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3 years ago

Find the length of the longest object that will fit inside a cylinder that has a radius of 3.25 inches and is 7 inches high.

Mathematics

1 answer:

ra1l [238]3 years ago

6 0

Answer:

9.5 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the length of the longest linear object of small dimensions that will fit across the space diagonal of the cylinder. The relevant length is that of the hypotenuse of a triangle whose legs are the diameter and height of the cylinder.

... length² = (3.25×2)² +7² = 91.25

... length = √91.25 ≈ 9.55249 ≈ 9.5 . . . inches

_____

Ordinarily, such a number would be rounded up, but that longer length will not fit. Hence it is appropriate to round the number down.

If the object can be curled up, more than 3.2 billion miles of DNA molecule would fit in the space.

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Verdich [7]

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Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Explain your answer to each question.

katovenus [111]

A) 3/7 is greater because 2 divided by 5 is .40 and 3 divided by 7 is .42 rounded

b) 3/10 = .3, 2/5 = .4, 14/30 = about .46, 1/2 =.5, and 8/15 = about .53

hope this helps :)

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4 years ago

If f(x) = x2 + 1 and g(x) = x - 4, which value is equivalent to (fog)(10)

aksik [14]

To get this f(g(10))

We do g(x)= 10-4= 6

This plug this into f(6)= 6^2 +1= 37

The answer is 37

8 0

3 years ago

Since 1936, the Gallup Organization has been asking Americans: "Are you in favor of the death penalty for a person convicted of

USPshnik [31]

Answer:

98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is [0.59 , 0.64].

Step-by-step explanation:

We are given that the results of the most recent survey; in a sample of 3100 females, 62% said that they were in favor of the death penalty for convicted murders.

Firstly, the pivotal quantity for 98% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of females who were in favor of the death penalty for convicted murders = 62%

n = sample of females = 3100

p = population proportion of all American females who support the death penalty

Here for constructing 98% confidence interval we have used One-sample z proportion statistics.

So, 98% confidence interval for the population proportion, p is ;

P(-2.33 < N(0,1) < 2.33) = 0.98 {As the critical value of z at 1% level

of significance are -2.33 & 2.33}

P(-2.33 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.33) = 0.98

P( $-2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.98

P( $\hat p-2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.98

98% confidence interval for p = [ $\hat p-2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.33 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.62-2.33 \times {\sqrt{\frac{0.62(1-0.62)}{3100} } }$ , $0.62+2.33 \times {\sqrt{\frac{0.62(1-0.62)}{3100} } }$ ]

= [0.59 , 0.64]

Therefore, 98% confidence interval for the proportion of all American females who support the death penalty for convicted murders is [0.59 , 0.64].

4 0

3 years ago

The medicine capsule shown consist of a cylinder with a hemisphere at each end. The total length of the capsule is 15 millimeter

sweet [91]

Answer:

The surface area of capsule is 235.5 mm².

Step-by-step explanation:

Given that,

Diameter = 5 mm

Total length = 15 mm

We need to calculate the radius of each hemisphere

Using formula of radius of hemisphere

$\text{radius of each hemisphere}=\text{radius of cylinder}$

$r=\dfrac{5}{2}$

$r=2.5\ mm$

We need to calculate the length of cylinder

Using formula of length

Length of cylinder = Total length of capsule-radius of left hemisphere- radius of right hemisphere

$\text{length of cylinder}=15-2.5-2.5$

$\text{length of cylinder}=10\ mm$

We need to calculate the surface area of capsule

Using formula of surface area of capsule

$\text{surface area of capsule}=\text{Curved surface area of cylinder}+\text{surface area of left hemisphere}+\text{surface area of right hemisphere}$

$\text{surface area of capsule}=2\pi rl+2\pi r^2+2\pi r^2$

$\text{surface area of capsule}=2\pi rl+4\pi r^2$

Put the value into the formula

$\text{surface area of capsule}=2\times3.14\times2.5\times10+4\times3.14\times(2.5)^2$

$\text{surface area of capsule}=235.5\ mm^2$

Hence, The surface area of capsule is 235.5 mm².

4 0

4 years ago