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Gnoma [55]
3 years ago
14

Prime factor 4x^2-81=0

Mathematics
1 answer:
rusak2 [61]3 years ago
8 0
Either one of these <span><span> x = 9/2 = 4.500
</span><span> x = -9/2 = -4.500
</span></span>
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4 0
3 years ago
A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. Whis is the next term in
podryga [215]
We are told that f(1) = -1.5, and that f(n+1) = -2f(n).
                                                 Then: f(2) = -2f(1) = -2(-1.5) = +3 (answer)

3 0
3 years ago
X+y=11 and 22X+15y=228
Lady_Fox [76]
X+y=11
22x+15y=228

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22x+165-15x=228
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7x=63
x=9

9+y=11
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The solution to the system of equations is (9,2)
6 0
3 years ago
11. Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x) 5 5 0 x , 0
NISA [10]

Question not properly presented

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x)

0 ------ x<0

x²/25 ---- 0 ≤ x ≤ 5

1 ----- 5 ≤ x

Use the cdf to obtain the following.

(a) Calculate P(X ≤ 4).

(b) Calculate P(3.5 ≤ X ≤ 4).

(c) Calculate P(X > 4.5)

(d) What is the median checkout duration, μ?

e. Obtain the density function f (x).

f. Calculate E(X).

Answer:

a. P(X ≤ 4) = 16/25

b. P(3.5 ≤ X ≤ 4) = 3.75/25

c. P(4.5 ≤ X ≤ 5) = 4.75/25

d. μ = 3.5

e. f(x) = 2x/25 for 0≤x≤2/5

f. E(x) = 16/9375

Step-by-step explanation:

a. Calculate P(X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(X ≤ 4) = F(x) {0,4}

P(X ≤ 4) = x²/25 {0,4}

P(X ≤ 4) = 4²/25

P(X ≤ 4) = 16/25

b. Calculate P(3.5 ≤ X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(3.5 ≤ X ≤ 4) = F(x) {3.5,4}

P(3.5 ≤ X ≤ 4) = x²/25 {3.5,4}

P(3.5 ≤ X ≤ 4) = 4²/25 - 3.5²/25

P(3.5 ≤ X ≤ 4) = 16/25 - 12.25/25

P(3.5 ≤ X ≤ 4) = 3.75/25

(c) Calculate P(X > 4.5).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(4.5 ≤ X ≤ 5) = F(x) {4.5,5}

P(4.5 ≤ X ≤ 5) = x²/25 {4.5,5}

P(4.5 ≤ X ≤ 5)) = 5²/25 - 4.5²/25

P(4.5 ≤ X ≤ 5) = 25/25 - 20.25/25

P(4.5 ≤ X ≤ 5) = 4.75/25

(d) What is the median checkout duration, μ?

Median is calculated as follows;

∫f(x) dx {-∝,μ} = ½

This implies

F(x) {-∝,μ} = ½

where F(x) = x²/25 for 0 ≤ x ≤ 5

F(x) {-∝,μ} = ½ becomes

x²/25 {0,μ} = ½

μ² = ½ * 25

μ² = 12.5

μ = √12.5

μ = 3.5

e. Calculating density function f (x).

If F(x) = ∫f(x) dx

Then f(x) = d/dx (F(x))

where F(x) = x²/25 for 0 ≤ x ≤ 5

f(x) = d/dx(x²/25)

f(x) = 2x/25

When

F(x) = 0, f(x) = 2(0)/25 = 0

When

F(x) = 5, f(x) = 2(5)/25 = 2/5

f(x) = 2x/25 for 0≤x≤2/5

f. Calculating E(X).

E(x) = ∫xf(x) dx, 0,2/5

E(x) = ∫x * 2x/25 dx, 0,2/5

E(x) = 2∫x ²/25 dx, 0,2/5

E(x) = 2x³/75 , 0,2/5

E(x) = 2(2/5)³/75

E(x) = 16/9375

4 0
3 years ago
Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12
Inessa05 [86]

Answer:

The solution of the equations are -6 and 1

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- We want to find the solution of the equation (x + 2) (x + 3) = 12

- <em>At first lets use the Foil method to multiply the two brackets</em>

 (x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)

 (x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term

 (x + 2) (x + 3) = x² + 5x + 6

∵ (x + 2) (x + 3) = 12

∴ x² + 5x + 6 = 12

- Subtract 12 from both sides

∴ x² + 5x - 6 = 0

- <em>Factorize the left hand side</em>

∵ x² = (x)(x)

∵ -6 = 6 × -1

∵ 6x + -1x = 5x

∴ (x + 6)(x - 1) = 0

- <em>Lets use the zero product property </em>

∵ (x + 6)(x - 1) = 0

∴ x + 6 = 0 ⇒ <em>OR</em> ⇒ x - 1 = 0

∵ x + 6 = 0

- Subtract 6 from both sides

∴ x = -6

∵ x - 1 = 0

- Add 1 to both sides

∴ x = 1

∴ The solution of the equations are -6 and 1

6 0
3 years ago
Read 2 more answers
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