p = 14.9 Eq. 2
n = cost of one notebook
p = cost of one pencil
From Eq. 1
n = 10 - 5p Eq. 3
From Eq. 2
n = 14.9 - 12p Eq. 4
Equalizing Eq. 3 and Eq. 4:
10 - 5p = 14.9 - 12p
12p - 5p = 14.9 - 10
7p = 4.9
p = 4.9 / 7
p = 0.7
From Eq. 3:
n = 10 - 5p
n = 10 - 5*0.7
n = 10 - 3.5
n = 6.5
Check:
From Eq. 2:
n + 12p = 14.9
6.5 + 12*0.7 = 14.9
6.5 + 8.4 = 14.9
Then:
1 pencil = $0.7
the centroid of a triangle is located 12 units from one of the vertices of a triangle. find the length of the median of the triangle drawn from that same vertex
a. 16
b. 18
c. 24
d. 36
e. 48
Length of the median of the triangle is b. 18
How to find the length of the median of a triangle?
Given that the centroid of a triangle is located 12 units from one of the vertices of a triangle. We need to find the length of the median of the triangle drawn from that same vertex.
Let ABC be a triangle.
Let AD be median of the triangle.
Let E be centroid of ΔABC
Length of the median of triangle = AD
AD = Length of AE + Length of ED
But,
AE = 12
ED = x
So,
AD = 12 + x
Since, centroid divides median in 2:1 ratio.
Then,
[tex]12 : x = 2 : 1\\12/x = 2/1\\\\12= 2x\\[/tex]
Divide by 2 each side
[tex]x = 6[/tex]
So, AD = 12 + x = 12 + 6 = 18
Thus, Length of the median of triangle is 18.
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pls answert this within 1 hour or else i will be DOOMED
In the fractions prompts given, the correct output are:
(1 ÷2) ÷ 4 = 1/8(1 ÷5) ÷ 2 = 1/10(1 ÷3) ÷ 5 = 1/15(1 ÷4) ÷ 4 = 1/16The solution to the problem for (1/2) ÷ 3 is given below.What is a fraction?A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.
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Solve the inequality for u.
48<5u+8
Simplify the answer as much as possible
Answer:
U=8
Step-by-step explanation:
48<5U+8
-5U<8-48
-5U<-40
-5U/-5<-40/+5
U>8
