A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row. Is the pattern an arithmetic sequence? Identify a and d. Write the 50th term of the sequence. Find the total number of logs in the first 10 rows.
Answers
Answer:
1) Is the pattern an arithmetic sequence?
Yes it is
2)Identify a and d.
a = First term = 2
d = Common difference = 2
3) Write the 50th term of the sequence.
50th term = 100
4) Find the total number of logs in the first 10 rows.
= 1010 logs
Step-by-step explanation:
Is the pattern an arithmetic sequence?
Yes it is
2) Identify a and d.
A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on,
The formula for arithmetic sequence =
an = a+ (n - 1)d
a = First term
d = Common difference
For the above question:
a = 2
d = Second term - First term
= 4 - 2
d = 2
3) Write the 50th term of the sequence.
Using the formula for arithmetic sequence
an = a+ (n - 1)d
a = 2
n = 50
d = 2
a50 = 2 + (50 - 1)2
= 2 + (49)2
= 2 + 98
= 100
The 50th term = 100
4)Find the total number of logs in the first 10 rows.
Sum of first n terms = n/2(a + l)
n = 10
a = first term = 2
We are told that there are 200 logs in the bottom row, hence:
l = last term = 200 logs
Hence,
Sn = 10/2×[ (2 + 200
= 5(202)
= 1010 logs
Related Questions
Find the y-intercept of the line y = 7/9x + 2/3
Answers
The y-intercept of the equation of line y = (7/9)x + 2/3 is 2/3.
What is the y-intercept of the given equation of line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of line in the question;
y = 7/9 x + 2/3
Simplify the right hand side
y = (7/9)x + 2/3
Using the slope-intercept form, the y-intercept is 2/3.
Therefore, the y-intercept in point form is (0,2/3).
Learn more about line intercepts here: brainly.com/question/14180189
#SPJ1
Which number is closest to 1/2
Answers
Answer:
0.56
it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%
statistics teachers often debate the best order n which to teach topics. one group of teachers likes to begin with data analysis. another group likes to teach design of studies first. to see which order is more effective in preparing students for the ap exam, an experiment was proposed. a large group of teachers, each of whom teaches two sections of statistics, volunteered to be a part of the experiment. each teacher will randomly assign one of their classes to begin with design, and the other to begin data analysis. which is the correct description of this design?
Answers
The correct description of the design is the experimental units are the individual students, the blocks are the teachers, and the response variable is the average AP Exam score for each classroom.
What is design of experiment?The area of applied statistics known as "design of experiments" deals with the planning, execution, analysis, and interpretation of controlled tests to identify the factors influencing the value of a parameter or group of parameters.
In order to see the response variable—the average AP test scores of each classroom—the study will apply treatments—begin with design and proceed with data analysis—on individual students as the experimental units. Depending on whether they like to begin the statistical themes with design or data analysis, the teachers are utilized as building blocks.
Therefore, the correct answer is option D .
To learn more about design of experiment refer here
https://brainly.com/question/1418338#
#SPJ4
Complete Question
Statistics teachers often debate the best order n which to teach topics. one group of teachers likes to begin with data analysis. another group likes to teach design of studies first. to see which order is more effective in preparing students for the ap exam, an experiment was proposed. a large group of teachers, each of whom teaches two sections of statistics, volunteered to be a part of the experiment. each teacher will randomly assign one of their classes to begin with design, and the other to begin data analysis. which is the correct description of this design?
A. The experimental units are the classrooms, the blocks are the teachers, and the response variable is the difference in average AP Exam score for each of the teacher's classes.
B. The experimental units are the teachers, there are no blocks, and the response variable is the average AP Exam score for each teacher.
C. The experimental units are the order of the topics, the blocks are the teachers, and the response variable is the average AP Exam score for all students who used each order of topics.
D. The experimental units are the individual students, the blocks are the teachers, and the response variable is the average AP Exam score for each classroom
The given planes intersect in a line. Find parametric equations for the line of intersection. [Hint: The line of intersection consists of all points (x, y, z) that satisfy both equations. Solve the system and designate the unconstrained variable as t .]
x + 2y + z = 1, 2x+5y + 32 = 4
Answers
The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t
To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:
1. x + 2y + z = 1
2. 2x + 5y + 32 = 4
Step 1: Solve for x from equation 1:
x = 1 - 2y - z
Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4
Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:
Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30
Step 4: Designate z as the parameter t:
z = t
Step 5: Substitute z with t in the expression for y:
y = 2t - 30
Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t
Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t
Note that we can choose any value of z for the parameter t, since z is unconstrained.
Learn more about Parametric:
brainly.com/question/15585522
#SPJ11
The window below has an area of 64 inches squared. What is the length of each side?
Answers
Answer:
The answer would be 8.
Step-by-step explanation:
What is the explicit formula for the arithmetic sequence?
an = 1.2 + (n - 1)1.5 an = 1.5 + (n − 1)1.2
an = 1.5+ (n - 1)3.9
an = 3.9+(n-1)1.5
Answers
Answer:
an = 1.2 + (n - 1) 1.5
Step-by-step explanation: opt A on edg
What is the value of
\(2 {x}^{ - 2} {y}^{ - 2} \)
for x = 3 and y = -2?
A.
\( \frac{1}{18} \)
B. 72
C.
\(2 {( - 6)}^{ - 4} \)
D. 1/648
Answers
Can someone show me an example on how to solve a y=mx+b equation?
Answers
Answer:
hey, good afternoon!
Step-by-step explanation:
here is an example: the cost of a pizza is 7.50 and you can add a topping for 0.65 cents. find the cost of the pizza with 6 toppings
y=mx+b
the x stands for the toppings and y is the cost. the rate is 0.65 cents and the orginal amount of money is b. so the equation would look like this:
y= .65x+7.50. x=6
y = 65(6)+7.50
=3.9+ 7.50= $11.50(answer)
the m is the rate of change in this question is 0.65 cents
b is initial/ fixed/ value once again in this qeustion it 7.50$
hope this helps. have a great day!
is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.
Answers
Yes, the P-value is the probability, assuming H0 is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.
The p-value is the probability of obtaining a statistic that is more or more extreme than that observed in experiment.
The p-value is calculated assuming the null hypothesis is true. Therefore, the lower the p-value, the stronger the evidence that the null hypothesis is false. That is, the lower the p-value, the stronger the evidence in favor of the alternative hypothesis.
The P-value is the observed test statistic (i.e., the data summary) that is as extreme as or more extreme than the currently observed test statistic under a statistical model that specifically assumes that the hypothesis is being tested. is the probability that It's true.
To learn more about p-value in hypothesis testing, refer:
https://brainly.com/question/14189134
#SPJ4
Complete question
is the P-value is the probability, assuming H0 is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.
The amunt of money that college students spend on rent each month is usually between $300 and $600. However, there are a few students who spend $1,300. What measure of spread would be most appropriate to measure the amount of money that college student spend on rent per month? Explain in detail why or why not one of the below measures would be used.
A. Median
B. Range
C. Standard Deviation
D. Inquartile Range
Answers
The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.
The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.
Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.
The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.
In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
Know more about Standard deviation here,
https://brainly.com/question/29115611
#SPJ11
3/8 of $32 restaurant bill = $ ?
Answers
Answer:
$12
Step-by-step explanation:
3/8 of $32 is the same as saying 3/8 x 32
32 x 3 = 96 (don't multiply 32 by 8 as well!!!!)
96/8 = 12
Answer:
The answer is 12.
Step-by-step explanation:
I have used an online Algebra calculator to help me with my answer so the answer is 100% correct.
PLEASE MARK BRAINLIEST.
Hope it helps.
What is the simplified value of the expression m/n if m=4/5 and n= −0.25
Answers
Answer:
The simplified value of the expression m/n if m=4/5 and n= −0.25 is -16.
Step-by-step explanation:
GIVE ME BRAINLEST!!!!!!!!!!!!!!!!!!!
A professional organizer charges an AED 10 consultation fee, plus AED 5 per hour. Her competitor charges an AED 11 consultation fee, plus AED 4 per hour.
Write and solve a system of equations to find the number of hours that the total charge will be the same. What will that charge be?
Enter the correct answer into the blank.
heeelp me
Answers
Answer: Let's let x be the number of hours worked. Then, the total charge for the first organizer is:
10 + 5x
The total charge for the second organizer is:
11 + 4x
To find the number of hours where the total charges are the same, we can set these two expressions equal to each other:
10 + 5x = 11 + 4x
Subtracting 4x from both sides gives:
10 + x = 11
Subtracting 10 from both sides gives:
x = 1
So the number of hours where the total charges are the same is 1 hour. To find the charge at that time, we can substitute x = 1 into either expression. Let's use the first organizer's expression:
10 + 5x = 10 + 5(1) = 15
So the charge at 1 hour is AED 15.
Step-by-step explanation:
log2 (X^2+3x+2)=1 state the universe and solve each of the following for x.
Answers
By "state the universe" I suppose you mean "domain". log₂(x ² + 3x + 2) is defined for
x ² + 3x + 2 = (x + 1) (x + 2) > 0 → x < -2 or x > -1
(To solve the inequality, consider values of x between the ones that make the expression exactly equal to 0, in this case x = -2 and x = -1. We have, for instance, for x = -3, that (-3)² + 3(-3) + 2 = 2 > 0, so x ² + 3x + 2 > 0 for all x < -2.)
Now solve the equation: Write both sides as powers of 2 to eliminate the logarithm on the left:
\(\log_2(x^2+3x+2)=1\implies 2^{\log_2(x^2+3x+2)}=2^1\implies x^2+3x+2=2\)
Solve the remaining quadratic:
x ² + 3x + 2 = 2
x ² + 3x = 0
x (x + 3) = 0
x = 0 or x = -3
Both of these solutions are within the presribed domain (-3 < -2 and 0 > -1), so we're done.
105 students in 3 Classes
Answers
Answer:
35
Step-by-step explanation:
just divide em
Someone please help me i dont understand this
What is the value of y ?
A. 30
B. 40
C. 120
D. 60
Answers
Answer:
The answer is d-60.
Step-by-step explanation:
The angles in a triangle have to add up to 180 degrees.
Answer:
The answer is D.
Step-by-step explanation:
Lets make an equation for this. Remember, that the sum of the interiors of a triangle is 180 degrees. 2y will represent the two angles, and we already have 60 degrees as one of the measures.
Equation: 2y+60=180
Now, simply subtract 60 from both sides
2y+60-60=180-60
This gives us 2y=120
Now divide both sides by 2
2y/2=120/2
y=60
So the answer is D. The value of y is 60 degrees.
need the answer for this
Answers
Answer:
60 degrees
Step-by-step explanation:
The point at C is a vertical angle.
Porque el 1 y el 20 no se consideran para formar grupos
Answers
El 1 y el 20 no se consideran para formar grupos debido a que tienen una propiedad especial en común. El número 1 es un elemento neutro en la multiplicación y el número 20 es un múltiplo común para todos los números del 1 al 20.
Por lo tanto, cualquier grupo que incluya 1 no afectará la multiplicación de los otros números del grupo y cualquier grupo que incluya 20 siempre tendrá un múltiplo común que lo hace irrelevante para la agrupación.
De esta manera, se evita la redundancia y se maximiza la eficiencia en la formación de grupos al resolver problemas de matemáticas o estadísticas.
For each equation, find y when x = -6. Then find x when y = 20.
A y = 6x +8
B. y = x
C. y = -x + 5
D.y = 6.5x+7
Answers
Answer:
A) x = 2
y = -28
B) x = 30
y = -4
C) x = -15
y = 11
D) x = 2
y = 46
Step-by-step explanation:
Hope this helps :D I'm in class so I can't explain rn I hope you understand the concept.
have a nice day
how many solutions are there to square root x =9
Answers
Answer:
There are 2 solutions to square root x = 9
They are 3, and -3
Step-by-step explanation:
The square root of x=9 has 2 solutions,
The square root means, for a given number, (in our case 9) what number times itself equals the given number,
Or, squaring (i.e multiplying with itself) what number would give the given number,
so, we have to find the solutions to \(\sqrt{9}\)
since we know that,
\((3)(3) = 9\\and,\\(-3)(-3) = 9\)
hence if we square either 3 or -3, we get 9
Hence the solutions are 3, and -3
Time left: 0:48:24
Question 11 of 50
What are the roots of the quadratic equation
x2+3x+2?
Answers
Answer:
-1 & -2
Step-by-step explanation:
x²+3x+2
x²+2x+x+2
(x²+2x)+(x+2)
x(x+2)+1(x+2)
(x+1)(x+2)
1) [A] Determine the factor of safety of the assumed failure surface in the embankment shown in the figure using simplified method of slices (the figure is not drawn to a scale). The water table is located 3m below the embankment surface level. the surface surcharge load is 12 KPa. Soil properties are: Foundation sand: Unit weight above water 18.87 KN/m Saturated unit weight below water 19.24 KN/m Angle of internal friction 28° Effective angle of internal friction 31° Clay: Saturated unit weight 15.72 KN/m Undrained shear strength 12 KPa The angle of internal friction 0° Embankment silty sand Unit weight above water 19.17 KN/m Saturated unit weight below water 19.64 KN/m The angle of internal friction 22 Effective angle of internal friction 26 Cohesion 16 KPa Effective cohesion 10 kPa Deep Sand & Gravel Unit weight above water 19.87 KN/m Saturated unit weight below water 20.24 KN/m The angle of internal friction 34 Effective angle of internal friction 36 [B] Calculate the factor of safety of the same assumed failure surface when sudden drawdown of the front water surface to the natural ground level.
Answers
The factor of safety using the simplified method of slices for the embankment is determined based on soil properties. Sudden drawdown affects stability by reducing water pressure on the failure surface.
[A] To determine the factor of safety using the simplified method of slices for the embankment shown, the following information is provided:
Foundation sand:Unit weight above water: 18.87 kN/m³
Saturated unit weight below water: 19.24 kN/m³
Angle of internal friction: 28°
Effective angle of internal friction: 31°
Clay:Saturated unit weight: 15.72 kN/m³
Undrained shear strength: 12 kPa
Angle of internal friction: 0°
Embankment silty sand:Unit weight above water: 19.17 kN/m³
Saturated unit weight below water: 19.64 kN/m³
Angle of internal friction: 22°
Effective angle of internal friction: 26°
Cohesion: 16 kPa
Effective cohesion: 10 kPa
Deep Sand & Gravel:Unit weight above water: 19.87 kN/m³
Saturated unit weight below water: 20.24 kN/m³
Angle of internal friction: 34°
Effective angle of internal friction: 36°
[B] To calculate the factor of safety of the same assumed failure surface when there is a sudden drawdown of the front water surface to the natural ground level, we need to consider the change in water pressure on the failure surface. The water pressure will decrease, reducing the driving forces acting on the embankment. This decrease in driving forces will affect the factor of safety calculation.
In summary, the factor of safety is a measure of the stability of the embankment. It considers the driving forces and resisting forces acting on the embankment. The simplified method of slices is used to calculate the factor of safety by dividing the embankment into slices and analyzing the forces acting on each slice individually. In the case of a sudden drawdown, the factor of safety will change due to the decrease in water pressure on the failure surface.
To learn more about friction visit:
https://brainly.com/question/24386803
#SPJ11
Please help me in this
Answers
Answer:
3
Step-by-step explanation:
as u add 2 + 1 from the 6 and 7 hours
pls answer this question only even numbers like 2,4,6....
Answers
Answer:
image is blur dear!!!
Step-by-step explanation:
Picture is there only answer number 7.
Answers
Surface area = ft^2
Volume = cm^3
Perimeter = in.
Explanation
Area is L x W so it is squared or
power of ^2
Volume is L x W x H so it is cubic or
power of ^3
Perimeter is 2L + 2W so it is inches,
no exponent
Your savings plan involves depositing funds in a continuous stream into an initially empty savings account at a rate given by S(t) = 1200 + 120 dollars per year. The savings account pays 2.07% interest.compounded continuously. To the nearest dollar, how much will be in the account at the end of 7 years? A. $9,810 B. $16,507 C. $10.491 D. $13,108
Answers
The amount in the account at the end of 7 years with continuous compounding interest is approximately $13,106.
To calculate the amount of money in the account at the end of 7 years, we need to consider the continuous compounding interest along with the continuous stream of deposits.
The continuous compound interest formula is given by the formula
\(A = Pe^{(rt),\)
where:
A = final amount
P = initial principal (the total amount of deposits made)
r = annual interest rate (as a decimal)
t = time in years
In this case, the interest rate is 2.07% or 0.0207 as a decimal, and the time is 7 years.
The continuous stream of deposits is given by the formula D(t) = (1200 + 120t), where:
D(t) = deposit amount at time t
t = time in years
To calculate the total amount in the account at the end of 7 years, we need to integrate the deposit function over the time period and add it to the compound interest formula.
∫[0,7] (1200 + 120t) dt = 1200t + 60t² evaluated from 0 to 7
= (12007 + 607²) - (12000 + 600²)
= 8400 + 2940
= 11340
Now we can calculate the final amount using the continuous compound interest formula:
\(A = 11340 \times e^{(0.0207*7)\)
\(A = 11340 \times e^{(0.1449)\)
A ≈ 11340 × 1.1553
A ≈ 13105.572
Rounding to the nearest dollar, the amount in the account at the end of 7 years is approximately $13,106.
Therefore, the correct option is D. $13,108.
Learn more about compound interest click;
https://brainly.com/question/14295570
#SPJ4
421.16 to nearest tenth
Answers
Answer:
421.20
Step-by-step explanation:
To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up.
Answer:
421.2
Step-by-Step Explanation:
you round up the .16 to 2 because the 6 is greater than 5 and the .1 is in the tenth place
How many different 5-digit PIN codes are there that only include the digits 7, 2, 4, 6, 9 and 3?
Answers
Answer:
720
Step-by-step explanation:
6*5*4*3*2=720
I really really need help and please show the steps so I can better understand it
I will mark brainliest obvi
Answers
The value of x is 7.
What are congruent triangles?
If all three of the matching sides and angles in two triangles are equal, the two triangles are said to be congruent.
It is given that the 2 triangles are congruent. So the matching sides are equal.
This means, TR=MN
Substitute the side lengths
3x-1=20
Move -1 to the right side
3x=20+1=21
x=21/3=7
So, the value of x is 7.
To learn more about the congruent triangles from the given link
https://brainly.com/question/1675117
#SPJ1
please help :(
thank you!
Answers
Answer:
pls stop deleting my answers brainly thx. also its b! ^-^
Step-by-step explanation: