Are potato chips three dimensional

Represent the following sentence as an algebraic expression, where "a number" is the

Aneli [31]

Answer: 3 - x

Step-by-step explanation: With

Subtraction be careful. 3 - x is not the same as x - 3. You have to keep the values given in order.

5 0

3 years ago

Approximately 5% of calculators coming out of the production lines have a defect. Fifty calculators are randomly selected from t

baherus [9]

Answer:

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Step-by-step explanation:

For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of calculators coming out of the production lines have a defect.

This means that $p = 0.05$

Fifty calculators are randomly selected from the production line and tested for defects.

This means that $n = 50$

What is the probability that exactly 2 calculators are defective?

This is P(X = 2). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{50,2}.(0.05)^{2}.(0.95)^{48} = 0.2611$

0.2611 = 26.11% probability that exactly 2 calculators are defective.

3 0

3 years ago

Simplify (4x^2+2)÷(2x^2-9x-5)

frosja888 [35]

Answer:

4.1 Pull out like factors :

4x2 + 2 = 2 • (2x2 + 1)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = 2x2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 2 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,2

of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 3.00 -1 2 -0.50 1.50 1 1 1.00 3.00 1 2 0.50 1.50

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

4.3 Factoring 2x2 - 9x - 5

The first term is, 2x2 its coefficient is 2 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 2 • -5 = -10

Step-2 : Find two factors of -10 whose sum equals the coefficient of the middle term, which is -9 .

-10 + 1 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 1

2x2 - 10x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-5)

Add up the last 2 terms, pulling out common factors :

1 • (x-5)

Step-5 : Add up the four terms of step 4 :

(2x+1) • (x-5)

Which is the desired factorization

Final result :

2 • (2x2 + 1) —————————————————— (x - 5) • (2x + 1)

5 0

2 years ago

the ratio of girls to boys in the sixth grade is 5:3. If there are 400 sixth graders, how many boys are there?

PilotLPTM [1.2K]

Answer:

boys = 250

girls = 150

Step-by-step explanation:

5g = 3b eq. 1

g + b = 400 eq. 2

g = girls

b = boys

From the eq. 2

g = 400 - b

Replacing this last eq. on eq. 1:

5(400-b) = 3b

5*400 + 5*-b = 3b

2000 - 5b = 3b

2000 = 3b + 5b

2000 = 8b

2000/8 = b

250 = b

From eq. 2

g + 250 = 400

g = 400 - 250

g = 150

Check:

from eq. 1

5*150 = 3*250 = 750

3 0

2 years ago

A square and a triangle have equal perimeters. The square has a perimeter of 4(x + 9), and the triangle has a perimeter of 3(x +

cricket20 [7]

Answer: x=36

4(x+9)=3(x+24)

4 0

3 years ago