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Alecsey [184]
3 years ago
5

Kite DCFE is inscribed in circle A shown below.

Mathematics
2 answers:
kogti [31]3 years ago
7 0

Answer:

∠DEF =56°

Step-by-step explanation:

We are given that arc DEF = 248°

So, arc DCF = 360°-248°

arc DCF = 112°

Now we are required to find the ∠DEF.

So, we will use Inscribed angle theorem.  

Inscribed angle theorem: The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.  

Intercepted arc = arc DCF = 112°

Inscribed angle = ∠DEF

⇒∠DEF = \frac{1}{2}arcDCF

⇒∠DEF = \frac{1}{2}\times 112^{\circ}

⇒∠DEF =56°

Hence the measure of ∠DEF =56°

Blababa [14]3 years ago
5 0

Answer:

\angleDEF=56^{\circ}

Step-by-step explanation:

We are given that a kite DCFE is inscribed in a circle A.

The measure of arc DEF=248^{\circ}

We have to find the measure of angle DEF.

arc DCF=360-arcDEF=360-248=112^{\circ}

Because complete angle =360 degrees

Inscribed angle theorem:It states that inscribed angle is equal to half of the measure of its  intercepted arc.

Therefore, \angle DEF=\frac{1}{2}\timesarcDCF

\angleDEF=\frac{1}{2}\times 112=56^{\circ}

Hence, the measure of angle DEF=56 degrees.

Answer:\angleDEF=56^{\circ}

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The equation in the form of the given expression is (0)² + (1)² = 1

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According to some of the trigonometry identity

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(sin0)² + (cos0)² = 1

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(0)² + (1)² = 1

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8 0
2 years ago
An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 42 and σ = 5.5.
alexandr1967 [171]

Answer:

a)P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

b) For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(42,25.5)  

Where \mu=42 and \sigma=5.5

And we want this probability:

P( X

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

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2 years ago
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katrin [286]
Answer: 108 degrees

============================================================

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minor arc AD = 72
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(minor arc AD) + (minor arc CD) = arc AC
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