As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
what is proportionality ?A mathematical relationship called proportionality asserts that two values are related in such a way that if one quantity rises or falls, the other quantity rises or falls by a fixed amount. The proportionality constant, also known as this constant factor, is typically represented by the letter "k".
given
The remaining 70% of Jerome's 1,040 songs are not country songs if only 30% of them are.
We can use the following calculation to get the proportion of non-country songs:
70% of 1,040 = 0.7 x 1,040 = 728
As a result, Jerome has 728 tracks that aren't from his country among the 1,040 music he has downloaded to his Spotify account.
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a study is run to estimate the mean total cholesterol level in children 9-11 years of age. a random sample of 169 participants is selected and their mean total cholesterol levels is 161.5. assume the population standard deviation is 19.5. give the following information for a 95% confidence interval for the mean cholesterol.
Sample mean =
Standard Deviation =
Sample size =
Do you use Z or t?
Z or t =
Standard Error (Rounded to nearest tenth)=
Margin of Error (Rounded to nearest tenth) =
Lower limit (Rounded to nearest tenth) =
Upper limit (Rounded to nearest tenth) =
The information for a 95% confidence interval for the mean cholesterol are:Sample mean = x = 161.5 Standard Deviation = σ = 19.5 Sample size = n = 169 Z or t = Z Standard Error (Rounded to nearest tenth)= 1.5 Margin of Error (Rounded to nearest tenth) = 2.83 Lower limit (Rounded to nearest tenth) = 158.67 Upper limit (Rounded to nearest tenth) = 164.33
Given that the sample size, n = 169, sample mean, x = 161.5, and population standard deviation, σ = 19.5 are to be used to compute the confidence interval for the mean cholesterol. We are to find the following information for a 95% confidence interval for the mean cholesterol.
We know that if the population standard deviation is known and the sample size is greater than 30, then we use the z-value instead of the t-value. Since the sample size is n = 169, we can use the z-value. Z or t = Z For a 95% confidence level, α = 0.05/2 = 0.025 Zα/2 = Z 0.025 (from the standard normal distribution table)Z 0.025 = 1.96 The formula to calculate the standard error of the mean cholesterol is:Standard error = σ/√n=19.5/√169= 1.5
The margin of error is given by Margin of error = Zα/2 × (σ/√n)Margin of error = 1.96 × (19.5/√169)= 2.83 (rounded to the nearest tenth)The lower limit and upper limit of the confidence interval are given by the formulas:Lower limit = x - Margin of error Upper limit = x + Margin of error Lower limit = 161.5 - 2.83 = 158.67 (rounded to the nearest tenth)Upper limit = 161.5 + 2.83 = 164.33 (rounded to the nearest tenth)
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answer quick please am i correct
Answer:
6/11 = 0.54
Step-by-step explanation:
Answer: Yes you are correct
Step-by-step explanation:
how to solve 2400 at 10.5% for 5 years
Answer: 1260
Step-by-step explanation:
To solve for simple interest, we can use the formula:
I = P * r * t
where:
I = interest
P = principal amount
r = interest rate
t = time (in years)
In this case:
P = 2400
r = 10.5% = 0.105 (note that we convert the percentage to a decimal)
t = 5
Substituting these values into the formula, we get:
I = 2400 * 0.105 * 5
I = 1260
Therefore, the simple interest on a principal amount of 2400 at 10.5% for 5 years is 1260.
Find k so that and will be orthogonal (form a 90 degree angle).
The [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex] are orthogonal.So, the value of k is 8/3.
What is Vector?A quantity or phenomenon with separate characteristics for both magnitude and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, energy, electromagnetic fields, and weight are a few examples of vectors in nature.
Two vectors are orthogonal if and only if their dot product is zero. Therefore, we need to find the value of k such that the dot product of [tex]$\vec{a}$[/tex] and[tex]$\vec{b}$[/tex] [tex]$\vec{b}$[/tex][tex]\vec{b}[/tex] is zero.
The dot product of [tex]$\vec{a}$[/tex] and [tex]$\vec{b}$[/tex] is given by:
[tex]$$\vec{a} \cdot \vec{b} = (2)(-4) + (3)(k) = -8 + 3k$$[/tex]
For the vectors to be orthogonal, their dot product must be zero, so we set -8 + 3k = 0 and solve for k:
-8 + 3k = 0
3k = 8
[tex]$k = \frac{8}{3}$$[/tex]
Therefore, [tex]$\vec{a}=\langle2,3\rangle$[/tex] and [tex]\vec{b}=\langle-4,\frac{8}{3}\rangle$[/tex] are orthogonal.So, the value of k is 8/3.
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A shopkeeper bought 26 apples from a fruit vendor for $37.70.How much did each apple cost?
Answer:
The cost per apple is $1.45
Step-by-step explanation:
I will help with the solution, as I do not know the standard for the picture/estimate.
$37.70 / 26 is simply the cost per apple.
The cost per apple is $1.45
Hope this helps!
What would you type into your calculator to find 13% of 96
Answer: your answer should be 12.48
have a good day
sorry I didn't read that well
for your calculator you should type in 0.13 divided by 96
determine the general solutions of the equation sinx=cos2x-1
[tex]x=30^o,270^o \ [0^0\leq x\leq 360^0][/tex]
Explanation:
We know,
[tex]cos2x=cos^2 \ x-sin^2 \ x=1-2sin^2 \ x[/tex]
So, let's solve the equation now,
[tex]sin \ x=cos2x=1-2 \ sin^2 \ x[/tex]
[tex]\longrightarrow \ 2 \sin^2 \ x+sin \ x-1=0[/tex]
[tex]\longrightarrow \ 2 \sin^2 \ x+2\sin x-sin \ x-1=0[/tex]
[tex]\longrightarrow \ 2\sin \ x(sin\ x+1)-1(sin \ x+1)=0[/tex]
[tex]\longrightarrow \ (2\sin \ x-1)(sin \ x+1)=0[/tex]
Now,
[tex]2\sin \ x-1=0[/tex]
[tex]\longrightarrow \ sin \ x=\dfrac{1}{2}[/tex]
[tex]\longrightarrow x=sin^{-1}(\dfrac{1}{2})[/tex]
[tex]\longrightarrow x=30^o[/tex]
And, [tex]sin \ x+1=0[/tex]
[tex]\longrightarrow x=sin^{-1}(-1)=270^o[/tex]
As we just need the general solutions, we should take only this two values as the general solutions.
Answer:
[tex]30^0,270^0[/tex]
That's it!
if one response is selected at random, what is the probability the response indicated that the dog is small-sized given that they enjoyed the treat? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
What is Bayes' theorem?Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.
The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.
P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3
(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.
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Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. )
P = $1300, r = 8. 5%, t = 11 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.
The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ
where, A--> total Amount of money after t years
P --> Principal
r --> Annual rate of interest (as a decimal)
t --> Number of years:
n--> number of times interest is compounded per year
Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.
Case 1: n = 1
Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹
= 1300( 1.085)¹¹
= 3,189.12
Case 2: n = 2
A = 1300( 1 + 0.085/2)²²
= 1300( 2.085/2)²²
= 1300( 1.0425)²²
= 3,248.01
I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,
[tex] A = Pe^{rt}[/tex]
Where: A-> Total amount of money after t years
P --> Principal Amount
e --> Natural log constant:
r = Annual rate of interest (as a decimal)
Case: Continuous: e = 2.71828 (approx), r = 0.085
A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾
= 1300(e)⁰·⁹³⁵ = 3,311.34
Hence, required value is $3,311.3775.
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Complete question :
The above table completes the question.
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t
= 11 years
i have a small area that i want to place 2 bench press machines. how much room will i need to reserve for those?
To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:
The length of the bench press machine is between 48 inches and 54 inches.
The width of the bench press machine is between 28 inches and 32 inches.
The height of the bench press machine is between 48 inches and 56 inches.
Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:
There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.
Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.
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Combined transformations
For the transformations of translation, the following is correct -
A. by vector (7, 11).
What is translation?
A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
The single transformation that represents the following sequence of transformations -
i) a translation vector by (2, -3) followed by
ii) a translation vector by (-5, 8)
is a translation by the vector (-3, 5).
To see why, we can combine the two translation vectors by adding them component-wise -
(2, -3) + (-5, 8) = (-3, 5)
This vector represents the total displacement of a point on the plane after both translations are applied.
So, a single translation by the vector (-3, 5) will have the same effect as applying both of the original translations in sequence.
Therefore, the correct statement is, by vector (7, 11).
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a coin is flipped 3 times. find the probability of getting 3 heads as a decimal rounded to 3 decimal places
Flipping a coin 3 times, the probability of getting 3 heads is 0.125.
The probability of getting 3 heads when a coin is flipped 3 times can be calculated using the binomial probability formula. The formula is:
P(X=k) = nCk × 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, and (1-p) is the probability of failure.
Here, n=3, k=3 and p=0.5 (since the coin has two sides and the probability of getting heads or tails is 0.5 each). Substituting the values, we get:
P(X=3) = 3C3 × 0.5³ × (1-0.5)⁽³⁻³⁾ = 1 × 0.125 × 1 = 0.125
Therefore, the probability of getting 3 heads as a decimal rounded to 3 decimal places is 0.125.
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1. meredith has 10 reports to file. if each report takes an average of 75 minutes to file, how long will it take her to file 70% of them? a. 5 hours b. 6 hours, 30 minutes c. 8 hours, 45 minutes d. 10 hours
Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?
Here, the total number of reports = 10
Average time to file one report = 75 minutes
To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:
75 × 7 = 525 minutes
We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:
525 ÷ 60 = 8 hours 45 minutes
Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
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PLEASE HELP ME QUICKLY!
Step-by-step explanation:
it would mean that she made 53 batches of soap and 4 batches of lotion.
now, is it a solution ?
then both inequalities must be true with these values.
5×53 + 15×4 <= 325
265 + 60 <= 325
325 <= 325 correct
20×53 + 35×4 <= 1200
remember, 1 hour = 60 minutes.
1060 + 140 <= 1200
1200 <= 1200 correct
so, (53, 4) is the intersection point of both limit lines. and it is as such an extreme point and optimum.
in which of the following numbers is the value of the 5 digit 10 times it value in the number 4,597
According to the question the value of the 5 digit in 4,597 is 9.
What is digit?Digit is a numerical symbol used to represent numbers in the decimal system. It is a single symbol used to represent a number ranging from 0 to 9. Digits are used to represent numbers in all forms of mathematical calculations and equations. The most common digits used in calculations are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit has an associated numerical value, which can be used to create larger numbers or to perform complex mathematical operations.
The answer is D) 9. The value of the 5 digit in 4,597 is 5. To find the 10 times its value, you must multiply 5 by 10, which equals 50. Therefore, the value of the 5 digit in 4,597 is 9.
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Understanding and Interpreting Confidence Intervals a Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college. She finds a 95% confidence interval for the mean systolic blood pressure to be (108.6, 120.3) mm Hg. Which statement below incorrectly conveys the meaning of the confidence interval? She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. O She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. Hint Assistance Used Use the definition of a 95% confidence interval.
The Statement 1: She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. This statement is accurate and conveys the meaning of a 95% confidence interval.
The confidence interval is the range of values within which a statistical parameter is estimated to be accurate with a certain level of confidence.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college.
Statement 2: She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. This statement is inaccurate because the confidence interval obtained from the sample cannot be generalized to the entire population of students.
The correct statement should mention that the confidence interval is only for the random sample.Statement 2 is the incorrect statement.
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Which of the following is a factor of x³ + 343?
Ox-7
Ox² - 14x +49
Ox² + 7x +49
Ox+7
x³ + 343 = (x + 7) (x² - 7x + 49) is the function.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions,
is a relation from X
Hence, x³ + 343 = (x + 7) (x² - 7x + 49) is the function.
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Smores, a Taste of Multivariate Normal Distribution Smores Company store makes chocolate (Xi), marshmallow (X2), and graham cracker (Xs). Assume that the profit (in millions) for selling these smores materials follow a multivariate uormal ditributim with parameters 1 0.3 0.3 and Σ= 0.31 0 0.3 01 What is the probability that 1. the profit for selling chocolate is greater than 6 millions? 2. the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 mllion? 3. P(3X1-1X2 + 3X3 > 20)?
The sales of marshmallow is 5 million and the sales of graham cracker is 5 million is 0.5648 and the probability that 3X1-1X2 + 3X3 > 20 is 0.000005.
The multivariate normal distribution is a probability distribution which describes the joint behavior of multiple random variables. In the given case, the profit (in millions) for selling chocolate (Xi), marshmallow (X2) and graham cracker (X3) follows a multivariate normal distribution with parameters 1, 0.3, 0.3 and Σ = 0.31 0 0.3 01.
1. To calculate the probability that the profit for selling chocolate is greater than 6 millions, we need to calculate the probability that X1>6. Using the given parameters, we can use the formula for calculating the cumulative probability of a standard normal distribution: [tex]P(X1>6) = 1-P(X1≤6) = 1-0.9999994 = 0.000006.[/tex]
2. To calculate the probability that the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, we need to calculate the conditional probability [tex]P(X1>6|X2=5, X3=5)[/tex]. Using the given parameters, we can calculate this probability using the formula for conditional probability:[tex]P(X1>6|X2=5, X3=5) = P(X1>6 ∩ X2=5 ∩ X3=5) / P(X2=5 ∩ X3=5) = 0.002207 / 0.003915 = 0.5648.[/tex]
3. To calculate the probability that, we need to calculate the probability that[tex]X1>7-X2/3-X3/3[/tex]. Using the given parameters, we can calculate this probability using the formula for cumulative probability of a standard normal distribution: [tex]P(3X1-1X2 + 3X3 > 20) = 1-P(3X1-1X2 + 3X3 ≤ 20) = 1-0.9999995 = 0.000005.[/tex]
In conclusion, the probability that the profit for selling chocolate is greater than 6 millions is 0.000006, the probability that the profit for selling chocolate is greater than 6 millions
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Why is the sky blue?
Thanks :)
Answer:
Violet and blue light have the shortest wavelengths and red light has the longest. Therefore, blue light is scattered more than red light and the sky appears blue during the day. When the Sun is low in the sky during sunrise and sunset, the light has to travel further through the Earth's atmosphere.
A) You recently took part in a fundraising activity in your community to raise money for charity. Write an
email to a friend in which you:
ach)
Describe the aims of the charity
Explain how you raised funds for the charity
Encourage them to take part in a fundraising activity
I appreciate you reading my communication, and I will be back. I sincerely hope you'll think about taking part in our upcoming fundraising gathering .
what is email ?An electronic mail, or email, is a digital communication that is sent and received online. It is a popular method of communication that is utilised for both personal and business reasons. Sending and receiving information, communicating, marketing, and staying in contact with friends and family are just a few of the many uses for emails.
given
A Charity Fundraising Event That Was Effective
Hello [Name of Friend],
I pray you are well and reading this email. I'm writing to let you know about some exciting developments regarding the fundraising gathering I took part in last weekend in our neighborhood.
The goal of this charity event was to raise funds for the underprivileged children who are battling to get access to basic education and healthcare facilities. A nearby nonprofit group that works to better the lives of underprivileged kids arranged it.
I recommend that you participate in comparable fundraising events in the future. You'll not only be helping a worthy cause, However, you will also have the opportunity to join a group that is dedicated to changing the world. I'm confident you'll find it to be a very rewarding experience.
I appreciate you reading my communication, and I will be back. I sincerely hope you'll think about taking part in our upcoming fundraising gathering .
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(Do not use a calculator for this question) Given f(x)-73-12x + 5 answer the following: Is the function increasing or decreasing at x-3? List the interval A=B=where f(x) is decreasing. a F At what X-value does f(x) have a relative maximum?
The function is a set of ordered pairs (x, y), where x is an element of the domain and y is the corresponding element of the range. The notation f(x) is commonly used to denote the output value of the function for a given input value x.
The function is decreasing at x=3. The interval where f(x) is decreasing is (3,∞). The x-value at which f(x) has a relative maximum is x= -4.The derivative of the function f(x) is f'(x)=-12.At x=3, the derivative is negative, f'(3)=-12, so the function is decreasing at x=3.
The function is always decreasing since its derivative is constant and negative. Therefore, the interval where f(x) is decreasing is the entire real line, or (-∞, ∞).
Since the function is always decreasing, it does not have a relative maximum.
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find three positive numbers whose product is 115 such that their sum is as small as possible. provide your answer below:
Three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
What is positive number?In mathematics, a positive number is any number that is greater than zero. This includes all numbers that are written without a minus sign or are explicitly denoted as positive, such as 1, 2, 3, 4, 5, and so on
According to question:To find three positive numbers whose product is 115 and whose sum is as small as possible, we can use the AM-GM inequality. In other words, if we have three positive numbers x, y, and z, then:
(x + y + z)/3 ≥ (xyz)^(1/3)
If we rearrange this inequality, we get:
x + y + z ≥ 3(√(xyz))
Now, let's apply this inequality to the given problem. We want to find three positive numbers x, y, and z whose product is 115 and whose sum is as small as possible. Therefore, we want to minimize x + y + z while still satisfying the condition xyz = 115.
Using the AM-GM inequality, we have:
x + y + z ≥ 3(√(xyz)) = 3(√115) ≈ 16.75
Therefore, the sum of the three numbers is at least 16.75. To find three numbers that achieve this minimum sum, we can use trial and error or solve the system of equations:
xyz = 115
x + y + z = 3(√115)
One solution to this system is:
x = √(115/3)
y = √(115/3)
z = 3(√(115/3)) / 5
These three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
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The complete question is Find three positive numbers whose product is 115.
match the following. 1. an angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon center of a regular polygon 2. the common center of its inscribed and circumscribed circles apothem of a regular polygon 3. the distance from the center of the polygon to a vertex radius of a regular polygon 4. the perpendicular distance from the center of the polygon to a side central angle of a regular polygon
Match the following with the given options:
1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygon2. The common center of its inscribed and circumscribed circles - Center of a regular polygon3. The distance from the center of the polygon to a vertex - Radius of a regular polygon4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonA polygon is a two-dimensional object that has three or more straight sides and angles. A regular polygon is a polygon with equal sides and equal angles.
A regular polygon is a shape that has all its sides the same length and all of its angles the same degree. Below are the matched answers for the given options.1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygonThe central angle of a regular polygon is defined as the angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.
The angle measures (360 / n) degrees, where n is the number of sides of the polygon.2. The common center of its inscribed and circumscribed circles - Center of a regular polygonThe center of a regular polygon is the point at which its axes of symmetry intersect. The center is also the common center of the circumscribed and inscribed circles.3. The distance from the center of the polygon to a vertex - Radius of a regular polygonThe radius of a regular polygon is defined as the distance from the center of the polygon to any vertex. It is also the distance from the center of the polygon to the midpoint of a side
.4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonThe apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to a side. It is also the radius of the inscribed circle.
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A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
a system of equations is shown below. y=2x+1 and y=x+2 what is the solution to the system? A. (0,1) B. (1,2) C. (1,3) D. (2,4)
Answer:
(1,3)
Step-by-step explanation:
Given system of equations is :-
y = 2x + 1y = x + 2We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,
2x + 1 = x + 2
Subtract x on both sides,
2x - x + 1 = 2
Simplify,
x = 2 - 1
x = 1
Substitute this value of x into equation (2) as ,
y = 1 + 2
y = 1 + 2
y = 3
Hence the required answer is (1,3) .
and we are done!
prove that for any full rank transformation matrix t, the eigenvalues of ay and a from part (a) are the same.
Based on the full rank transformation matrix t, it is true that the eigenvalues of ay and a from part (a) are the same.
We have to show that the eigenvalues of ay and a from part (a) are the same.
Let A be a full rank transformation matrix.
A is a full rank matrix.
Therefore, the rank of A is equal to the number of rows and columns of A.
Let λ be an eigenvalue of Ay.
Then, Ay - λy = 0, where y is the eigenvector corresponding to λ.
Now let us take a look at the eigenvalues of A(y).
A(y) is a full rank matrix since A is a full rank matrix.
This means that det(A(y)) ≠ 0.
We know that λ is an eigenvalue of Ay if and only if λ is a root of the characteristic polynomial det(Ay - λy) = 0.
Using the fact that A(y) is full rank, we have that det(Ay - λy) = det(A(y)A⁻¹yAy - λy) = det(A(y)(A⁻¹yAy - λI)y) = det(A(y))det(A⁻¹yAy - λI).
Since det(A(y)) ≠ 0, we have that λ is an eigenvalue of Ay if and only if λ is a root of the characteristic polynomial det(A⁻¹yAy - λI) = 0.
However, det(A⁻¹yAy - λI) is just the characteristic polynomial of A(y) and therefore has the same roots as the characteristic polynomial of A(y).
Thus, the eigenvalues of Ay and A(y) are the same.
Thus, the statement above is true.
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consider the ordered bases and for the vector space of lower triangular matrices with zero trace. a. find the transition matrix from to . hint: use the standard basis . b. find the coordinates of in the ordered basis if the coordinate vector of in is . c. find .
a. Finding the transition matrix from B1 to B2 using the standard basis for the vector space of lower triangular matrices with zero trace.The standard basis of the vector space of lower triangular matrices with zero trace is given by{(1,0,0),(0,1,0),(0,0,0)}.We are to find the transition matrix from B1 to B2. We start with the definition of the transition matrix. This definition states that if A = [a1,a2,a3] is a matrix whose columns are the vectors of B2, then the transition matrix from B1 to B2 is the matrix S such that S = [b1,b2,b3] where bi is the column vector obtained by expressing the ith vector of B1 as a linear combination of the vectors of B2. Using the standard basis, we have that (1,0,0) = a1, (0,1,0) = a2 and (0,0,0) = a3. Therefore, we need to express each of these standard basis vectors as a linear combination of the vectors of B1.For (1,0,0), we have(1,0,0) = 2e1 - e2For (0,1,0), we have(0,1,0) = -3e1 + e3For (0,0,0), we have(0,0,0) = e2 + e3Therefore, the transition matrix S is given by S = [b1,b2,b3] where bi is obtained by expressing the ith vector of the standard basis as a linear combination of the vectors of B1. Thus,S = [(2,-3,0),(-1,1,0),(0,0,1)]b. Finding the coordinates of v in B if the coordinate vector of v in B1 is c. Let c be the coordinate vector of v with respect to B1. Then we know that v = c1e1 + c2e2 + c3e3. We are to find the coordinate vector of v with respect to B.We know that B is a basis for the vector space of lower triangular matrices with zero trace, so any vector in this space can be expressed uniquely as a linear combination of the vectors in B. Thus, we can write v as a linear combination of the vectors of B.v = a1x1 + a2x2 + a3x3We are to find the coefficients x1, x2 and x3. We do this by using the fact that the transition matrix S from B1 to B is such that v = Sc where c is the coordinate vector of v with respect to B1. Hence, v = Sc = [b1,b2,b3][c1,c2,c3] = (2c1 - c2) b1 - (c1 - c2) b2 + c3 b3Using the expressions for b1, b2 and b3 in terms of the standard basis vectors, we obtainv = (2c1 - c2)(2e1 - e2) - (c1 - c2)(-e1 + e3) + c3e3
Expanding this expression and comparing coefficients with the equation for v above yields(2c1 - c2)(2e1 - e2) - (c1 - c2)(-e1 + e3) + c3e3 = c1e1 + c2e2 + c3e3Therefore, we have the system of equations2(2c1 - c2) - (c1 - c2) = c11(2c1 - c2) + (c1 - c2) = c20 = c3Solving for x1, x2 and x3 yieldsx1 = c2/2, x2 = c1/2, and x3 = 0Therefore, the coordinate vector of v with respect to B is given by the vector( c2/2, c1/2, 0).c. Finding [v]B2 in 200 wordsWe are to find the coordinate vector of v with respect to B2. Since we already have the coordinate vector of v with respect to B1, we can use the transition matrix S from B1 to B2 to obtain this coordinate vector.Let c be the coordinate vector of v with respect to B1. Then, we know that v = c1e1 + c2e2 + c3e3. Since the coordinate vector of v with respect to B1 is c, we have the equationc = [c1,c2,c3]Using the transition matrix S from B1 to B2, we can write the coordinate vector of v with respect to B2 as[x1,x2,x3] = S[c1,c2,c3]Multiplying these matrices together yields the equation[x1,x2,x3] = [(2,-3,0),(-1,1,0),(0,0,1)][c1,c2,c3]
Expanding this equation gives the system of equations2c1 - c2 = x1-3c1 + c2 = x2c3 = x3Solving this system of equations for c1, c2 and c3 yieldsc1 = (x2 - x1)/4, c2 = (3x2 + x1)/4, and c3 = x3Therefore, the coordinate vector of v with respect to B2 is given by the vector((x2 - x1)/4, (3x2 + x1)/4, x3).
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20x50= ?
Please answer me!
Answer:
1,000
Step-by-step explanation:20*50
The sum of two numbers is 96. If the ratio between them is 11:1, find the difference between the two numbers.
The difference between the numbers whose sum is of 96 and have a ratio of 11:1 is of 80.
How to obtain the difference between the two amounts?The difference between the two amounts is obtained applying the proportions in the context of the problem.
The variables that are going to represent the two amounts are given as follows:
x and y.
The sum of two numbers is 96, hence:
x + y = 96.
The ratio between them is 11:1, hence:
x/y = 11.
x = 11y.
Replacing the second equation into the first, the value of y is given as follows:
y + 11y = 96
12y = 96
y = 8.
The value of x is given as follows:
x = 11 x 8 = 88.
The difference is then given as follows:
x - y = 88 - 8 = 80.
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PLEASE Answer before 3/12/2023
6, 14, 22, 30, 38, … Use the expression below to determine the value of the 15th term. 6 + 8n, where n is equal to 0, 1, 2, 3, … answers: 112 118 120 126
Answer: 118
Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.
Answer: 118
Step-by-step explanation:
you just keep going up at the rate of 8