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Sergeu [11.5K]
3 years ago
9

What is the measure of ACE in the diagram below? A. 46 B. 104 C. 29 D. 58

Mathematics
2 answers:
sergeinik [125]3 years ago
7 0
Answer : C
***HOPE THIS HELP YOU***
beks73 [17]3 years ago
3 0

Answer:

C

Step-by-step explanation:

The secant- secant angle ACE is half the difference of the measures of the intercepted arcs, that is

∠ ACE = \frac{1}{2} (AE - BD ) = \frac{1}{2} (104 - 46)° = \frac{1}{2} × 58° = 29° → C

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The numbers​ 1, 2,​ 3, 4, and 5 are written on slips of​ paper, and 2 slips are drawn at random one at a time without replacemen
mamaluj [8]
<h2>Answer:</h2>

(a)

The probability is :  1/2

(b)

The probability is :  1/2

<h2>Step-by-step explanation:</h2>

The numbers​ 1, 2,​ 3, 4, and 5 are written on slips of​ paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2)   (1,3)    (1,4)    (1,5)

(2,1)   (2,3)   (2,4)   (2,5)

(3,1)   (3,2)   (3,4)   (3,5)

(4,1)   (4,2)   (4,3)   (4,5)

(5,1)   (5,2)   (5,3)   (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

               P(A|B)

We know that it could be calculated by using the formula:

P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}

Hence, based on the data we have:

P(A\bigcap B)=\dfrac{1}{20}

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is:  (4,5) )

and

P(B)=\dfrac{2}{20}

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

               P(A|B)

Hence, based on the data we have:

P(A\bigcap B)=\dfrac{1}{20}

( since, the only outcome out of 20 outcomes is:  (3,5) )

and

P(B)=\dfrac{2}{20}

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}

7 0
3 years ago
Complete each statement with a number that makes the statement true. A._____ &lt; 7°c. B.___&lt;-3°c. C.-0.8°c &lt;_____ &lt; -0
IrinaVladis [17]

A. 6c

B. -5c

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D. 2c

Just a few you could use.

5 0
3 years ago
Which statements are true?
Rina8888 [55]

Answer:

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Step-by-step explanation:

Absolute value is the distance to zero, and it is always positive. That means the positive and negative versions of a number have the same absolute value. That means the first one is true, and the second and third ones are false. For the last one, -6 is closer to zero, so that means it would be true (The absolute value of -6 is 6, and the absolute value of -7 is 7).

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Is 9.78083 a rational number
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4 0
3 years ago
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Serhud [2]

Answer:

The area of a rhombus is 18\sqrt{3} square units.

Step-by-step explanation:

Side length of rhombus = 6 units.

Interior angle of rhombus = 120°

another Interior angle of rhombus = 180°-120° = 60°.

Draw an altitude.

In a right angled triangle

\sin \theta=\frac{opposite}{hypotenuse}

\sin (60)=\frac{h}{6}

\frac{\sqrt{3}}{2}=\frac{h}{6}

Multiply both sides by 6.

3\sqrt{3}=h

The height of the rhombus is 3\sqrt{3}.

Area of a rhombus is

Area=base\times height

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Area=18\sqrt{3}

Therefore, the area of a rhombus is 18\sqrt{3} square units.

8 0
2 years ago
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