Step-by-step explanation:
I cannot really identify and read the provided answer options.
the solution to the sequence 2, 6, 10, 14, 18, ... is
an = 4×(n-1) + 2
recursive that is
a1 = 2
an = an-1 + 4
please pick the right option in your original problem definition that fits to this solution.
The recursive formula that represents the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.
This fixed value is called the common difference, and it is the same for all terms in the sequence.
We have,
The given sequence has a common difference of 4 between its consecutive terms.
To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.
Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:
[tex]a_2 = a_1 + 4[/tex]
Similarly, we can represent the third term (a3) as:
[tex]a_3 = a_2 + 4[/tex]
Substituting the value of a2 from the above equation, we get:
[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]
We can continue this pattern to find the recursive formula for the nth term of the sequence:
[tex]a_n = a_{n-1} + 4[/tex]
where [tex]a_1[/tex]= 2
Thus,
The recursive formula for the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
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An College student complained that the cost of textbooks was too high. She randomly surveyed 36 other students and found that the mean amount of money spent for textbooks was $121.60. If the standard deviation of the population was $6.36, find the best point estimate. Show your work.
Answer:
The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.
Step-by-step explanation:
Best point estimate:
The best point estimate of a population mean is the sample mean.
In this question:
The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.
10 mugs and 2 plates cost £54
8 mugs and 2 plates cost £46
Write down and solve simultaneous equations
(M is the cost of a mug and p is the cost of a plate, in £
Answer:
mug = 4
plate = 7
Step-by-step explanation:
10 x + 2y =54
8x + 2y = 46
2x = 8
x = 4
2y = 14
y = 7
Is each statement true for parallelogram DEFG? Drag each statement into the correct box.
DF=EG
EF=DG
∠DEG ≅ ∠FGE
The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
What is Quadrilateral?a quadrilateral is a four-sided polygon, having four edges and four corners.
DEFG is a parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
DF=FG is a true statement.
The diagonal passing through a parallelogram are equal in length.
EF=DG is a true statement
The opposite sides of a parallelogram are equal.
∠DEG ≅ ∠FGE are congruent angles.
Because the opposite angles of a triangle are equal in meausure.
Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
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Please help with this question ive been asking for half an hourrrr
answer asap pls
Ill mark brainlist
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Calls to a customer service center last on average 2.8 minutes with a standard deviation of 1.4 minutes. An operator in the call center is required to answer 75 calls each day. Assume the call times are independent. What is the expected total amount of time in minutes the operator will spend on the calls each day
Answer:
The expected total amount of time the operator will spend on the calls each day is of 210 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n-values of normal variable:
Suppose we have n values from a normally distributed variable. The mean of the sum of all the instances is [tex]M = n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Calls to a customer service center last on average 2.8 minutes.
This means that [tex]\mu = 2.8[/tex]
75 calls each day.
This means that [tex]n = 75[/tex]
What is the expected total amount of time in minutes the operator will spend on the calls each day
This is M, so:
[tex]M = n\mu = 75*2.8 = 210[/tex]
The expected total amount of time the operator will spend on the calls each day is of 210 minutes.
Write this ratio as a fraction in simplest form without any units. 6 weeks to 49 days You can use the table below to help convert the units.
Step-by-step explanation:
6 weeks : 49 days
42 days : 49 days
42/49(HCF is 7, so divide both values by 7)
that will equal to 6/7
Is -40/8 positive or negative?
Answer:
Negative. The answer gives - 5
Answer:
Negative
Step-by-step explanation:
-40/8 is equivalent to -5. Since -5 or "negative five" is negative (as it states), the equation is negative.
Shen started to run on a treadmill after setting its timer for 93 minutes. The display says that he has finished 69% of his run. How many minutes have gone by?
Round your answer to the nearest tenth.
Answer:
64.2 minutes
Step-by-step explanation:
We are given that
Shen set timer to run=93 minutes
He has finished his run=69%
We have to find total number of minutes have gone by.
69% of 93
=[tex]\frac{69}{100}\times 93[/tex]
By using
a%[tex]=\frac{a}{100}[/tex]
69% of 93=[tex]\frac{6417}{100}[/tex]
69% of 93=64.17 min
69% of 93[tex]\approx 64.2min[/tex]
Hence, 64.2 minutes have gone by.
why museums are regarded as information resources?
Step-by-step explanation:
everything can be found in the picture
Answer:
Hello There!!
Step-by-step explanation:
Museums are regarded as information resources because there are historical things and artifacts there.
hope this helps,have a great day!!
~Pinky~
2 sin x cos x – sin x = 0
Answer: PiN, Pi/3+2PiN, 5Pi/3+2PiN
Step-by-step explanation: Use formula sheet
Pls Help I will give Brainliest!
Answer:
Step-by-step explanation:
A band played an encore at 2 of its last 4 shows. Considering this data, how many of the
band's next 14 shows would you expect to have an encore?
shows
The number of times that the band played an encore at 7 out of the next 14 shows.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.
We may use the following percentage to determine how many of the following 14 performances will likely have an encore:
1/2 = x/14
14 = 2x
x = 7
Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.
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Which region represents the solution to the given system of inequalities?
Answer:
The intersection region shown in the graph attached is the solution of the system of inequalities
What is the correct written expression for the variable expression: (3 - x)/7
3 divided by the difference of 7 and x
or
the difference of 3 divided by 7 and x
Answer:
3 divided by 7 and x=-1.5*x
Step-by-step explanation:
Someone please help, thank you
Step-by-step explanation:
everything can be found in the picture
Answers:
(a) [tex]n = 2(r+m)[/tex]
(b) [tex]n = \frac{h^2}{9}[/tex]
===========================================
Work Shown:
Part (a)
[tex]\frac{n}{2} - m = r\\\\\frac{n}{2} = r+m\\\\n = 2(r+m)[/tex]
In the second step, I added m to both sides. Afterward, I multiplied both sides by 2 to fully isolate n.
------------------------
Part (b)
[tex]3\sqrt{n} = h\\\\\sqrt{n} = \frac{h}{3}\\\\n = \left(\frac{h}{3}\right)^2\\\\n = \frac{h^2}{3^2}\\\\n = \frac{h^2}{9}\\\\[/tex]
First I divided both sides by 3. After that, I squared both sides. The (h/3) squares to (h^2)/9.
Evaluate the following integral on the region R in xy-plane
An obvious substitution would be to take u = x - y and v = x + 2y, so that 0 < u < 1 (which follows from y = x ==> x - y = 0 and y = x - 1 ==> x - y = 1), and 0 < v < 1.
Solve for x and y in terms of u and v :
u - v = (x - y) - (x + 2y) = -3y ==> y = (v - u)/3
2u + v = 2 (x - y) + (x + 2y) = 3x ==> x = (2u + v)/3
Compute the Jacobian and its determinant:
[tex]J=\begin{bmatrix}D_ux&D_vx\\D_uy&D_vy\end{bmatrix}=\begin{bmatrix}\dfrac23&\dfrac13\\\\-\dfrac13&\dfrac13\end{bmatrix} \implies |\det(J)|=\dfrac13[/tex]
Now in the integral, we have
[tex]\displaystyle\iint_R\frac{x+2y}{\cos(x-y)}\,\mathrm dx\,\mathrm dy = \frac13\int_0^1\int_0^1\frac{v}{\cos(u)}\,\mathrm du\,\mathrm dv \\\\ \displaystyle= \frac13\left(\int_0^1v\,\mathrm dv\right)\left(\int_0^1\sec(u)\,\mathrm du\right) \\\\ \displaystyle= \frac13\bigg(\frac{v^2}2\bigg)\bigg|_0^1\bigg(\ln|\sec(u)+\tan(u)|\bigg)\bigg|_0^1 \\\\ \displaystyle= \boxed{\frac16\ln(\sec(1)+\tan(1))}[/tex]
Evaluate the integral.
∫ 17/ (x^3 − 27) dx
Answer:
??????????????????????????
i need help
can someone help me
ty
a.
Answer:
1170cm^3
Step-by-step explanation:
Break it into two prisms. 5 x 9 x 15 and 11 x 3 x 15. Find the volume of each and add.
(5 x 9 x 15) + (11 x 3 x 15)
675 + 495
1170cm^3
b.
Answer:
846cm^2
Step-by-step explanation:
Add each side's area together.
(9x15) + (5x15) + (6x15) + (3x15) + (12x15) + (11x15) + (5x9) + (5x9) + (11x3) + (11x3)
135 + 75 + 90 + 45 + 180 + 165 + 45 + 45 + 33 + 33
846 cm^2
Answer:
(a)1170 cm^3
(b)846 cm^2
Step-by-step explanation:
(a) Rectangle #1= 11 x 3 = 33 cm^2
Rectangle #2 = 5 x 9 = 45 cm^2
Volume = 45 + 33 = 78 x 15 = 1170 cm^3
(b) First find the surface are of all 8 faces in the prism and then add them all.
1st face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2
2nd face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2
3rd face = 15 x 3 = 45 cm^2
4th face = 15 x 6 = 90 cm^2
5th face = 15 x 9 = 135 cm^2
6th face = 15 x 5 = 75 cm^2
7th face = 15 x 12 = 180 cm^2
8th face = 15 x 11 = 165 cm^2
1st + 2nd + 3rd +4th + 5th+ 6th + 7th + 8th = 846 cm^2
Hope this helps!
A binary operation is defined on the set of real numbers ℝ by
x ∆ y = x²− 2xy + y
²
; x, y ∈ ℝ.
i. Find m such that 2 ∆ − 5 = √m
ii. Simplify ((n+1) ∆ y)/n
; n ≠ 0
Answer:
I. m = 2401
II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]
Step-by-step explanation:
I. Determination of m
x ∆ y = x² − 2xy + y²
2 ∆ − 5 = √m
2² − 2(2 × –5) + (–5)² = √m
4 – 2(–10) + 25 = √m
4 + 20 + 25 = √m
49 = √m
Take the square of both side
49² = m
2401 = m
m = 2401
II. Simplify ((n+1) ∆ y)/n
We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:
x ∆ y = x² − 2xy + y²
(n+1) ∆ y = (n+1)² – 2(n+1)y + y²
(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²
(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1
(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1
(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1
(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1
(n+1) ∆ y = (n – y + 2)(n – y) + 1
((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n
((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]
A circle P is circumscribed about a regular hexagon ABCDEF
Arcs AB, BC, CD, DE, EF, FA are all equal
Select one:
a. False
b. True
Answer: True
Explanation:
Let point G be the center of both the hexagon and the circle.
The measure of arc AB is the same as central angle AGB, both of which are 360/6 = 60 degrees. This applies to the other arc measures as well. The full 360 degree circle is split up into 6 equal pieces, each piece being 60 degrees.
For brainlest:)))) answer
Answer:
0Step-by-step explanation:
There are not rotational symmetry.
Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.6.
Independently, she then decides whether or not to buy a CD, with a probability of 0.2 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.
Answer:
this probability is 0.68
Step-by-step explanation:
the probability she buys fruit but not a CD is
0.6 × (1 - 0.2) = 0.48
the probability she buys a CD by not fruit is
0.2 × (1 - 0.6) = 0.08
the probability that she buys both is
0.6 × 0.2 = 0.12
the probability that she buys fruit or a CD or both is adding all 3 probabilities :
0.48 + 0.08 + 0.12 = 0.68
A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the
orange.
By what percentage is the grapefruit heavier than the apple?
pls answer
Grapefruit=108
Orange=100
Apple=90
a) (108-90)/90*100 = 18/90*100=20%
b) (108-90)/108= 18/108*100=16 2/3%
Answer:
The grapefruit is 20% heavier than the orange:)
Step-by-step explanation:
Let the weight of orange be x.
This means that the weight of grapefruit is:
1.08x
( Since grapefruit is: 8% heavier than orange )
Also, the weight of apple is 10% lighter than apple.
This means that the weight of apple is: 0.90 x
Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables
Answer:
3:1
Step-by-step explanation:
90:30 simplified is 3:1
This is a 30-60-90 triangle. What is the measure of x?
[3⋅5]7=
help pls anyone pls help me
A money box contains only 10-cent
and 20-cent coins. There are 33
coins with a total value of $4.60.
How many coins of each?
Answer:
Below in bold.
Step-by-step explanation:
x + y = 33 where x = 10 cent coin and y = 20 cent coin
10x + 20y = 460
Multiply first equation by 10:
10x + 10y = 330
Subtract this from the second equation:
10y = 130
y = 13
So there are 13 20c coins
and 33 - 13 = 20 10c coins.
What is the volume of the solid figure?
help pls
Answer:
B, 4x6x7 and 1x3x3.
Step-by-step explanation:
First, remember the formula: V=LWH (Volume equals length times width times height). Lastly, find the equations that match that formula, therefor B, 4x6x7 and 1x3x3 matches the formula, so B is your correct answer.
To find the percentage, what I did was that I divided 55 and 163 and the answer I got was 33%. However, my answer was incorrect. Because my answer was incorrect, how do I go about this problem?
Answer:
200
Step-by-step explanation:
You were right to divide 55 by 163. The problem, however, asks for the answer to be rounded to the nearest tenth.
Therefore, 55 / 163 = 0.3374 = 33.7%
Hope this helps!
is the sum of two rational numbers sometimes zero ture or false?
Answer:
True.
Step-by-step explana
-4/5 + 4/5 is 0