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3 years ago

N-31/4 =2 simple equation

Mathematics

1 answer:

Zanzabum3 years ago

6 0

Answer:

n = 5.75

Step-by-step explanation:

original equation

n - 31/4 = 2

multiply everything by 4

n * 4 - 31/4 * 4 = 2 * 4

simplify

4n - 31 = 8

add 31 to both sides

4n - 31 + 31 = 8 + -31

simplify

4n = -23

divide both sides by 4

4n/4 = -23/4

simplify

n = 5.75

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A tetrahedron is a triangular pyramid with 4 equilateral faces. Han has a box of tetrahedrons with each of the 4 vertices marked

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Theoretically, the number of the vertex comes at the top must be equal for infinitely many numbers of trials, but it's a tedious job to roll the dice for a large number of times. Rolling the tetrahedron only 10 times will not predict the correct result.

Han suspects that this tetrahedron is weighted in some way to make 1 appear more often than the other numbers.

So, check his suspect experimentally with the help of the concept of center of mass. A fair tetrahedron must have the center of mass at the center of the body.

The given tetrahedron has 4 equilateral triangular faces, so at first, measure all the sides of triangular faces and make sure that all are having the same length.

Then, conduct an experiment to check the location of the center of mass.

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For the center of mass to be located at the center of the tetrahedron, the base must be parallel to the ground (flat ground).i.e the hanging string must be perpendicular to the base for all the four cases.

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3 years ago

Researchers studying starfish collected two independent random samples of 40 starfish. One sample came from an ocean area in the

krek1111 [17]

Answer:

The test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

Step-by-step explanation:

The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.

The hypothesis to test this can be defined as follows:

H₀: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ = p₂.

Hₐ: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ ≠ p₂.

The two-proportion z-test would be used to perform the test.

A sample of n = 40 starfishes are selected from both the ocean areas.

It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of the 40 starfish from the south, 11 were found to be over 8 inches in length.

Compute the sample proportion of starfish from north that were over 8 inches in length as follows:

$\hat p_{n}=\frac{6}{40}=0.15$

Compute the sample proportion of starfish from south that were over 8 inches in length as follows:

$\hat p_{s}=\frac{11}{40}=0.275$

The test statistic is:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

Compute the combined proportion P as follows:

$P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125$

Compute the test statistic value as follows:

$z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}$

$=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$

Thus, the test statistic for the appropriate test is $\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}$ .

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qaws [65]

Answer:

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Step-by-step explanation:

Remember that complementary angles always add up to 90°.

We know that the two complementary angles are represented by (x) and (x+14). In other words:

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So, let's solve for x.

First, combine like terms:

$2x+14=90$

Let's isolate the x by subtracting 14 from both sides:

$(2x+14)-14=(90)-14$

The left cancels. Subtract on the right:

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Divide both sides by 2:

$\frac{2x}{2}=\frac{76}{2}$

The left side cancels. Divide on the right:

$x=38\textdegree$

So, the value of x is 38°.

And we're done!

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4 years ago