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3 years ago

Factor 7y^2-21y^3 completely

1 answer:

8 0

Well you can take out a 7 and y^2 since both have it.
-3y should be your answer because you got rid of 7y^2 and then you have to divide -21/7 to get -3. Also if you take y^2 from y^3 you are left with just a "y".

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Chris is building a model out of wire. He has a length of wire that measures 9/10 of a yard. If he cuts it into 5 equal parts, t

bazaltina [42]

$\displaystyle\\\frac{9}{10}~~\text{of a yard}~~=\frac{9}{10}~\text{yards}\\\\\frac{1}{5}~\text{from}~\frac{9}{10}~\text{yards}=\frac{1}{5}\times\frac{9}{10}=\frac{9}{50}~\text{yards each piece}$

3 0

3 years ago

4 more than one third of a number n is 6. An equation is? The solution is n =?

harkovskaia [24]

Answer:

$\frac{1}{3}$ n + 4 = 6

Step-by-step explanation:

Given problem:

4 more than one third of a number n is 6

Unknown:

The equation = ?

Solution of the number = ?

Solution:

let the number = n

So, 4 more than one third of a number;

One third of n = $\frac{1}{3}$ n

4 more;

$\frac{1}{3}$ n + 4

is 6;

$\frac{1}{3}$ n + 4 = 6 (equation of the expression)

Let us now solve the equation:

$\frac{1}{3}$ n + 4 = 6

$\frac{1}{3}$ n = 6 - 4

$\frac{1}{3}$ n = 2

n = 6

5 0

3 years ago

From past experience, a company has found that in carton of transistors: 92% contain no defective transistors 3% contain one def

jasenka [17]

Answer:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

LEt X the random variable who represent the number of defective transistors. For this case we have the following probability distribution for X

X 0 1 2 3

P(X) 0.92 0.03 0.03 0.02

We can calculate the expected value with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

8 0

4 years ago

The product of buvo numbers is 21. If the first number is-3 which equation represents this situation and what is the second numb

8_murik_8 [283]

Answer:

- 3 + x = 21

X = 24

Step-by-step explanation:

- 3 + x = 21

X = 21 + 3

X = 24

6 0

3 years ago

in spencers garden the number of rose bushes is 7 less than 1.5 times the number of carnation bushes. If the number of carnation

Step2247 [10]

<span>1.5 times the number of carnation bushes.
If the number of carnation bushes is c.
R = 1.5c - 7
Hope this helps:-)</span>

7 0

4 years ago