Use the method of completing the square to transform the quadratic equation into the equation form (x + p)^2 = q. 6+12x+3x^2=0

The Patterson family has 3 kids, 1 boy and 2 girls. Suppose that for each birth, the probability of a boy birth is 1/2, and the

elena-14-01-66 [18.8K]

Answer:

$Probability = \frac{1}{8}$

Step-by-step explanation:

Given

Represent Boys with B and Girls with G

$P(B) = \frac{1}{2}$

$P(G) = \frac{1}{2}$

Required

Find the probability or having 1 boy 2 girls

Since the order is not important, the probability is calculated as follows;

$Probability = P(B) * P(G) * P(G)$

Substitute $\frac{1}{2}$ for P(B) and P(G)

$Probability = \frac{1}{2} * \frac{1}{2} * \frac{1}{2}$

$Probability = \frac{1 * 1 * 1}{2 * 2 *2}$

$Probability = \frac{1}{8}$

<em>Hence, the fractional probability is </em> $\frac{1}{8}$ <em></em>

7 0

3 years ago

Which of the following pairs of numbers contains like fractions? A. 5⁄6 and 10⁄12 B. 3⁄2 and 2⁄3 C. 3 1⁄2 and 4 4⁄4 D. 6⁄7 and 1

ElenaW [278]

<h2>Hello!</h2>

The answers are:

A.

$\frac{5}{6}$ and $\frac{10}{12}$

D.

$\frac{6}{7}$ and $1\frac{5}{7}$

To find which of the following pairs of numbers contains like fractions, we must remember that like fractions are the fractions that share the same denominator.

We are given two fractions that are like fractions. Those fractions are:

Option A.

$\frac{5}{6}$ and $\frac{10}{12}$

We have that:

$\frac{10}{12}=\frac{5}{6}$

So, we have that the pairs of numbers

$\frac{5}{6}$

and

$\frac{5}{6}$

Share the same denominator, which is equal to 6, so, the pairs of numbers contains like fractions.

Option D.

$\frac{6}{7}$ and $1\frac{5}{7}$

We have that:

$1\frac{5}{7}=1+\frac{5}{7}=\frac{7+5}{7}=\frac{12}{7}$

So, we have that the pair of numbers

$\frac{6}{7}$

and

$\frac{12}{7}$

Share the same denominator, which is equal to 7, so, the pairs of numbers constains like fractions.

Also, we have that the other given options are not like fractions since both pairs of numbers do not share the same denominator.

The other options are:

$\frac{3}{2},\frac{2}{3}$

and

$3\frac{1}{2},4\frac{4}{4}$

We can see that both pairs of numbers do not share the same denominator so, they do not contain like fractions.

Hence, the answers are:

A.

$\frac{5}{6}$ and $\frac{10}{12}$

D.

$\frac{6}{7}$ and $1\frac{5}{7}$

Have a nice day!

3 0

3 years ago

The perimeter of this kite is 108 cm.

taurus [48]

Answer:

n is equal to 26

Step-by-step explanation:

Equation: n+ n + (n+2) +(n+2) = 108

so: 2n + 2(n+2) = 108

2n + 2n + 4 = 108

4n + 4 = 108

4n = 108 - 4

4n = 104

n = 104/4

n = 26

6 0

2 years ago

Solve for n -3n-5=16

Nezavi [6.7K]

Answer:

n = -7

Step-by-step explanation:

Solve for n:

-3 n - 5 = 16

Hint: | Isolate terms with n to the left-hand side.

Add 5 to both sides:

(5 - 5) - 3 n = 5 + 16

Hint: | Look for the difference of two identical terms.

5 - 5 = 0:

-3 n = 16 + 5

Hint: | Evaluate 16 + 5.

16 + 5 = 21:

-3 n = 21

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 n = 21 by -3:

(-3 n)/(-3) = 21/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

n = 21/(-3)

Hint: | Reduce 21/(-3) to lowest terms. Start by finding the GCD of 21 and -3.

The gcd of 21 and -3 is 3, so 21/(-3) = (3×7)/(3 (-1)) = 3/3×7/(-1) = 7/(-1):

n = 7/(-1)

Hint: | Simplify the sign of 7/(-1).

Multiply numerator and denominator of 7/(-1) by -1:

Answer: n = -7

7 0

3 years ago

Read 2 more answers

A helicopter leaves bristol and flies due east for 10 miles.Then the helicopter flies 8miles north before landing. What is the d

DedPeter [7]

Answer:

The distance of the helicopter from the bristol is approximately 1<u>2.81 miles</u>

Step-by-step explanation:

Given:

Helicopter flies 10 miles east of bristol.

Then the helicopter flies 8 miles North before landing.

To find the direct distance between the helicopter and bristol.

Solution:

In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter

The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.

On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.

Applying Pythagorean theorem to find the hypotenuse of the triangle.

$Hypotenuse^2=Short\ leg^2+Shortest\ leg^2$

$Hypotenuse^2=10^2+8^2$

$Hypotenuse^2=100+64\\Hypotenuse^2=164$

Taking square root both sides.

$\sqrt{Hyptenuse^2}=\sqrt{164}\\Hypotenuse = 12.81\ miles$

Thus, the distance of the helicopter from the bristol is approximately 12.81 miles

6 0

3 years ago