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3 years ago

Find the circumference of a circle with a radius of 35 inches in terms of pie add to the nearest 10th of an inch

Mathematics

2 answers:

vladimir1956 [14]3 years ago

8 0

$\overline{ \underline{ \boxed{ \frak{Given }}}}$

Find the circumference of a circle with a radius of 35 inches in terms of pie add to the nearest 10th of an inch

$\overline{ \underline{ \boxed{ \frak{Solution}}}}$

Given that :

Radius = 35 inches

π = 3.14

Formula for getting the circumference :

$\star \: \underline{ \pink{\boxed{\frak{Circumference_{(Circle)} = 2πr}}}}$

Putting the values in the formula we get :

$\twoheadrightarrow \frak{Circumference_{(Circle)} = 2 \times 3.14 \times 35 \: in}$

$\twoheadrightarrow \frak{Circumference_{(Circle)} = 3.14 × 70 in }$

$\twoheadrightarrow \frak{Circumference_{(Circle)} = 219.8 \: inches}$

Henceforth, the circumference is 219.8 inches

But we are given to convert it into the nearest 10th

As 8 > 5

The Circumference of the Circle will be 220 inches

ser-zykov [4K]3 years ago

7 0

Circumference of circle = 2 π r

π = 3.14
r = 35 inches

Now , Substuting the values

Circumference of circle = 2 × 3.14 × 35

Circumference of circle = 6.28 × 35

Circumference of circle = 219.8 inches

Nearest 10ᵗʰ of 219.8 is 220

Hence , the Circumference of circle is 220 Inches.

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In a test of weight loss programs, 40 randomly selected adults used the Atkins weight loss program. After 12 months, their mean

natulia [17]

Answer:

90% confidence interval for the mean weight loss for all such subjects is [0.82 lbs, 3.38 lbs].

Step-by-step explanation:

We are given that in a test of weight loss programs, 40 randomly selected adults used the Atkins weight loss program.

After 12 months, their mean weight loss was found to be 2.1 lbs., with a standard deviation of 4.8 lbs.

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

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight loss of 40 adults = 2.1 lbs

s = sample standard deviation = 4.8 lbs

n = sample of adults = 40

$\mu$ = population mean weight loss

Here for constructing 90% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

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

P(-1.685 < $t_3_9$ < 1.685) = 0.90 {As the critical value of t at 39 degree

of freedom are -1.685 & 1.685 with P = 5%}

P(-1.685 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.685) = 0.90

P( $-1.685 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.685 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.685 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X +1.685 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.685 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.685 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $2.1-1.685 \times {\frac{4.8}{\sqrt{40} } }$ , $2.1+1.685 \times {\frac{4.8}{\sqrt{40} } }$ ]

= [0.82 , 3.38]

Therefore, 90% confidence interval for the true mean weight loss for all such subjects is [0.82 lbs, 3.38 lbs].

Interpretation of this confidence interval is that we are 90% confident that the mean weight loss for all such subjects will lie between 0.82 lbs and 3.38 lbs.

So, if our true mean weight will be between 0.82 lbs and 2.1 lbs then we can say that the Atkins program appear to be effective. But it is somewhat appear to be practical kind of aspect.

5 0

3 years ago

Substitution X=4y x+2y=12

lorasvet [3.4K]

Answer:

4y + 2y = 12

solved; y = 2

Step-by-step explanation:

put the 2 y values together to get 6y. Then divide both sides by 6 to icolate y to get 2.

Have a great day!

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8 0