The recursive formula is;
1. a₁ = 16
aₙ = a - 11
2. a₁ = 4
a₂ = 5a
How to determine the value
The formula that is used for calculating the nth term of an arithmetic sequence is expressed as;
an = a + (n -1 )d
Such that the parameters of the formula are;
an is the nth termsa is the first termn is the number of termsd is the common differenceRecursive sequence an = aₙ₋₁+ d.
Now, substitute the values, we get;
1. a₁ = 16
d = -11
when n = 2
aₙ = a₂₋₁ + (-11)
aₙ = a - 11
2. a₁ = 4
r = 5
a₂ = 5a
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In a certain investigation: 460 persons were involved in the study: and based on an enquiry on their age. it was known that 75% of them were 22 or more years. The following frequency distribution shows the age composition of the persons under study. Find the mean and modal life of condensers_ Mid; age in years No. of persons 18 f; 23 28 33 90 122 ; 38 56 48 24 20 33'
Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.
What does a percentage actually mean?In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.
Here,
The following algorithm must be used to determine the mean age:
=> mean = (all years added together) / (total number of persons)
The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:
=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)
=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25
=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)
According to the information provided, there are 460 people in total.
=> mean = 17745.25 / 460
=> mean = 17745.25 / 460
As a result, the average lifespan is roughly 38.552 years.
The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.
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What are the roots of the quadratic equation 0 = 2x² + 12x-14?
1,6, -7
2,12,-14
-7,1
-1,7
The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.
What is a quadratic equation?Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.
In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
So, the roots of 0 = 2x² + 12x-14 are:
2x² + 12x-14 = 0
2x² + 14x - 2x -14
2x(x + 7) - 2(x + 7)
(2x - 2) (x + 7)
Now, use the zero product property as follows:
2x - 2 = 0
2x = 2
x = 2/2
x = 1
And
x + 7 = 0
x = -7
Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.
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Correct question:
What are the roots of the quadratic equation 0 = 2x² + 12x-14?
a. 1,6, -7
b. 2,12,-14
c. -7,1
d. -1,7
Determine the following attributes of the graph below please i only have 8 mins to turn this in 20 points pleaseeee
For the following function, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, for the graph in this problem, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.Hence:
The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).What is the maximum and the minimum value?We have to look at the values of y on the interval, hence:
The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).More can be learned about functions at https://brainly.com/question/24808124
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A set of quiz scores has a mean of 78 and a standard deviation of 9. Using a common grading scale where 60 and above is a passing score, what percentage of the
students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.
Answer:
97.5% of the students passed this test.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 78, standard deviation of 9.
What percentage of the students passed this test?
Above 60.
60 = 78 - 2*9
So 60 is two standard deviations below the mean.
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
Of the 50% above, all passed.
Of the 50% below, 95%(within 2 standard deviations of the mean) passed.
So
\(p = 0.5 + 0.5*0.95 = 0.975\)
97.5% of the students passed this test.
Answer for ten points!
Answer:
Step-by-step explanation:
I don’t get this how do these things work please explain
Answer:
Ok, so:
-The number of people who like tea are represented in the first column.
-The number of people who dislike tea are represented in the second column.
-The number of people who like coffee are represented in the first row.
-The number of people who dislike coffee are represented in the second row.
This works like a multiplication chart:
People who like tea and coffee are represented in the top left square. People who dislike tea and coffee are represented in the box that coordinates to T' and C' (If you find T' and C' and run your fingers along the column/row until they run into each other, you'll find it.) The same is true for other combinations.
At the bottom of the first column is the total number of people who like tea. At the right-most part of the first row, is the total number of people who like coffee.
(52 people like tea, 80 people were surveyed)
I hope this helps you understand, please ask any clarifying questions you need! : )
how can I cheat on ixl other than the inspect element or a person to help me.
Answer:
Don't cheat, there is your answer.
Step-by-step explanation:
How do I find the quotient for 42.6 ÷ 0.07
Answer:
Step-by-step explanation:
42.6 divided by 0.07 is 608.571428
Regular division.
How do I do this?
.
.
Answer:
the answer is 4 i believe
Step-by-step explanation:
1 pts the number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day. a random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. describe the sampling distribution of the sample mean
The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day centered around population mean.
This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
1. The number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day.
2. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated.
3. The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day.
4. This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
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Can someone help me with this question please?
What is the equation of the line that passes through the points (2,-4) and (0,-4)?
Answer:
0
Step-by-step explanation:
\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-4-(-4)}{0-2} = \frac{0}{-2} = 0\)
Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= help (formulas) Is the differential equation 9ty+ety′=yt2+81 linear and homogeneous, linear and nonhomogeneous, or nonlinear?
Answer:
\(p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }\)
g(t) = 0
And
The differential equation \(9ty + e^{t}y' = \frac{y}{t^{2} + 81 }\) is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -
\(9ty + e^{t}y' = \frac{y}{t^{2} + 81 }\)
\(e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0\)
By comparing with y′+p(t)y=g(t), we get
\(p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }\)
g(t) = 0
And
The differential equation \(9ty + e^{t}y' = \frac{y}{t^{2} + 81 }\) is linear and homogeneous.
What does the 49 days until Fourth of July there are seven days in a week and how many weeks will it be Fourth of July
Answer:
It will be Fourth of July in 7 weeks.
Step-by-step explanation:
Since you know that there are seven days in a week, you can use a rule of three to find the amount of weeks in 49 days that is the number of days until Fourth of July:
7 days → 1 week
49 days → x
x=(49*1)/7
x=7
According to this, the answer is that it will be Fourth of July in 7 weeks.
Mrs. Ricks is painting a fence that is 4 1/6 yards long. She stops when she is 3/5 done. How much of the fence did Mrs. Ricks paint?
Answer: If the fence is 4 1/6 yards long, we can first convert this to an improper fraction:
4 1/6 = (6*4 + 1)/6 = 25/6 yards
If Mrs. Ricks stops when she is 3/5 done, then she has painted:
(3/5)(25/6) = (325)/(5*6) = 15/2 = 7 1/2 yards
Therefore, Mrs. Ricks painted 7 1/2 yards of the fence.
Step-by-step explanation:
A box of cereal is halfway full. How much cereal is in the box? 14 in 2 in 8.8 in
Answer:
I'm honestly proud of myself for getting this right, the answer is 123.2
Step-by-step explanation:
14 x 8.8 x 2 divides by 2 and that's your answer pretty self-explanatory and simple
find the points of D(-3,-1), E(-1,2), F(4,-2) after a rotation 180° about the origin ASAP PLEASE ILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
D = 3,1
E = 1,-2
F= -4,2
Round the number to 3
significant figures.
0.2590100
Answer:
0.259
Step-by-step explanation:
There are some rules in determining what numbers are significant figures.
All non-zero numbers are significant.Zeroes between two non-zero numbers are significant.Zeroes at the front of a number are not significant.Trailing zeroes are only significant if there is a decimal point.We can determine how many significant figures the number currently has.
The first zero is not significant.2, 5, 9, and 1 are significant because they are non-zero numbers.The zero between 9 and 1 is significant because it is a captive zero.The zeroes at the end of the number are significant because they are trailing zeroes.There are currently seven significant figures. In order to round the number to three significant figures, we must round it to the thousandths place, or the 9.
The rounding rules are:
If the digit in the place after the number we are rounding is less than 5, you round down (or in other words, keep the number the same; Ex: 74 becomes 70)If that digit is greater than 5, you round up (Ex: 78 becomes 80)Since 0 is less than 5, the number rounded to 3 significant figures is 0.259.
Which statement about 6x2 7x – 10 is true? one of the factors is (x 2). one of the factors is (3x – 2). one of the factors is (2x 5). one of the factors is (x – 5).
One of the factors of the given quadratic expression is (x+2).
The given quadratic expression is:
\(6x^{2} +7x-10\)
What is a quadratic expression?Any expression of the form \(ax^{2} +bx+c\) is called a quadratic expression where a≠0.
Splitting the middle term of the given expression
\(6x^{2} +12x-5x-10\)
\(6x(x+2)-5(x+2)\)
\((x+2)(6x-5)\)
Hence, one of the factors of the given quadratic expression is (x+2).
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Please help!
Rewrite the rational exponent as a radical. (2 points)
Answer:
Answer: 3) \(\sqrt{5}\)
Step-by-step explanation:
Radical Form and Exponent Form
A radical can be expressed as a rational exponent following the identity:
\(\displaystyle \sqrt[m]{x^n}=x^\frac{n}{m}\)
We should also recall that:
\((x^n)^m=x^{nm}\)
We are given the expression:
\(\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}\)
Applying the power of power:
\(\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\left(5^{\frac{3}{4}\cdot \frac{2}{3}}\right)\)
Simplifying:
\(\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=5^{\frac{1}{2}}\)
Converting to radical form:
\(\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\sqrt{5}\)
Answer: 3) \(\sqrt{5}\)
Please help! Correct answer only, please! I need to finish this assignment this week. Determine the value of the following if it is possible. If it is not possible, explain.
Answer:
Option D is the correct answer
Step-by-step explanation:
Since, dimensions of both the matrices are different, hence they cannot be added.
Amber's rectangular patio is 30 feet
long. The ratio of length to the
width is 4 to 2. What is the width of
Amber's patio in yards?
(Hint: 3 feet = 1 yard)
HELP PLEASE
30 POINTS + BRAINLYEST!!!!!
(no links please)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use pi = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)
Cone:
radius r = 4 inches
height h = 18 inches
volume = πr²h/3 = (3.14)(4²)(18)/3 ≈ 301.44 cm³
Cylinder:
r = 4 inches
h = 3 inches
volume = πr²h = (3.14)(4²)(3) = 904.32 cm³
Volume of cylinder is three times the volume of cone
-20x2 + x + 12
Factor
Answer:
[x-3] [x+4]
Step-by-step explanation:
You look to see if you spot the appropriate factors strait away. If you can not immediately determine them you have to consider all of the potential ones and reason out which ones work.
can someone help asap
Answer:
3 4/9-1 1/2= 1 17/18
Step-by-step explanation:
Answer:
3 4/9-1 1/2= 1 17/18
Step-by-step explanation:
A time for the 100 meter sprint of 14.5 seconds at a school where the mean time for the 100 meter sprint is 17.6 seconds and the standard deviation is 2.1 seconds. A) −1.5; not unusual B) −3.1; unusual C) 1.5; not unusual D) −1.5; unusual
Since the probability is less than 5%, which is the conventional threshold for unusual results, we can conclude that the time of 14.5 seconds is unusual for this school's 100 meter sprint. Therefore, the correct answer is D) −1.5; unusual.
To solve this question, we need to calculate the z-score using the formula:
z = (x - μ) / σ
Where x is the individual time, μ is the mean time, and σ is the standard deviation.
Substituting the given values, we get:
z = (14.5 - 17.6) / 2.1 = -1.48
Since the calculated z-score is negative, we need to refer to the standard normal distribution table to find the corresponding probability. Looking up the z-score -1.48 in the table, we find that the probability is 0.0694 or approximately 6.94%.
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answer for this and example
Answer:
e would equal a half because it's in the middle
Robert ate lunch at 11:am. He ate a snack4and a half hours later. What time did he eat his snack
If Robert ate lunch at 11:am and he ate a snack 4and a half hours later, Robert ate his snack at 3:30 pm
To find out what time Robert ate his snack, we need to add 4 and a half hours to the time he ate lunch.
Since he ate lunch at 11:00 am, we can convert this time to 24-hour format by adding 12 hours to get 11:00 + 12:00 = 23:00.
Next, we add 4 and a half hours to 23:00 by converting the half hour to minutes and adding it to the minutes portion of the time:
23:00 + 4 hours + 30 minutes = 27:30
However, since there are only 24 hours in a day, we need to convert this time back to 12-hour format. To do this, we subtract 12 hours from 27:30 to get 15:30.
Therefore, Robert ate his snack at 3:30 pm (or 15:30 in 24-hour format).
In summary, we added 4 and a half hours to the time Robert ate lunch, converted the resulting time to 24-hour format, subtracted 12 hours to account for the excess of 24 hours, and then converted the time back to 12-hour format to obtain the time Robert ate his snack.
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The average number of words in a romance novel is 64,182 and the standard deviation is 17,154. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to two decimal places. A. X ~ N( , ) B. Find the proportion of all novels that are between 50,000 and 60,000 words.
The proportion of all novels that are between 50,000 and 60,000 words is approximately 0.
A. The random variable X, representing the number of words in a randomly selected romance novel, follows a normal distribution with a mean (μ) of 64,182 and a standard deviation (σ) of 17,154.
B. To find the proportion of all novels that are between 50,000 and 60,000 words, we need to calculate the area under the normal curve between those two values.
First, we need to standardize the values using the z-score formula:
z₁ = (50,000 - μ) / σ
z₂ = (60,000 - μ) / σ
Substituting the given values:
z₁ = (50,000 - 64,182) / 17,154
z₂ = (60,000 - 64,182) / 17,154
Calculating these z-scores will give us the standardized values.
Next, we need to find the corresponding cumulative probabilities for each z-score using a standard normal distribution table or a statistical calculator.
Let's assume we find P(Z < z1) = P(Z < z2) = p.
The proportion of all novels between 50,000 and 60,000 words is given by:
Proportion = P(z1 < Z < z2)
= P(Z < z2) - P(Z < z1)
= p - p
= 0
Since the probabilities are the same, the proportion of novels between 50,000 and 60,000 words is approximately 0.
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Janelle has one dime and several nickels in her coin purse. The table below describes the relationship between the number of nickels, n, and the total value of the coins in her coin
purse in cents, c
If Janelle has 8 nickels in her coin purso, what is the total value of the coins?
52 cents
50 cents
48 cents
46 cents
Answer:
Graph the solution set for the inequalityy > 2x - 5 by following these steps: Step 1: Identifythe slope and y-intercept. slope = y-intercept = -4. 2.
Step-by-step explanation:
GRADE 9 MATH TEXTBOOK QUESTION PLEASE HELP ME someone help me answer all of question 4??? ASAPP