What is the solution to -3x+5?

Which choice is equivalent to the expression shown below? -3(3y-2x) +2(5x-4y)

kap26 [50]

Answer:

-17y + 16x

Step-by-step explanation:

-3(3y - 2x) + 2(5x - 4y) = -9y + 6x + 10x - 8y = -17Y + 16X.

If it is helpful, plz give me Brainliest.

7 0

3 years ago

What is the image of point (4, 5) after a counterclockwise rotation of 270º about the origin?

andriy [413]

A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin.

Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

A clockwise rotation of 90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, a counterclockwise rotation of 270º about the origin which is equivalent to a clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)

Therefore, a counterclockwise rotation of 270º about the origin of the point (4, 5) will result in an image with the coordinate of (5, -4) (option C)

3 0

3 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

2 years ago

Herman and Helga had a combined gross income of $391,200 in 2009. When filing their federal income tax return with the Married F

viva [34]

33% depending on if your numbers is the same as mine

7 0

3 years ago

Read 2 more answers

Use the formula R = 6e12.77x, where x is the blood alcohol concentration and R, as a percent, is the risk of having a car accide

kenny6666 [7]

Well, It depends. It is either the mathematical term for 100% - 50%, or 6e*Ehq8deh. So, It is either 1389D9238 or c793-sk2. So try plotting the database point. Hope this helps :)

3 0

3 years ago

Read 2 more answers