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Given:

The sequence is:

[tex]-3,5,13,21...[/tex]

To find:

The explicit formula for the given sequence then find the 47th term.

Solution:

We have,

[tex]-3,5,13,21...[/tex]

The difference between two consecutive terms are:

[tex]5-(-3)=8[/tex]

[tex]13-5=8[/tex]

[tex]21-13=8[/tex]

The given sequence has a common difference. So, the given sequence is an arithmetic sequence with first term -3 and common difference 8.

The explicit formula for an arithmetic sequence is:

[tex]a_n=a+(n-1)d[/tex]

Where, a is the first term and d is the common difference.

Putting [tex]a=-3[/tex] and [tex]d=8[/tex] in the above formula, we get

[tex]a_n=-3+(n-1)8[/tex]

[tex]a_n=-3+8n-8[/tex]

[tex]a_n=8n-11[/tex]

Putting [tex]n=47[/tex], we get

[tex]a_{47}=8(47)-11[/tex]

[tex]a_{47}=376-11[/tex]

[tex]a_{47}=365[/tex]

Therefore, the explicit formula for the given sequence is [tex]a_n=8n-11[/tex] and the 47th term is 365.

Answer:

Step-by-step explanation:

1.[tex](3x)( {x}^{2} {y}^{3} )[/tex]

= [tex]3 {x}^{3} {y}^{3} [/tex]

2.[tex](5 {a}^{3} b)(2ab)[/tex]

=[tex]10 {a}^{4} {b}^{2} [/tex]

Answer:

6*4+8=32

Step-by-step explanation:

32-8=24

24/6=4

so 6*4=24

24+8=32

6x+8=32

6x+8-8=32-8

6x=24

6x÷6=24÷6

X=4

Answer is 4

Might be a bit confusing but hope that helps :)

Answer: Hi. The height of the tree is 27 ft

Step-by-step explanation:

Answer link- https://socratic.org/answers/601885

Answer:

It would be 12. Do you need me to explain or are you good?

Step-by-step explanation:

Answer:

6√2

Step-by-step explanation:

Answer:

I dont see the whole question

Step-by-step explanation:

Answer:

Remember the relation:

Distance = Speed*Time.

Then if we define:

y = distance

x = time

Speed = 50km/hr

Then we can write the relation between distance and time is:

y = (50km/hr)*x

This is the equation we need to graph.

To graph it, we can just find two points of that equation, and then draw a line that connects them:

For example if we have x = 0hr then:

y = (50km/hr)*0hr = 0km

then we have the point (0hr, 0km)

If now we use the point x = 1hr, then:

y = (50km/hr)*1hr  = 50km

Then we also have the point (1hr, 50km)

Now we can draw these two points and connect them by a line, that line is the graph of the equation.

The graph of the equation can be seen below:

Answer:

[tex]y = \frac{2}{3} x[/tex]

Step-by-step explanation:

Hope it is helpful...

Answer:

is B and E. They both equal 81

Answer:

7/15

Step-by-step explanation:

P(appetizers with cheese) = number with cheese / total = 1/5

P(entrees with cheese) = number with cheese / total = 1/3

It is the P(a) + P(b) - P(a and b)

We cannot double count the cheese and cheese event)

P( cheese and cheese) = 1/3 * 1/5 = 1/15

1/5 + 1/3 - 1/15

3/15 + 5/15 -1/15

8/15 - 1/15

7/15

Explanation:

This is because cosine is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

In this case, 20 is the adjacent side to the reference angle C. The hypotenuse is the longest side 29.

Answer:

r = 16, q = 16√2

Step-by-step explanation:

This is a 45° 45° 90° triangle. In this type of triangle, the legs of said shape will be equal and the hypotenuse will be the leg length multiplied by √2.

Therefore, r = 16 and q = 16√2.

Answer:

r = 16, c = 22.63

Step-by-step explanation:

tan 45° = 16/r

r = 16/ tan 45°

r = 16

c² = a² + b²

c² = 16² + 16²

c² = 256 + 256

c² = 512

c = 22.63

Answer:

Number of hours= 7.5

Step-by-step explanation:

Giving the following information:

Amount saved= $35

Hourly rate= $6

Total objective= $80

To calculate the number of hours to be saved, we need to use the following formula:

Number of hours= difference needed / hourly rate

Number of hours= (80 - 35) / 6

Number of hours= 45/6

Number of hours= 7.5

Answer:

no

Step-by-step explanation

3,6,9

Answer:

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Step-by-step explanation:

The amount of profit y made by the company from selling each widget at x price is modeled by the equation:

[tex]y=-x^2+72x-458[/tex]

Since this is a quadratic with a negative leading coefficient, its maximum will occur at its vertex point. We want to find the price that the widget should be sold to make the maximum profit. So, we want to find the x-coordinate of the vertex. This is given by the formula:

[tex]\displaystyle x=-\frac{b}{2a}[/tex]

In this case, a = -1, b = 72, and c = -458. Substitute and evaluate:

[tex]\displaystyle x=-\frac{72}{2(-1)}=36[/tex]

In order to make the maximum profit, the company should sell each widget at (the currency isn't given, so I'll be assuming USD) $36.

Answer:

3

Step-by-step explanation:

tan 60 = root(3)

tan² 60 = {root (3)}²

tan² 60 = 3

Answer:

[tex]\$0.41[/tex]

Step-by-step explanation:

Convert millimeters to meters:

[tex]50\:\mathrm{mm}=0.05\:\mathrm{m}[/tex]

At a price of $8.20 per meter, the total price would be [tex]$8.20\cdot 0.05=\boxed{\$0.41}[/tex]

Answer:

10

Step-by-step explanation:

When multiplying numbers of the same base the exponents are added

therefor

n + 10 = 20

n = 10

Answer:

10

Step-by-step explanation:

y^n × y^10 = y^20

y^(n+10) = y^20

n+10 = 20

n = 20-10

n = 10

Answer:

approximately 1,925,000

Step-by-step explanation:

700,000 * 0.07 = 49,000    this would be the growing rate per year.

49,000 * 1,225,000    this would be the population grown in 25 years.

700,000 + 1,225,000 = 1,925000    this would be the total population that was in the city and the population that has grown in the 25 years.

Hope this helps

You want all of the answers or just one?

Answer:

Step-by-step explanation:

opposite sides of a parallelogram are equal . So,

NM = OL

2x + 5 = x + 10

2x - x = 10 - 5

x = 5

substitute the value of x

NM = 2x + 5

=2*5 + 5

=15

for NO also substitute 5 inplace of x

Answer:

[tex]122 - 71 = 51 \\ m < 51[/tex]

Answer:

DBC= 40˚

Step-by-step explanation:

Since we already know what ABC and ABD is we could use these information to get what DBC is.

Since ABD and DBC adds together to sum up to ABC we could use this info to create this equation:

ABD+DBC=ABC

Replace ABD and ABC with the number that it is equal to

71˚+DBC=112˚

Move 71˚ to the other side by subtracting

DBC=112˚-72˚

Which is 40˚

So the answer is 40˚

Hope this helped!

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Initial number of users

[tex]N_0=100[/tex] [tex]\text{growth rate=doubles every seven days}[/tex]

[tex]100\% \longrightarrow 7\ days\\\\\frac{100}{100} \longrightarrow 7\ days\\\\1 \longrightarrow 7\ days\\\\[/tex]

When:

[tex]N=N_0\ 2^{rt}\\\\[/tex]

    [tex]=100\times 2^{rt}\\\\=100\times 2^{t\cdot \frac{1}{7}}\\\\=100\times 2^{ \frac{t}{7}}\\\\[/tex]

Checking the value:

After 14 days:

[tex]N=100\times 2^{ \frac{14}{7}}=400\\\\100 \overset{100\ days}{\rightarrow} 200 \overset{7 \ days}{\rightarrow}\ 400[/tex]

Answer:

x= 2.67

y= 7

Step-by-step explanation:

I want you to know that I might be wrong.

I times 3 and 2.67 which gave me 8.

3 * 2.67 equals= 8.01

I added 8.01 to 7 which gave me 15.

Answer:

Smaller number = 15

Larger number = 29

Step-by-step explanation:

Let smaller number be S

Let larger number be  L

Given :

Sum = 44. That is , S + L = 44

Smaller number is 14 less than larger number. That is , S = L - 14

Therefore the equations are :

                                          S + L = 44 ------(1)

                                          S = L -  14 ------(2)

Substitute (2) in ( 1 )

(L - 14 ) + L = 44

L - 14 + L = 44

2 L = 44 + 14

2 L = 58

L = 29

Substitute L in (1) : S = L - 14 = 29 - 14 = 15

Answer:

Larger Number: 29

Smaller Number: 15

Step-by-step explanation:

By assigning the letters "L" and "S", to the larger number and smaller number respectively, we can solve this using simultaneous equations:

L+S = 44

L-14 = S

By substituting S = L-14 into the first equation, we get:

L+L-14 = 44 (add 14 to both sides)

L+L = 58 ( divide by 2 as L+L becomes 2L)

L=29

When L= 29, S= 29-14 which is 15

Answer:

13122

Step-by-step explanation:

an = 6 x 3^(n - 1)

n = 8

a8 = 6 x 3^(8 - 1) = 6 x 3^7 = 6 x 2187 = 13122

The above person is Correct, they deserve more Rating

--to brainly staff*     If you delete this answer, something is wrong with this world, im trying to help the people who are unsure about the above answer having a low rating, to tell them that it is the correct answer. Thank you

Answer: D

Step-by-step explanation:

I’m like 90% sure it’s D ‍♀️

Answer:

D

Step-by-step explanation:

Domain is how far the graph goes left to right.

The left arrow goes left into -infinity forever

The right arrow goes down and to the right forever, into infinity

Answer:

Step-by-step explanation:

Given:

Total number of worker = 7

Find;

1] Mean of worker's salary

2] Mean of worker's salary[Excluding Deva's income]

Computation:

Mean = Sum of all observation / Total number of observation

1] Mean of worker's salary = [13,500 + 27,500 + 13,750 + 79,000 + 18,750 + 27,500 + 15,000] / 7

Mean of worker's salary = [194,500] / 7

Mean of worker's salary = £27,785.71 (Approx.)

2] Mean of worker's salary[Excluding Deva's income] = [13,500 + 27,500 + 13,750 + 18,750 + 27,500 + 15,000] / 6

Mean of worker's salary[Excluding Deva's income] = [115,500]/7

Mean of worker's salary[Excluding Deva's income] = £16,500 (Approx.)

Answer:

C

Step-by-step explanation:

2ab * sqrt[3](192ab^2) - 5 * sqrt[3](81 a^4b^5) =

= 2ab * sqrt[3](4^3 * 3 * a * b^2) - 5 * sqrt[3](3^3 * 3 * a^3 * a * b^3 * b^2)

= 2ab * 4 sqrt[3](3 * a * b^2) - 5 * 3 * a * b * sqrt[3](3 * a * b^2)

= 8ab * sqrt[3](3 * a * b^2) - 15ab * sqrt[3](3 * a * b^2)

= -7ab * sqrt[3](3ab^2)

Answer: C