M(-2,-6) Across the y-axis: Across the x-axis

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is

Scorpion4ik [409]

Answer:

26 ounces of 55% solution
104 ounces of 80% solution

Step-by-step explanation:

Let x represent the quantity of 80% solution. Then 130-x is the amount of 55% solution. The total amount of salt in the mix is ...

0.80x +0.55(130 -x) = 0.75·130

0.25x = 0.20·130 . . . . . . . subtract 0.55(130)

x = 0.20/0.25(130) = 104

130-x = 26

She should use 26 ounces of 55% solution and 104 ounces of 80% solution.

5 0

3 years ago

What is the range of f(x) = 3X + 9?<br> {yly<9}<br> {yly>9}<br> {yly> 3}<br> {yly<3}

4vir4ik [10]

Answer:

the set of all real numbers

Step-by-step explanation:

f(x) = 3X + 9 is a polynomial, and so both the domain and the range are "the set of all real numbers."

None of your answer choices match this. Check with your teacher if you can.

7 0

2 years ago

The pendulum swings at an arc of 30 cm and its successive swings reduced to 10% of the previous swings. What is the total distan

OleMash [197]

Answer:

$S_g= 33.333cm$

Step-by-step explanation:

From the question we are told that

Arc of 30 cm

10% reduction after each swing

Generally sum of geometric sequence is given by the equation

$S_g=\frac{a(1-r^n)}{1-r}$

Mathematically solving for total distance traveled we have

$S_g=\frac{30(1-(0.10^5)}{1-(0.10)}$

$S_g=\frac{30}{0.9}$

Therefore the total distance traveled by the pendulum after 5 swings

$S_g= 33.333cm$

3 0

3 years ago

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population pro

Gnom [1K]

Answer:

A sample of 1068 is needed.

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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population proportion?

We need a sample of n.

n is found when M = 0.03.

We have no prior estimate of $\pi$ , so we use the worst case scenario, which is $\pi = 0.5$

Then

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

$0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.03\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.03}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}$

$n = 1067.11$

Rounding up

A sample of 1068 is needed.

8 0

2 years ago

An arc has a length of 123.53 millimeters and a radius of 28 millimeters. What is the measure of the angle of the sector in degr

nadezda [96]

Answer:

Step-by-step explanation:

The formula for arc length in terms of degrees is

$A.L.=\frac{\theta}{360}*2\pi r$ and we have everything we need to fill in to find the angle measure.

$123.53=\frac{\theta}{360}*56\pi$ which is the same as

$123.53=\frac{56\pi \theta}{360}$ and

$360(123.53)=56\pi \theta$ and

$\frac{360(123.53)}{56\pi}=\theta$ so

θ = 253°

4 0

2 years ago