All swimming equipment is on sale with a 15% discount. A snorkeling set regularly sells for $45. Find the discount.

Minchanka [31]

(a) 1A 2A 3A 1B 2B 3B (6 possible outcomes

(b) Possible outcomes for A or 1 are 1A 2A 3A and 1B ( 4 outcomes) therefore:
Probabilty = 4/6 = 2/3

6 0

3 years ago

Can someone PLEASE explain in simple terms which trigonometric ratio to use, like tangent, cosine, or sine, and WHY?

natulia [17]

Answer:

Use law of Cosines or Tangent

Step-by-step explanation:

This is a SAS triangle, where you have have an angle adjacent to two side lengths. But given that it is a right triangle, you can find the hypotenuse by just using the tangent formula. You can find the quantity of any angle by applying tan= opposite side/adjacent side length.

However, lets say you want to find the opposite side, side XZ, you can use the law of cosine which basically states:

c=a^2+b^2﹣2abcos(angle number). But since it is a right triangle, just use the hypotenuse theorem which states: C^2 = A^2 + B^2

The answer for XZ would thus be: squareroot of 136 or 2(34)^1/2.

Hope this helps :)

7 0

3 years ago

In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet.

Alex777 [14]

Answer:

$0.025 = 2.33\sqrt{\frac{0.79*0.21}{n}}$

Option d.

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:

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

79 percent of adults age 18 years and older in the United States use the Internet.

This means that $\pi = 0.79$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.33$ .

Which of the following should be used to find the sample size (n) needed?

We have to find n for which $M = 0.025$

So the equation is:

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

$0.025 = 2.33\sqrt{\frac{0.79*0.21}{n}}$

Option d.

4 0

3 years ago

What is the volume of a cylinder of 8in by 0.5 ft in cubic inches

Naily [24]

The volume of cylinder is 1205.76 cubic inches

Solution:

We have to find the volume of cylinder

The volume of cylinder is given by formula:

$V = \pi r^2h$

Where "r" is the radius and "h" is the height of cylinder

Given dimensions are:

Radius = 8 inches

Height = 0.5 feet

Convert feet to inches

1 feet = 12 inches

Therefore,

0.5 feet = 12 x 0.5 = 6 inches

Thus, we have got,

height = 6 inches

Substitute r = 8 inches and h = 6 inches in formula:

$V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76$

Thus volume of cylinder is 1205.76 cubic inches

7 0

3 years ago

Given f'(x) = (x-4)(4-2x), find the x-coordinate for relative maximum on the graph of f(x)

antiseptic1488 [7]

Answer:

The coordinate of the relative maximum is x=4.

Step-by-step explanation:

Given that the derivative of the function $f(x)$ is $f'(x) = (x-4)(4-2x)$ , the maxima and minima or the critical points can be found where $f'(x)=0,$ that is:

$f'(x) = (x-4)(4-2x)=0.$

The solutions to this equation are $x=4$ and $x=2.$

Now, if the second derivative $f''(x)$ for a function $f(x)$ is negative at a critical point, then the critical point is the relative maximum.

Therefore we want to see at which of the two critical points is $f''(x)$ negative. The second derivative is:

$\frac{\mathrm{d f'(x)}}{\mathrm{d}x}=f''(x)=-4(x-3).$

Now $f''(4)$ is $-4$ , and $f''(2)$ is $+4$ , therefore we deduce that the relative maxium is located at $x=4$ , because there the second derivative $f''(x)$ is negative.

4 0

3 years ago