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3 years ago

What is the length of the blue in the circle o below

Mathematics

2 answers:

iVinArrow [24]3 years ago

8 0

Answer:

Option D. 8.53 units

Step-by-step explanation:

we know that

The triangle OAB is congruent with the triangle OCD

because

OA=OB=OC=OD=radius circle O

AB=CD

therefore

The height of both triangles is equal to 8.53 units

The segment blue is equal to 8.53 units

Ganezh [65]3 years ago

3 0

Answer:

D. 8.53 units

Step-by-step explanation:

In the given circle, we can form two triangles:

i) ΔAOB connecting the radius OA and OB

ii) ΔCOD connecting the radius OC and OD.

We know that all the radius in a circle are the same measure.

We are given AB = 12.48 = CD 12.48 units.

Therefore, by SSS (Side-side-side) postulate the triangles AOB and COD are the congruent.

Therefore, the height of the triangle must be equal.

The height of triangle AOB is 8.53 units

The blue line is the height of the triangle COD.

Therefore, the length of the blue is 8.53 units.

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What should be the value of x so that the three consecutive terms will be in GP 2x+2, 16 and 64x. Also find the sum of first 10

Alexxandr [17]

Answer:

<em>Sum of the first ten terms = 1,398,100</em>

Step-by-step explanation:

Given the geometric progression 2x+2, 16, 64x...

Since they are in GP, their common ratio is expressed as;

16/2x+2 = 64x/16

16/2(x+1) = 4x

8/x+1 = 4x

Cross multiply

4x(x+1) = 8

4x²+4x = 8

4x²+4x - 8 = 0

divide through by 4

x²+x - 2 = 0

Factorize

x²+2x-x- 2 = 0

x(x+2)-1(x+2) = 0

(x-1)(x+2) = 0

x = 1 and -2

Hence the values of x are 1 and -2

Get the common ratio;

r = 16/2x+2

Since x = 1

r = 16/2(1)+2

r = 16/4

r = 4

Sum of the first n terms is expressed as;

Sn = a(rⁿ-1)/r-1

a = 2x+2

a = 2(1)+2

a = 4

Substitute;

S10 = 4(4^10 - 1)/4 - 1

S10 = 4(1,048,576-1)/3

S10 = 4,194,300/3

S10 = 1,398,100

Hence the sum of the first ten terms is 1,398,100

5 0

3 years ago

I need help can someone help me

solong [7]

D. Meters is your answer

5 0

4 years ago

Help me please ASAP!!!!

nydimaria [60]

Answer:

i need this too

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A fenced in rectangular region with the dimensions 4 yards by 8 yards is suddenly expanded by the same distance in each dimensio

Korolek [52]

Answer:

The distance added to each dimension is 2 yards.

Step-by-step explanation:

The initial dimensions of the rectangular fence is 8 yards by 4 yards.

The initial area of the rectangular fence = area of a rectangle

area of a rectangle = length x width

So that,

The initial area of the fence = 8 x 4

= 32

The initial area of the fence is 32 square yards.

But, with the new dimensions, area = 60 square yards.

(4 + x) x (8 + x) = 60

$x^{2}$ + 12x + 28 = 60

$x^{2}$ + 12x - 32 = 0

(x + 14) = 0 or (x - 2) = 0

x = -14 or x =2

Thus, x = 2

The distance added to each dimension is 2 yards.

4 0

3 years ago

Construct a 99% confidence interval to estimate the population proportion with a sample proportion equal to 0.36 and a sample s

vivado [14]

Using the z-distribution, the 99% confidence interval to estimate the population proportion is: (0.2364, 0.4836).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 99% confidence level, hence $\alpha = 0.99$ , z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$ , so the critical value is z = 2.575.

The estimate and the sample size are given by:

$\pi = 0.36, n = 100$ .

Then the bounds of the interval are:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 - 2.575\sqrt{\frac{0.36(0.64)}{100}} = 0.2364$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 + 2.575\sqrt{\frac{0.36(0.64)}{100}} = 0.4836$

The 99% confidence interval to estimate the population proportion is: (0.2364, 0.4836).

More can be learned about the z-distribution at brainly.com/question/25890103

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8 0

2 years ago