Math / Data & Statistics

QuestionThe central angle of sector $U$ is $90^{\circ}$ . What is the probability that the spinner lands on $U$ ?
Simplify your answer and write it as a proper fraction.

Studdy Solution

STEP 1

1. The spinner is divided into four equal sectors.
2. Each sector has a central angle of $90^\circ$ .
3. The total angle in a circle is $360^\circ$ .
4. The probability of the spinner landing on a sector is proportional to the central angle of that sector.

STEP 2

1. Determine the total angle of the circle.
2. Calculate the fraction of the circle represented by sector $U$ .
3. Simplify the fraction to find the probability.

STEP 3

The total angle of a circle is:
$360^\circ$

STEP 4

The central angle of sector $U$ is $90^\circ$ . The fraction of the circle that sector $U$ represents is:
$\frac{90^\circ}{360^\circ}$

STEP 5

Simplify the fraction:
$\frac{90}{360} = \frac{1}{4}$
The probability that the spinner lands on sector $U$ is:
$\boxed{\frac{1}{4}}$

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QuestionThe central angle of sector $U$ is $90^{\circ}$ . What is the probability that the spinner lands on $U$ ?
Simplify your answer and write it as a proper fraction.

Studdy Solution

STEP 1

1. The spinner is divided into four equal sectors.
2. Each sector has a central angle of $90^\circ$ .
3. The total angle in a circle is $360^\circ$ .
4. The probability of the spinner landing on a sector is proportional to the central angle of that sector.

STEP 2

1. Determine the total angle of the circle.
2. Calculate the fraction of the circle represented by sector $U$ .
3. Simplify the fraction to find the probability.

STEP 3

The total angle of a circle is:
$360^\circ$

STEP 4

The central angle of sector $U$ is $90^\circ$ . The fraction of the circle that sector $U$ represents is:
$\frac{90^\circ}{360^\circ}$

STEP 5

Simplify the fraction:
$\frac{90}{360} = \frac{1}{4}$
The probability that the spinner lands on sector $U$ is:
$\boxed{\frac{1}{4}}$

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QuestionThe central angle of sector UUU is 90∘90^{\circ}90∘. What is the probability that the spinner lands on UUU ?Simplify your answer and write it as a proper fraction.

Studdy Solution

STEP 1

1. The spinner is divided into four equal sectors.2. Each sector has a central angle of 90∘90^\circ90∘.3. The total angle in a circle is 360∘360^\circ360∘.4. The probability of the spinner landing on a sector is proportional to the central angle of that sector.

STEP 2

1. Determine the total angle of the circle.2. Calculate the fraction of the circle represented by sector UUU.3. Simplify the fraction to find the probability.

STEP 3

The total angle of a circle is:360∘ 360^\circ 360∘

STEP 4

The central angle of sector UUU is 90∘90^\circ90∘. The fraction of the circle that sector UUU represents is:90∘360∘ \frac{90^\circ}{360^\circ} 360∘90∘​

STEP 5

Simplify the fraction:90360=14 \frac{90}{360} = \frac{1}{4} 36090​=41​ The probability that the spinner lands on sector UUU is:14 \boxed{\frac{1}{4}} 41​​

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionThe central angle of sector $U$ is $90^{\circ}$ . What is the probability that the spinner lands on $U$ ?
Simplify your answer and write it as a proper fraction.

1. The spinner is divided into four equal sectors.
2. Each sector has a central angle of $90^\circ$ .
3. The total angle in a circle is $360^\circ$ .
4. The probability of the spinner landing on a sector is proportional to the central angle of that sector.

1. Determine the total angle of the circle.
2. Calculate the fraction of the circle represented by sector $U$ .
3. Simplify the fraction to find the probability.

The total angle of a circle is:
$360^\circ$

The central angle of sector $U$ is $90^\circ$ . The fraction of the circle that sector $U$ represents is:
$\frac{90^\circ}{360^\circ}$

Simplify the fraction:
$\frac{90}{360} = \frac{1}{4}$
The probability that the spinner lands on sector $U$ is:
$\boxed{\frac{1}{4}}$