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2 years ago

Is it possible to construct a triangle with the given lengths? 17, 37, 53

Mathematics

1 answer:

kvv77 [185]2 years ago

7 0

Answer:

Yes

Step-by-step explanation:

In any triangle, the sum of any two sides must be larger than the third side. To test this, we only actually need to pick the two shorter sides. In this case, the following inequality is true:

$17+37>53,\\54>53,\\\text{True}\:\checkmark$

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Sgagwhjdbwjjahavajansmkshsgsbsnkdjfhdbdbdjdqhahr

Nezavi [6.7K]

Answer:

huh?

Step-by-step explanation:

huh what does "sgagwhjdbwjjahavajansmkshsgsbsnkdjfhdbdbdjdqhahr" mean?

5 0

3 years ago

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,91

Maurinko [17]

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that $n = 3900, \pi = \frac{1911}{3900} = 0.49$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032$

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

3 0

2 years ago

Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end be

MaRussiya [10]

Using limits, it is found that the end behavior of the function is given as follows:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

<h3>How to find the end behavior of a function f(x)?</h3>

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In this problem, the function is:

$f(x) = \frac{8x - 1}{2x - 9}$

Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4$ .

$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4$ .

Hence the correct statement is:

As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.

More can be learned about limits and end behavior at brainly.com/question/27950332

#SPJ1

7 0

2 years ago

Please help on two math questions. I don’t understand how to do them.

Sidana [21]

When you represent intervals on the number line, you're including full dots, excluding empty dots, and you're considering numbers highlighted by the line.

In the first case, you've highlighted everything before -2 (full dot, thus included), and everything after 1 (empty dot, excluded). So, the set would be

$x\leq -2 \lor\ x>1$

or, in interval notation,

$(-\infty,-2]\cup (1,\infty)$

In the second case, you are looking for all numbers between -3 and 5. This interval is symmetric with respect to 1: you're considering all numbers that are at most 4 units away from 1, both to the left and to the right.

This means that the difference between your numbers at 1 must be at most 4, which is modelled by

$|x-1|\leq 4$

where the absolute values guarantees that you'll pick numbers to the left and to the right of 1.

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3 years ago

Which of the following is an example of a culture maintaining traditional ways?

ddd [48]

Answer:

Amish driving buggies and using horses and mules instead of tractors

Step-by-step explanation:

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3 years ago