7,16,30,49,73,?
find next number in series​

Answers

Answer 1

Let A be the first sequence, and denote by [tex]a_n[/tex] the n-th term in A.

Consider the forward differences of A :

16 - 7 = 9

30 - 16 = 14

49 - 30 = 19

73 - 49 = 24

Call this sequence of first differences B, so that for n ≥ 1,

[tex]b_n=a_{n+1}-a_n[/tex]

where [tex]b_n[/tex] is the n-th term of B.

Now consider the forward differences of B, which is another sequence we'll call C :

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

Then if [tex]c_n[/tex] is the n-th term of C, we have for all n ≥ 1,

[tex]c_n=b_{n+1}-b_n=5[/tex]

which gives

[tex]b_{n+1} = b_n+5[/tex]

This tells us B is an arithmetic sequence - the first term is 9 and the difference between consecutive terms is 5, so we have for n ≥ 1,

[tex]b_n = 9 + 5(n-1) = 5n + 4[/tex]

Plug this into the recurrence for A :

[tex]a_{n+1} = a_n + b_n = a_n + 5n + 4[/tex]

We don't need to solve for [tex]a_n[/tex], fortunately; we just want the next term, which would be

[tex]a_6 = a_5 + 5^2 + 4 = 73 + 25 + 4 = \boxed{102}[/tex]


Related Questions

What angle is this
A. Vertical
B. Adjacent
C. Supplementary
D. Complementary
Can be multiple answers ​

Answers

Answer:

A and D

Step-by-step explanation:

Find the area of each figure. Round to the nearest tenth if necessary.

Answers

Answer:

1. semicircle=14.1372mm

parallelogram=40 mm

54.1372 mm^2

2. 180 ft

hope this helps

have a good day :)

Step-by-step explanation:

if sin= 3/4 what are the values of cos 0 and tan 0

Answers

Answer:

Your choice is correct

Step-by-step explanation:

The first choice

How to graph 5a-6b=18

Answers

Answer:

[tex]a = \frac{ - 6}{5} b + \frac{18}{5} [/tex][tex]b = \frac{ - 5}{6} a + 3[/tex]

Step-by-step explanation:

Let's solve for a .

[tex]5a+6b=18[/tex]

Step 1: Add -6b to both sides.

[tex]5a+6b+−6b=18+−6b[/tex]

[tex]5a=−6b+18[/tex]

Step 2: Divide both sides by 5.

[tex] \frac{5a}{5} = \frac{ - 6b + 18}{5} [/tex][tex]a = \frac{ - 6}{5} b + \frac{18}{5} [/tex]

Let's solve for b.

[tex]5a+6b=18[/tex]

Step 1: Add -5a to both sides.

[tex]5a+6b+−5a=18+−5a[/tex]

[tex]6b=−5a+18[/tex]

Step 2: Divide both sides by 6.

[tex] \frac{6b}{6} = \frac{ - 5a + 18}{6} [/tex][tex]b = \frac{ - 5}{6} a + 3[/tex]Hope it is helpful....

Plz help me well mark brainliest if correct.....?

Answers

Answer:

B. 8 x 12

Step-by-step explanation:

First of all, it has an area of 96

So lets find the multiplication pair that equals 96.

10 x 10 = 100        NO

6 x 16 = 96           YES

8 x 12 = 96           YES

Now we have two equations: 8 x 12 and 6 x 16

Perimeter of 40 means:

2(a+b) = 40

Lets input the two equations:

2(8+12) = 2 x 20 = 40

2(6+16) = 2 x 22 = 44

So the dimensions that works is 8 x 12

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

A rectangle with a length of 5cm and width of 2cm is cut diagonally. What is the area of one of the triangles formed?

PLEASE LEAVE STEPS!

Answers

Answer:

5cm^2

Step-by-step explanation:

l=5 w=2

Area= 5×2

=10cm^2

Area of triangle= 10/2

=5cm^2

calculate the distance between the points J = ( -7, 6) and F = ( -1, 1 ) in coordinate plane

Answers

Step-by-step explanation:

d=√(x2-x1)²+(y2-y1)²

d=√(-1+-7)²+(1+6)²

d=√(-8)²+(7)²

d=√64+49

d==√113

d=10.6

Khan Question :) will make brainliest <3

Answers

Answer:

150[tex]\pi[/tex]

Step-by-step explanation:

Use the formula [tex]\pi[/tex]r^2h

The radius is 5 and the height is 6

so [tex]\pi[/tex](5)^2(6)

=150[tex]\pi[/tex]

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm.
(a) State the hypotheses to test whether the mean is smaller than it is supposed to be.
(b) What is the test statistic?
(c) At α = .05, what is the critical value for this test?
(d) What is your conclusion?

Answers

Answer:

|z(s)| <  |z(c)|

Then  z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm

Step-by-step explanation:

Goal mean     μ  =  56 gm

standard deviation   σ  = 0,77

From random sample:

mean    x  = 55,82

sample size  n  = 49

We assume a normal distribution ( is a manufacturing controlled process)

a) Hypothesis Test:

Null Hypothesis                         H₀          x   =  μ

Alternative Hypothesis             Hₐ           x  <  μ

Alternative hypothesis is telling us that the test is a one-tail test to the left

as n > 30 we use the normal distribution.

b)  z(s) =  ( x  -  μ  ) / σ / √n

z(s)  =  55.82  -  56 ) * 7 / 0,77

z(s)  = 0,18*7/0,77

z(s)  =  - 1.6363

c)  if  significance level is α  = 0.05  then  α/2 = 0,025

Then from  z table, z  score for  0,025     z(c) = -1.96

d)  Comparing  z(c)  and z(s) modules

|z(s)| <  |z(c)|

Then  z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm

If something cost $60 and it has a markdown of 40% what is the sale price

Answers

Answer:

Your total is now $36

Step-by-step explanation:

Multiply 60 times 40%

and it will show that you saved $24

subtract $60 - $24

there's your answer.

Click on the graph below to create a triangle with vertices at the following points.
(-5,0), (-5,9), (0,9)

Answers

Well, since you didn’t upload the picture we can’t really show you the points, but all you do, is for the first one you go 5 up on the graph, and 0 to the side. and then just keep going!

Lexi is hiking a trail that is 7.5 miles long. She stops to take a break after hiking 3.8 miles of the trail. Which equation can be used to find how many miles, m, Lexi has left to hike

Answers

Answer:

7.5 - 3.8 = m

Step-by-step explanation:

The equation can be used to determine the number of miles (m) Lexi has left to hike will be m + 3.8 = 7.5.

What is subtraction?

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

Lexi is hiking a trail that is 7.5 miles long. She stops to take a break after hiking 3.8 miles of the trail.

Then the equation can be used to determine the number of miles (m) Lexi has left to hike will be

Let m be the number of miles left. Then we have

m + 3.8 = 7.5

Subtract 3.8 on both sides, then we have

m = 3.7

More about the subtraction link is given below.

https://brainly.com/question/4319655

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plwaseeee helppp!! plelalslsllslslz

Answers

Answer:

45 degrees

opposite angles are the same so

30+30=60

105+105=210

210+60=270

360-270=90

but since we have 2 angles we divide it by 2

so angle 1 is 45 degrees

hope it helps :)

Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding if they ran a red light?

Answers

Answer:

four out of 100 (4%)

Step-by-step explanation:

5.3 in.
8 in.
4 in.
8 in.

Answers

Answer: 58.6

Step-by-step explanation:

4 x 8 = 32

4 x 5.3 = 21.2

4 x 2.7 = 10.8 / 2 = 5.4

32 + 21.2 + 5.4 = 58.6


On a coordinate plane, a single transformation will be performed on square RSTU.
Select three transformations of square RSTU that would result in a congruent figure.



A a translation 3 units up and 8 units to the right

B a rotation of 270 counterclockwise about the origin

C a dilation by a scale factor of 1 with respect to the origin
a dilation by a scale factor of 1.5 with respect to the origin

E
a dilation by a scale factor of -2 with respect to the origin

Answers

Answer:the answer is ABC

Step-by-step explanation:

I had this on my exit ticket and my teacher reviewed the question and told me it was correct

What is the real number of ∞?

Answers

Answer:

Infinity is not a real number, its an idea.

Step-by-step explanation:

An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can't compete with infinity.

The owner of a restaurant wants to collect data to find out the customers' opinions on the variety of appetizers offered on the menu. Which group should she survey to collect the best data? ANSWERRR QUCIKK A.
thirty customers who asked to share their opinions of the appetizers with the chef
B.
fifty randomly selected customers who dined at the restaurant
C.
sixty members of the local community
D.
the first fifty customers who dine at the restaurant without ordering an appetizer

Answers

Fifty randomly selected customers who dined at the restaurant will be best to collect the data thus, option (B) is correct.

What is sampling?

Sampling is collecting some items in a lot randomly to predict opinions about the lot.

For example; the Selection of goods, selection of people

Sampling is a useful technique because if we do it for all samples then it will take time and cost as well.

As per the given,

To find out the customers' opinions on the variety of appetizers offered on the menu we need to take randomly customers and the customers who dine at the restaurant because if they did not dine then they didn't know the verities.

The random selection gives the exact results.

Hence "Fifty randomly selected customers who dined at the restaurant will be best to collect the data".

To learn more about sampling,

https://brainly.com/question/13287171

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Solve using square roots: (x-6)^2=144

Answers

x^2-12x+36-144=0

x^2-12x-108=0

(x-18)(x+6)

X=18,-6

Which of the following shows the solution to m + 5 > -1?

Answers

it is D. m+5>-1, subtract 5 from both sides to get m>-6. there is no equals to which tells us that there is an open circle around -6. D is the only one that matches this

-90 + x = 180
What is the answer ?

Answers

Answer:

x = 270

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

-90 + x = 180

Step 2: Solve for x

[Addition Property of Equality] Add 90 on both sides:                                  x = 270

Answer:

x = 270

Step-by-step explanation:

- 90 + x = 180

Add 90 to each side of the equation.

- 90 + 90 + x = 180 + 90

Combine like terms.

x = 270


4. For his garden, Clay has a mixture of 12
white corn seeds, 24 yellow corn seeds, and
16 bicolor corn seeds. If he reaches for a
seed without looking, what is the probability
that Clay will plant a bicolor corn seed first?

Answers

Answer:

I believe about 30.8%

please help!!! urgently i dont get this

Answers

Answer:

4

Step-by-step explanation:

I already know the answer I just need someone to explain step by step how to solve it. I need to know the process ​

Answers

Step-by-step explanation:

First Multiply two of the numbers, for example, 15 x 6 and then multiply that by the last number, 90 x 13 and thats your answer. Hope it helps!

The amount of rain last month? Numerical or categorical data?

Answers

Answer:

categorical

Step-by-step explanation:

One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 35 individuals who consider themselves to be avid Internet users results in a mean time of 1.99 hours watching television on a weekday.

Required:
Determine the likelihood of obtaining a sample mean of 1.99 hours or less from a population whose mean is presumed to be 2.45 hours.

Answers

Answer:

Step-by-step explanation:

Robyn can rent an unfurnished apartment for $850 per month. The landlord requires first and last months' rent, plus a security deposit of $350. How much will Robyn have to pay before she can rent this apartment?

Answers

Answer:

2,050 dollars is how much she will have to pay

Step-by-step explanation:

1) Which division expression is the given figure below modeling?
10 points
A) 2/3=4
B) 4 = 2/3
C) 4x2/3
D) 2/3 x 4
Figure to use with Problem #1​

Answers

4/8=32 in think that’s the answer

Adam borrowed $16,780 at 12.5 percent for 10 years. What is his monthly payment?

A: $240.31
B: $245.83
C: $230.12
D: $229.81

Answers

ANSWER:

245.83

Step-by-step explanation:

16,780/100=167.8

167.8 x 1.465= 245.827

Using unitary method, Adam's monthly payment is 245.83 dollar.

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Monthly payment with 12.5% interest rate for 10 years per 100 dollar is 1.465 dollar.

Monthly payment with 12.5% interest rate for 10 years per 1 dollar is 0.01465 dollar.

Monthly payment with 12.5% interest rate for 10 years per 16780 dollar is 1.465 * 16780 dollar = 245.83 dollar.

Learn more about unitary method here

https://brainly.com/question/22056199

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Jared has some birds and dogs in his backyard. He counts a total of 12 heads and 30 legs. How many birds and dogs are in Jared's garden?

Answers

Answer:

12, because both dogs and birds only have 12 heads

12 Jared has 12 birds
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