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3 years ago

Please help me out!!!!!

Mathematics

1 answer:

valentina_108 [34]3 years ago

5 0

Answer:

Option (5)

Step-by-step explanation:

f(x) is a function with the degree of 3, having zeros as x = 2, 2t, -2t

And f(1) = -15

Option (1)

f(x) = 2x³- 2x² + 2x - 30

f(1) = 2(1)³ - 2(1)² + 2(1) - 30

= 2 - 2 + 2 - 30

= -28 ≠ -15

Therefore, Option (1) is not the answer.

Option (2)

f(x) = 2x³ + 2x² + 2x - 30

f(1) = 2(1)³ + 2(1)² + 2(1) - 30

= 2 + 2 + 2 - 30

= 6 - 30

= -24 ≠ -15

Therefore, Option (2) is not the answer.

Option (3)

f(x) = 3x³ - 6x² + 12x - 12

f(1) = 3(1)³ - 6(1)² + 12(1) - 12

= 3 - 6

= -3 ≠ -15

Therefore, Option (3) is not the answer.

Option(4)

f(x) = 48x³- 9x² + 12x - 24

f(1) = 48(1)³ - 9(1)² + 12(1) - 24

= 48 - 9 + 12 - 24

= 27 ≠ -15

Therefore, Option (4) is not the answer.

Option (5)

f(x) = 3x³- 6x² + 12x - 24

f(1) = 3(1)³- 6(1)² + 12(1) - 24

= 3 - 6 + 12 - 24

= -15

Therefore, Option (5) is the correct option.

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Answer: 74.5% of the measurements fall within one standard deviation of the average.

Step-by-step explanation:

The total number of measurements given is 2 + 12 + 10 + 33 + 40 + 76 + 80 + 65 + 52 + 22 + 12 + 5 + 11 = 420

If the mean is 21 mm and one standard deviation is 0.23 mm, then one standard deviation from the mean would be

21 ± 0.23

The lower limit is 20.77 mm

The upper limit is 21 + 0.23 = 21.23 mm

The number of measurements that fall within this range are

20.8 × 40

20.9 × 76

21.0 × 80

21.1 × 65

21.2 × 52

The total number of measurements that fall within this range is

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3 years ago

Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

kirill115 [55]

Answer:

f(x) = $x^{4}$ + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + $\sqrt{2}$ is a zero then - 1 - $\sqrt{2}$ is also a zero

$\sqrt{3}$ is a zero then - $\sqrt{3}$ is also a zero

Thus the corresponding factors are

(x - (- 1 + $\sqrt{2}$ ) ), (x - (- 1 - $\sqrt{2}$ ) ), (x - $\sqrt{3}$ ), (x - (- $\sqrt{3}$ )), that is

(x + 1 - $\sqrt{2}$ ), (x + 1 + $\sqrt{2}$ ), (x - $\sqrt{3}$ ), (x + $\sqrt{3}$ )

The polynomial is then the product of the roots

f(x) = (x + 1 - $\sqrt{2}$ )(x + 1 + $\sqrt{2}$ )(x - $\sqrt{3}$ )(x + $\sqrt{3}$ )

= ((x + 1)² - ( $\sqrt{2}$ )²)((x² - ( $\sqrt{3}$ )²)

= (x² + 2x + 1 - 2)(x² - 3)

= (x² + 2x - 1)(x² - 3) ← distribute

= $x^{4}$ - 3x² + 2x³ - 6x - x² + 3

= $x^{4}$ + 2x³ - 4x² - 6x + 3

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4 years ago

Is this answer is correct

Yuliya22 [10]

Yes, this answer is correct.

3 0

3 years ago

Read 2 more answers

The reported unemployment is 5.5% of the population. What measurement scale is used to measure unemployment? Select one: a. Nomi

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Answer:

c. Interval or ratio

Step-by-step explanation:

There exists the following measurement scales:

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3 years ago

A researcher studying the sleep habits of teens will select a random sample of n teens from the population to survey. The resear

kati45 [8]

Answer:

D. The center remains constant, and the area in the tails of the distribution decreases.

Step-by-step explanation:

Hello!

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3 years ago