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2 years ago

What is the side length of the smallest square plate on which a 28-cm chopstick can fit along a diagonal without any overhang?

Mathematics

2 answers:

Zepler [3.9K]2 years ago

7 0

Answer:

19.8

Step-by-step explanation:

you have 28 divide it by 2 and then multiply it by the square root of 2

vladimir2022 [97]2 years ago

4 0

2727262622626262626❤️❤️❤️❤️

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In the data set, what is the variance? 6 8 1 9 4

Juli2301 [7.4K]

The answer is s² ≈ 10.3

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3 years ago

A right circular cone is undergoing a transformation in such a way that the radius of the cone is increasing at a rate of 1/2 in

Ivenika [448]

Answer:

The volume is decreasing at the rate of 1.396 cubic inches per minute

Step-by-step explanation:

Given

Shape: Cone

$\frac{dr}{dt} =\frac{1}{2}$ --- rate of the radius

$\frac{dh}{dt} =-\frac{1}{3}$ --- rate of the height

$r = 2$

$h = \frac{1}{3}$

Required

Determine the rate of change of the cone volume

The volume of a cone is:

$V = \frac{\pi}{3}r^2h$

Differentiate with respect to time (t)

$\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})$

Substitute values for the known variables

$\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)$

$\frac{dV}{dt} = -\frac{\pi}{3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{7*3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{21}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{88}{63}$

$\frac{dV}{dt} =-1.396in^3/min$

The volume is decreasing at the rate of 1.396 cubic inches per minute

3 0

2 years ago

What does this number apply to??

topjm [15]

Hey there!

The opposite of the square root of 25 is -5, and this is an <u>integer and a rational number and a real number.</u>

<u></u>

Hope it helps and have a great day!

4 0

2 years ago

Read 2 more answers

SGA is doing a fundraiser to sell candles for project graduation. Small candles cost $4.00 and large candles cost $6.00. They ha

mafiozo [28]

Given:

Cost of small candles = $4.00

Cost of large candles = $6.00

They have at most 50 candles, and want to make at least $100.

To find:

The system of linear inequalities represents the situation.

Solution:

Let x be the number of small candles and y be the number of large candles.

At most 50 candles means total candles must be less than or equal to 50.

$x+y\leq 50$

Want to make at least $100. It means, the total sales must be greater than or equal to $100.

$4x+6y\geq 100$

Therefore, the inequalities in the system of linear inequalities are $x+y\leq 50$ and $4x+6y\geq 100$ .

3 0

2 years ago

News article reports that "Americans have differing views on two potentially inconvenient and invasive practices that airports c

OverLord2011 [107]

Answer:

1) p1=0.83

2) p2=0.81

3) Option B

4) p=0.82

5) s=0.03

6) z=0.67

7) P=0.50

8) Do not reject H0

Step-by-step explanation:

1) The proportion of Republicans who think the full-body scans should be applied in airports is equal to the ratio between the republicans that think it should over the total Republicans in the poll:

$p=X/n=258/311=0.83$

2) The proportion of Democrats who think the full-body scans should be applied in airports is equal to:

$p=X/n=294/363=0.81$

3) As we want to know if there is a difference in the proportions calculated, not if one is higher or lower than the other, the correct option is B:

$H_0:p_1-p_2=0\\\\H_a:p_1-p_2\neq0$

4) The pooled estimate of a proportion is the average of both proportions:

$\bar{p}=\frac{p_1+p_2}{2}= \frac{0.83+0.81}{2}=0.82$

5) The standard error can be calculated as:

$s=\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1} +\frac{\bar{p}(1-\bar{p})}{n_2}} \\\\s=\sqrt{\frac{0.82*0.18}{311} +\frac{0.82*0.18}{363}} \\\\s=\sqrt{0.00047+0.00041} =\sqrt{0.00088}=0.03$

6) The z-statistic can be calculated as:

$z=\frac{p_1-p_2}{s}=\frac{0.83-0.81}{0.03}=\frac{0.02}{0.03}=0.67$

7) The P-value for z=0.67 is P=0.50 (from the standard normal distribution table).

$2P(Z>|z|)=0.50286$

8) If the significance level is 0.01, the P-value is bigger than the significance level. The effect is not significanct. The null hypothesis is not rejected.

There is not enough evidence to say that both proportions are different.

A. Do not reject H0

8 0

2 years ago

What is the side length of the smallest square plate on which a ​28-cm chopstick can fit along a diagonal without any​ overhang?

What is the side length of the smallest square plate on which a 28-cm chopstick can fit along a diagonal without any overhang?