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2 years ago

Solve the following equation for x. 12x^2-36x=0

Mathematics

1 answer:

OlgaM077 [116]2 years ago

6 0

$\qquad\qquad\huge\underline{{\sf Answer}}♨$

Let's solve for x ~

$\qquad \sf \dashrightarrow \:12 {x}^{2} - 36x = 0$

$\qquad \sf \dashrightarrow \:12 x({x}^{} - 3) = 0$

$\qquad \sf \dashrightarrow \:12x = 0 \: \: or \: \: x - 3 = 0$

$\qquad \sf \dashrightarrow \:x = 0 \: \: or \: \: x = 3$

Therefore, the possible values of x are 0 and 3

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A recipe requires 1\4 of a cup of cranberries for 1 batch. How many beaches of scones can be made using 6 1/2 cups of cranberrie

TiliK225 [7]

Answer:

Step-by-step explanation:

1 batch is 1/4 cups of cranberries.

This means that we have to find the number of groups of 1/4 in 6 1/2 cups to find the number of batches.

(The decimal forms of these numbers are 6.5 and 0.25)

6.5/0.25=26

There are 26 batches

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2 years ago

Need answer to. Add 3x-3and4x^2-6x

Dahasolnce [82]

3x-3+4x^2-6x
4x^2-6x+3x-3 (arrange them in order)
4x^2-3x-3

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3 years ago

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

Alexus [3.1K]

Answer:

a) 18.94% probability that the sample mean amount purchased is at least 12 gallons

b) 81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c) The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

For sums, we can apply the theorem, with mean $\mu$ and standard deviation $s = \sqrt{n}*\sigma$

In this problem, we have that:

$\mu = 11.5, \sigma = 4$

a. In a sample of 50 randomly selected customers, what is the approximate 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 1 subtracted by the pvalue of Z when X = 12.

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

By the Central Limit theorem

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

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

$Z = 0.88$

$Z = 0.88$ has a pvalue of 0.8106.

1 - 0.8106 = 0.1894

18.94% probability that the sample mean amount purchased is at least 12 gallons

b. In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at most 600 gallons.

For sums, so $mu = 50*11.5 = 575, s = \sqrt{50}*4 = 28.28$

This probability is the pvalue of Z when X = 600. So

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

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

$Z = 0.88$

$Z = 0.88$ has a pvalue of 0.8106.

81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c. What is the approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers.

This is X when Z has a pvalue of 0.95. So it is X when 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 approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

5 0

3 years ago

The length of a rectangular board is 10 cm longer than its with. The width of the board is 26cm. The board is cut into 9 equal p

Margaret [11]

Answer: 26 cm × 4 cm or

36 cm × 2.89 cm

Step-by-step explanation:

The diagram of the board is shown in the attached photo

Width of the rectangular board is given as 26 cm

The length of a rectangular board is 10 cm longer than its with. This means that

Length of rectangular board = 26 +10 = 36 cm.

Area of rectangular board = length × width. It becomes

36 × 26 = 936cm^2

The board is cut into 9 equal pieces. This means that the area of each piece would be the area of the board divided by 9. It becomes

936 /9 = 104cm^2

The dimensions of the piece would be

Since area of each piece is 104 cm^2 and the width of the bigger board still corresponds to one side of each piece, the other side of each piece will be 104 /26 = 4 cm

Also, the board could have been cut along the length such that one side of the cut piece corresponds to the length of the original board (36 cm)

and the other side becomes

104 /36 = 2.89 cm

The possible dimensions are

26 cm × 4 cm or

36 cm × 2.89 cm