5, 6 5/12, 6.45, 11/2 from least to greatest

Please help with this

ivolga24 [154]

the value of x is 50 because the degrees of a triangle will always be 180 degrees

3 0

4 years ago

How to factor 6n2 - 6n - 12

alexandr402 [8]

We see that in these 3 terms, 6 is a common factor. So, let's factor out a 6:

$6n^2-6n-12 = 6(n^2-n-2)$

We can set this equal to 0 and factor by using the quadratic formula which is:

$x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

So, let's do just that:

$6(n^2-n-2) = 0$

Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:

$\frac{1 \pm \sqrt{(-1)^2-4(1)(-2)} }{2(1)} = \frac{-1 \pm \sqrt{1-(-8)} }{2}$

$\frac{-1 \pm \sqrt{9} }{2} = {1, -2}$

So, we can write this as:

$6n^2 - 6n - 12 = 6(n-1)(n+2)$

Notice that the 6 comes back because it was only temporarily mad. And that the roots have opposite signs in the parentheses because to find the roots, you need to set each parentheses equal to 0 and solve for n. With that in mind, your final answer is 6(n-1)(n+2). Hope I could help you!

7 0

3 years ago

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

k0ka [10]

Part A:

From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.

Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

$standard \ deviation= \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{30}} = \frac{0.4}{5.477} =0.073$

Part C:

The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

$P(X\ \textgreater \ x)=1-P(X\ \textless \ x) \\ \\ =1-P\left(z\ \textless \ \frac{x-\mu}{\sigma/\sqrt{n}} \right)$

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that <span>the average number of moths in 30 traps is greater than 0.7</span> given by:

$P(X\ \textgreater \ 0.7)=1-P(X\ \textless \ 0.7) \\ \\ =1-P\left(z\ \textless \ \frac{0.7-0.6}{0.073} \right)=1-P(z\ \textless \ 1.369) \\ \\ =1-0.91455=\bold{0.0855}$

7 0

4 years ago

Jada’s teacher ask her to write a three-digit number that uses the digit 4 once and the digit 7 twice. The value of one 7 needs

viva [34]

477

The value of the first 7 from the left is 70.

If you divide 70 by 10, you get the value of the second seven, 7.

Another way to know this is equivalent fractions:

1/10 = 7/10

10 X 7 = 70
1 X 7 = 7

6 0

4 years ago

Suppose given an isosceles triangle with a leg measuring 5 in. Two lines are drawn through some point on the base, each parallel

enot [183]

We have an isosceles triangle and 2 lines that are drawn through some ( any ) point on the base. The both lines are parallel to one of the legs. Then those lines with the legs of the triangle make a parallelogram. We can say that x and y are the sides of the parallelogram. Then: x + y = 5 in. And the perimeter of the parallelogram: P = 2 x + 2 y = 2 * ( x + y ).
P = 2 * 5 = 10 in. The rest is in the attachment.
Answer: The perimeter of the constructed parallelogram is 10 inches.

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5 0

4 years ago