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3 years ago

Solve for x ax+ b= r

Mathematics

1 answer:

Alexxx [7]3 years ago

7 0

Answer:

$x = \dfrac{r - b}{a}$

Step-by-step explanation:

$ax + b = r$

Subtract b from both sides.

$ax = r - b$

Divide both sides by a.

$x = \dfrac{r - b}{a}$

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A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyl

LuckyWell [14K]

Answer:

A sample of 16577 is required.

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 $1 - \frac{\alpha}{2}$ .

The margin of error is of:

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

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use $\pi = 0.5$ , which is when the largest sample size will be needed.

The sample size is n for which M = 0.01. So

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

$0.01 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.01\sqrt{n} = 2.575*0.5$

$\sqrt{n} = \frac{2.575*0.5}{0.01}$

$(\sqrt{n})^2 = (\frac{2.575*0.5}{0.01})^2$

$n = 16576.6$

Rounding up:

A sample of 16577 is required.

8 0

2 years ago

A football player punts a ball. The path of the ball can be modeled by the equation y = –0.004x2 + x + 2.5, where x is the horiz

Galina-37 [17]

The answer is 252.5 ft

y = –0.004x² + x + 2.5
Let's take y = 0 and we'll get the quadratic equation:

–0.004x² + x + 2.5 = 0
The general formula for quadratic equation is:
ax² + bx + c = 0

a = -0.004
b = 1
c = 2.5

$x_{1,2} = \frac{-b+/- \sqrt{ b^{2}-4ac} }{2a} =\frac{-1+/- \sqrt{ 1^{2}-4*(-0.004)*2.5} }{2*(-0.004)} = \frac{-1+/- \sqrt{1+0.04} }{-0.008} = \\ 
=\frac{-1+/- \sqrt{1.04} }{-0.008} = \frac{-1+/-1.02}{-0.008}$

$x_1=\frac{-1+1.02}{-0.008} = \frac{0.02}{-0.008} = -2.5 \\ 
x_2=\frac{-1-1.02}{-0.008} = \frac{2.02}{-0.008} = 252.5$

Since distance cannot be negative (x1), the correct answer is x2 = 252.5 ft

5 0

3 years ago

Read 2 more answers

What is the answer to 1-2x=-3x+2

scZoUnD [109]

Answer:

x=1

Step-by-step explanation:

1-2x=-3x+2

-1=-x

1=x

8 0