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
kotykmax [81]
3 years ago
15

What is the measure of θ in radians? Enter an exact expression.

Mathematics
1 answer:
Sonja [21]3 years ago
4 0

Answer:

The answer is \frac{7\pi }{6}

Step-by-step explanation:

Just did this problem

You might be interested in
When an automobile is stopped with a roving safety patrol,each tire is checked for tire wear, and each headlight is checkedto se
ryzh [129]

Answer:

a) Joint ptobability distribution

\begin{pmatrix}  &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}

b) P(X<= 1 and Y <= 1) = P(X<= 1) * P(Y<=1) = 0.56

c) P(X + Y = 0)=0.3

d) P(X + Y <= 1)=0.53

Step-by-step explanation:

We have to construct the joint probability table with the marginal probabilities of X and Y.

X can take values from 0 to 2, and Y can take values from 0 to 4.

We can calculate each point of the joint probability as:

P(x,y)=P_x(x)*P_y(y)

Then, the joint probabilities are:

X=0 Y=0 Px=0.5 Px=0.6 P(0,0)=0.3

X=0 Y=1 Px=0.5 Px=0.1 P(0,1)=0.05

X=0 Y=2 Px=0.5 Px=0.05 P(0,2)=0.025

X=0 Y=3 Px=0.5 Px=0.05 P(0,3)=0.025

X=0 Y=4 Px=0.5 Px=0.2 P(0,4)=0.1

X=1 Y=0 Px=0.3 Px=0.6 P(1,0)=0.18

X=1 Y=1 Px=0.3 Px=0.1 P(1,1)=0.03

X=1 Y=2 Px=0.3 Px=0.05 P(1,2)=0.015

X=1 Y=3 Px=0.3 Px=0.05 P(1,3)=0.015

X=1 Y=4 Px=0.3 Px=0.2 P(1,4)=0.06

X=2 Y=0 Px=0.2 Px=0.6 P(2,0)=0.12

X=2 Y=1 Px=0.2 Px=0.1 P(2,1)=0.02

X=2 Y=2 Px=0.2 Px=0.05 P(2,2)=0.01

X=2 Y=3 Px=0.2 Px=0.05 P(2,3)=0.01

X=2 Y=4 Px=0.2 Px=0.2 P(2,4)=0.04

We can write it in the form of a matrix:

\begin{pmatrix}  &Y=0&Y=1&Y=2&Y=3&Y=4\\X=0&0.3&0.05&0.025&0.025&0.1\\ X=1&0.18&0.03&0.015&0.015&0.06 \\ X=2&0.12&0.02&0.01&0.01&0.04\end{pmatrix}

b) From the joint probability P(X<= 1 and Y <= 1) is equal to

P(X\leq 1 \& Y \leq 1)=P(0,0)+P(0,1)+P(1,0)+P(1,1)\\\\P(X\leq 1 \& Y \leq 1)=0.3+0.05+0.18+0.03=0.56

We can calculate P(X<= 1) * P(Y<=1)

P_x(X\leq 1)=P_x(0)+P_x(1)=0.5+0.3=0.8\\\\P_y(Y\leq1)=P_y(0)+P_y(1)=0.6+0.1=0.7\\\\P_x(X\leq1)*P_y(Y\leq1)=0.8*0.7=0.56

Both calculations give the same result.

c) Probability of no violations

P(X+Y=0)=P(0,0)=0.3

d) P(X + Y <= 1)

P(X+Y \leq 1)=P(0,0)+P(0,1)+P(1,0)\\\\P(X+Y \leq 1)=0.3+0.05+0.18=0.53

5 0
3 years ago
50 POINTS!
Furkat [3]

Answer:

1.

a) 357 inches³ of water more would be required to fill the tank

b) Riley is not correct, the volume of the larger aquarium is 27

   times larger than the volume of the smaller on

c) Riley is not correct, the surface area of the larger aquarium is 9

   times the surface area of the smaller one

2.

a) There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) The surface area of the shipping box is 567 inches²

Step-by-step explanation:

1.

a) * Lets study the first aquarium:

- The formula for volume is V = l × w × h

∴ It is a rectangular box of dimensions 16 in , 8.5 in , 10.5 in

∴ Its volume = 16 × 8.5 × 10.5 = 1428 inches³

* The full capacity of this aquarium is 1428 inches³

- Riley noticed that it 3/4 full of water, then still can fill with

 1/4 to be full

- Why 1/4 because 1 - 3/4 = 1/4

∴ The volume of 1/4 the aquarium = 1/4 × 1428 = 357 inches³

* There are 357 inches³ of water more would be required to fill the tank

b) * Lets talk about the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their volumes will be (3 : 1)³

- Because we will multiply each dimension by 3 and they

  are 3 dimensions, that means 3 × 3 × 3 ⇒ 3³

∴ The ratio between their volumes = 27 : 1

∴ Riley is not correct because the volume of the larger aquarium is 27

   times larger than the volume of the smaller aquarium

c) * Similar for the surface area of the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their surface area will be (3 : 1)²

- Because we will multiply each dimension by 3 and to get the

 surface area we multiply each two dimensions for the six faces

 and then add them

∴ The ratio between their surface area = 9 : 1

∴ Riley is not correct because the surface area of the larger aquarium

  is 9 times larger than the surface area of the smaller aquarium

2.

a) * Lets think about this situation

- We want to fill some office supplies boxes of side length

 4.5 inches inside the shipping box of dimensions 18 in , 9 in , 4.5 in

- That means the volume of the shipping box is how many times

 the volume of the office supplies box

∴ The number of office supplies boxes = the volume of shipping box ÷ the volume of the office supplies box

∵ the volume of shipping box = 18 × 9 × 4.5 = 729 inches³

∵ the volume of the office supplies box = 4.5 × 4.5 × 4.5 = 91.125 inches³

∴ The number of office supplies boxes = 729 ÷ 91.125 = 8 boxes

* There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) Look to the Net of the shipping box

- The net has 6 faces shaped rectangles

- Each two faces are congruent

- To find the surface area we will add all the areas of the 6 faces

- Two faces with dimensions 18 in and 9 in

∴ Their areas = 2 (18 × 9) = 324 inches²

- Two faces with dimensions 18 in and 4.5 in

∴ Their areas = 2 (18 × 4.5) = 162 inches²

- Two faces with dimensions 4.5 in and 9 in

∴ Their areas = 2 (4.5 × 9) = 81 inches²

∴ The total surface area = 324 + 162 + 81 = 567 inches²

* The surface area of the shipping box is 567 inches²

3 0
3 years ago
What is the equation of the line that passes through the point (-6,-8) and has a slope of 1/3​
Arturiano [62]

y + 8 = 1/3 (x+6)

With the given information, we can use the point-slope formula, , to write the equation of the line. Substitute values for the  , , and  in the formula to do so.

The  represents the slope, so substitute  in its place. The  and  represent the x and y values of one point the line intersects, so substitute -6 for  and -8 for . This gives the following answer and equation (just make sure to convert the double negatives into positives:  

8 0
2 years ago
There are six nickels and seven dimes in your pocket. Five of the nickels and three of the dimes are Canadian. The others are US
ira [324]
B!



hope this helps, it just seems like the best answe.
7 0
3 years ago
Which list correctly orders A,B and C from least to greatest when A=-8,B= |-6|, and C=|11|
stiks02 [169]

Answer: it is A, b, c

just did the exam

3 0
3 years ago
Read 2 more answers
Other questions:
  • Please help me <br> I have to solve the triangle with the law of sines
    5·2 answers
  • If John has 69 apples and eats 66 apples how many does he have left?
    10·1 answer
  • What is the volume of a cylinder with a radius of 7 and the height of 9​
    7·2 answers
  • Please help me! Thank you! I only need help with a)
    10·1 answer
  • (98 - 78) x 11 juhjjgghjnbhjhbjnbjmjjhjhjh
    15·2 answers
  • Quadratic function question<br>​
    10·1 answer
  • Solve. Chanasia has 6.25 gallons of paint. She wants to use 2/5 of the paint to paint her living room. How many gallons of paint
    13·1 answer
  • A quantity with an initial value of 510 decays exponentially at a rate of 0.05% every 7
    11·1 answer
  • Pls help i’m on the verge of tears
    13·1 answer
  • Directions: Simplify the following monomials (if possible).
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!