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frutty [35]
3 years ago
14

Greatest common factor of 24x^8+6x^5+9x^2

Mathematics
1 answer:
spayn [35]3 years ago
7 0
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Nidhi is creating a rectangular garden in her backyard. The length of the garden is 10 feet. The perimeter of the garden must be
Basile [38]

Answer:

The range of width is 10 ≤ W ≤ 28

Step-by-step explanation:

* lets study the meaning of compound inequality

- If x is greater than a and x is smaller than b, then x is between a and b

∵ x > a and x < b

∴ The compound inequality is ⇒ a < x < b

# Ex: ∵ x > -2 and x < 10

∴ The compound inequality is ⇒ -2 < x < 10

- If x is greater than or equal a and x is smaller than or equal b, then

 x is from a and b

∵ x ≥ a and x ≤ b

∴ The compound inequality is ⇒ a ≤ x ≤ b

# Ex: ∵ x ≥ -2 and x ≤ 10

∴ The compound inequality is ⇒ -2 ≤ x ≤ 10

* Now lets solve the problem

- The garden in the shape of a rectangle with dimensions length (L)

 and width (W)

- The length of the garden is 10 feet

- The perimeter (P) of the garden is at least 40 feet and not more than

  76 feet

∵ L = 10 feet

∵ P = 2L + 2W

- At least means greater than or equal (≥) and not more than means

 smaller than or equal (≤)

∴ P ≥ 40 feet

∴ P ≤ 76 feet

- lets use the rule of the perimeter

∴ 2(10) + 2(W) ≥ 40 ⇒ simplify

∴ 20 + 2W ≥ 40 ⇒ subtract 20 from both sides

∴ 2W ≥ 20 ⇒ divide both sides by 2

∴ W ≥ 10 ⇒ (1)

- Do similar with P ≤ 76

∴ 2(10) + 2(W) ≤ 76 ⇒ simplify

∴ 20 + 2W ≤ 76 ⇒ subtract 20 from both sides

∴ 2W ≤ 56 ⇒ divide both sides by 2

∴ W ≤ 28 ⇒ (2)

- From (1) and (2)

∴ 10 ≤ W ≤ 28 ⇒ compound inequality

* The range of the width is from 10 feet to 28 feet

5 0
2 years ago
Tennis Replay In the year that this exercise was written, there were 879 challenges made to referee calls in professional tennis
tiny-mole [99]

Answer:

a. 0.0209 = 2.09% probability that among the 879 challenges, the number of overturned calls is exactly 231.

b. 231 is less than 2.5 standard deviations above the mean, which means that 231 overturned calls among 879 challenges is not a significantly high result.

Step-by-step explanation:

For each challenge, there are only two possible outcomes. Either it was overturned, or it was not. The probability of a challenge being overturned is independent of any other challenge. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Significantly high:

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

If a value is more than 2.5 standard deviations above the mean, this value is considered significantly high.

25% of the challenges are successfully upheld with the call overturned.

This means that p = 0.25

879 challenges

This meas that n = 879

a. If the 25% rate is correct, find the probability that among the 879 challenges, the number of overturned calls is exactly 231.

This is P(X = 231). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 231) = C_{879,231}.(0.25)^{231}.(0.75)^{648} = 0.0209

0.0209 = 2.09% probability that among the 879 challenges, the number of overturned calls is exactly 231.

b. If the 25% rate is correct, find the probability that among the 879 challenges, the number of overturned calls is 231 or more. If the 25% rate is correct, is 231 overturned calls among 879 challenges a result that is significantly high

The mean is:

E(X) = np = 879*0.25 = 219.75

The standard deviation is:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{879*0.25*0.75} = 12.84

219.75 + 2.5*12.84 = 251.85 > 231

231 is less than 2.5 standard deviations above the mean, which means that 231 overturned calls among 879 challenges is not a significantly high result.

5 0
2 years ago
If MrBeast bought 69 Lamborghini's and bought 420 Rolex watches how many items in all would he have bought altogether?
timama [110]
It’ll be 489 altogether

have a great day :)
6 0
3 years ago
Read 2 more answers
Anjali rented a bike from Julio's Bikes. It
Leni [432]

Answer:

8 Hours Because 6×8=48 Plus The Cost Was 10$ You Would Just Do 48 + 10 = 58

Step-by-step explanation:

6 × 8 =48 + 10 = 58

7 0
3 years ago
What is the area of a rectangle with the length of 43 inches and a width of 25 inches?
Lorico [155]
1.72 is the area to the rectangle 
4 0
2 years ago
Read 2 more answers
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