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3 years ago

Determine if the sequence is arithmetic. If it is, find the common difference.

Mathematics

1 answer:

mr_godi [17]3 years ago

7 0

Answer:

In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.

So we just need to take different pairs of consecutive terms and see if their difference is always the same:

1) The differences are:

32 - 35 = -3

29 - 32 = -3

26 - 29 = -3

So yes, this is an arithmetic sequence and the common difference is -3

2) The differences are:

-23 - (-3) = -20

-43 - (-23) = -20

-63 - (-43) = -20

This is an arithmetic sequence, and the common difference is -20

3) The differences are:

-64 -(-34) = -30

-94 -(-64) = -30

-124 -(-94) = -30

This is an arithmetic sequence and the common difference is -30

4) The differences are:

-40 -(-30) = -10

-50 - (-40) = -10

-60 - (-50) = -10

This is an arithmetic sequence and the common difference is -10

5) The differences are:

-9 - (-7) = -2

-11 - (-9) = -2

-13 - (-11) = -2

This is an arithmetic sequence, and the common difference is -2

6) The differences are:

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

This is an arithmetic sequence, and the common difference is 5.

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Find X. <br> pls & thank you :)

diamong [38]

Answer:

<u>The correct answer is D. 69</u>

Step-by-step explanation:

Let's recall that if an exterior angle has its vertex where two rays share an endpoint outside a circle, the measure of that exterior angle is found by dividing the difference between the measures of the intercepted arcs by two.

Therefore, we have:

x = (Measure of arch CD - Measure of arch BD)/2

Replacing with the real values:

x = (210 - 72)/2

x = 138/2 = 69°

<u>The correct answer is D. 69</u>

5 0

4 years ago

The rate of change in sales for Garmin from 2008 through 2013 can be modeled by

Zina [86]

Answer:

a) The model for the sales of Garmin is represented by $S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112$ .

b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

Step-by-step explanation:

a) The model for the sales of Garmin is obtained by integration:

$S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt$

$S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C$ (1)

Where $C$ is the integration constant.

If we know that $t = 9$ and $S(t) = 2.9$ , then the model for the sales of Garmin is:

$-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9$

$C = 47.112$

The model for the sales of Garmin is represented by $S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112$ .

b) The average sales of the Garmin from 2008 through 2013 ( $\bar{S}$ ) is determined by the integral form of the definition of average, this is:

$\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt$ (2)

$\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112 \right]} \, dt$

$\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8) \right]$ $\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)$

$\bar{S} = 2.5$

The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.

7 0

3 years ago

Algebra help (picture is included)

SVETLANKA909090 [29]

$\boxed {\boxed {\text {Volume = base area x height}}}$

Base Area = 2 x 2 = 4 cm²

Volume = 4 x 3.5 = 14 cm³

Answer: 14 cm³

3 0

4 years ago

10 POINTS PLZ HELP A GIRL OUT

Georgia [21]

Answer:

201

Step-by-step explanation:

What you do is you first find the formula which is 3.14(r^2)(h/3)

So it will be 3,14(4^2)(12/3). why it is 4 is because a radius is half the length of the circle and they gave you the length of the full circle so you half it.

Your answer is 200.96 but to the nearest whole number is 201.

3 0

3 years ago

What is the probability if a penny lands on heads 30 times after being tossed 50 times?

Firlakuza [10]

The probability will be equal to 60%.

<h3>What is probability?</h3>

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The best thing to do here is to put it into a fraction. as 30 landed heads up, 20 (50-30) must be tails.

You can then put this into a fraction, which becomes 20/50.

To turn this into a decimal, you can then divide 1 by 50

1/50= 0.02

As you've got 22 lots of this, you then need to multiply 0.02 by 20.

0.2x20= 0.40

To find the percentage, you've then got to multiply the decimal by 100.

100x0.40= 40.

Therefore, 40% of the tosses would be tails

As you've found what one percentage is, you simply need to take this number away from 100 to find the other, rather than having to go through the process again.

100-40= 60

To know more about probability follow

brainly.com/question/24756209

#SPJ1

7 0

2 years ago