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Viefleur [7K]
3 years ago
5

If a math student Square both legs of a right triangle and the results were 441 and 400, what is the length of the hypotenuse of

a triangle?​
Mathematics
1 answer:
kolezko [41]3 years ago
7 0

Answer:

29 \\

Solution:

According to the Pythagorean Theorem, is that the square of the hypotenuse is equal to the sums of squares of the two legs in which if you take the square root of the sum you are going to get the actual length of the hypotenuse but the two legs are already squared so all you have to do now is sum them and take the square root of it.

\sqrt{441  +  400}  \\  \sqrt{841} \\ 29

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3/5 of a condductors club went on a camping trip. 39 people went how mant stayed home
mafiozo [28]
39 / 3/5 = 

39 *5 = 195 / 3 = 65

65-39 = 26 people stayed home
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3 years ago
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.

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2 years ago
Four students had the following amounts of money in their pockets: $3.14, $.67, $2.45, and $1.14. How much money did they have t
Butoxors [25]
A. $7.40
Adding $3.14 to $0.67 equals $3.81
You then could add $2.45 to $3.81 and get $6.26
Finally you add $1.14 to $6.26 and get $7.40
7 0
3 years ago
Read 2 more answers
In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is
zheka24 [161]

Answer:

f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

Step-by-step explanation:

Let:

M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y

This is and exact equation, because:

\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}

So, define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)

The solution will be given by:

f(x,y)=C_1

Where C1 is an arbitrary constant

Integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y):

f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}

Substitute into \frac{\partial f(x,y)}{\partial y} =N(x,y)

2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y

Integrate \frac{dg(y)}{dy} with respect to y:

g(y)=\int\ {8y} \, dy =4y^2

Substitute g(y) into f(x,y):

f(x,y)=2x^2+4y^2+2xy

The solution is f(x,y)=C1

f(x,y)=2x^2+4y^2+2xy=C_1

Solving y using quadratic formula:

y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )

4 0
3 years ago
A 51-foot ladder is leaning up against a building . The top of the ladder reaches the wall at a height of 50 feet . How far is t
alexandr402 [8]
If 50^2 +b^2=51^2 then
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           b^2=100
              b=10
4 0
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