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PLEASE HELP... What do you do when none of the variables cancel out while solving systems by elimination?

Vitek1552 [10]

Answer:

multiply one or both of the equations until a variable can cancel out

3 0

3 years ago

How many cups of sorbet are used in 8 cups of punch? (Punch Recipe:: Ginger Ale: 40% | Orange Juice: 25% | Pineapple Juice: 20%

Wittaler [7]

54.4 Cups of soebet are used in 8 cups of punch.

6 0

3 years ago

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne

Leto [7]

Answer:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.

This means that $n = 533, \pi = \frac{351}{533} = 0.6585$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 - 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6247$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 + 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6923$

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

6 0

3 years ago

Find the value of c so that the polynomial p(x) is divisible by (x-3). p(x) =-x^3+cx^2-4x+3. c=?

Vilka [71]

Answer:

$\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}$

Step-by-step explanation:

A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,

$\sf \implies p(x)=- x^3+cx^2-4x+3$

And the factor is ,

$\sf \implies g(x) = x + 3$

Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0

$\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}$

<h3>Hence the value of c is (-14)/3 .</h3>

4 0

3 years ago

Three angles of a hexagon are congruent. The other three angles are also congruent, each with a measure twice that of the first

Serga [27]

The sum of the interior angles of a hexagon is 720 degrees. If 3 angles are congruent, each with measure x degrees, and the other 3 angles are also congruent to each other, each with measure 2x degrees, then the total sum of all 6 angles would be 3x + 3(2x) = 9x. If this is equal to 720, then x = 80 degrees, while 2x = 160 degrees.
Therefore, there are 3 80-degree angles and 3 160-degree angles.

3 0

3 years ago