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3 years ago

A DVD has a diameter of 34 centimeters. What is the area of the DVD? Round your answer to the nearest

Mathematics

2 answers:

alex41 [277]3 years ago

4 0

Answer:

Area of the circle = $907.46\;cm^2$

Step-by-step explanation:

Diameter of the DVD = $34\;cm$

$Radius=\dfrac{34}{2}=17\;cm$

Area of the circle= $\pi \times r^2$

As,

$\pi =\dfrac{22}{7}=3.14$

Area is:

$=3.14\times 17\times 17\\\\=3.14\times 289\\\\=907.46\;cm^2$

Area of the circle is: $907.46\;cm^2$

nata0808 [166]3 years ago

3 0

Answer:

907.46cm

Step-by-step explanation:

Area of Cirlce = πr^2

R= 17

R^2= 289

289 x 3.14 = 907.46

907.46cm

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Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to hav

Svetllana [295]

Answer:

She needs a sample of at least 385.

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 $Z = 1.96$ .

How large a sample should she take to achieve this?

She needs a sample of size at least n.

n is found when M = 0.04.

We do not know the true population proportion, so we use $\pi = 0.5$ , which is the case for which we are going to need the largest sample size.

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

$0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.05\sqrt{n} = 1.96*0.5$

Dividing both sides by 0.05

$\sqrt{n} = 19.6$

$(\sqrt{n})^{2} = 19.6^{2}$

$n = 384.2$

Rounding up

She needs a sample of at least 385.

3 0

3 years ago

I need help with answers A,B,C

mezya [45]

The first one is two goals per game I believe

8 0

3 years ago

Ryan made 95 ounces of of apple jelly he puts the same amount in 6 jars about how much jelly does each jar have

goldfiish [28.3K]

Answer:

15.83 ounces

Step-by-step explanation:

95/6 is about 15.83

Use division to divide things evenly

7 0

3 years ago

Let g represent Mia’s score. Which expression represents 57 more than 3 times Mia’s score?

My name is Ann [436]

Answer

Step-by-step explanation:

3g+57

6 0

3 years ago

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

3 years ago