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Bess [88]
3 years ago
6

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ou

nce. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
Mathematics
1 answer:
GalinKa [24]3 years ago
3 0

Answer:

The right solution is:

(a) 0.8849

(b) 12.28%

(c) 4.9935

(d) 28004

Step-by-step explanation:

Given:

Mean,

= 4.5

Standard deviation,

= 0.3

(a)

P(x > 4.14)

As we know,

⇒ z = \frac{4.14-4.5}{0.3}

      =-1.20

then,

⇒ P(z>-1.20) = P(z

                          =0.8849

(b)

P(4.8 < x < 5.04)

= P(\frac{4.8-4.5}{0.3} < \frac{x-\mu}{\sigma} < \frac{5.04-4.5}{0.3} )

= P(1

= P(z

= 0.9641 -0.8413

= 0.1228

or,

= 12.28 (%)

(c)

P(x > x) = 0.05

z value will be,

= 1.645

⇒ 1.645 = \frac{x - 4.5}{0.3}

         x = 4.9935

(d)

P(x < 5.01)

⇒ z = \frac{x- \mu}{\sigma}

      =\frac{5.01-4.5}{0.3}

      =1.7

P(z < 1.70) = 0.9554

⇒ n = \frac{27875}{0.9954}

       =28004

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Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

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using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

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10/20 is simplified to 1/2

k = 1/2

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2 years ago
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Anastaziya [24]

Answer:

35

Step-by-step explanation:

If they won 4/5 then they lost 1/5. If 1/5 is 7 then you need five 7s.

7 × 5 = 35

4 0
3 years ago
Read 2 more answers
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