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Maru [420]
2 years ago
6

A cylindrical water tank of height 4 m is used to fill containers with dimensions 20 cm X 30 cm X 50 cm. If the tank can fill ex

actly 200 of these containers, find its base radius. (Take Pi = 3.14)
Mathematics
1 answer:
faltersainse [42]2 years ago
5 0

Answer:

0.35cm

Step-by-step explanation:

Step 1

We find the volume of the container.

The formula = Length × Width × Height

Length = 20cm

Width = 30cm

Height = 50cm

The volume of the tank = 20cm × 30cm × 50cm

= 30000 cm³

Step 2

We are told that:

The tank can fill exactly 200 of these containers

We have to find the volume that 1 cylinder will contain

Hence,

200 containers = 30000 cm³

1 container = x

Cross Multiply

200 × x = 30000cm³

x = 30000cm³/200

x = 150cm³

Step 3

We find the base radius of the cylindrical tank

Height = 4m

Convert to cm

1m = 100cm

4m = x

Cross Multiply

x = 4 × 100cm = 400cm

Volume of the cylinder = πr²h

Radius = √V/πh

Radius = √150/π × 400

Radius = 0.35 cm

Therefore, base radius = 0.35cm

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33/8 + 2 1/3

= 33/8 + 7/3

= 155/24

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3 years ago
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6 times -2 is -12.

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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:

<em>The question is incomplete:</em>

<em>The significance level is 0.05.</em>

<em>The data is:</em>

<em>Brand X: 91, 100, 88, 89</em>

<em>Brand Y: 99, 96, 94, 99</em>

<em>Brand Z: 83, 88, 89, 76</em>

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

Now we calculate the F statistic as:

F=MSB/MSE=172/23.78=7.23

The degrees of freedom of the numerator are:

dfn=a-1=3-1=2

The degrees of freedom of the denominator are:

dfd=N-a=3*4-3=12-3=9

The P-value of F=7.23, dfn=2 and dfd=9 is:

P-value=P(F>7.23)=0.01342

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

3 0
3 years ago
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Answer:

6

Step-by-step explanation:

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The greatest common factor is the product of the common factors at their lowest exponents.

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7 0
3 years ago
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fgiga [73]

Answer:

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Step-by-step explanation:

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5 0
2 years ago
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