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2 years ago

PLEASE HELP

Mathematics

1 answer:

babunello [35]2 years ago

7 0

The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2

Given that the softball diamond is square in shape.

Let the side of the square i.e. distance between consecutive bases is x

The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.

Using the Pythagorean theorem we have:

x² +x²= c²,

where c is the distance from the 1st base to the 3rd base.

Combining similar terms gives us

2x²=c²

Taking the square root of both sides we have

√2x²= √c²

⇒x√2=c

⇒c=x√2

This is the expression for the distance from the 1st base to the 3rd base in terms of side length.

Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.

Learn more about the Pythagorean theorem

here: brainly.com/question/231802

#SPJ10

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Answer:

a) ii. This is a left-tailed test.

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c) -1.301

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e) Option i) The data supports the claim that college students get less sleep than the general population.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 7 hours

Sample mean, $\bar{x}$ = 6.87 hours

Sample size, n = 45

Alpha, α = 0.10

Sample standard deviation, s = 0.55 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 7\text{ hours}\\H_A: \mu < 7\text{ hours}$

a) We use one-tailed(left) t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{6.87 - 7}{\frac{0.55}{\sqrt{45}} } =-1.59$

c) Now,

$t_{critical} \text{ at 0.10 level of significance, 44 degree of freedom } = -1.301$

Since,

$t_{stat} < t_{critical}$

d) We fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis and conclude that mean number of hours of sleep for all college students is less than 7 hours.

e) Option i) The data supports the claim that college students get less sleep than the general population.

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Step-by-step explanation:

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Answer:

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