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DanielleElmas [232]
3 years ago
12

Enter what that means? Help someone.

Mathematics
1 answer:
Luda [366]3 years ago
7 0

\frac{x^2}{3} is the same as \frac{1}{3}x^2

Dividing by 3 is the same as multiplying by the fraction 1/3

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What is the solution set of (x - 2)(x - 3) = 2?
Deffense [45]

Answer:

X = 4, 1

Step-by-step explanation:

Multiplying out

X^2 - 2x - 3x +6 = 2

X^2 - 5x +4 = 0

Factoring:

X^2 - 4x - X +4

X(x-4) - 1(x-4)

(x-1)(x-4)=0

X= 1, 4

8 0
2 years ago
The function f is defined by f(x)=5x+k, where k is a constant. Find k, if the value of f at x=2 is equal to 14.
yKpoI14uk [10]

Answer:

k = 4

Step-by-step explanation:

f(x)=5x+k

Let x =2

f(2) = 5*2 +k

f(2) = 10+k

We know f(2) = 14

14 = 10+k

Subtract 10 from each side

14-10 = 10+k-10

4 =k

4 0
3 years ago
Read 2 more answers
What is the area of the polygon shown below? (in the image). A. 322 mm^2 B. 364 mm^2 C. 520 mm^2 D. 584 mm^2 Show all work pleas
GalinKa [24]

Answer:

A. 322 mm^2

Step-by-step explanation:

First split the shape into two (a rectangle and a triangle).

Then calculate the area of those shapes.

Rectangle: 20 x 14 =  280 mm^2

Triangle: 6 x 14 / 2 = 42 mm^2

Add them together.

280 + 42 = 322 mm^2

3 0
3 years ago
Read 2 more answers
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let
vladimir1956 [14]

Answer:

a) P(X ≤ 2) = 0.87

b)  P(X ≥ 5) = 0.01

c) P(1 ≤ X ≤ 4) = 0.71

d) P ( X = 0 ) = 0.28

e) σ(X) = 1.09 , E(X) = 1.25

Step-by-step explanation:

Given:

- Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.05)

Where, n = 25 and p = 0.05

Find:

(a) Determine P(X ≤ 2).(b) Determine P(X ≥ 5).(c) Determine P(1 ≤ X ≤ 4).(d) What is the probability that none of the 25 boards is defective?(e) Calculate the expected value and standard deviation of X.

Solution:

- The probability mass function for a binomial distribution is given by:

                         P ( X = x ) = nCr * (p)^r * ( 1 - p )^(n-r)

a) P(X ≤ 2):

                         P(X ≤ 2) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 )

                         = (0.95)^25 + 25*0.05*0.95^24 + 25C2*0.05^2*0.95^23

                         = 0.87

b) P(X ≥ 5):

            P(X ≥ 5) = 1 - [P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

            = 1 - [ 0.87 + 25C3*0.05^3*0.95^22 + 25C4*0.05^4*0.95^21]

            = 1 - 0.98994

            = 0.01

c) P(1 ≤ X ≤ 4):

            P(1 ≤ X ≤ 4) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

            = ( 0.87 - 0.95^25) + 0.11994

           = 0.71

d) P( X = 0 )

            P ( X = 0 ) = 0.95^25 = 0.28

e) E(X) & σ(X):

            E(X) = n*p

            E(X) = 25*0.05 = 1.25

            σ(X) = sqrt ( Var (X) )

            σ(X) = sqrt ( n*p*(1-p) ) = sqrt ( 25*0.05*0.95 )

            σ(X) = 1.09

4 0
2 years ago
Laura is three times as old as Luci. In 5 years, the sum of their ages will be 30. What are the current ages of Laura and Luci?
Inga [223]
Firstly you would do 30 - 10 = 20, so their ages combined is 20, Laura has to be 15, and Luci has to be 5.

Second, 4 years ago, Peter was 15 and Sylvia was 5, and also in 5 years Sylvia will be 14 and Peter will be 24.

Hope this helps.
7 0
3 years ago
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