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Find the sum, if it exists, of the infinite geometric series that is related to the infinite geometric sequence {1,521, ; 1,369 ; 1,232; ...}. Round the value of r to the nearest hundredth, if needed

S = 16,643
S = 15,210
The infinite geometric series diverges.
S = 12,560

Step-by-step explanation:

Hope you can correct you question

Answer:

16

Step-by-step explanation:

Given

A coin

[tex]n = 7[/tex] --- Number of flips

[tex]x \to heads[/tex]

Required

Which can't be the value of x

From the question, we understand that the coin was flipped 7 times.

This means that, the highest occurrence of head is:

[tex]x = 7[/tex]

And the list is:

[tex]x = 0[/tex]

So, the range of x is:

[tex]x = \{0,1,2,....,7\}[/tex]

In the above range, only (16) is out of range.

Hence:

[tex]x \ne 16[/tex] --- Number of heads can't be 16

Answer:

D

Step-by-step explanation:

It is D because there are only 3 sides given. I understand where you were going with B, but there is no angle given, (and you cannot prove one either), so the answer is simply D.

A - There is no angle, triangle does not matter

B - There is no angle, triangle is correct

C - It is similar, they have the same scale factor

D - There are 3 sides, and the triangle is correct

Answer:

x < 7

Step-by-step explanation:

-8x + 40> -16

Subtract 40 from each side

-8x + 40-40> -16-40

-8x >-56

Divide each side by -8, remembering to flip the inequality

-8x/-8 < -56/-8

x < 7

Answer:

B) positive x-axis.

Step-by-step explanation:

angle to be in standard position, its vertex is at the origin and the initial side lies along the positive x axis

Answer:

Positive x axis

Step-by-step explanation:

The angle lies in standard position means it begins from Q1

The first side must be x axis

Then in Q1 x>0 so it's positive x axis

Answer:

126

Step-by-step explanation:

1200 x .021=25.20 interest per year

25.20x5=126

assumes no compounding

Answer:

Step-by-step explanation:

angle 2 and angle 3 are complementary angle because their sum is 90 degree as they are perpendicular.

Answer:

Cost of a coffee = $1.5

Cost of a muffin = $1.25

Step-by-step explanation:

Given:

Cost of 3 coffee and 2 muffins = $7

Cost of 2 coffee and 4 muffins = $8

Find:

Cost of each

Computation:

Assume;

Cost of a coffee = a

Cost of a muffin = b

So,

3a + 2b = 7 .......... Eq1

2a + 4b = 8 .......... Eq2

Eq1 x 2

6a + 4b = 14 ......... Eq3

From Eq3 - Eq2

4a = 6

a = 1.5

Cost of a coffee = $1.5

3a + 2b = 7

3(1.5) + 2b = 7

4.5 + 2b = 7

b = 2.5/2

b = 1.25

Cost of a muffin = $1.25

Answer:

∠1 = ∠8

Step-by-step explanation:

Because they are ALTERNATE EXTERIOR ANGLE

Answer:

∠1 = ∠8

Step-by-step explanation:

Because alternate exterior angles are equal.

Also there is no angle given so you cant work them out.

simply put:

∠1 = ∠8

∠1 = ∠4

∠3 = ∠2

∠1 = ∠5

∠2 = ∠6

∠2 = ∠7

∠5 = ∠8

∠4 = ∠8

∠7 = ∠6

∠7 = ∠3

Let me know if I missed out on anymore! It was long that's why.

Hope this kind of explained it :)

Answer:

Can you insert a picture?  and then I could help you.

Step-by-step explanation:

Answer:

Brianne would earn 5 dollars an hour so the graph should look something like this.

Answer:80^w2−48

Step-by-step explanation:

Answer:

If You Factor it it will be (w+8) (5w2-3)

Step-by-step explanation:

Answer:

where is the question?

Step-by-step explanation:

Given:

Consider the rule of a sequence is:

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

To find:

The 6th term generated by the given rule.

Solution:

We have,

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

Substituting [tex]n=6[/tex] in the above rule, we get

[tex]T_6=\dfrac{6^2-6}{2}[/tex]

[tex]T_6=\dfrac{36-6}{2}[/tex]

[tex]T_6=\dfrac{30}{2}[/tex]

[tex]T_6=15[/tex]

Therefore, the 6th term generated by the given rule is 15.

Answer:

A. Based on the procedure by which this figure was generated, it is likely that the population proportion is between 44.5% and 51.5%.

Step-by-step explanation:

Confidence interval:

We build a confidence interval from a sample proportion, to get an estimate of where the population proportion should likely be.

48% of voters surveyed favored the reelection of Congressman Porkbarrel, with a margin of error of 3.5%.

48 - 3.5 = 44.5%.

48 + 3.5 = 51.5%.

Following the concept of a confidence interval, the population proportion is likely to be between 44.5% and 51.5%, and thus, the correct answer is given by option A.

Answer:

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

Step-by-step explanation:

Given

[tex]x + zy = 2[/tex]

Required

Rewrite to show y-intercept

We have: [tex]x + zy = 2[/tex]

Subtract x from both sides

[tex]zy = 2-x[/tex]

Divide both sides by z

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

The y intercet is: [tex]\frac{2}{z}[/tex]

Answer:

.....

Step-by-step explanation:

Up and down

Answer:

Step-by-step explanation:

1 is 60 2 i 60 and 3 is 61 ;)

Answer:

7

Step-by-step explanation:

Divide 14 by 2

Answer:

P(rolling five distinct values) = 1/3888

Step-by-step explanation:

We are told that I the fair sided dice, 6 is replaced with 5.

Thus,the numbers are now;

1,2,3,4,5,5.

This means a total of 6 possible numbers appearing.

Now, in these 6 numbers there are only 5 distinct numbers since 5 occurs twice.

P(1) = 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 2/6

Thus,probability of rolling 5 distinct values = 1/6 × 1/6 × 1/6 × 1/6 × 2/6 = 1/3888

Answer:

x = 133

Step-by-step explanation:

x + 14 = 147

x (+ 14 - 14) = 147 - 14

x = 133

Answer:

15.2

Step-by-step explanation:

mean=average

to find the mean, add up all of the numbers and divide by the # of numbers that there are

4+5+6+12+12+12+14+16+22+23+28+28=182

182/12=15.2

Answer:

11.3 to 1DP.

Step-by-step explanation:

The mean = sum of the numbers / 12.

= 136/12

= 11.333

Answer:

48

Step-by-step explanation:

138-90(right angled triangle)=48

Answer:

(4a^5b^6)^4 = 256a^20b^24

Step-by-step explanation:

Answer: k = 8

Step-by-step explanation:

-3k + 30 = 6

-3k = -24

k = 8

Answer:

k = 8

Step-by-step explanation:

6 = -3(k - 10)

Divide each side by -3

6/-3 = -3/-3 *(k - 10)

-2 = k-10

Add 10 to each side

-2+10 = k-10+10

8 = k

Answer:

Step-by-step explanation:

I dont know how to do the box thing, but I added all the things and boys read more.

girls:1870

boys:1952

The diffrence (when subracting) is 82

Answer:

[tex]sin(\theta) = \frac{\sqrt{17} }{7}[/tex]

Step-by-step explanation:

We know that:

sin(x)^2 + cos(x)^2 = 1

And we know that:

[tex]cos(\theta) = \frac{4\sqrt{2}}{7} }[/tex]

We want to find the value of the sine function evaluated in theta.

If we replace that in the first equation, we get:

[tex]sin(\theta)^2 + cos(\theta)^2 = 1[/tex]

[tex]sin(\theta)^2 + (\frac{4*\sqrt{2} }{7}) ^2 = 1[/tex]

[tex]sin(\theta)^2 + (\frac{4^2*\sqrt{2}^2 }{7^2}) = 1[/tex]

[tex]sin(\theta)^2 + (\frac{16*2 }{49}) = 1[/tex]

Now we can just isolate the sine part of that equation, so we get:

[tex]sin(\theta)^2 = - (\frac{16*2 }{49}) + 1 = \frac{-32}{49} + \frac{49}{49} = \frac{-32 + 49}{49} = \frac{17}{49}[/tex]

[tex]sin(\theta) = \sqrt{\frac{17}{49} } = \frac{\sqrt{17} }{\sqrt{49} } = \frac{\sqrt{17} }{7}[/tex]

(We can't simplify the fraction anymore)

Answer:

7 * 9 = 63

63 for when both of the triangles are combined, 31.5 for one triangle.

Rectangle = 18 * 22 = 396

396 + 63

459 cm^2

Answer:

The least amount is $75.50

Step-by-step explanation:

Given

[tex]p \to profit[/tex]

[tex]x \to amount[/tex]

[tex]p = -0.5x^2 + 36x - 231[/tex]

Required

The smallest amount to make at least 363

We have:

[tex]p = -0.5x^2 + 36x - 231[/tex]

Rewrite as:

[tex]-0.5x^2 + 36x - 231=p[/tex]

Substitute 363 for p

[tex]-0.5x^2 + 36x - 231 = 363[/tex]

Collect like terms

[tex]-0.5x^2 + 36x - 231 + 363 = 0[/tex]

[tex]-0.5x^2 + 36x + 132 = 0[/tex]

Using quadratic formula, we have:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

[tex]a = -0.5; b= 36; c = 132[/tex]

So, we have:

[tex]x = \frac{-36 \± \sqrt{36^2 - 4*-0.5*132}}{2*-0.5}[/tex]

[tex]x = \frac{-36 \± \sqrt{1560}}{-1}[/tex]

[tex]x = \frac{-36 \± 39.50}{-1}[/tex]

Split

[tex]x = \frac{-36 + 39.50}{-1}; x = \frac{-36 - 39.50}{-1}[/tex]

[tex]x = \frac{3.50}{-1}; x = \frac{-75.50}{-1}[/tex]

[tex]x = 75.50[/tex] and [tex]x = -3.50[/tex]

The amount can't be negative.

So:

[tex]x = 75.50[/tex]

Hence, the least amount is $75.50