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3 years ago

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A circular park of diameter 40 feet is surrounded by a concentric road of uniform width. If the area of the road is 84 pi square

feet, find its width.
a 6 feet
b 2 feet
c 3 feet
d 4 feet

1 answer:

Dominik [7]3 years ago

4 0

Answer:

Step-by-step explanation:

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Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enroll

Papessa [141]

Answer:

The 95% confidence interval for the average number of units that students in their college are enrolled in is between 11.7 and 12.5 units.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 45 - 1 = 44

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2\frac{1.5}{\sqrt{45}} = 0.4$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 12.1 - 0.4 = 11.7 units

The upper end of the interval is the sample mean added to M. So it is 12.1 + 0.4 = 12.5 units

The 95% confidence interval for the average number of units that students in their college are enrolled in is between 11.7 and 12.5 units.

8 0

2 years ago

Water use in the summer is normally distributed with a mean of 311.4 million gallons per day and a standard deviation of 40 mill

r-ruslan [8.4K]

Answer: 0.965

Step-by-step explanation:

Given : Water use in the summer is normally distributed with

$\mu=311.4\text{ million gallons per day}$

$\sigma=40 \text{ million gallons per day}$

Let X be the random variable that represents the quantity of water required on a particular day.

Z-score : $\dfrac{x-\mu}{\sigma}$

$\dfrac{350-311.4}{40}=0.965$

Now, the probability that a day requires more water than is stored in city reservoirs is given by:-

$P(x>350)=P(z>0.965)=1-P(z$

We can see that on comparing the above value to the given P(X > 350)= 1 - P(Z < b) , we get the value of b is 0.965.

4 0

3 years ago

Line m in xy plane contains the points (2,4) and (0,1) which of the following is the equation of M

HACTEHA [7]

Answer:

The equation of line M in slope intercept form is $y=\frac{3}{2}x+1$

The equation of line M in standard form is $3x-2y=-2$

Step-by-step explanation:

step 1

Find the slope of line M

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

(2,4) and (0,1)

substitute

$m=\frac{1-4}{0-2}$

$m=\frac{-3}{-2}$

$m=\frac{3}{2}$

step 2

Find the equation of the line M in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{3}{2}$

$point\ (0,1)$

substitute

$y-1=\frac{3}{2}(x-0)$

$y-1=\frac{3}{2}x$ ----> equation in point slope form

step 3

Find the equation of line M in slope intercept form

$y=mx+b$

Isolate the variable y in the equation of the line in point slope form

$y-1=\frac{3}{2}x$

Adds 1 both sides

$y=\frac{3}{2}x+1$

step 4

Find the equation of the line M in standard form

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=\frac{3}{2}x+1$

Multiply by 2 both sides

$2y=3x+2$

$3x-2y=-2$ ---> equation in standard form

7 0

3 years ago

six friends are going to buy a pizza. Their chices are to biu 2 medium 10-inch diameter pizzas for 7:00 each, or 1 large 14 inch

11111nata11111 [884]

For this question, we want to find out the greatest amount of area of pizza for the least amount of money:

So we have two pizzas with a 10 in. diameter. Let us take one of those pizzas.

The formula for area of a circle is $\pi r ^2$ ; So the area for one of these 10 in. pizzas would be $\pi (5)^2$ or 25 $\pi$ .

We have two of these pizzas, so the total area that we would get with $14 would be 25 $\pi$ *2 or 50 $\pi$ .

For the second case, we have one pizza with a 14 in. diameter.

The area of this pizza will be $\pi (7)^2$ or 49 $\pi$ .

So for $15 we can buy 49 $\pi$ worth of pizza.

The best deal would be to buy the two medium pizzas of 10 inch diameter, because for $14, you get 50 $\pi$ .

5 0

3 years ago

(X-4) (x+2)=16 <br> What’s the standard form

Reika [66]

Step-by-step explanation:

$(x - 4)(x + 2) = 16 \\ {x}^{2} + (- 4 + 2)x + ( - 4) \times 2= 16 \\ {x}^{2} - 2x - 8 - 16 = 0 \\ {x}^{2} - 2x - 24 = 0 \\ is \: the \: standard \: form.$

8 0

3 years ago

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