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3 years ago

If the polynomial function P has real coefficients and if a + bi is a zero of P, then Incorrect:________

Mathematics

1 answer:

ivolga24 [154]3 years ago

5 0

Answer:

a -bi
2 -i

Step-by-step explanation:

If a polynomial has real coefficients, complex zeros come in conjugate pairs.

If a+bi is a zero, then so is a-bi. (a-bi is the conjugate of a+bi)

If 2+i is a zero, then so is 2-i.

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Many states assess the skills of their students in various grades. One program that is available for this purpose is the Nationa

Nataly [62]

Answer:

A score of 314 is needed to be in the top 25% of students who take this exam.

Step-by-step explanation:

We are given that one of the tests provided by the NAEP assesses the reading skills of twelfth-grade students. In recent years, the national mean score was 289 and the standard deviation was 37.

Let X = <u><em>scores of the tests provided by the NAEP</em></u>

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = national mean score = 289

$\sigma$ = standard deviation = 37

Now, we have to find how high a score is needed to be in the top 25% of students who take this exam, that means;

P(X > x) = 0.25 {where x is the required score}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-289}{37}$ ) = 0.25

P(Z > $\frac{x-289}{37}$ ) = 0.25

In the z table, the critial value of z that represents the top 25% of the area is given as 0.6745, that is;

$\frac{x-289}{37}=0.6745$

${x-289}=0.6745\times 37$

x = 289 + 24.96 = 313.96 ≈ 314

Hence, a score of 314 is needed to be in the top 25% of students who take this exam.

7 0

3 years ago

C6.1 PA1 short term decision Artisan Metalworks has a bottleneck in their production that occurs within the engraving department

laila [671]

Answer: $4850

Step-by-step explanation:

The other information related to the question is:

Direct materials = $3.50

Direct labor = $1.10

Variable overhead = $0.45

Fixed overhead = $2.80

Total = $7.85

Based on the information given in the question, the increase in the profit will be calculated as the contribution from the 3000 extra units minus the worker's salary.

Contribution from 3000 units will be:

= (Selling price - Direct materials - Direct labor - Variable overhead) × 3000

= ($25 - $3.50 - $1.10 - $0.45) × 3000

= $19.95 × 3000

= $59850

Increase on Profit:

= $59850 - $55000

= $4850

5 0

3 years ago

Find the area to the nearest hundredth

Savatey [412]

Answer:

9.0586 OR

9.06

Step-by-step explanation:

IDK, used fusion 360

6 0

3 years ago

What happens to the graph of the line y = mx + b if the value of b is decreased?

ollegr [7]

Answer:

The lines moves lower.

Step-by-step explanation:

The steepness of a line is related to the slope, m.

b is the y-intercept, not the slope.

b is where the line intersects the y-axis.

Changing b changes the vertical position of the line.

Answer: The lines moves lower.

7 0

2 years ago

6. The diagram on the right shows the cross-section of a cylindrical pipe with water lying in the bottom. a) If the maximum dept

riadik2000 [5.3K]

Answer:

404 cm³ Anyway... Look down here for my explanation.

Step-by-step explanation:

Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.

We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area 88.8/360*area of circle - ½*7*788.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

Volume of water = cross-sectional area * length

13.5 * 30 cm³

404 cm³

6 0

2 years ago