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3 years ago

In the diagram below, AB and bc are tangent to o. What is the measure of ac?

Mathematics

2 answers:

DanielleElmas [232]3 years ago

4 0

Answer:

Option D. $150\°$

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$m\angle ABC=\frac{1}{2}[arc\ ADC-arc\ AC]$

substitute the given values

$30\°=\frac{1}{2}[210\°-arc\ AC]$

$60\°=[210\°-arc\ AC]$

$arc\ AC=210\°-60\°=150\°$

Tom [10]3 years ago

4 0

Answer:

Option (D) is correct.

Step-by-step explanation:

OA is perpendicular to AB

OC is perpendicular to BC

Radius from the center is perpendicular to the tangent.

In quadrilateral ABCO,

∠ABC+∠BCO+∠AOC+∠OAB=360°

30°+90°+∠AOC+90°=360°

∠AOC+210°=360°

∠AOC=360°-210°

∠AOC=150°

Hence, arc AC=150°

Thus, the correct answer is option (D)

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Given the data: 0.90 1.42 1.30 1.55 1.63 1.32 1.35 1.47 1.95 1.66 1.96 1.47 1.92 1.35 1.05 1.85 1.74 1.65 1.78 1.71 2.29 1.82 2.

yKpoI14uk [10]

Answer:

Step-by-step explanation:

a) Mean means the average we add all the values in data and divide it by the total number

Mean= 0.9+1.42+1.3+1.55+1.63+1.32+1.35+1.47+1.95+1.66+1.96+1.47+1.92+1.35+1.05+1.85+1.74+1.65+1.78+1.71+2.29+1.82+2.06+2.14+1.27

Mean= 40.61

Mean= 1.624

Place the values in correct order starting from least

0.9,1.05,1.27,1.30,1.32,1.35,1.35,1.42,1.47,1.47,1.55,1.63,1.65,1.66,1.71,1.74,1.78,1.82,1.85,1.92,1.95,1.96,2.06,2.14,2.29

Median = 1.65 ( this is the middle value odf the data given)

Mode = 1.35 and 1.47

Variance =

in order to find the variance we subtract each data value with mean and square it and then divide all with the total sample size

σ2 = (0.9-1.624)²+ (1.42-1.624)²+(1.3-1.624)²+(1.55-1.624)²+(1.63-1.624)²+(1.32-1.624)²+(1.35-1.624)²+(1.47-1.624)²+(1.95-1.624)²+(1.66-1.624)²+(1.96-1.624)²+(1.47-1.624)²+(1.92-1.624)²+(1.35-1.624)²+(1.05-1.624)²+(1.85-1.624)²+(1.74-1.624)²+(1.65-1.624)²+(1.78-1.624)²+(1.71-1.624)²+(2.29-1.624)²+(1.82-1.624)²+(2.06-1.624)²+(2.14-1.624)²+(1.27-1.624)²

σ2= 2.764

σ2 = 0.1105

Standard Deviation = √σ2

σ -= √0.1105

σ = 0.332

Coefficient of variance = Here we divide standard deviation by mean and multiply by 100

Coefficient of Variance = (0.332÷ 1.624) × 100

Coefficient of Variance = 20.47

7 0

3 years ago

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet,

babunello [35]

Answer:

15 feet

Step-by-step explanation:

It is given that Quadrilateral ABCD is similar to Quadrilateral EFGH. This means that the corresponding sides of these two quadrilateral will be in the same proportion.

i.e.

Ratio of two corresponding sides would be the same. We are given longest three sides of ABCD and shortest two sides of EFGH. Let the 4th sides of ABCD i.e. the shortest side be x.

So, the ratio of the shortest sides of two quadrilaterals would be the same as the ratio of second shortest sides.

So,

$x:6=30:12\\\\\frac{x}{6}=\frac{30}{12}\\\\ x=\frac{30}{12} \times 6\\\\ x = 15$

So, the 4th side on quadrilateral ABCD would be 15 feet. None of the options match with the answer.

8 0

3 years ago

Write the following numbers used in these statements in scientific notation. (Note: Some of these numbers have been rounded.)

lutik1710 [3]

Answer:

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

Step-by-step explanation:

We have given that radius of earth is 4000 miles

4000 miles can be written as 4×1000

We have to written 4000 miles in scientific form

We know that 1000 can be written in scientific form as $1000=10^3$

So $4000miles =4\times 1000=4\times 10^3miles$

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

5 0

3 years ago

At the Dessert Island Pastry Cafe, there are 2 cakes for every 7 donuts and 11 brownies for every 3 cakes. What is the ratio of

Westkost [7]

Answer: 22/21

Step-by-step explanation:

2 cakes : 7 donuts → 6 cakes : 21 donuts

3 cakes : 11 brownies → 6 cakes : 22 brownies

22 brownies : 21 donuts

Now, simply write this as a fraction. 22/21

7 0

3 years ago

Read 2 more answers

the population of two towns were equal in a particular year. subsequently the population of one town increases by 8 % and the po

VashaNatasha [74]

Ooh, this is a tough one. I'll try my best to answer.

Ok, for the town that decreased in population it would of gone to 21551.38 citizens. For the one that increased in population by 8% it would be 24761.16.

Hope that helps!

8 0

3 years ago