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
mash [69]
3 years ago
14

What is the image of the point (3,2)(3,2) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin?

Mathematics
1 answer:
BARSIC [14]3 years ago
4 0

Answer: = (-2,3)

Step-by-step explanation:

  • Rotation is a transformation of a figure by rotating it for a specific angle about a fixed point.

Here, fixed point = origin = (0,0)

Transformation rule for rotation of  90^{\circ}counterclockwise about the origin:

(x,y)\to (-y,x)

Then, the image of the point (3,2) =  (-2,3)

Hence, the image of the point (3,2) after a rotation of  90^{\circ}counterclockwise about the origin = (-2,3)

You might be interested in
Factor the polynomial.<br> 8m^2 + 4m
Arisa [49]

Answer:4m(2m+1)

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was ca
Yanka [14]

Answer:

a. P(X = 0)= 0.001

b. P(X = 1)= 0.001

c. P(X=2)= 0.044

d. P(X=3)= 0.117

e. P(X=4)= 0.205

f. P(X=5)= 0.246

g. P(X=6)= 0.205

h. P(X=7)= 0.117

i. P(X=8)= 0.044

j. P(X=9)= 0.001

k. P(X=10)= 0.001

Step-by-step explanation:

Hello!

You have the variable X with binomial distribution, the probability of success is 0.5 and the sample size is n= 10 (I suppose)

If the probability of success p=0.5 then the probability of failure is q= 1 - p= 1 - 0.5 ⇒ q= 0.5

You are asked to calculate the probabilities for each observed value of the variable. In this case is a discrete variable with definition between 0 and 10.

You have two ways of solving this excersice

1) Using the formula

P(X)= \frac{n!}{(n-X)!X!} * (p)^X * (q)^{n-X}

2) Using a table of cummulative probabilities of the binomial distribution.

a. P(X = 0)

Formula:

P(X=0)= \frac{10!}{(10-0)!0!} * (0.5)^0 * (0.5)^{10-0}

P(X = 0) = 0.00097 ≅ 0.001

Using the table:

P(X = 0) = P(X ≤ 0) = 0.0010

b. P(X = 1)

Formula

P(X=1)= \frac{10!}{(10-1)!1!} * (0.5)^1 * (0.5)^{10-1}

P(X = 1) = 0.0097 ≅ 0.001

Using table:

P(X = 1) = P(X ≤ 1) - P(X ≤ 0) = 0.0107-0.0010= 0.0097 ≅ 0.001

c. P(X=2)

Formula

P(X=2)= \frac{10!}{(10-2)!2!} * (0.5)^2 * (0.5)^{10-2}

P(X = 2) = 0.0439 ≅ 0.044

Using table:

P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.0547 - 0.0107= 0.044

d. P(X = 3)

Formula

P(X = 3)= \frac{10!}{(10-3)!3!} * (0.5)^3 * (0.5)^{10-3}

P(X = 3)= 0.11718 ≅ 0.1172

Using table:

P(X = 3) = P(X ≤ 3) - P(X ≤ 2) = 0.1719 - 0.0547= 0.1172

e. P(X = 4)

Formula

P(X = 4)= \frac{10!}{(10-4)!4!} * (0.5)^4 * (0.5)^{10-4}

P(X = 4)= 0.2051

Using table:

P(X = 4) = P(X ≤ 4) - P(X ≤ 3) = 0.3770 - 0.1719= 0.2051

f. P(X = 5)

Formula

P(X = 5)= \frac{10!}{(10-5)!5!} * (0.5)^5 * (0.5)^{10-5}

P(X = 5)= 0.2461 ≅ 0.246

Using table:

P(X = 5) = P(X ≤ 5) - P(X ≤ 4) = 0.6230 - 0.3770= 0.246

g. P(X = 6)

Formula

P(X = 6)= \frac{10!}{(10-6)!6!} * (0.5)^6 * (0.5)^{10-6}

P(X = 6)= 0.2051

Using table:

P(X = 6) = P(X ≤ 6) - P(X ≤ 5) = 0.8281 - 0.6230 = 0.2051

h. P(X = 7)

Formula

P(X = 7)= \frac{10!}{(10-7)!7!} * (0.5)^7 * (0.5)^{10-7}

P(X = 7)= 0.11718 ≅ 0.1172

Using table:

P(X = 7) = P(X ≤ 7) - P(X ≤ 6) = 0.9453 - 0.8281= 0.1172

i. P(X = 8)

Formula

P(X = 8)= \frac{10!}{(10-8)!8!} * (0.5)^8 * (0.5)^{10-8}

P(X = 8)= 0.0437 ≅ 0.044

Using table:

P(X = 8) = P(X ≤ 8) - P(X ≤ 7) = 0.9893 - 0.9453= 0.044

j. P(X = 9)

Formula

P(X = 9)= \frac{10!}{(10-9)!9!} * (0.5)^9 * (0.5)^{10-9}

P(X = 9)=0.0097 ≅ 0.001

Using table:

P(X = 9) = P(X ≤ 9) - P(X ≤ 8) = 0.999 - 0.9893= 0.001

k. P(X = 10)

Formula

P(X = 10)= \frac{10!}{(10-10)!10!} * (0.5)^{10} * (0.5)^{10-10}

P(X = 10)= 0.00097 ≅ 0.001

Using table:

P(X = 10) = P(X ≤ 10) - P(X ≤ 9) = 1 - 0.9990= 0.001

Note: since 10 is the max number this variable can take, the cummulated probability until it is 1.

I hope it helps!

4 0
3 years ago
Lia, Phil, and Cam collect a total of 200.30 dollars for a holiday fundraiser. Phil collects 12.80 dollars more than Lia. Cam co
kramer

Answer:

 Lia collects $ 37.5 ,  Phil collects  $50.3  and Cam collects dollars $ 112.5 .

Step-by-step explanation:

Let us assume that the dollar collect by the Lia be x .

As given

Lia, Phil, and Cam collect a total of 200.30 dollars for a holiday fundraiser.

Phil collects 12.80 dollars more than Lia.

Phil collects dollars = 12.80 + x

As given

Cam collects 3 times as much as Lia.

Cam collects dollars = 3x

Than the equation becomes

x + 12.80 + x + 3x  = 200.30

12.80 +  5x  = 200.30

5x =  200.30 - 12.80

5x = 187.5

x = \frac{187.5}{5}

x = $ 37.5

Thus

Lia collects dollars =  $ 37.5

Phil collects dollars = 12.80 + 37.5

                                = $50.3  

Cam collects dollars = 3 × 37.5

                                  = $ 112.5

Therefore the  Lia collects $ 37.5 ,  Phil collects  $50.3  and Cam collects dollars $ 112.5 .

5 0
3 years ago
The marked price of
Tju [1.3M]

Answer:

MP =  Rs. 1500

SP =  Rs. 1230

Step-by-step explanation:

Let the Cost Price (CP) be x

<u>Then Market Price (MP):</u>

  • MP = x+ 20% = 1.2x

<u>Discounted Selling Price (SP):</u>

  • SP = MP - 18% = 0.82*1.2x = 0.984x

<u>Since the difference between CP and SP is Rs.20:</u>

  • x - 0.984x = 20
  • 0.016x = 20
  • x= 20/0.016
  • x = 1250

<u>Then:</u>

  • MP = 1.2*1250= Rs. 1500

and

  • SP = 1500*0.82 = Rs. 1230

3 0
3 years ago
Help, what are the next three numbers??
artcher [175]

Answer:

1.3, 1.6, 1.9

Step-by-step explanation:

Add .3 each time

8 0
3 years ago
Read 2 more answers
Other questions:
  • two vertices of an isosceles triangle in the coordinate plane have coordinates (0,0) and (2a,0). Where might the third vertex be
    5·1 answer
  • A water bottle holds a volume of 2 cups. Is the volume of 5 water bottles greater than 4 pints?
    12·2 answers
  • Use a model to divide. 1/2÷3​
    9·1 answer
  • Find the total surface area.<br> 8 km<br> 4 km<br> 3.9 km<br> 2 km<br> 8 km
    11·1 answer
  • Determine the following product: 2a(4a^3-3a-1)
    8·1 answer
  • The value of x is the same for both equations below. Solve for x.<br> x+3=6 and 6×=18
    15·1 answer
  • A student pulls a rope with a force of 20 N to the left. Another student pulls on the
    8·1 answer
  • Please help me, I need to have this answered by tomorrow at the latest and I'm lost.
    10·1 answer
  • Enter the solutions from least to greatest. H (x)=(-4x -3)(x -3)h(x)=(−4x−3)(x−3)h, left parenthesis, x, right parenthesis, equa
    5·1 answer
  • Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pen
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!