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kirill115 [55]
3 years ago
8

Convert y + 3 = -3(x + 5) to standard form.

Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0
Hi there!

y  + 3 =  - 3(x + 5)
First we need to work out the parenthesis, which can for instance be done using rainbow technique.

y + 3 =  - 3x  -  15
Now subtract 3 from both sides.

y =  - 3x  - 18
And finally add 3x to both sides.

3x + y =  - 18
The 4th answer choice is correct.



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nikitadnepr [17]

Answer:

7% R=18 6=4

Step-by-step explanation:

6 0
3 years ago
A poll in 2017 reported that 705 out of 1023 adults in a certain country believe that marijuana should be legalized. When this p
just olya [345]

Answer:

1. d. (0.652, 0.726)

2. b. (0.661, 0.718)

a. The margin of error of a 90​% confidence interval will be less than the margin of error for the 95​% and 99​% confidence intervals because intervals get wider with increasing confidence level.

Step-by-step explanation:

Data given and notation  

n=1023 represent the random sample taken in 2017    

X=705 represent the people who thinks that believe that marijuana should be legalized.

\hat p =\frac{705}{1023}=0.689 estimated proportion of people who thinks that believe that marijuana should be legalized.

z would represent the statistic in order to find the confidence interval    

p= population proportion of people who thinks that believe that marijuana should be legalized.

Part 1

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

0.689 -2.58 sqrt((0.689(1-0.689))/(1023))=0.652

0.689 + 2.58sqrt((0.56(1-0.689))/{1023))=0.726

And the 99% confidence interval would be given (0.652;0.726).

We are 99% confident that about 65.2% to 72.6% of people  believe that marijuana should be legalized

d. (0.652, 0.726)

Part 2

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

And replacing into the confidence interval formula we got:

0.689 - 1.96((0.689(1-0.689))/(1023))=0.661

0.689 + 1.96 ((frac{0.56(1-0.689))/(1023))=0.718

And the 95% confidence interval would be given (0.661;0.718).

We are 95% confident that about 66.1% to 71.8% of people  believe that marijuana should be legalized

b. (0.661, 0.718)

Part 3

Would be lower since the quantile z_{\alpha/2} for a lower confidence is lower than a quantile for a higher confidence level.

The margin of error of a 90​% confidence interval will be less than the margin of error for the 95​% and 99​% confidence intervals

If we calculate the 90% interval we got:

For the 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution. The quantile for this case would be 1.64.

And replacing into the confidence interval formula we got:

0.689 - 1.64 ((0.689(1-0.689))/{1023))=0.665

0.689 + 1.64 ((0.56(1-0.689))/(1023))=0.713

And the 90% confidence interval would be given (0.665;0.713).

We are 90% confident that about 66.5% to 71.3% of people  believe that marijuana should be legalized.

The intervals get wider with increasing confidence level.

So the correct answer is:

a. The margin of error of a 90​% confidence interval will be less than the margin of error for the 95​% and 99​% confidence intervals because intervals get wider with increasing confidence level.

6 0
3 years ago
The side lengths of a right triangle are 18 cm, 24 cm, and 30 cm. You are asked to find the area of the triangle by using A = 1/
vekshin1

Answer:

1. Use the Adjacent and opposite side (Ignore the Hypotenuse)

Or use HERO'S FORMULA based on the information given

2. Area = 216cm^2

Step-by-step explanation:

There are three to four ways we can go about finding the area of a triangle. And a these would be dependent on the information given about the triangle.

From the question, you said the three side lengths are given. In such case, we employ the HERO FORMULA.

HERO FORMULA:

Area = √ s(s-a)(s-b)(s-c)

where s = 1/2(a + b + c)

a, b, c are the three sides

But since the question insisted that we use 1/2* base * height. Let's use our know of right angle to dissolve that.

A right angle triangle has three sides. The longest is always the Hypotenuse.

Let's take it this way.

Hypotenuse = 30cm

Opposite= 18cm

Adjacent = 24cm

Area = 1/2 * base * height

Area = 1/2 * 18 * 24

Area = 1/2 * 432

Area = 216cm^2

We ignored the longest side, (the Hypotenuse)

6 0
3 years ago
I have this huge project that is worth half my grade, but my partner won't help at all. What should I do?
marusya05 [52]
Blackmail them. Kidding ask the teacher for a new partner or just do it on your own and tell the teacher to give you all the points then,
6 0
3 years ago
Read 2 more answers
Hello, I really need help with this!
yuradex [85]
1. Given
2. Definition of Supplementary Angles
3. First Substitution
4. Subtraction property of Equality
5. Second Substitution
6. Exterior Side in Opposite Rays
7. If corresponding angles are equal, then lines are parallel
5 0
3 years ago
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