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Amiraneli [1.4K]
3 years ago
15

The length of a rectangle should be 8 meters longer than 7 times the width. If the length must be

Mathematics
1 answer:
nikdorinn [45]3 years ago
8 0

Answer:

The restrictions for x would be 14 > x > 5.

Step-by-step explanation:

Let the length of the rectangle be y and the width be x.

That being said, the equation would be as follows:

y = 7x + 8

y - 8 = 7x

x = \frac{y-8}{7}

Therefore, substituting the two values of y into the equations, we would get:

x = \frac{43-8}{7}

x = \frac{35}{7}

x = 5

And:

x = \frac{106-8}{7}

x = \frac{98}{7}

x = 14

Therefore, x would be between 5 and 14, and the restrictions for x would be 14 > x > 5.

Hope this helped!

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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

​(c) What percentage of organs weighs less than 260 grams or more than 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
3 years ago
What is the product of -3xy^2 and (2x^2 - 4y)
ICE Princess25 [194]

Answer:

 2 • (x2 - 2y)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 2x2 -  4y

Step  2  :  See below

Step  3  :  See below

Pulling out like terms :

3.1     Pull out like factors :

Answer:  2 • (x2 - 2y)

<em><u>Hope this helps.</u></em>

6 0
3 years ago
The price of 1 gallon of milk has increased $3.24 to $4.05. What is the percentage
AURORKA [14]
4.05 - 3.24 = 0.81
(0.81 / 3.24)*100 = 25%
5 0
4 years ago
Please help me!! Will give brainlyist
prohojiy [21]

Answer: We cannot see the picture, can you use it as a different file.

5 0
3 years ago
If f(x) = [x] – 5, what is f(8.6)?<br> 3<br> 4<br> 8<br> 9
shutvik [7]

Answer:

Step-by-step explanation:

The strange thing about the greatest integer function is that the number you are evaluating the function at is not actually the number unless its an integer.  The rule is to round down, ALWAYS, if you are dealing with a value of x that is not an integer.  In other words, you are NOT evaluating the function at 8.6, you have to round down to 8 and evaluate it there.  8 - 5 = 3

3 0
4 years ago
Read 2 more answers
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