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Anni [7]
2 years ago
10

In her calculations, Rosita will be using the square root of 2 often. She wants to use as few digits as possible, but at the sam

e time have sufficient precision. How should Rosita round the square root of 2 so that the approximation times 5 is greater than 7.05?
Mathematics
1 answer:
Sladkaya [172]2 years ago
6 0

Testing the multiplication for each case, it is found that she should round the square root of 2 to three decimal digits.

<h3>What is the square root of 2?</h3>

The square root of 2 is given by:

\sqrt{2} = 1.41421356237

With one decimal digit, the result of the multiplication is:

5 \times \sqrt{2} = 5 \times 1.4 = 7 < 7.05

With two decimal digits, the result of the multiplication is:

5 \times \sqrt{2} = 5 \times 1.41 = 7.05 = 7.05

With three decimal digits, the result of the multiplication is:

5 \times \sqrt{2} = 5 \times 1.414 = 7.07 > 7.05

Hence, she should round the square root of 2 to three decimal digits.

You can learn more about rounding at brainly.com/question/17248958

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The strength of a cable is proportional to the square of its diameter. If a 2-cm cable will support 800kg, how much will a 3-cm
xz_007 [3.2K]
Strength [is proportional to] d^2
strength1/(d1)^2 = strength2/(d2)^2
800kg/(2cm)^2 = strength2/(3cm)^2
strength2 = 800 kg * (3 cm)^2/(2 cm)^2
strength2 = 800 kg * 3^2/2^2
strength2 = 800 kg * 9/4
strength2 = 1800 kg
3 0
3 years ago
What is the greatest common factor of 3x^2-9x
sp2606 [1]
The answer is 3x.
Factor out 3x and u get 3x(x-3).
3 0
3 years ago
Five ninths plus four sixths have a nice day Owo
Nat2105 [25]

Answer:

<em>Shoyo here!</em>

Step-by-step explanation:

1.22222222222

hehe, that's a long number- have a nice day! <3

8 0
3 years ago
A sample size 25 is picked up at random from a population which is normally
Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

Sample of 25:

This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

(a) P(X<99)

This is the pvalue of Z when X = 99. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{99 - 100}{1.2}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

Z = \frac{X - \mu}{s}

Z = \frac{100 - 100}{1.2}

Z = 0

Z = 0 has a pvalue of 0.5

X = 98

Z = \frac{X - \mu}{s}

Z = \frac{98 - 100}{1.2}

Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
3 years ago
Write an inequality to describe the region. the region between the yz-plane and the vertical plane x = 3
deff fn [24]

Write an inequality to describe the region is x < 0 < 3

Inequalities in three dimensions:

When an inequality representing a region in three dimensions contains only one of the three variables, then the other two variables have no restrictions. We use inequalities to describe solid regions in three dimensions.

Answers and Explanation:

The y z - plane is represented by the equation x = 0

As the region is between this plane and the vertical plane x = 3, we will get the inequality 0 < 0 < 3

Thus, the desired inequality is  

0 < 0 < 3.

Learn more about inequalities at:

brainly.com/question/14408811

#SPJ4

4 0
2 years ago
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