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3 years ago

The lengths of a triangle are 12 and 23 meters find the range of possible lengths for the third side

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

6 0

Answer: 11 < x < 35

suppose: the length of the third side is x

because x is the third side of a triangle

=> 23 - 12 < x < 23 + 12

⇔ 11 < x < 35

Step-by-step explanation:

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A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 wo

levacccp [35]

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for 2 worthless stone selection),

X = 1200(1 worthless stone & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

$(^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435$

Thus;

$Pr (X = 0) = \dfrac{(^8_2)}{435}$

$Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644$

$P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}$

$P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}$

$P(X =1200) = \dfrac{ (8) ( 22) }{435}$

$P(X =1200) =0.4046$

$Pr (X = 2400) = \dfrac{(^{22}_2)}{435}$

$Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310$

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046) + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

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3 years ago

What is 2/5 ÷ 2/3 i need help

ki77a [65]

Answer:

0.6

Step-by-step explanation:

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2 years ago

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Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x –

mafiozo [28]

Answer:

0 = x2 - 9x + 20

Step-by-step explanation:

y + 5x = x² + 10 Simplify this equation

- 5x - 5x

y = x² - 5x + 10

Set both equations equal to each other since they both equal y

x² - 5x + 10 = 4x - 10

-4x - 4x

x² - 9x + 10 = -10

+ 10 + 10

x² - 9x + 20 = 0

If this answer is correct, please make me Brainliest!

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3 years ago

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Answer:

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3 years ago

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algol [13]

Answer:

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Step-by-step explanation:

9 x 60 to get the minutes then add the extra 15

555/538 (minutes over miles)

1.0315 x 60 to get back to hours

61.89 miles per hour

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3 years ago