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Natalija [7]
2 years ago
11

Draw the region that satisfies all three of the inequalities; x < 3, y > 2, y < 2x+3​

Mathematics
1 answer:
FrozenT [24]2 years ago
3 0

Check the picture below.

the line you drew for y = 2x +3 is correct, now recall that the line for x = 3 is just a vertical line, in red, and that y = 2 is just a horizontal line, in green.

now all lines are solid because all are using ⩽ or ⩾, meaning the borderline is included, and you can do a "true" "false" region check if you wish, but less than 3 is to the left of the red one, greater than 2 is above the green one and less than 2x + 3 is just to its left.

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The difference of twice a number G and 10 is 24.<br><br> Please help me as I'm stumped! Thank you!
arlik [135]
 Twice the number G is 2×G.
The difference between 2G and 10 is 24.
2G - 10 = 24
2G = 24 + 10
2G = 34
G = 34/2
G = 17
8 0
3 years ago
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Adult tickets to a play cost $22.00 Tickets for children cost $15.00. Tickets for a group of 11 people cost a total of $228.00.
Mademuasel [1]
There would be 2 children and 9 adults

Explanation: $22x 9 adults= 198
$15x 2 children= 30
Then you add them together and 198+30 = $228
6 0
3 years ago
Need help with my practice for a test please give awnser and show your work so i know how to do :)
docker41 [41]

Answer:

Step-by-step explanation:

2 * 2 = 4u² (area of the central square)

2 * 2 : 2 = 2u² (area of one congruent triangle)

4 + 2 + 2 = 8u²

(u = units)

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2 years ago
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A national survey conducted in 2011 among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War
Drupady [299]

Answer:

a)z=4.658

p_v =P(z>4.65)=1-P(z  

b) Using the significance level assumed \alpha=0.05 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is  higher than 50%.

c) The 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

Step-by-step explanation:

I )Part a

1) Data given and notation

n=1507 represent the random sample taken  

X represent the Americans who thinks that the Civil War is still relevant to American politics and political life

\hat p estimated proportion of Americans who thinks that the Civil War is still relevant to American politics and political life in the sample

p_o=0.5 is the value that we want to test since the problem says majority    

\alpha=0.05 represent the significance level (no given, but is assumed)  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

p= population proportion of Americans who thinks that the Civil War is still relevant to American politics and political life

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life exceeds 50%(Majority). :  

Null Hypothesis: p \leq 0.5

Alternative Hypothesis: p >0.5

We assume that the proportion follows a normal distribution.  

This is a one tail upper test for the proportion of  union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion \hat p is significantly (different,higher or less) from a hypothesized value p_o".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =1507*0.5=753.5>10

n(1-p_o)=1507*(1-0.5)=753.5>10

3) Calculate the statistic  

The statistic is calculated with the following formula:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}

On this case the value of p_o=0.5 is the value that we are testing and n = 1507.

z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1507}}}=4.658

The p value for the test would be:

p_v =P(z>4.65)=1-P(z  

II) Part b

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

Based on the alternative hypothesis the p value would be given by:

p_v =P(z>4.65)=1-P(z  

Using the significance level assumed \alpha=0.05 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is  higher than 50%.

III) Part c

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 90% confidence interval the value of \alpha=1-0.9=0.1 and \alpha/2=0.05, 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:

0.56 - 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.527

0.56 + 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.593

And the 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

And this result agrees with the result of part b, since the interval not contains the value of 0.5 we can conclude that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life it's higher than 0.5 at 90% of confidence.

7 0
2 years ago
!ANSWER FAST! <br><br> !ANSWER FAST!<br><br> !ANSWER FAST!
Anna007 [38]

Answer:

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Step-by-step explanation:

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HOPE THIS HELPS

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8 0
3 years ago
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