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3 years ago

Solve this quadratic equation by completing the square. x^2+4x=15

Mathematics

1 answer:

AlekseyPX3 years ago

7 0

Answer:

x = -2 ±sqrt( 19)

Step-by-step explanation:

x^2 + 4x = 15

Take the coefficient of x

Divide by 2

4/2 =2

Square it

2^2 = 4

Add it to each side

x^2 + 4x+4 = 15+4

(x+2)^2 = 19

Take the square root of each side

sqrt( (x+2)^2) =±sqrt( 19)

x+2 = ±sqrt( 19)

Subtract 2 from each side

x+2-2 = -2 ±sqrt( 19)

x = -2 ±sqrt( 19)

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3 years ago

The school fair committee needs enough pizzas for 275 people. Each pizza has 8 slices. How many pizzas does the committee need t

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Step-by-step explanation:

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3 years ago

Consider a binomial experiment with n = 10 and p = 0.10. (a) Compute f(0). If required, round your answer to four decimal places

ss7ja [257]

Answer:

(a) The value of f (0) is 0.3487.

(b) The value of f (2) is 0.1937.

(d) The value of P (X ≥ 1) is 0.6513.

(e) The value of E (X) is 1.

(f) The value of V (X) is 0.9 and σ is 0.9487.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameter n = 10 and p = 0.10.

The probability mass function of X is:

$P(X=x)={10\choose x}0.10^{x}(1-0.10)^{10-x};\ x=0,1,2,3...$

(a)

Compute the value of f (0) as follows:

f (0) = P (X = 0)

$={10\choose 0}0.10^{0}(1-0.10)^{10-0}\\=1\times 1\times 0.348678\\=0.348678\\\approx0.3487$

Thus, the value of f (0) is 0.3487.

(b)

Compute the value of f (2) as follows:

f (2) = P (X = 2)

$={10\choose 2}0.10^{2}(1-0.10)^{10-2}\\=45\times 0.01\times 0.43047\\=0.1937115\\\approx0.1937$

Thus, the value of f (2) is 0.1937.

(c)

Compute the value of P (X ≤ 2) as follows:

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

$=\sum\limits^{0}_{2} {{10\choose x}0.10^{x}(1-0.10)^{10-x}}\\=0.3487+0.3874+0.1937\\=0.9298$

Thus, the value of P (X ≤ 2) is 0.9298.

(d)

Compute the value of P (X ≥ 1) as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

= 1 - 0.3487

= 0.6513

Thus, the value of P (X ≥ 1) is 0.6513.

(e)

Compute the expected value of X as follows:

$E(X)=n\times p$

$=10\times 0.10\\=1$

Thus, the value of E (X) is 1.

(f)

Compute the variance of X as follows:

$V(X)=np(1-p)$

$=10\times 0.10\times (1-0.10)\\=0.90$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{V(X)}$

$=\sqrt{0.90}\\=0.94868\\\approx0.9487$

Thus, the value of V (X) is 0.9 and σ is 0.9487.

8 0

4 years ago

Convert 920 centimeters to meters. help

bixtya [17]

9.2 m

Because 1 cm = 0.01 m

So 920 x 0.01 = 9.2

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3 years ago

Read 2 more answers

Would appreciate help with an explanation

frosja888 [35]

The Answer Is AB=20.25

27/16=x/12

x=20.25

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3 years ago