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xeze [42]
3 years ago
5

The height of the trunk is 26 inches the length of the trunk is 50 inches. The tv is 54 inches wide. And 96 inches in height Use

the Pythagorean theorem to calculate the length of the diagonal of the trunk.

Mathematics
1 answer:
Sav [38]3 years ago
6 0

Answer:

The length of the diagonal of the trunk is 56.356011 inches

Step-by-step explanation:

According to the given data we have the following:

height of the trunk= 26 inches

length of the trunk= 50 inches

According to the Pythagorean theorem, to calculate the length of the diagonal of the trunk we would have to calculate the following formula:

length of the diagonal of the trunk=√(height of the trunk∧2+length of the trunk∧2)

Therefore, length of the diagonal of the trunk=√(26∧2+50∧2)

length of the diagonal of the trunk=√3176

length of the diagonal of the trunk=56.356011

The length of the diagonal of the trunk is 56.356011 inches

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maks197457 [2]
Just multiply the bases and add up the exponents.

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6 0
3 years ago
Solve the system by substitution.<br> [-2.5x+y = 13.5<br> 12.25x - y=-12.25
IrinaK [193]

Answer:

x = 5/39 , y = 539/39

Step-by-step explanation:

Solve the following system:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

In the first equation, look to solve for y:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:

y - (5 x)/2 = 27/2

Add (5 x)/2 to both sides:

{y = 1/2 (5 x + 27)

12.25 x - y = -12.25

Substitute y = 1/2 (5 x + 27) into the second equation:

{y = 1/2 (5 x + 27)

1/2 (-5 x - 27) + 12.25 x = -12.25

(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

In the second equation, look to solve for x:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:

(39 x)/4 - 27/2 = -49/4

Add 27/2 to both sides:

{y = 1/2 (5 x + 27)

(39 x)/4 = 5/4

Multiply both sides by 4/39:

{y = 1/2 (5 x + 27)

x = 5/39

Substitute x = 5/39 into the first equation:

{y = 539/39

x = 5/39

Collect results in alphabetical order:

Answer: {x = 5/39 , y = 539/39

5 0
3 years ago
If f(x)=8-10x and g(x)=5x+4 what is the value of (fg)(-2)?
Shalnov [3]
First, calculate f(g(x))==> you plug (5x+4) in the value of x in f(x)

==>f(g(x))= 8-[10(5x+4)===>8-50x-40===>f(g(x))= -50x  + 32

& f(g(-2))= -100+32 =68.

There is a mistake in your answers, it should be 68 & not 78
6 0
2 years ago
Suppose a poll is taken that shows that 765 out of 1500 randomly​ selected, independent people believe the rich should pay more
Zanzabum

Answer:

z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775  

p_v =P(z>0.775)=0.219  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

Step-by-step explanation:

Data given and notation

n=1500 represent the random sample taken

X=765 represent the successes

\hat p=\frac{765}{1500}=0.51 estimated proportion of successes

p_o=0.5 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5:  

Null hypothesis:p \leq 0.5  

Alternative hypothesis:p > 0.5  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775  

Statistical decision  

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.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(z>0.775)=0.219  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

8 0
3 years ago
A sheet of glass has a density of 2.5g/cm^3. WHat is the density of the glass in kg/m^3?
larisa [96]
The answer is 0.0025kg/0.01m^3

5 0
2 years ago
Read 2 more answers
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