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3 years ago

Use the subtraction method to solve the system of equations. Choose the correct ordered pair. 2x-y=6

Mathematics

1 answer:

Ber [7]3 years ago

8 0

Answer:

Check for (3, 0)

Put x = 3 and y = 0 in equation 2x – y = 6

2(3) – (0) = 6

6 = 6

<h2>True statement. </h2>

(3,0) is a solution of 2x – y = 6.

(ii) Check for (0, 6)

Put x = 0 and y = 6 in 2x – y = 6

2 x 0 – 6 = 6-6 = 6

<h2>False statement. </h2>

⇒ (0, 6) is not a solution of 2x – y = 6.

(iii) Check for (2, -2)

Put x = 0 and y = 6 in 2x – y = 6

2 x 2 – (-2) = 6

4 + 2 = 6

6 = 6

<h2>True statement. </h2>

⇒ (2,-2) is a solution of 2x – y = 6.

(iv) Check for (√3, 0)

Put x = √3 and y = 0 in 2x – y = 6

2 x √3 – 0 = 6

2√3 = 6

<h2>False statement. </h2>

⇒(√3, 0) is not a solution of 2x – y = 6.

(v) Check for (1/2, -5)

Put x = 1/2 and y = -5 in 2x – y = 6

2 x (1/2) – (-5) = 6

1 + 5 = 6

6 = 6

<h2>True statement. </h2>

⇒ (1/2, -5) is a solution of 2x – y = 6.

Step-by-step explanation:

Hope it is helpful......

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What is the distance between points M(6,-6) and Z(2,-3), to the nearest tenth?

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3 years ago

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var

Andrei [34K]

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96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

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

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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.

In this question:

$\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5$

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

$Z = \frac{3765 - 3639}{59.5}$

$Z = 2.12$

$Z = 2.12$ has a pvalue of 0.983

X = 3513

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

$Z = \frac{3513 - 3639}{59.5}$

$Z = -2.12$

$Z = -2.12$ has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

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Nimfa-mama [501]

<em>Answer:</em>

<em>a is greater than 1, so a−1 is positive.</em>

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<em>The distance between a and 1 appears to be less than the distance between 1 and 0, so it looks like a is less than 2. Thus a−2 is negative.</em>

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<em>b is negative, so −b is positive.</em>

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<em>The distance between a and 0 appears to be less than the distance between b and 0, so it looks like |a| is less than |b|. Since b is negative and a is positive, a+b is negative.</em>

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<em>Since |a| and |b| are both greater than 1, |ab| is also greater than 1 (this builds on the intuition students gained in fifth grade as in 5.NF.5). ab is negative since a is positive and b is negative. Thus, ab+1 is negative.</em>

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3 years ago

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