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3 years ago

15 POINT QUESTION! Multiply and simplify. (4x−2)(3x^2−2x+1)

2 answers:

7 0

To answer this, first, you need to multiply the first bracket to the second bracket. Then, it will show like this: 4x(3x^2)-4x(2x)+4x(1)-2(3x^2)-2(-2x)-2(1)= 12x^3-8x^2+4x-6x^2+4x-2.
Then simplify them by adding or subtracting the same objects (same exponents and same variables). If they don't have the same objects, just let them be.
The final answer will be: -12x^3-14x^2+8x-2

Crazy boy [7]3 years ago

6 0

The correct answer is 12x³-14x²+8x-2.

Explanation:
We use the distributive property:
4x*3x² - 4x*2x + 4x*1 - 2*3x² - 2*(-2x) - 2*1 = 12x² - 8x² + 4x - 6x² + 4x - 2.

Combining like terms, we have 12x³-14x²+8x-2.

You might be interested in

A number when divided by 18 has a quotient of 132 and a remainder of 9. What is the number?

postnew [5]

$\frac{n}{18} = 132 + \frac{9}{18}$
$n = 2376 + 9 
$
$n = 2385$

8 0

4 years ago

The mean hourly wage for employees in industries is currently $24.57. Suppose we take a sample of employees from the manufacturi

Mashutka [201]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ = $24.57

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $24.57

(b) The P-value of the test statistics is 0.1212.

(c) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using P-value approach.

(d) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using critical value approach.

Step-by-step explanation:

We are given that a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the U.S industries.

Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour.

Let $\mu$ = population mean hourly wage in the manufacturing industry.

(a) Null Hypothesis, $H_0$ : $\mu$ = $24.57 {means that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ $24.57 {means that the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the U.S industries}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean wage in the manufacturing industry = $23.89/hr

σ = population standard deviation = $2.40/hr

n = sample of employees from the manufacturing industry = 30

So, the test statistics = $\frac{23.89-24.57}{\frac{2.40}{\sqrt{30} } }$

= -1.55

The value of z test statistics is -1.55.

(b) Now, the P-value of the test statistics is given by;

P-value = P(Z < -1.55) = 1 - P(Z $\leq$ 1.55)

= 1 - 0.9394 = 0.0606

For two-tailed test P-value is calculated as = 0.0606 $\times$ 2 = 0.1212

Since, the P-value of the test statistics is higher than the level of significance as 0.1212 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.

(d) Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.

6 0

3 years ago

Step by step to find the scientific notation for 1.3 x 10^9?

lakkis [162]

Answer:

117000000000

Step-by-step explanation:

117000000000

=1.17^11

or 1.17e+11

8 0

3 years ago

What is the tangent ratio for angle A?

Rasek [7]

Hi there!

Tangent = opposite/adjacent

The side opposite angle A is side CB, which equals 6.
The side adjacent to angle A is side CA, which equals 8.

Therefore, the tangent ratio of angle A is 6/8, or 3/4.

The correct answer is OPTION D.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

6 0

3 years ago

Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and

Elenna [48]

Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

3 0

3 years ago