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1 year ago

7

Peter is making green paint by mixing blue and yellow paint in a cuboid container, shown below. The container has width of 30cm

and length of 40cm and is full. He mixes blue paint and yellow paint in the ratio 2: 3. Peter uses 8.4 litres of blue paint. Calculate the height of the container

1 answer:

dusya [7]1 year ago

4 0

Answer: height = 17.5cm

Step-by-step explanation: Peter mixes blue and yellow paint in the ratio 2:3, which means:

$\frac{2}{3} = \frac{8.4}{x}$

$x = \frac{8.4*3}{2}$

x = 12.6L

The container is full with the two paints, so total volume:

V = 12.6 + 8.4

V = 21L

Knowing that 1L = 1dm³ and sides of cuboid is measure in cm:

V = 21dm³ = 21000cm³

Volume of a cuboid is calculated as:

V = width*length*height

Height of the container is

height = $\frac{V}{width*length}$

height = $\frac{21000}{30*40}$

height = 17.5cm

The height of the container is 17.5cm.

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Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

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The sample proportion is p=0.26.

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The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328$

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

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2 years ago

Y is inversely proportional to x.<br> Complete the table.<br> х<br> 15<br> 6<br> у<br> 5<br> 10

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Answer:

When x = 15, y= 2

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Step-by-step explanation:

This is a question in inverse proportion. In this proportion, an increase in one quantity would lead to a decrease in the other and vice versa.

We are to complete the table using the relationship between x and y.

Given:

y is inversely proportional to x = y ∝ 1/x

∝ = proportional to

y ∝ 1/x

y = k × 1/x

Where k = constant of proportionality

To understand the relationship between y and x, we need to find the value of k.

y = k × 1/x

From the table,

When x = 6, y = 5

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y = 30/x

The above relationship would enable us find the missing parts.

When x = 15, y= ?

y = 30/15

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When y= 10, x= ?

10 = 30/x

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a quarter of a book a month

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2 years ago

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Answer: $(15.263,\ 17.537)$

Step-by-step explanation:

According to the given information, we have

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Critical value for 95 percent confidence interval :

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Required 95% confidence interval : $(15.263,\ 17.537)$

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1 year ago

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Answer:

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1 year ago