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tester [92]
3 years ago
15

10x^4+7x^3-12x^2

Mathematics
1 answer:
VashaNatasha [74]3 years ago
8 0
10x^4+ 7x^3-12x^2
= x^2(10x^2+ 7x- 12)
= x^2(10x^2 -8x+ 15x -12)
= x^2[ 2x(5x-4)+ 3(5x-4)]
= x^2(5x-4)(2x+3)

x^2(5x-4)(2x+3)= 0
⇒ x= 0
or 5x-4= 0
or 2x+3= 0
⇒ x= 0
or x= 4/5
or x= -3/2

The final answer is x= 0 or x= 4/5 or x= -3/2~

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Answer:

\triangle CBA \sim\triangle EFD

Step-by-step explanation:

\triangle CBA \sim\triangle EFD is the appropriate similarity statement.

5 0
3 years ago
This question is too hard
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Answer:

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Total number of dried fruits is 21, while the total number of nuts is 33.

Step-by-step explanation:

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Anna wants to buy a car in two years and wants to have $10,000 for the purchase. How much will Anna need to deposit today in an
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$9,050.25

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6 0
3 years ago
Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations. Assume that the popu
aleksley [76]

Answer:

b. Student-t with 48 degrees of freedom

Step-by-step explanation:

For this case we need to use a Two Sample t Test: equal variances.

Assumptions

When running a two-sample equal-variance t-test, the basic assumptions are "that the distributions of the two  populations are normal, and that the variances of the two distributions are the same".

Let \bar x and \bar y be the sample means of two sets of data of size n_x and n_y respectively. We assume that the distribution's of x and y are:

x \sim N(\mu_x ,\sigma_x =\sigma)

y \sim N(\mu_y ,\sigma_y=\sigma)

Both are normally distributed but without the variance equal for both populations.

The system of hypothesis can be:

Null hypothesis: \mu_x =\mu_y

Alternative hypothesis: \mu_x \neq \mu_y

We can define the following random variable:

t=\frac{(\bar x -\bar y)-(\mu_x -\mu_y)}{s\sqrt{\frac{1}{n_x}+\frac{1}{n_y}}}

The random variable t is distributed t \sim t_{n_x +n_y -2}, with the degrees of freedom df=n_x +n_y -2= 20+30-2=48

And the pooled variance can be founded with the following formula:

s^2=\frac{(n_x -1)s_x^2 +(n_y-1)s_y^2}{n_x +n_y -2}

So on this case the best answer would be :

b. Student-t with 48 degrees of freedom

5 0
3 years ago
500 principal earning 3% compound monthly, after 10 years.
mamaluj [8]

Answer:

D. $674.68

Step-by-step explanation:

We will use the well known equation for compound interest

A = P(1 + \frac{r}{n})^{nt}

Where

  • A is the final total
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  • r is the interest rate as a decimal
  • n is the number of times the interest is compounded each year
  • t the number of years

Plugging in what we know from the question:

A = 500(1+\frac{0.03}{12})^{12 \times 10}\\A = 500(1.34935355)\\A = 674.68

So the answer is D.

Hope this helps!

4 0
3 years ago
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