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3 years ago

can anyone solve this step by step its 3x-2y=5 3x+y=8 in substitution please they are both the same problem

Mathematics

1 answer:

Assoli18 [71]3 years ago

6 0

3x-2y=5

3x+y=8

Rewrite the second equation as y = -3x +8

Substitute that into the first equation for y:

3x-2(-3x+8) = 5

Use distributive property:

3x +6x -16 = 5

Combine like terms:

9x - 16 = 5

Add 16 to both sides:

9x = 21

Divide both sides by 9:

x = 21/9

x = 7/3

Replace X in the first equation and solve for y:

3(7/3) -2y = 5

7 - 2y = 5

Subtract 7 from both sides:

-2y = -2

Divide both sides by -2:

y = 1

The solution is (7/3, 1)

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Factor completely 3x^2− x − 4.

Mamont248 [21]

(x+1) x (3x-4) is the answer

3 0

3 years ago

Read 2 more answers

The weight of an organ in adult males has a bell-shaped distribution with a mean of 350 grams and a standard deviation of 45 gr

Svetach [21]

Answer:

a) About 68% of the data would be between 305 grams to 395 grams

b) About 95% of organs weighs between 260 grams and 440 grams

c)About 5% of organs weighs less than 260 grams or more than 440 grams

d) About 97% of organs weighs between 215 grams and 440 grams

Step-by-step explanation:

The empirical rule formula:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

(a) About 68% of organs will be between what weights?

We would be applying the First rule of the Empirical formula to this.

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

Mean = 350 grams

Standard deviation = 45 grams

Hence,

350 grams - 45 grams

= 305 grams

350grams + 45grams

= 395 grams

Therefore about 68% of the data would be between 305 grams to 395 grams

(b) What percentage of organs weighs between 260 grams and 440 grams?

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ - 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Therefore, about 95% of organs weighs between 260 grams and 440 grams

Let try the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 - 2(45)

= 350 - 90

= 260

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Since, about 95% of organs weighs between 260 grams and 440 grams, the percentage of organs weighs less than 260 grams or more than 440 grams is calculated as:

100% - 95%

= 5%

Therefore, percentage of organs weighs less than 260 grams or more than 440 grams is 5%

(d) What percentage of organs weighs between 215 grams and 440 grams?

For 215 grams, we apply the 3rd rule to confirm

= 3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

Mean = 350 grams

Standard deviation = 45 grams

μ - 3σ

= 350 - 3(45)

= 350 - 135

= 215.

Hence, 99% of the organs weigh 215 grams

For 440, from the solve questions above, we know the second rule applies.

Hence,

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean = 350 grams

Standard deviation = 45 grams

μ + 2σ

= 350 + 2(45)

= 350 + 90

= 440

Hence,

99% + 95%/ 2

= 194% / 2

= 97%

Therefore, about 97% of organs weighs between 215 grams and 440 grams

4 0

4 years ago

To find the difference of 7 - 3 5/12 how do you rename the 7

Anettt [7]

Hi! Here's how you do this problem:

1. You want to turn the 7 into 6 12/12

2. Subtract the two

6 12/12 - 3 5/12 = 3 7/12

So your answer is 3 7/12. Hope I helped!

3 0

3 years ago

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4639 miles, with a standard

WINSTONCH [101]

Answer:

0.9808 = 98.08% probability that the mean of a sample of 32 cars would differ from the population mean by less than 181 miles

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 normally distributed samples can be 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$