309, 303, 297,...
Find the 31st term.
Answers
The 31st term of the given sequence will be 129.
What is an arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
\(T_n = a + (n-1)d\)
Given sequence;
309, 303, 297,...
The first term, a1 = 309
The common difference, d = 303 - 309 = -6
The 31st term will be
n = 31
\(T_n = a + (n-1)d\)
\(T_{31} = 309 + (31-1)(-6)\\\\T_{31} = 309 + (30)(-6)\\\\T_{31} = 309 + (-180)\\\\T_{31} = 129\)
Hence, The 31st term of the given sequence will be 129.
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ1
Related Questions
14 points help me please
Answers
Answer:
B. 0.8 meters
Step-by-step explanation:
Divide 2.4 by 3 and you will get 0.8
find the value of X, y and z
ans: x=50 y= 50 z=50
Answers
The value of x , y and z in the parallel line is 50 degrees.
How to find the angle in parallel line?When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.
Therefore, let's use the angle relationships to find the angle, x, y and z as follows:
Therefore,
x = 360 - 310(sum of angles in a point)
x = 50 degrees
Therefore,
x = y(alternate interior angles)
Alternate interior angles are congruent.
Hence,
y = 50 degrees
Therefore,
x = z(alternate interior angles)
z = 50 degrees.
learn more on angles here: https://brainly.com/question/17043791
#SPJ1
Given the function f(x)=5x−6 find f(4).
Answers
Answer:
f(4)=14
Step-by-step explanation:
f(x)=5x-6
f(4)=5(4)-6
f(4)=20-6
f(4)=14
Answer:
f(4) = 14
Step-by-step explanation:
f(x) = 5x -6
f(4) = 5(4) - 6
f(4) = 20 - 6
f(4) = 14
Find the area of the triangle.
Answers
Answer:
its 10k
Step-by-step explanation:
would be what ur looking for
For the system of differential equations x'(t) = -9/5 x + 5/3 y + 2xy y' (t) = - 18/5 x + 20/3 y - xy the critical point (x_0, y_0) with x_0 > 0, y_0 >, y_0 > is x_0 = 2/3 y_0 = 2/5 Change variables in the system by letting x(t) = x_0 + u(t), y(t) = y_o + v(t). The system for u, v is Use u and v for the two functions, rather than u(t) and v(t) For the n, v system, the Jacobean matrix at the origin is A = -1 3 -4 6 You should note that this matrix is the same as J(x_0, y_0) from the previous problem.
Answers
The system of differential equations after the change of variables is given by u'(t) = -3/5 u + 2/3 v + (4/9)x_0v + 4/15 u^2 + 4/15 uv and v'(t) = -4v + 6u + (8/3)x_0u - (2/3)y_0 - 2uv, with the Jacobian matrix A = [-1, 3; -4, 6] at the origin.
How to find Jacobian matrix?The given system of differential equations:
x'(t) = -9/5 x + 5/3 y + 2xy
y'(t) = -18/5 x + 20/3 y - xy
Critical point:
x_0 = 2/3, y_0 = 2/5
New variables:
x(t) = x_0 + u
y(t) = y_0 + v
New system of differential equations in terms of u and v:
u'(t) = -3/5 u + 2/3 v + (4/9)x_0v + 4/15 u^2 + 4/15 uv
v'(t) = -4v + 6u + (8/3)x_0u - (2/3)y_0 - 2uv
Jacobian matrix at the origin:
A = [-1, 3; -4, 6]
Learn more about differential equations
brainly.com/question/31583235
#SPJ11
Select the correct answer. a cylinder has a radius of 10 inches and a height of 6 inches. about what is its volume in cubic inches? use 3.14 for π. a. 60 cu. in. b. 188.4 cu. in. c. 628 cu. in. d. 1,884 cu. in.
Answers
Answer:
Its d
Step-by-step explanation:
because you square 10 and you get 100 and you have to multiply 6 with 100 which is 600 and then you multiply the 3.14 which gives you 1,884
PLEASE MARK AS BRAINLIEST
a restaurant sells burritos for $8.00 each. The cost of the meat is $1.50 and the cost of the other ingredients is $1.00 for each burrito.
Money made from selling burritos is positive . The cost of making burritos is negative. Profit is the money left after paying the cost.
How much profit would the restaurant make by selling 100 burritos?
1. How much money would the restaurant take in by selling 100 burritos?
Answers
Answer:
$550
Step-by-step explanation:
Answer:
The restaurant would take in $550 by selling 100 burritos
Step-by-step explanation:
First, we need to add all the expenses together and multiply by 100
1.50 + 1.00 = 2.50
2.50 x 100= 250
We know that the restaurant would charge $800 in total for the 100 burritos so now we subtract what it costs to make them.
800 - 250 = 550
Our final answer would be $550
Which of the following is true when using the empirical rule for a set of sample data? Select one: a. Approximately 68% of all observations are in the interval + s. b. Almost all observations are in the interval #2s. c. Approximately 68% of all observations are in the interval + 2s. d. Approximately 95% of all observations are in the interval + S.
Answers
When using the empirical rule for a set of sample data, the following statements are true: Approximately 68% of all observations are in the interval ± 1s (one standard deviation from the mean),Almost all observations are in the interval ± 3s (three standard deviations from the mean),Approximately 95% of all observations are in the interval ± 2s (two standard deviations from the mean),This statement, "Approximately 95% of all observations are in the interval + S", is incorrect.
When using the empirical rule for a set of sample data, the following statements are true:
a. Approximately 68% of all observations are in the interval ± 1s (one standard deviation from the mean).
b. Almost all observations are in the interval ± 3s (three standard deviations from the mean).
c. Approximately 95% of all observations are in the interval ± 2s (two standard deviations from the mean).
d. This statement, "Approximately 95% of all observations are in the interval + S", is incorrect. The empirical rule states that approximately 68% of all observations are in the interval ± 1s, not just "+ s".
Therefore, the correct answer is (c) Approximately 68% of all observations are in the interval + 2s.
To learn more about empirical rule : brainly.com/question/30573266
#SPJ11
When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is __
O 31.6% O 46.3% O 44.5% O43.6%
Answers
When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is 46.3%.
The given problem is an example of confidence intervals in statistics. The formula for finding the confidence interval in percentage is given below:
Confidence Interval in Percentage = P ± Z Score x √ (PQ/n)
where
P = Sample proportion
Q = 1 - P
n = Sample Size
Z Score is obtained from the Z-Table where the confidence level is given.
To obtain the upper limit, the following formula should be used:
Upper Limit of the Confidence Interval = P + Z Score x √ (PQ/n)
Substitute the given values of the question into the formula:
P = 114/293 = 0.3891
Q = 1 - 0.3891 = 0.6109
n = 293
The upper limit for the 90% confidence interval is given by the Z-Table at 1.645:
Upper Limit of the Confidence Interval = 0.3891 + 1.645 x √ [(0.3891 x 0.6109)/293]
≈ 0.3891 + 1.645 x 0.0467
≈ 0.3891 + 0.07701
≈ 0.4661 = 46.3%
Therefore, the answer is 46.3%.
To know more about confidence interval visit:
https://brainly.com/question/32546207
#SPJ11
Please help me out!!
Answers
Answer:
60 in³
Step-by-step explanation:
Prism A is 2×3×5 which is 30in³
Prism B is 2 times the height, which means it is 4×3×5 which is 60
The scatter plot shows the time spent studying, x, and the quiz score, y, for each of 25 students
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact ett
(b) using your equation from part (a), predict the quiz score for a student who spent 50 minutes studying
Note that you can use the graphing tools to help you apprimate the line.
Answers
a). y = 0.833x + 20 is a rough equation for the line that best fits the data.
b). A student who spent fifty minutes studying received a quiz score of 62.
Describe equation ?A mathematical statement that demonstrates the equality of two expressions is known as an equation. In most cases, it has two sides and an equal sign "=" in the centre. The left-hand side (LHS) and right-hand side (RHS) of the equation refer to the expressions on each side of the equal sign.
In mathematics, equations are used to depict connections between quantities or to resolve issues. They may include constants, which are fixed values that never change, as well as variables, which are symbols that denote uncertain values.
Depending on the maximum power of the variable in the equation, equations can be linear, quadratic, cubic, or of a higher degree. Depending on the quantity of terms and the complexity of the expressions used, they may also be simple or complex.
The line that fits the data the best is:
y = mx + c --------------> (1)
(a) Now, we use the points \((x_1,y_1)=(0,20)\) and \((x_2,y_2)=(60,70)\) to find the line of best fit.
So, slope
\(m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{70-20}{60-0}\\ \\m=\frac{50}{60} \\\\m=\frac{5}{6}\)
Thus, (1) becomes
y= x + c --------------> (2)
Now, using (0,20) in (2)
20 = .0 + c = c=20
Consequently, the correct formula for the line of best fit is
y= x + 20 -----------> (3)
or y = 0.833x + 20
(b) For quiz score after 50 min, put x= 50 in (3)
y = . 50 +20= 41.66 + 20 = 61.67
Therefore, the quiz's final score after 50 minutes will be roughly y = 62.
To know more about Equation, visit:
https://brainly.com/question/29174899
#SPJ1
3
Period
Date
5. If a teacher were to distribute sheets of
paper so that each student got two
sheets, there would be 8 sheets
remaining. However, if three sheets
were given to each student, the teacher
would be 11 sheets short. Which
equation could be used to find how
many students are in the class?
Answers
If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11.
A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
Let number of students in class be denotes as "x",
If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,
If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,
So, the equation which is used to find number of students in class is 2x+8=3x-11,
Therefore, the correct option is (d).
Learn more about Equation here
https://brainly.com/question/19626
#SPJ1
The given question is incomplete, the complete question is
If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?
(a) 2(x - 8) = 3(x + 11)
(b) 2(x + 8) = 3(x - 11)
(c) 2x-8 = 3x + 11
(d) 2x+8 = 3x - 11
Outliers: 2. 38, 42, 77, 47, 74, 51, 48, 41, 82, 72, 74, 129 find the Median: Q3: QI: IQR:
Answers
The median of the given data is 52, the lower quartile (Q1) is 41, the upper quartile (Q3) is 74, and the interquartile range (IQR) is 33.
Median: 52
Q1: 41
Q3: 74
IQR: 33
1. Arrange the numbers in ascending order: 38, 41, 42, 47, 48, 51, 72, 74, 74, 77, 82, 129
2. Count the number of data points: 12
3. Calculate the median by adding the two middle numbers and dividing by two: (47 + 48) / 2 = 52
4. Calculate the lower quartile (Q1) by finding the median of the lower half of the data: 41
5. Calculate the upper quartile (Q3) by finding the median of the upper half of the data: 74
6. Calculate the interquartile range (IQR) by subtracting the lower quartile from the upper quartile: 74 - 41 = 33
Learn more about median here
https://brainly.com/question/15323584
#SPJ4
30 Children lined up to jump
rope 9 children joined them
4. Children left to get a drink of
water How many children
were left in the line?
Answers
30 children lined up to jump rope 9 children joined them so total number of children in the line 30+9=39 4 children left to get a drink of water. Therefore, the total number of children left in the line was 39-4=35 .
Initially, there were 30 children lined up to jump rope. Later, 9 children joined them, making the total number of children in the line 30+9=39. However, after some time, 4 children left to get a drink of water. Therefore, the total number of children left in the line was 39-4=35.
To understand the solution, we can use basic arithmetic operations. First, we add the number of children who joined the line to the initial number of children to find the total number of children in the line, which is 30+9=39. Then, we subtract the number of children who left the line from the total number of children in the line to find the number of children left in the line, which is 39-4=35.
In conclusion, after 4 children left to get a drink of water, there were 35 children left in the line. It is important to pay attention to the changes in the number of children and use basic arithmetic operations to find the solution.
Considering the given terms, initially there were 30 children in the line. 9 children joined them, increasing the number to 39. Then, 4 children left to get a drink of water, so there were 35 children left in the line.
Learn more about basic arithmetic operations here :
https://brainly.com/question/32046154
#SPJ11
Write a recursive formula for the sequence below. Use the variable "n" for your formula in your answer.
{2, -8, 32, -128, 512, ... }
Answers
Answer:
\(\begin{cases}a_1 = 2\\\\a_{n} = -4*a_{n-1}\end{cases}\)
============================================
Explanation:
The first line of the answer says "the first term is 2".
The second line says "take any term and multiply by -4 to get the next term".
The \(a_n\) represents the nth term while \(a_{n-1}\) is the term just before it.
The second line shown above is the same as writing \(a_{n+1} = -4*a_n\)
---------------
The -4 is found by dividing any term over its previous one
-8/2 = -4
32/(-8) = -4
-128/32 = -4
512/(-128) = -4
This shows the common ratio is -4 and this sequence is geometric.
Can you have a triangle with two right angles?
Answers
Answer:
no
Step-by-step explanation:
because there are two angles
My Answer ↓
No. You cannot have a triangle with two right angles due to the concept that a triangle can only have 3 sides. Therefore, a triangle can only have 1 right angle.
Lamont has purchased 20 trading cards and wants to have at least 50 trading cards. Write and solve an inequality to nd the number of trading cards Lamont needs. Select all of the true statements.
Answers
Given:
Lamont has purchased 20 trading cards.
He wants to have at least 50 trading cards.
To find:
The inequality for the number of trading cards Lamont needs and solve it.
Solution:
Let x be the number of trading cards Lamont needs.
He has 20 trading cards. So,
Total cards = x + 20
It is given that, he wants to have at least 50 trading cards. It means, total card must be greater than or equal to 50.
\(x+20\geq 50\)
Subtract 20 from both sides.
\(x+20-20\geq 50-20\)
\(x\geq 30\)
Therefore, the required inequality is \(x+20\geq 50\) and solution is \(x\geq 30\).
The number of trading cards that Lamont needs will be at least 30 trading cards.
From the information given, we are informed that Lamont has purchased 20 trading cards and wants to have at least 50 trading cards.
Therefore, the number that will be needed more will be:
= 50 - 20 = 30
Therefore, he'll need at least 30 more cards.
Read related link on:
https://brainly.com/question/14058435
Find 160% of 90 ??????
Answers
Answer:144
Step-by-step explanation:
Answer:
the answer is 144
160/100×90=144
for infinity car wash, the arrival rate is 9 / hour and the service rate is 12 / hour. the arrival and service distributions are not known so we can't use the m/m/1 formulas. if the average waiting time in the line is 25 minutes, then how many customers (waiting and being served) are at the carwash?
Answers
There are approximately 4 customers (waiting and being served) at the carwash on average
Since the arrival and service distributions are not known, we cannot use the M/M/1 formulas to solve this problem. Instead, we can apply Little's Law, which asserts that the average customer count in a stable system equals the arrival rate times the average customer dwell duration.
25 minutes = 60/25 hours
= 0.4167hours
In this case, we are given that the arrival rate is 9/hour and the average waiting time in the line is 25 minutes. We need to convert the waiting time to hours by dividing by 60
We can determine an average number of customers in the system using Little's Law.
Average number of customers = Arrival rate × Average time in system
= 9 customers/hour × 0.4167 hours
= 3.75
≈ 4 customers
Therefore, there are approximately 4 customers (waiting and being served) at the carwash on average
Learn more about Little's Law here
https://brainly.com/question/29538196
#SPJ4
Solve the given equation. Check your solution and show all your work. 7/10 r = 4 3/5
(this is the last question i have on my test i swear)
Answers
Answer: R= 30.1
Step-by-step explanation: 10r = 7*43/1
10r= 301/1
10r= 301
10/10
R= 30.1
Type the missing number in this sequence,3, 9,_,24,33,43,54
Answers
Answer: 18
Step-by-step explanation:
Simplify the expression.
Answers
Answer:
x
Step-by-step explanation:
(log to the base 3) of 27^x can be re-written as
x*(log to the base 3) of 27, which is equivalent to:
x*(log to the base 3 of 3^3) = x
So the answer is simply " x "
Help please ! Please
Answers
Answer:
15, 8, 25 The teacher payed 0.40 per book.
Step-by-step explanation:
4/10 = 2/5 Simplify the 4/10 to find the unit rate.
15: 2/5 = 6/x Set up your proportion.
2x =30 Cross multiply
/2 /2 Divide both sides by 2 to isolate x
x =15
8: 2/5 = x/20 Set up proportion
40 =5x Cross multiply
/5 /5 Divide both sides by 5 to isolate x
8 =x
25: 2/5 = 10/x Set up proportion
2x =50 Cross multiply
/2 /2 Divide both sides by 2 to isolate x
x =25
Graph: y=mx+b To graph, you will need to use y=mx+b format
y= 2/5 x+2 2/5 is your unit rate. Your rate changes every 2 books bought. To graph, start at (0,2) and go up 2 and to the right 5, plot. Continue moving up 2 and to the right 5 to graph.
The teacher payed 0.40 per book because 2/5 simplifies to 0.40.
Travis bought 14 tickets to the school play for 54$. Children tickets cost $3 and adult tickets cost $5. How many adult tickets did he buy?
Answers
Answer:
Step-by-step explanation:
Let x be the number of adult tickets Travis bought, and y be the number of children tickets he bought.
We know that Travis bought a total of 14 tickets, so x + y = 14.
We also know that the total cost of the tickets was $54, so 5x + 3y = 54.
We can use the first equation to solve for y in terms of x: y = 14 - x.
Substituting this into the second equation, we get:
5x + 3(14 - x) = 54
Simplifying and solving for x, we get:
5x + 42 - 3x = 54
2x + 42 = 54
2x = 12
x = 6
Therefore, Travis bought 6 adult tickets and 14 - 6 = 8 children tickets.
to find maximum wage of number equality of boy adult and child.
I mean: 48 = 6.8
12 person from here
2 person remain
6 $ remain as well
6 = 2 child ticket
so the answer is 6
Which procedure is especially likely to result in strong emotional responses such as crying or other displays of distress
Answers
A procedure that is especially likely to result in strong emotional responses such as crying or other displays of distress is the administration of a painful or uncomfortable stimulus.
When individuals experience pain or discomfort, it is common for them to display strong emotional responses such as crying or distress. This is because pain is a powerful stimulus that triggers both physiological and emotional reactions.
Various procedures can elicit such emotional responses, particularly those involving painful or uncomfortable stimuli. For example, medical procedures like injections, surgeries, or dental treatments that involve physical discomfort can lead to strong emotional reactions.
Additionally, emotionally challenging situations such as receiving distressing news, experiencing traumatic events, or undergoing intense psychological interventions may also provoke strong emotional responses.
The intensity of emotional responses can vary depending on individual differences, past experiences, and the specific context in which the procedure or stimulus is encountered. It is important to provide appropriate support and care to individuals who may experience these emotional reactions to ensure their well-being and emotional comfort.
Learn more about procedures here:
https://brainly.com/question/27176982
#SPJ11
please help.. just how many times am i gonna have to post the same question over and over again to get an actual answer
Answers
Sarah is going to invest $280 and leave it in an account for 9 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Sarah to end up with $410?
Plzzz helppp
Answers
Answer:
4.2%
Step-by-step explanation:
Is 11 over 20 greater than 1 or less than 1
Answers
Answer:
11/20 is less than
Step-by-step explanation:
Since 11/20 is a fraction and 1 is a whole number.
Use the scenario below to ansuer questions 9-11. Raymond purchased a new tractor for his wheat farm. He estimates that the tractor will depreciate in value by about 8.5% per year as shown in the table below. AGE OF TRACTOR IN YEARS X o 1 VALUE OF TRACTOR (U.S. DOLLARS) f(x) 165,000 151,000 138,140 126,400 115,660 105,830 9. 2 What will be the estimated value of the tractor when it is 6 years old? 6 3 4 5 200000 У 180000 10. The graph shows the function f(x) = 165000(0.915) where f(x) is the value of Raymond's tractor after x years. What does poini (10, 67873) represent in the situation? 160000 165,000(0.915) 140000 120000 100000 Value of Teactor (collars) 800001 (10.87873) 60000 11. Using the function equation and a graphing utility, in how many years will the tractor be worth less than $50,000? 40000 20000 0 0 -2 2 16. 12 14 after 13 years 8 10 Time (years) -20000
Answers
Given:
\(f(x)=165000(0.915)^x\)Find-: what does point (10,67873) represent.
Sol:
\(f(x)=165000(0.915)^x\)Where,
\(\begin{gathered} f(x)=\text{ The value of random tractor } \\ \\ x=\text{ year} \end{gathered}\)At point.
\((10,67873)\)Point (10, 67873) represents after the 10-year value of the random tractor is 67873.
Check value for x = 10 year.
\(\begin{gathered} f(x)=165000(0.915)^x \\ \\ f(10)=165000(0.915)^{10} \\ \\ f(10)=67873 \end{gathered}\)BRAILYEST The area of a square poster is 37 in.2. Find the length of one side of the poster to the nearest tenth of an inch. The length of one side of the poster is nothing in.
Answers
Answer:
Length of the square poster = 6.1 in
Step-by-step explanation:
Area of a square poster = 37 in^2
Area of a square = length^2
37 = lenght ^2
Find the square root of both sides
√37 = √ length ^2
Length = 6.0828 in
Approximately
Length of the square poster = 6.1 in