1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ser-zykov [4K]
3 years ago
6

Can someone explain this to me please

Mathematics
1 answer:
IrinaVladis [17]3 years ago
3 0

Answer:

c. 36·x

Step-by-step explanation:

Part A

The details of the circle are;

The area of the circle, A = 12·π cm²

The diameter of the circle, d = \overline {AB}

Given that \overline {AB} is the diameter of the circle, we have;

The length of the arc AB = Half the the length of the circumference of the circle

Therefore, we have;

A = 12·π = π·d²/4 = π·\overline {AB}²/4

Therefore;

12 = \overline {AB}²/4

4 × 12 = \overline {AB}²

\overline {AB}² = 48

\overline {AB} = √48 = 4·√3

\overline {AB} = 4·√3

The circumference of the circle, C = π·d = π·\overline {AB}

Arc AB = Half the the length of the circumference of the circle = C/2

Arc AB = C/2 = π·\overline {AB}/2

\overline {AB} = 4·√3

∴ C/2 = π·4·√3/2 = 2·√3·π

The length of arc AB = 2·√3·π cm

Part B

The given parameters are;

The length of \overline {OF} = The length of \overline {FB}

Angle D = angle B

The radius of the circle = 6·x

The measure of arc EF = 60°

The required information = The perimeter of triangle DOB

We have;

Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;

The length of \overline {OD} = The length of \overline {OB}

The length of \overline {OB} = \overline {OF} + \overline {FB} = \overline {OF} + \overline {OF} = 2 × \overline {OF}

∴ The length of \overline {OD} = 2 × \overline {OF} = The length of \overline {OB}

Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;

∠EOF = The measure of arc EF = 60° = ∠DOB

Therefore, in ΔDOB, we have;

∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°

∵ ∠D = ∠B, we have;

∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°

∠D = ∠B = 120°/2 = 60°

All three interior angles of ΔDOB = 60°

∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal

Therefore;

The length of \overline {OD} = The length of \overline {OB} = The length of \overline {DB}  = 2 × \overline {OF}

The perimeter of ΔDOB = The length of \overline {OD} + The length of \overline {OB} + The length of \overline {DB} = 2 × \overline {OF} + 2 × \overline {OF} + 2 × \overline {OF} = 6 × \overline {OF}

∴ The perimeter of ΔDOB = 6 × \overline {OF}

The radius of the circle = \overline {OF} = 6·x

∴ The perimeter of ΔDOB = 6 × 6·x = 36·x

You might be interested in
Name two 2 digit factors whose product is greater than 200 but less than 600
Alexxandr [17]
10 and 21, 10*21=210 
3 0
3 years ago
Read 2 more answers
Write a quadratic function f whose only zero is −10.
Radda [10]

function is: f(x)=(x+10)^2

4 0
3 years ago
Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis
nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = <u><em>the interval of time between the eruptions</em></u>

So, X ~ N(\mu=72, \sigma^{2} =23^{2})

The z-score probability distribution for the normal distribution is given by;

                            Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( \frac{X-\mu}{\sigma} > \frac{82-72}{23} ) = P(Z > 0.43) = 1 - P(Z \leq 0.43)

                                                           = 1 - 0.6664 = <u>0.3336</u>

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let \bar X = <u><em>sample mean time between the eruptions</em></u>

The z-score probability distribution for the sample mean is given by;

                            Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P(\bar X > 82 min)

       P(\bar X > 82 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{82-72}{\frac{23}{\sqrt{13} } } ) = P(Z > 1.57) = 1 - P(Z \leq 1.57)

                                                           = 1 - 0.9418 = <u>0.0582</u>

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let \bar X = <u><em>sample mean time between the eruptions</em></u>

The z-score probability distribution for the sample mean is given by;

                            Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P(\bar X > 82 min)

       P(\bar X > 82 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{82-72}{\frac{23}{\sqrt{34} } } ) = P(Z > 2.54) = 1 - P(Z \leq 2.54)

                                                           = 1 - 0.9945 = <u>0.0055</u>

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

6 0
3 years ago
Which names are other ways to name ∠1?
vesna_86 [32]
∠1 is an angle formed by the two lines PF and YF at point F

We can also call this angle as ∠PFY because it indicates the point F in the middle where the angle is formed

We can call this angle as ∠YFP because it also indicates the point F in the middle where the angle is formed

we can also call this angle ∠F since F is the point where the angle is formed.

Correct answer: ∠PFY, ∠YFP, ∠F
4 0
3 years ago
Using pemdas what’s the correct solution
SSSSS [86.1K]

4- 2/3 (4-1/6) divided by 3/4

parenthesis first

4 - 2/3 (3 5/6) divided by 3/4

change to an improper fraction (6*3+5)/6

4 - 2/3 ( 23/6)divided by 3/4

4 - 46/18 divide by3/4

copy dot flip

4 - 46/18 * 4/3

4 - 23/9 * 4/3

4 - 92/27

get a common denominator of 27

4*27/27 -92/27

108/27 - 92/27

16/27

4 0
3 years ago
Read 2 more answers
Other questions:
  • Mr. Lloyd wants to build a dollhouse for a starter this is a proportional to their house he might have to live in this house and
    15·1 answer
  • What is the difference in the measures of the radii of cylinder Y and cylinder Z, in inches?
    14·2 answers
  • Can someone answer the questions pls
    9·1 answer
  • There are 108 flights from an airport, 20 of which are longer than 3 hours.
    7·1 answer
  • The dimensions of a 3-ft by 6-ft rectangle are multiplied by 1/3. How is the area affected?
    14·1 answer
  • Find the vertex f(x)=2(x+14)^2-6
    14·1 answer
  • Which equation can be used to find the measure of Arc E H G?
    12·2 answers
  • Pls can someone help me
    6·1 answer
  • During a sale, Betty found swing sets on sale for $145 that had previously cost $500. What is
    15·1 answer
  • Determine whether the set of points represent a function relationship.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!