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3 years ago

Is the term (x+2) a factor of the polynomial f(x)=x^3-10x^2+27x-12

Mathematics

1 answer:

Viefleur [7K]3 years ago

6 0

No.

f(-2) = -114, not zero.
(x-4) is the only rational factor of f(x).

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A tap is filling a 10-liters tank at the speed of 5 liters per minute.

SVETLANKA909090 [29]

Answer:

<em />

<em>It takes</em><u> 2.5 minutes </u><em>to fill the tank.</em>

Explanation:

The net speed or net rate for filling the 10-liters tank is equal to the speed the tap is filling less the speed the water is leaking through the hole located at the bottom of the tank:

Net rate = rate of filling - rate of leaking

Net rate = 5 liters/minute - 1 liter/minute

Net rate = 4 liters/minute

Thus, consiedering the tank is empty at the beginning, the time is:

Time = Volume of the tank / net rate of filling

Time = 10 liters / (4liters/minute)

Time = 2.5 minutes ← answer

4 0

3 years ago

A sports news station wanted to know whether people who live in the North or the South are bigger sports fans. For its study, 17

Free_Kalibri [48]

Using the z-distribution, it is found that the 95% confidence interval for the difference is (-1.3, -0.7).

<h3>What are the mean and the standard error for each sample?</h3>

Considering the data given:

$\mu_S = 3.8, n = 175, s_S = \frac{1.7}{\sqrt{175}} = 0.1285$

$\mu_N = 4.8, n = 152, s_N = \frac{1.2}{\sqrt{152}} = 0.0973$

<h3>What is the mean and the standard error for the distribution of differences?</h3>

The mean is the subtraction of the means, hence:

$\overline{x} = \mu_S - \mu_N = 3.8 - 4.8 = -1$

The standard error is the square root of the sum of the variances of each sample, hence:

$s = \sqrt{s_S^2 + s_N^2} = \sqrt{0.1285^2 + 0.0973^2} = 0.1612$

<h3>What is the confidence interval?</h3>

It is given by:

$\overline{x} \pm zs$

We have a 95% confidence interval, hence the critical value is of z = 1.96.

Then, the bounds of the interval are given as follows:

$\overline{x} - zs = -1 - 1.96(0.1612) = -1.3$

$\overline{x} + zs = -1 + 1.96(0.1612) = -0.7$

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

4 0

2 years ago

At 10:00 a.m. the temperature is –3.4°F. The temperature increases 0.5°F each hour for the next 6 hours. If the temperature drop

Marat540 [252]

Answer:

-3.4+3=-0.4 -0.4-5.3=-5.7 (-5.7F)

Step-by-step explanation:

Brainlist plz

3 0

2 years ago

Drag and drop the correct surface area to match the cube. cube with edge length = 3.2 m 12.8 m²19.2 m²51.2 m²61.44 m²

Ira Lisetskai [31]

- Surface Area of a Cube = 6(L)²
- Surface Area of this cube = 6(3.2)²
= 61.44 m²

3 0

3 years ago

Second time posting this. Please help!! :)

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

$\frac{480+24(x-40)}{x}$

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

5 0

3 years ago