An arithmetic sequence is described by the function f(n) = -3n + 7.
Determine the first five terms of this sequence

Answer:

x = 12

y = 12√3

Step-by-step explanation:

=======================================================

Explanation:

The sequence {3,11,19,...} is arithmetic since we are adding 8 to each term to get the next one

etc. This means the common difference is d = 8.

The first term is a = 3

Let's use this formula

S = n*(2*a + d(n - 1) )/2

so we can find the sum of the first n terms. In this case, n = 35

So,

S = n*(2*a + d(n - 1) )/2

S = 35*(2*3 + 8(35 - 1) )/2

S = 35*(6 + 8(34))/2

S = 35*(6 + 272)/2

S = 35*(278)/2

S = 35*139

S = 4865

[tex]4865[/tex] is the  the sum of the first [tex]35[/tex] terms of the following series [tex]3, 11, 19...[/tex]

What is arithmetic sequence?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2

The sequence  [tex]{3,11,19,...}[/tex]   is arithmetic since we are adding [tex]8[/tex] to each term to get the next one as shown below:

[tex]3+8 = 11\\11+8 = 19[/tex]

This means the common difference is [tex]d = 8.[/tex]

The first term is [tex]a = 3[/tex]

Number of terms [tex]=n=35[/tex]

Sum of the series

[tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{35}{2} (2[/tex]×[tex]3+34[/tex]×[tex]8)[/tex]

[tex]=35[/tex]×[tex]139[/tex]

[tex]=4865[/tex]

Hence, we can conclude that the sum of the first [tex]35[/tex] terms of the following series is [tex]4865[/tex]

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Explanation + answers

Because there are lengths going from 0 to 1, the lines must mean either decimals or fractions (we'll use fractions for this.)

1. There are twelve lines from 0 and 1, which we can use as the denominator for our fraction. This means the length of each line is 1/12.

2. In order to find where K's point is at, we simply need to count until we get to it. After counting, I see that K is on point 8/12, which we can simplify to get a smaller number. If we simplify once, we get 4/6, which we can again simplify to get 2/3. This gives us the answer K is on point 8/12 or 2/3.

Answer:

$0.90

Step-by-step explanation:

So first you need to find the rate (showing how much money it costs to run for 1 hour) so you get 0.60 and divide it by 4 and its 0.15, then multiply 0.15 by 6 and get 0.90

Answer:

True

Step-by-step explanation:

They are the same dimensions

Answer:

I think its true because there both the same shape and dimension

Answer:

389,120

Step-by-step explanation:

Answer: D

Step-by-step explanation:

the 4th one nzoabsjqnnansiwwna

Answer:

17

Step-by-step explanation:

Add (4 + 5) = 9 then multiply by 3 = 27 - 12 = 15 +2 = 17

Answer:

[tex]3(4 + 5) - 12 + 2 = 17[/tex]

Step-by-step explanation:

[tex]3(4 + 5)[/tex]

break it down into PEMDAS

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

[tex]3 \times 4 = 12[/tex]

[tex]3 \times 5 = 15[/tex]

[tex]15 + 12 = 27[/tex]

[tex]3(4 + 5) = 27[/tex]

move onto your second part

[tex]27 - 12 + 2[/tex]

[tex]27 - 12 = 15[/tex]

[tex]15 + 2 = 17[/tex]

your final part would be to put it all back together with your answer show an.

[tex]3(4 + 5) - 12 + 2 = 17[/tex]

Answer:

Step-by-step explanation:

65

Answer:

500

Step-by-step explanation:

10*50=500

Answer:

1a. 3y = 18

1b. y + 7 = 18

1c. 2y + 4 = 18

Step-by-step explanation:

In each case, let's take the red boxes to be constant why the the green boxes represents the variable, y.

Thus,

1a. There are only 3 green boxes which gives us 18, therefore, the equation that expresses this would be:

3y = 18

1b. We have 7 red boxes which represents the constant, 7.

We also have 1 green box which represents the variable, y. Therefore, the equation that expresses this would be:

y + 7 = 18

1c. We have 4 red boxes = 4

We have 2 green boxes = 2y

Therefore, we would have:

2y + 4 = 18

Answer:

he has already ran 35 miles

turn 70% into a decimal .70 than multiply that by 50 and you get 35

Answer:

35

Step-by-step explanation:

1 bracelet costs $7

5 bracelets is 7*5=35

As we can see with the numbers they gave us every bracelet costs 7 dollars, 1 =7, 2=14 and so on. With this information we can just take the number 5 and multiply it by 7 which would equal 35. Or you could add 7 to 21 and then 7 to 28. Whichever one works for you.

Hope this helped

Answer:

6x⁴ + 26x³ + 8x²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

(6x² + 2x)(x² + 4x)

Step 2: Expand

Answer:

D. $13.76 million is the correct answer :)

Step-by-step explanation:

The solution is, $13.76 was the predicted profit in year 10.

Here, we have,

Given : the equation is,

y=-0.34x^2 + 4.43x + 3.46.

To Find : Using the quadratic regression equation, what was the predicted profit in year 8

Solution :

y=-0.34x^2 + 4.43x + 3.46.

Where y is profit and x is year

Substitute x = 10

y=-0.34* 10^2 + 4.43*10+ 3.46.

or, y = 13.76

So, Option D is true

Hence the predicted profit in year 10 is $13.76.

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Answer: positive force → balanced force → negative force

Step-by-step explanation: I just did it

Answer:

A

Step-by-step explanation:

edg

Answer:2,460

Step-by-step explanation:

Just use a calculator

820x3=2,460

Answer:

See below.

Step-by-step explanation:

I've never seen one asked quite this way, but I think I have it figured out.

The objective here is to get the right answer for each square. The answer is either the one next to the 'x', which means you put an 'x' in the tic-tac-toe square or the answer is the one next to the 'O', which means you put an 'O' in the tic-tac-toe square.

I will number them boxes 1-3 on the top row, 4-6 for the next, and 7-9 for the bottom row.

Box 1: In a fraction, you subtract the bottom exponent from the top exponent, so the proper exponent is 10 - 2 = 8. That is an O for g^8.

Box 2: A power raised to a power - multiply the exponents. 2*6=12. That is an X for m^12 for box 2.

Box 3: for multiplying the same base, you add the exponents. 4+5=9. That gives us y^9, which is a X for box 3.

Box 4: j is a factor four times, so that is j^4. That puts an O in Box 4.

Box 5: In a fraction, you subtract the bottom exponent from the top exponent, so we get -2 - (-6) = -2 + 6 = 4. The correct expression is h^4, so we have an X for box 5.

Box 6: A power to a power, you multiply the exponents so the first part becomes m^8. Now we have m^8 * m^5. For multiplying the same base, you add the exponents. 8+5=13. That gives us m^13, which puts an O in box 6.

Box 7: The top is a power to a power so we multiply the exponents. 4*5=20. The top is b^20.

On the bottom, for multiplying the same base, you add the exponents. 2+3=5, so the bottom is b^5.

Now we have a fraction, (b^20)/(b^5). In a fraction, you subtract the bottom exponent from the top exponent, so we have 20 - 5 = 15, and thus b^15. That gives us an X for box 7.

Box 8: A fraction IS a division, so we do divisons and fractions the same way. The p^3 on the left is the top (numerator) and the p^2 part is the bottom (denominator). So 3-2=1. But P^1 is just P, so we have an O for box 8.

Box 9: For the numerator, it is a power to a power so we multiply the exponents and get k^12.

For the denominator, we are multiplying the same base, so you add the exponents. 7 + (-5) = 2, and we get k^2 for the denominator

Now we have the fraction of k^12 OVER k^2.  In a fraction, you subtract the bottom exponent from the top exponent. 12-2=10. We get k^10, giving us an X for box 9.

So here is what we get for tic-tac-toe.

0   X   X

O   X   0

X   O   X

We get 3 in a row in boxes 3, 5, and 7. The exponents in those problems are 9, 4, and 15 respectively. The product of thse 3 numbers is 540.

This was a LOT of steps, so I encourage you to check every little multiplication and addition I did.

Hope this helps.

Answer:

its 300

Step-by-step explanation:

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

[tex]P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312[/tex]

Probability of having an emergency locator and not being discovered:

20% of 28%. So

[tex]P(A cap B) = 0.2*0.28 = 0.056[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105[/tex]

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

[tex]P(A) = 1 - 0.5312 = 0.4688[/tex]

Probability of not having an emergency locator and being discovered:

34% of 72%. So

[tex]P(A \cap B) = 0.34*0.72 = 0.2448[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522[/tex]

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

[tex]P(A \cap B) = 0.66*0.72 = 0.4752[/tex]

Probability of being discovered, given that it has the emergency recorder:

[tex]p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946[/tex]

This question asks for P(X = 7) when [tex]n = 10[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064[/tex]

0.064 = 6.4% probability that 7 of them are discovered.

Answer:

1. y intercept is 6 and the slope is 1/2x

2. y intercept is 7 and the slope is 4x

3. y intercept is 1 and the slope is -2/3x

4. y intercept is 3 and the slope is 5/2x

5. y intercept is 4 and the slope is -x

6. y intercept is 9 and the slope is -8/3x

Step-by-step explanation:

hope this helps I just finished learning this. this should be right

Answer:

1) slope= 1/2 or 0.5

  y intercept= -6

2) slope= 4

  y intercept= -7

3) slope= - 2/3 or -0.66666---->

  y intercept= -1

4) slope= 5/2 or 2.5

  y intercept= 3

5) slope= -1

  y intercept= 4

6) slope= -8/3 or 2.66666666667

  y intercept= 9

Answer:

576 cm²

Step-by-step explanation:

10x15=150

10x15=150

12x15=180

1/2x8x12=48

1/2x8x12=48

150+150+180+48+48=576

Answer:n>10

Step-by-step explanation:b

Answer:

im pretty sure the h represents hours bc there is min on the other so 22x60=1320.  so 1320L

Step-by-step explanation:

Answer:

all you have to do is graph i dont see what i can help you with im

sorry

Step-by-step explanation:

NoAnswer:

Step-by-step explanation: