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telo118 [61]
3 years ago
8

The nth term of a sequence is 3(n + 3).

Mathematics
1 answer:
attashe74 [19]3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula

n = 1 : 3(1 + 3) = 3 × 4 = 12

n = 2 : 3(2 + 3) = 3 × 5 = 15

n = 3 : 3(3 + 3) = 3 × 6 = 18

n = 4 : 3(4 + 3) = 3 × 7 = 21

The first 4 terms are 12, 15, 18, 21

Substitute n = 50 into the n th term formula

n = 50 : 3(50 + 3) = 3 × 53 = 159 ← 50 th term

Equate n th term formula to 100, that is

3(n + 3) = 100

3n + 9 = 100 ( subtract 9 from both sides )

3n = 91 ( divide both sides by 3 )

n = 30.333...

Thus the first term to have a value larger than 100 is the 31 st term

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4. 700 J of work is used to push an object for 12 seconds. What is the power of this machine?
s2008m [1.1K]

Answer:

58.3333333333

Step-by-step explanation:

3 0
3 years ago
A circle is centered at the point (5, -4) and passes through the point (-3, 2).
harina [27]

Answer:

The answer to your question is:

             (x - 5)² + (y + 4)² = 10²     or         (x - 5)² + (y + 4)² = 100

Step-by-step explanation:

Data

Center (5, - 4)

Point ( -3 , 2)

Formula

d = √ ((x2- x1)² + (y2 - y1)²)

(x - h)² + (y - k)² = r²

Process

Radius

d = √ ((-3 - 5)² + (2 + 4)²)

d = √ ((-8)² + (6)²)

d = √ 64 + 36

d = √100

d = 10 units

Circle

                           (x - 5)² + (y + 4)² = 10²

                             (x - 5)² + (y + 4)² = 100

8 0
3 years ago
Leon receives a birthday gift of $50 from his parents. Each week he saves $5.00. How many weeks will it take for him to save $12
lubasha [3.4K]

Answer:

14 weeks. the equation would be a.

Step-by-step explanation:

120-50=70   70/5=14 it will take him 14 weeks to get 120 if he saves 5 a week on top of the additional 50 he already has.

3 0
2 years ago
A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 125 is selected and is used to estimate
Mrrafil [7]

Answer:

a:  0.8884

b: 0.9934

Step-by-step explanation:

We have µ = 300 and σ = 70.  The sample size, n = 125.  

For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:

P(292 < x < 308).

We need to find the z-scores that correspond to these values using the given data.  See attached photo 1 for the calculation of these scores.

We have P(292 < x < 308) = 0.8884

Next we want the probability of the sample mean to be within 17 units of the population mean, so we want the values from 283 to 317.  We want to find

P(283 < x < 317)

We need to find the z-scores that correspond to these values.  See photo 2 for the calculation of these scores.

We have P(283 < x < 317) = 0.9934

5 0
3 years ago
Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16). Wha
Rudik [331]
The point P has coordinates (x,y) = (-2,6) so x = -2 and y = 6

Replace x and y with those values into the rule given
So,
(x,y) ---> (x-2, y-16)
turns into
(-2,6) ---> (-2-2, 6-16) = (-4,-10)

P = (-2,6)
P ' = (-4,-10) 

The answer is -10 because your teacher just wants the y coordinate of point P'
4 0
3 years ago
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