the perimeter of a semicircle is 108 cm what is the perimeter of the square drawn on the diameter of the semicircle

Mathematics

1 answer:

Andreas93 [3]3 years ago

4 0

Answer:

Step-by-step explanation:

the perimeter of the semi-circle would be the diameter plus the circumference of half of the circle.

They want to know the perimeter of a square using the diameter of the sem-circle as ONE side, so the perimeter of the square would be 4 times the ONE side.

We should recall:

diameter = 2 times the radius circumference of a cirlce = 2π r

How do we find the diameter of the of the semi circle?

The perimeter of the semi circle is given as 108 cm

Perimeter of the semicirle = 2r + π r diameter plus semi circumference

108 = r ( 2 + π) factor out the r and solve for r

108 / (2 + π) = r divide both sides by ( 2 + r)

Now we know r, the perimeter of the squqre is 4 times 2r or 8r

perimeter of square = 8 [ 108 / (2 + π) ] π I used 3.14

= 864 / 5.14

= 168.1 cm I got rounded to nearest tenth

When I re-checked by work I found a few math, logic and calculation errors. Please re-check my answer for any more mistakes.

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In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$