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3 years ago

The diagram shows a logo made from 3 circles.

Mathematics

1 answer:

Cloud [144]3 years ago

3 0

Answer:

% area of the shaded region = 33%

Step-by-step explanation:

Radius of the middle circle = 7 cm

Radius of the inner circle = 4 cm

Area of the middle circle = πr²

= π(7)²

= 49π

Area of the inner circle = π(4)²

= 16π

Area of the shaded region= 49π - 16π

= 33π

Area of the outermost circle = π(10)²

= 100π

% area of the shaded region = $\frac{\text{Area of the shaded region}}{\text{Area of the inner circle}}\times 100$

= $\frac{33\pi }{100\pi }\times 100$

= 33%

Therefore, area of the shaded region is 33% of the complete logo.

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2. Following are the marks obtained by a batch of 10 students in a

timurjin [86]

Answer:

Students level of knowledge is higher in accountancy (Y) compared to statistics (X).

Step-by-step explanation:

The level of knowledge of the students in each subject can be known by comparing the mean score of the subjects.

Marks of the students in statistics (X) are: 63 64 62 32 30 60 47 46 35 28

mean = $\frac{63 +64+62+32+30+60+47+46+35+28}{10}$

= $\frac{467}{10}$

= 46.7

The mean mark of students in statistics (X) is 46.7.

Marks of students in accountancy (Y) are: 68 66 35 42 26 85 44 80 33 72

mean = $\frac{68+66+35+42+26+85+44+80+33+72}{10}$

= $\frac{551}{10}$

= 55.1

The mean mark of students in accountancy (Y) is 55.1.

It can be inferred that students level of knowledge is higher in accountancy (Y) compared to statistics (X).

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3 years ago

What is -9x+6y=18 in slope intercept form?

Scrat [10]

The answer to this question would be
y
=
1
6
x
+
3

8 0

3 years ago

Read 2 more answers

35 bus together to pick apples they pay the total of 5 and 1/2 of apples. if each person takes home 1/3 of apples, how many appl

Lady_Fox [76]

Answer:

I do not know, if you ca rewrite that would be helpful

Step-by-step explanation:

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3 years ago

-4x+5y=17 4x+6y=-6 solve using elimination<br><br>SHOW WORK

Ber [7]

-4x+4x +5y +6y = 17-6

11y=11

divide both side by 11 to isolate y

y=1

4x+6(1) = -6

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3 0

3 years ago

(a) Suppose anxn has finite radius of convergence R and an ≥ 0 for all n. Show that if the series converges at R, then it also c

valina [46]

Answer:

a) See the proof below.

b) $\sum \frac{(-x)^n}{n}$

Step-by-step explanation:

Part a

For this case we assume that we have the following series $\sum a)n x^n$ and this series has a finite radius of convergence $R$ and we assume that $a_n \geq 0$ for all n, this information is given by the problem.

We assume that the series converges at the point $x= R$ since w eknwo that converges, and since converges we can conclude that:

$\sum a)n R^n < \infty$

For this case we need to show that converges also for $x=-R$

So we need to proof that $\sum a_n (-R)^n < \infty$

We can do some algebra and we can rewrite the following expression like this:

$\sum a_n (-R)^n = \sum (-1)^n a)n R^n$ and we see that the last series is alternating.

Since we know that $\sum a_n x^n$ converges then the sequence { $a_n R^n$ } must be positive and we need to have $lim_{n\to \infty} a^n R^n = 0$

And then by the alternating series test we can conclude that $\sum a_n (-R)^n$ also converges. And then we conclude that the power series $a_n x^n$ converges for $x=-R$ ,and that complete the proof.

Part b

For this case we need to provide a series whose interval of convergence is exactly (-1,1]

And the best function for this $\frac{(-x)^n}{n}$

Because the series $\sum \frac{(-x)^n}{n}$ converges to $-ln(1+x)$ when $|x|$ using the root test.

But by the properties of the natural log the series diverges at $x=-1$ because $\sum \frac{1}{n} =\infty$ and for $x=1$ we know that converges since $\sum \frac{-1}{n}$ is an alternating series that converges because the expression tends to 0.

6 0

3 years ago