Solve the equation 4y-1.9=6.3

The table shows the price for different numbers of board games:

zlopas [31]

Answer:

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

= 7/2

= 3.5

For the point (4, 14)

k = y/x

= 14 / 4

= 7/2

= 3.5

For the point (5, 17.50)

k = y/x

= 17.5 / 5

= 3.5

For the point (9, 31.50)

k = y/x

= 31.50 / 9

= 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

= 7

The price of 4 board game

y = 3.5 (4)

= 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

6 0

2 years ago

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample

fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

37% of the company's orders come from first-time customers.

This means that $p = 0.37$

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that $n = 225$

Mean and standard deviation:

$\mu = p = 0.37$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322$

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

$Z = \frac{0.38 - 0.37}{0.0322}$

$Z = 0.31$

$Z = 0.31$ has a pvalue of 0.6217

X = 0.26

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

$Z = \frac{0.26 - 0.37}{0.0322}$

$Z = -3.42$

$Z = -3.42$ has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0

2 years ago

The target temperature for a laboratory is 72° Fahrenheit. It

myrzilka [38]

The inequality |t - 72| ≤ 2 represents the target temperature for a laboratory is 72° Fahrenheit, and it can vary by up to 2° option (D) is correct.

<h3>What is inequality?</h3>

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

The question is incomplete.

The complete question is in the picture, please find the attached picture.

We have:

The target temperature for a laboratory is 72° Fahrenheit. It can vary by up to 2°.

Target temperature = 72 degree Fahrenheit

It can vary by up to 2°. (the highest limit)

The temperature in the laboratory represented by t

Now,

inequality represents this situation is:

|t - 72| ≤ 2

Thus, the inequality |t - 72| ≤ 2 represents the target temperature for a laboratory is 72° Fahrenheit, and it can vary by up to 2° option (D) is correct.

Learn more about the inequality here:

brainly.com/question/19491153

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