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2 years ago

What is the area of a circle with a diameter of 15. 8cm? To the nearest hundredth

Mathematics

1 answer:

klio [65]2 years ago

7 0

Answer:

see below

Step-by-step explanation:

First we need to find the radius

r =d/2 = 15.8/2 = 7.9 cm

The area of a circle is given by

A = pi r^2

= pi ( 7.9) ^2

=62.41 pi

Using 3.14 for pi

195.9674

To the nearest hundredth

195.97

Using the pi button

196.0667975

To the nearest hundredth

196.07

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Leo is constructing a tangent line from point Q to circle P. What is his next step?

bezimeni [28]

Answer:

hello your question has a missing diagram attached below is the missing diagram

answer :

Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )

Step-by-step explanation:

when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between the given circles and then construct a line through it

6 0

2 years ago

23, 24, 25, 26, and 27

Debora [2.8K]

23. Option A: 4p + 175 = 375

24. $50 per monthly payment if the down payment is $175

25. Option C: 28x + 64 = 456

26. $14 for a haircut

27.
a. See the diagram attached. It was drawn on Google Drawing so obviously not to scale but you get the gist.

b.

Not quite sure what a verbal model is but with the diagram you should be able to describe it.

4 bookshelves, 2 on each side, in an entertainment center and a middle section of 30 inches wide all add up in its entirety to equal 90 inches.

c.

4x + 30 = 90

d.

4x = 60
x = 15

The bookcases are each 15 inches wide

5 0

3 years ago

Suppose that the expected value of a measurement is 2.0 m. Which of the following sets of measurements is the MOST accurate? A.

zavuch27 [327]

Answer:

C is probably the answer

Step-by-step explanation:

1.9 Is approximately 2

2.3 Is approximately 2

2.2 is also approximated to 2

1.8 Is also approximately 2

4 0

3 years ago

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confide

salantis [7]

Answer:

With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

Step-by-step explanation:

We are given that a random sample of 60 home theater systems has a mean price of$131.00. Assume the population standard deviation is$18.80.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean price = $131

$\sigma$ = population standard deviation = $18.80

n = sample of home theater = 60

$\mu$ = population mean

Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $131-1.645 \times {\frac{18.8}{\sqrt{60} } }$ , $131+1.645 \times {\frac{18.8}{\sqrt{60} } }$ ]

= [127.01 , 134.99]

Therefore, 90% confidence interval for the population mean is [127.01 , 134.99].

Now, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean price = $131

$\sigma$ = population standard deviation = $18.80

n = sample of home theater = 60

$\mu$ = population mean

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $131-1.96 \times {\frac{18.8}{\sqrt{60} } }$ , $131+1.96 \times {\frac{18.8}{\sqrt{60} } }$ ]

= [126.24 , 135.76]

Therefore, 95% confidence interval for the population mean is [126.24 , 135.76].

Now, with 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

7 0

3 years ago

A government bureau publishes annual price figures for new mobile homes. A simple random sample of 36 new mobile homes yielded t

Oliga [24]

Answer:

The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).

Step-by-step explanation:

The question is incomplete:

The prices in thousands of dollar are:

66.6, 69.8, 58.4, 57.3, 63.1, 61.8, 56, 72.7, 61.8,

66.9, 72.6, 63.1, 58.7, 65.9, 61.1, 56.1, 49.9, 72.6,

49, 56.4, 72.6, 60.1, 65, 64.8, 56.5, 52, 53.2,

56.4, 75.4, 76.3, 60.5, 74.6, 57, 69.2, 62.7, 77.2.

We have a sample of n=36 new mobile homes.

The mean of this sample is:

$M=(1/36)\sum_{i=1}^{36}x_i=\dfrac{2273.3}{36}=63.147$

The population standard deviation is σ=7.5 (in thousands of dollars).

The critical value of z for a 99.7% CI is z=2.97.

Then, we can calculate the margin of error as:

$E=z\cdot \sigma/\sqrt{n}=2.97*7.5/\sqrt{36}=22.275/9=2.475$

Now we can calculate the lower and upper bound of the confidence interval as:

$LL=\bar X-E=63.147-2.475=60.672\\\\UL=\bar X+E=63.147+2.475=65.622$

The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).

8 0

3 years ago