write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
Answers
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
According to the task content, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
Consequently, the required expression is an arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
Ultimately, The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term of the arithmetic sequence is given by the expression; T (n) = 1 + 7 (n -1).
Read more on arithmetic sequence;
https://brainly.com/question/22972770
#SPJ1
Related Questions
can someone write these in decimals plz and thank u
Answers
Answer:
2. 0.075
3. 0.416
4. 20.3
5. 1.32
6. 0.503
7. 12.11
8. 0.214
Determine the center and radius of the following circle equation:
X2+ y2 – 10x + 16y + 25 = 0
Help ASAP pls!!!
Answers
Radius is 8
Question 12 (1 point)
The degree of each term in the binomial expansion of (x - y)5 is
4
5
-5
6
.
Answers
=================================================
Explanation:
Let's consider the expression (x-y)^2. It expands out to x^2-2xy+y^2. The terms are:
x^2-2xyy^2Each of those terms either has a single variable with an exponent of 2, or has the exponents add to 2. Think of 2xy as 2x^1y^1.
In short, this means that the degree of each monomial term is 2.
----------
Now consider (x-y)^3. It expands out into x^3-3x^2y+3xy^2+y^3.
We have terms that either have a single variable and the exponent is 3, or the exponents add to 3. The degree of each term is 3.
----------
This pattern continues.
In general, for (x-y)^n, where n is any positive whole number, the degree of each term in the expansion is n. If you picked any term, added the exponents, then the exponents will add to n.
1. Determine whether line KM and line ST are Parallel, Pers
Line KM has a slope of 5/8
Line ST has a slope of -8/5
Answers
Answer:
Since the slope of KM and ST are different, they are not parallel
Step-by-step explanation:
Slope of line KM = \(\frac{5}{8}\)
Slope of ST = \(-\frac{8}{5}\)
Determine whether the lines are perpendicular;
Solution:
We can use the slope of a line to determine whether they are perpendicular or parallel to one another.
Parallel lines do not meet one another
Perpendicular lines cross one another at an angle of 90°
Two lines are parallel if their slopes are the same;
Since the slope of KM and ST are different, they are not parallel
Question 1
A school bus weighs 6
tons. How many pounds does a school bus weigh?
O 6,500 pounds
12,000 pounds
O
12,500 pounds
13,000 pounds
Answers
2000 x 6 = 12000
12000 Pounds
Answer:
12,000
Step-by-step explanation:
one ton = 2000 pounds then multiply that by 6 and you have your answer
In ΔPQR, \text{m}\angle P = (4x+11)^{\circ}m∠P=(4x+11) ∘ , \text{m}\angle Q = (2x+1)^{\circ}m∠Q=(2x+1) ∘ , and \text{m}\angle R = (7x-14)^{\circ}m∠R=(7x−14) ∘ . Find \text{m}\angle P.m∠P.
Answers
Answer:
67°
Step-by-step explanation:
According to angle sum property of a triangle, sum of all the angles of a triangle is equal to 180°.
In ΔPQR,
∠P + ∠Q + ∠R = 180°
Put ∠P = (4x+11)°, ∠Q = (2x+1)° and ∠R = (7x-14)°
\(4x+11+2x+1+7x-14=180\\13x-2=180\\13x=182\\x=14\)
So,
m∠P = [4(14)+11]° = 67°
Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.
Answers
Answer:
a) The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
We are 95% confident that the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is within 9,009 and 10,585 steps.
b) No, we can not use the confidence interval to estimate the probability of individual values. It can onlybe used to make inference about the population mean.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=9,797.
Ths sample standard deviation is s=2,313.
The sample size is N=61.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2313}{\sqrt{61}}=\dfrac{2313}{7.81}=296.15\)
The degrees of freedom for this sample size are:
\(df=n-1=61-1=60\)
The t-value for a 99% confidence interval and 61 degrees of freedom is t=2.66.
The margin of error (MOE) can be calculated as:
\(MOE=t\cdot s_M=2.66 \cdot 296.15=787.84\)
Then, the lower and upper bounds of the confidence interval are:
\(LL=M-t \cdot s_M = 9797-787.84=9009\\\\UL=M+t \cdot s_M = 9797+787.84=10585\)
The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
b) The value of 8,500 steps is outside the confidence interval, but this means that it is an unusual value for the mean number of steps for all people in New York City who wear an activity tracker.
We can not use the confidence interval to estimate the probability of individual values.
The activity tracking devices.
The activity tracker re those devices such as watches and a bands that tells you about your physical activity such as skipping, running, and walking. They simply count the steps and tell you about the daily goals and targets. They are quite effective for monitoring blood pressure and more.
Thus answer is 9,009, 10,585 workers, 9,009, and 10,585 steps and population mean.
As per the question, the smart trackers are used by the new york people on a daily basis and they measure the footsteps of the people. A sample of random 61 people was taken and selected on the basis of the tracers. It was found that with these statistical tests a 99% confidence interval was taken for the mean on a typical workday for all people working in City that is 9,009, 10,585. The 95% confidence that the mean number of steps taken by workers of the City was within 9,009 and 10,585 steps.The confidence interval can be used to estimate the probability of the individual values. It can be used for drawing inferences for the population mean.Learn more about the trackers are electronic.
brainly.com/question/17434350.
can you solve this question?
Answers
By the MVT, there is at least one point c in (0, 6) such that f'(c) = -c/√(36 - c²) = -6/6 = -1, and we have found that c ≈ 4.24.
What is Mean Value Theorem (MVT)?The Mean Value Theorem (MVT) states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
For the given function f(x) = √(36 - x²) on the interval [0, 6], we can check if MVT can be applied as follows:
Continuity: The function f(x) is continuous on the closed interval [0, 6] because it is a square root of a polynomial, and polynomials are continuous everywhere.
Differentiability: To check if f(x) is differentiable on the open interval (0, 6), we can take its derivative:
f'(x) = (-x)/√(36 - x²)
The derivative exists and is continuous everywhere on the open interval (0, 6), except at x=6 where it is undefined (because the square root becomes 0). However, since c must be in the open interval (0, 6), the MVT can still be applied.
Therefore, by MVT, there exists at least one point c in (0, 6) such that:
f'(c) = (f(6) - f(0))/(6 - 0)
To find c, we can first calculate f(6) and f(0):
f(6) = √(36 - 6²) = √(36 - 36) = 0
f(0) = √(36 - 0²) = √36 = 6
Then we can calculate the derivative f'(x):
f'(x) = (-x)/√(36 - x²)
Setting f'(c) equal to (f(6) - f(0))/(6 - 0) and solving for c:
(-c)/√(36 - c²) = -6/6
c/√(36 - c²) = 1
c²/(36 - c²) = 1
c² = 36 - c²
2c² = 36
c² = 18
c = ±√18
Since c must be in the interval (0, 6], the only possible value of c is c = √18 ≈ 4.24.
Learn more about mean value theorem here: https://brainly.com/question/19476767
#SPJ1
What are the coordinates of the point on
the directed line segment from (1, 2) to
(8,9) that partitions the segment into a
ratio of 6 to 1?
Answers
Answer:
Step-by-step explanation:
=√((x2 – x1)² + (y2 – y1)²)
=√((8 – 1)² + (9 – 2)²)
=√((7)² + (7)²)
=√(49 + 49)
=√(2 • 49)
=7√2
Divide the line segment into 7 parts equally:
=(7√2)/7
=1√2
Multiply to 6 and 1 to get 6:1 ratio:
= 6(1√2)
= 6√2
Final Answer: 6√2 and √2.
The surface area of a sphere is 615.44 square meters. Which equation can be used to find the radius of the sphere? Recall the formula S A = 4 pi r squared. 615.44 = 4 pi r 615.44 = 4 pi r squared 615.44 = (4 pi r) squared 615.44 = 4 pi r squared + 2 pi r
Answers
\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=615.44 \end{cases}\implies 615.44=4\pi r^2 \\\\\\ \cfrac{615.44}{4\pi }=r^2\implies \sqrt{\cfrac{615.44}{4\pi }}=r\)
Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
Answers
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
To learn more about distance click on,
https://brainly.com/question/28658621
#SPJ1
ASAPP PLEAASSEE!!!
Nathan deposits $940 every 2 months into his daughter's RESP. If the account earns 3.99% / annual, compound quarterly, how much will be in the account after 25 years?
Answers
There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.
To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (amount in the account after 25 years)
P = Principal amount (amount deposited every 2 months)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.
Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.
Now, we can substitute these values into the formula:
A = 940(1 + 0.0399/4)^(4*25)
Calculating the exponent first:
(1 + 0.0399/4)^(4*25) ≈ 2.703236
Now, substituting the calculated exponent and the number of deposits into the formula:
A = 940 * 2.703236 * 150 ≈ $594,311.34
Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.
It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.
For more such questions on compounded visit:
https://brainly.com/question/24274034
#SPJ8
PLEASE HELP FOR 5 STAR AND BRAINLIST TYSM
Answers
Answer:
Step-by-step explanation:
1) 792÷ 36=22
2) 1/2 ÷ 3 = 1/6
3) D
4) its 10,00 cause 7.741 x 10 = 77,410
5) the answer in decimal is 60.089
You can use these steps to work out the amount of income tax you pay each month.
Work out
monthly salary - 987.5
Work out
answer to Step 1 +5
Step 1
Step 2
Cho has a salary of £24 000 per year.
Helen has a salary of £1720 per month.
How much more income tax does Cho pay than Helen each month?
Answers
The amount more in income tax that Cho pays than Helen each month would be £56.
How to find the income tax ?First, find Helen's yearly salary :
= 1, 720 x 12
= £ 20, 640
Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.
Cho 's monthly tax would be:
= (( 24, 000 - 12, 570 ) x 20 % ) / 12
= £ 190. 50
Helen's monthly tax :
= (( 20, 640 - 12, 570 ) x 20 % ) / 12
= £ 134.50
The difference is therefore :
= 190. 50 - 134.50
= £56
Find out more on income tax at https://brainly.com/question/20704728
#SPJ1
Which of the following gives the circumference, C, of a circle with a radius of 4?
OC 4T
OC=4T²
OC=8T
O C=16T
Answers
The circumference of a circle with a radius of 4 is 8π.
What is the circumference of a circle with a radius of 4?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is the distance around a circle or the length of a circle. It is expressed mathematically as;
C = 2πr
Where r is radius and π is constant pi.
Given that the radius of the circle is 4 units.
Plug into the above formula.
C = 2πr
C = 2 × π × 4
C = 8π
Therefore, the circumference is 8π.
Option C) 8π is the correct answer.
Learn more about circles here: https://brainly.com/question/20693416
#SPJ1
Pls help due in 5 min
What is the total amount of the most common amount and the least common amount of milk drank daily?
Answers
Answer:
50/87
Step-by-step explanation:
A woman invests $8000 in an account that earns 4.5% simple interest. If the money is invested for 5 years, how much money is in the account at the end of the 5 year period?
Answers
Answer:
180000
Step-by-step explanation:
4.5 x 5 = 22.5
22.5 x 8000 = 180000
If 5x + 2 =12x- 5, then x = ?
Answers
Answer:
x = 1
Step-by-step explanation:
First, move all the variables to one side by subtracting 5x on both sides:
5x + 2 = 12x - 5
2 = 7x - 5
Add 5 to both sides:
7 = 7x
1 = x
Answer:
x=1
Step-by-step explanation:
5x + 2 =12x- 5
Subtract 5x from each side
5x-5x + 2 =12x-5x- 5
2 = 7x-5
Add 5 to each side
2+5 = 7x-5+5
7 = 7x
Divide each side by 7
7/7 = 7x/7
1 =x
Find the area of the trapezoid.
( The answer 10.5 is not correct )
Answers
Answer:
42 units
Step-by-step explanation:
Area of a trapezoid is always 1/2(b1+b2)*h
so here base 1 is 4 units, and base 2 is 10 units. When we add these we get 14, divided by 2 which is 7, and multiplied by height of 6, which is 42
last year a company made a profit of one and a quarter million dollars.Each year the company reinvests 1/3 of the profit How much of this profit eill they reinvest
Answers
Answer:
$83,333
Step-by-step explanation:
1 000 000*1/4
250 000
250 000*1/3 = 83 333.33
Joe is asked to prove that the sum of the interior angles (, , and ) of the triangle he has drawn equals 180°. His triangle is represented in the diagram above, and his work is shown below.
Answers
The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.
What is angle sum property of triangle?The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.
To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.
To know more about isosceles, visit:
https://brainly.com/question/9872652
#SPJ1
write an equation of the line that passes through the points (0,-2),(3,13)
Answers
Answer: y = 5x-2
Step-by-step explanation:
Which distribution is positively skewed?
O A.
О в.
0000
0000
::.
18
22 24 26
02 4 6 8 10 12 14 16 18 20 22 24 26 28 30
which is it
Answers
From the four options the positively skewed distribution is fourth one.
Hence the correct option is given by (D).
Positively skewed distribution is a distribution with its tail is more pronounced on the right side than it is on the left. Since the distribution is positively skewed, then the value is positive.
The median, mode and other statistical observation data are on left side of the arithmetic mean.
The graph for positively skewed distribution is given by,
Clearly from the given four graphs, fourth graph that is option (D) is looking like positively skewed distribution.
Hence the correct option will be (D).
To know more about positively skewed distribution here
https://brainly.com/question/20905823
#SPJ1
question down below thanks
Answers
Hassan is cooking some rice the recipe says he needs 450 grams of rice for 6 people.how many kilograms of rice would he need for 18 people
Answers
Answer:
so if we take 450 an divide it by 6 you get 75. So take 75 times 18 and you get 1,350 so he would need 1,350 kilograms of rice for 18 people
Step-by-step explanation:
hope this helps :D
Makesha lost 58.5 pounds in 18 weeks. Find her rate of loss in pounds per week.
Answers
I dont get this question equation
y=0.5 (6) - 4
I know that 0.5 is equivalent to 1/2 but I just don’t get this question
Answers
To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:
y = 3 - 4
Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:
y = -1
Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.
Answer
\(\pink\sf{y=-1}\)
Step-by-step explanation
I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).
We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:
\(\sf{y=3-4}\)
And now we just simplify the last part:
\(\sf{y=-1}\)
∴ answer: y = -1
how to get point of intersection of two lines
Answers
Where the 2 lines meet in the middle to form an X
Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS
SOMEONE HELP! PLEASE!
Answers
The two column proof showing that ΔWXZ ≅ ΔYXZ is as shown below
From the given triangle, we see that;
Given: WX ≅ XY, XZ bisects WXY
Prove: ΔWXZ ≅ ΔYXZ
The two column proof for the above is as follows;
Statement 1; WX ≅ XY, XZ bisects 2
Reason 1; Given
Statement 2: ∠WXZ ≅ YXZ
Reason 2; Angle bisector
Statement 3; XZ ≅ XZ
Reason 3: Reflexive property of congruence
Statement 4: ΔWXZ ≅ ΔYXZ
Reason 4: SAS Congruence Postulate
Read more about two column proof at; https://brainly.com/question/1788884
#SPJ1
Pls I don’t have much time explain it clearly thank u.
Answers
Explanation
let's remember how to multiply terms with variables and exponents
let
a, b, c,m, n ,o and p integers
x and y variables, so
\(\begin{gathered} ax^m\cdot bx^n=(a\cdot b)x^{m+n} \\ \text{also} \\ ax^my^n\cdot bx^oy^p=(a\cdot b)x^{m+o}y^{n+p} \end{gathered}\)Step 1
hence, do the operation usign the properties
\(\begin{gathered} 4v^5u^7\cdot2v\cdot5u^6 \\ 4v^5u^7\cdot2v\cdot5u^6=(4\cdot2\cdot5)v^{5+1}u^{7+6} \\ 4v^5u^7\cdot2v\cdot5u^6=(40)v^6u^{13} \\ 4v^5u^7\cdot2v\cdot5u^6=40v^6u^{13} \end{gathered}\)therefore, the answer is
\(40v^6u^{13}\)i hope this helps yo