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alexgriva [62]
3 years ago
7

What is the square root of 144

Mathematics
2 answers:
zimovet [89]3 years ago
6 0

Answer: 12

Step-by-step explanation: To solve this problem, first notice that the square root of 144 is a perfect square. In other words, it's possible to find a whole number multiplied by itself which equals 144.

Since 144 factors as 12 x 12, the square root of 144 is 12.

Dmitrij [34]3 years ago
3 0
The square root of 144 is 12
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A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many
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The total surface area of the triangular prism that has a height of h and the side length of a is given below.

\rm a(\dfrac{\sqrt3}{2} \ a + 3h)

<h3>What is a triangular prism?</h3>

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.

A box is in the shape of an equilateral triangular prism.

If the box is to be covered with paper on its lateral sides.

Let a be the side length of the equilateral triangle and h be the height of the prism.

Then the surface area of the triangular prism will be

Surface area = 2 × area of triangle + 3 × area of the rectangle

The area of the triangle will be

\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}

The area of the rectangle will be

\rm Area \ of \ rectangle = a \ h

Then the total surface area will be

\rm Surface\ area =  2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area =  a(\dfrac{\sqrt3}{2} \ a + 3h)

More about the triangular prism link is given below.

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2 years ago
Sofie claims to be a tasting expert. To test her abilities, someone bakes Sofie a cake using 3 of the following
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Summing all the ingredients to get the total sample size, we applied the formula for obtaining the probability which is

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Answer:

Option b - not significantly greater than 75%.

Step-by-step explanation:

A random sample of 100 people was taken i.e. n=100

Eighty of the people in the sample favored Candidate i.e. x=80

We have used single sample proportion test,

p=\frac{x}{n}

p=\frac{80}{100}

p=0.8

Now we define hypothesis,

Null hypothesis H_0 : candidate A is significantly greater than 75%.

Alternative hypothesis H_1 : candidate A is not significantly greater than 75%.

Level of significance \alpha=0.05

Applying test statistic Z -proportion,

Z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}

Where, \widehat{p}=80\%=0.80 and p=75%=0.75

Substitute the values,

Z=\frac{0.80-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}

Z=\frac{0.80-0.75}{\sqrt{\frac{0.1875}{100}}}

Z=\frac{0.05}{0.0433}

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The p-value is

P(Z>1.1547)=1-P(Z

P(Z>1.1547)=1-0.8789

P(Z>1.1547)=0.1241

Now, the p-value is greater than the 0.05.

So we fail to reject the null hypothesis and conclude that the A is not significantly greater than 75%.

Therefore, Option b is correct.

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