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2 months ago

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Frank reasoned that in the number 0.555, the value of the 5 in the thousands place is ten times as great as the 5 in the hundred

th place is he correct explain

2 answers:

Inessa [12.5K]2 months ago

5 0

Answer:

Frank is mistaken.

Step-by-step explanation:

It is given: Frank maintains that in 0.555, the 5 in thousands place has a value tenfold that of the 5 in hundredths place.

To determine: Is he correct explain?

Solution:

Ones Tenths Hundredths Thousandths

0 5 5 5

The expanded form results in $0\times 1+5\times \frac{1}{10}+5\times \frac{1}{100}+5\times \frac{1}{1000}$

The 5 in the thousandths position is $\frac{1}{10}$ times the value of the 5 in hundredths position.

Consequently, Frank's assertion is incorrect.

zzz [12.3K]2 months ago

3 0

The provided number is 0.555, which can also be expressed as

$0+ \frac{1}{10}*5 + \frac{1}{100}* 5+ \frac{1}{1000} * 5$

In examining the digits post-decimal, each subsequent digit decreases to 1/10 of the preceding one.

Thus, the assertion that "the value of the 5 in the thousands place is ten times as great as the 5 in the hundredth place" is incorrect.

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Write the perimeter of the floor plan shown as an algebraic expression in x.

Leona [12618]

To determine the perimeter, we sum the lengths of all sides.

Looking at the diagram, we find the perimeter is calculated as follows:
P = 11 + (x - 2) + (11 - 3) + [(x - 2) - (x - 11)] + (x - 11)
= 11 + x - 2 + 8 + 9 + x - 11
= 2x + 15.

Final expression: 2x + 15

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3 months ago

Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the me

babunello [11817]

Answer:

a) There is an 18.94% chance that the sample mean of the amount purchased will be at least 12 gallons.

b) There is an 81.06% chance that the total gasoline purchased will not exceed 600 gallons.

c) The estimated value for the 95th percentile of the total consumption by 50 randomly chosen customers is 621.5 gallons.

Step-by-step explanation:

The solution to this query involves applying the normal probability distribution and the central limit theorem.

Normal probability distribution

Issues involving normally distributed samples can be addressed using the z-score formula.

In a dataset characterized by mean $\mu$ and standard deviation $\sigma$ , the z-score for a value X is expressed as:

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

The z-score indicates how many standard deviations a particular value is from the mean. After calculating the z-score, we reference the z-score table to find its corresponding p-value, which represents the probability that a measure is less than X, essentially giving us X's percentile. By subtracting the p-value from 1, we find the chance that the measure exceeds X.

Central Limit Theorem

The Central Limit Theorem posits that for a normally distributed variable X, with mean $\mu$ and standard deviation $\sigma$ , the distribution of sample means with size n approximates a normal distribution characterized by mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

Even when dealing with a skewed variable, the Central Limit Theorem remains applicable as long as n is no less than 30.

For sums, this theorem can likewise be employed, accompanied by mean $\mu$ and standard deviation $s = \sqrt{n}*\sigma$ .

In this scenario, we are given that:

$\mu = 11.5, \sigma = 4$

a. For a group of 50 randomly selected customers, what is the estimated probability that the sample mean amount purchased is at least 12 gallons?

Here we have $n = 50, s = \frac{4}{\sqrt{50}} = 0.5657$

This probability is derived from 1 minus the p-value of Z corresponding to X = 12.

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

According to the Central Limit Theorem

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

$Z = \frac{12 - 11.5}{0.5657}$

$Z = 0.88$

$Z = 0.88$ yields a p-value of 0.8106.

1 - 0.8106 = 0.1894

Therefore, there is an 18.94% chance that the sample mean amount purchased is at least 12 gallons.

b. For a group of 50 randomly selected customers, what is the estimated probability that the total amount of gasoline purchased does not exceed 600 gallons?

Regarding sums, we have $mu = 50*11.5 = 575, s = \sqrt{50}*4 = 28.28$

This probability equals the p-value of Z when X = 600. Hence,

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

$Z = \frac{600 - 575}{28.28}$

$Z = 0.88$

$Z = 0.88$ displays a p-value of 0.8106.

Thus, there is an 81.06% chance that the total gasoline purchased will be 600 gallons or less.

c. What is the approximate figure for the 95th percentile regarding the total purchases by 50 randomly chosen customers?

This value corresponds to X when Z indicates a p-value of 0.95, which occurs at Z = 1.645.

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

$1.645 = \frac{X- 575}{28.28}$

$X - 575 = 28.28*1.645$

$X = 621.5$

The 95th percentile estimate for the total amount purchased by 50 randomly selected customers stands at 621.5 gallons.

5 0

2 months ago

What is a31 of the arithmetic sequence for which a5=3.2 and a9=12.0?

zzz [12365]

The formula for an arithmetic sequence:

$a_n=a_1+(n-1)d$

We are given:

$a_5=3.2,\ a_9=12.0$

Determine d (the common difference)

$a_9-a_5=4d\\\\4d=12.0-3.2\\\\4d=8.8\ \ \ |:4\\\\d=2.2$

Calculate a31:

$a_{31}=a_5+26d\\\\a_{31}=3.2+26\cdot2.2=60.4$

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2 months ago

Use the table to find the residual points. A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4,

Leona [12618]

Answer:

What is the variation for each successive input?

✔ 1

What is the variation for each successive output?

✔ 0.35

What is the rate of variation for the correlation?

✔ 0.35

Step-by-step explanation:

The change per input is 1 since the inputs are 10,11,12,13.

The change for each successive output is 0.35 because we must subtract 4.1 from 3.75.

Thus, the rate of variation for the correlation is likewise 0.35.

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2 months ago

An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid h

Svet_ta [12734]

Response:

Volume of the trapezoidal prism = 15x^2 cubic units

Detailed explanation:

First, let’s calculate the area of the trapezoidal bases.

The lengths of the parallel sides are x and 2x, averaging to 1.5x.

The height stands at x

Consequently, area of the trapezoidal base comes out to be 1.5x * x = 1.5x^2

The volume of this prism is computed as area of the base multiplied by height

(the length is not a factor, but height certainly is)

Thus, 1.5x^2 * 10 yields 15x^2

5 0

2 months ago