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
Ludmilka [50]
3 years ago
7

An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the minor arc that is in

tercepted by the knife measures 120 degrees, find the length of the diameter of the plate. Round your final answer to two decimal places.
Mathematics
1 answer:
ankoles [38]3 years ago
7 0

The diameter of the plate is 9.24 inches

Step-by-step explanation:

Let us consider the radius to be 'r'

Angle = 120°

Chord length = 8 inches

Chord length = 2rsin(θ/2)

8 = 2r sin(120/2)

8 = 2r sin60°

8/2 = r (√3/2)

4/(√3/2) = r

r = 8/√3

r = 8/1.73

r = 4.62 inches

Diameter of the plate = 2(4.62)

= 9.24 inches

The diameter of the plate is 9.24 inches

You might be interested in
The Coast Starlight Amtrak train runs from Seattle to Los Angeles. The mean travel time from one stop to the next on the Coast S
Goshia [24]

Solution :

a).

Given :

R = 0.636, $S_x = 99$, $S_y=113, M_x=108, M_y=129$

Here R = correlation between the two variables

        $S_x , S_y$ =  sample standard deviations of the distance and travel time between the two train stops, respectively.

      $M_x, M_y$ = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, b_1  $=R \times \left(\frac{S_y}{S_x}\right)$

                            $=0.636 \times \left(\frac{113}{99}\right)$

                            = 0.726

Therefore, the slope of the regression line b_1 is 0.726

The equation of the regression line is given by :

$\overline {y} = b_0+b_1 \overline x$

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line $b_0$ is given by :

$b_0=M_y-(b_1 \times M_x)$

  = 129 - (0.726 x 108)

  = 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b).\text{ The slope of the line predicts that it will require 0.726 minutes} for each additional mile travelled.

The intercept of the line, $b_0$ = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because  it seems we have travelled zero  distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). $R^2=0.404$

This means that the model accounts for around 40.4% variation in the travel time.

3 0
3 years ago
Assume that lines that appear to be tangent are tangent. O is the center of the circle. In degrees, what is the value of x?
Nastasia [14]

9514 1404 393

Answer:

  145

Step-by-step explanation:

In this geometry, the central angle (x°) and the external angle (35°) are supplementary.

  x° = 180° -35°

  x = 145

4 0
2 years ago
A. 4<br> b. 5<br> c. 9<br> d. 25
trapecia [35]
5t=45
45/5=9

The answer is C
Hope I helped
7 0
3 years ago
Determine if the statement is always, sometimes or never true. Equilateral triangles are isosceles triangles.
tia_tia [17]
Never .. isoscels is unequal. I'm pretty sure
7 0
3 years ago
Which is NOT a right triangle
Ira Lisetskai [31]

Answer:f i’m pretty sure

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • Draymond green averaged 5.1 field goal shot attempts per game. Stephen curry averaged 10.2 field goal shot attempts per game. Ho
    5·1 answer
  • What the Answer please?
    11·1 answer
  • Solve x3 = 125 over 27
    12·2 answers
  • Charlotte earns $1,595 per month at her job. She will receive a 7% raise. How much more money will Charlotte earn each year afte
    14·2 answers
  • A taxi cab charges $0.55 per mile in addition to a $1.75 flat rate fee. Susie has $10 to spend on a taxi cab ride. The taxi driv
    5·2 answers
  • The scale of a drawing is 1 in.:4ft. Find the drawing length that would be used to represent an actual length of 24ft.
    12·1 answer
  • Factor completely: 5x^2-11x+6
    6·1 answer
  • (2x + 3y - 4) – (5x + 2)​
    15·1 answer
  • Someone help me with this, it’s due today
    12·2 answers
  • Miguel made $286 for 13 hours of work.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!