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AysviL [449]
3 years ago
11

One number exceeds another by -1. the sum of the numbers is 5. what are the numbers?

Mathematics
1 answer:
maks197457 [2]3 years ago
4 0
X-y=-1
x+y=5
y=x+1
x+x+1=5
2x+1=5
2x=4
x=2
y=x+1
y=2+1
y=3
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Suppose 52% of the population has a college degree. If a random sample of size 563563 is selected, what is the probability that
amm1812

Answer:

The value is  P(| \^ p -  p| < 0.05 ) = 0.9822

Step-by-step explanation:

From the question we are told that

    The population proportion is  p =  0.52

     The sample size is  n  =  563      

Generally the population mean of the sampling distribution is mathematically  represented as

           \mu_{x} =  p =  0.52

Generally the standard deviation of the sampling distribution is mathematically  evaluated as

       \sigma  =  \sqrt{\frac{ p(1- p)}{n} }

=>      \sigma  =  \sqrt{\frac{ 0.52 (1- 0.52 )}{563} }

=>      \sigma  =   0.02106

Generally the  probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

            P(| \^ p -  p| < 0.05 ) =  P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 ))

  Here  \^ p is the sample proportion  of persons with a college degree.

So

 P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) = P(\frac{[[0.05 -0.52]]- 0.52}{0.02106} < \frac{[\^p - p] - p}{\sigma }  < \frac{[[0.05 -0.52]] + 0.52}{0.02106} )

Here  

    \frac{[\^p - p] - p}{\sigma }  = Z (The\ standardized \  value \  of\  (\^ p - p))

=> P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) = P[\frac{-0.47 - 0.52}{0.02106 }  <  Z  < \frac{-0.47 + 0.52}{0.02106 }]

=> P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) = P[ -2.37 <  Z  < 2.37 ]

=>  P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) = P(Z <  2.37 ) - P(Z < -2.37 )

From the z-table  the probability of  (Z <  2.37 ) and  (Z < -2.37 ) is

  P(Z <  2.37 ) = 0.9911

and

  P(Z <  - 2.37 ) = 0.0089

So

=>P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) =0.9911-0.0089

=>P( - (0.05 - 0.52 ) <  \^ p <  (0.05 + 0.52 )) = 0.9822

=> P(| \^ p -  p| < 0.05 ) = 0.9822

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3 years ago
Use the graph to find the cost of 6 show tickets.
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The lines y = 2x - 1 and y = -2x + 3 intersect at exactly one point which means this system has exactly one solution. so the system is consistent and independent 
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Answer for no.9:

144.5cm^2

Step-by-step explanation:

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3 years ago
Find the correct values for the variables that make the statement cos(h)=x/y true.
Stels [109]

Answer:

The sum of the measures of the angles in a triangle is equal to 180 degree.

In triangle FGH;

\angle F + \angle G + \angle H = 180^{\circ}

or

\angle H = 180^{\circ} -{\angle F + \angle G}

Substitute the given values from the given figure we have;

\angle H = 180^{\circ} -{33^{\circ} + 90^{\circ}}

\angle H = 180^{\circ} -{123^{\circ}}

Simplify:

\angle H = 57^{\circ}

Given that:

\cos H = \frac{x}{y}

Using Cosine ratio:

\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}

In a given figure:

Base = GH = x and Hypotenuse = FH = y = 80 cm

Then;

\cos 57^{\circ}= \frac{x}{80}

or

x = \cos 57^{\circ} \cdot 80  

x = 0.54463903501 \cdot 80 \approx 43.57 cm

Therefore, the value of :

H = 57^{\circ}

x = 43.57 cm

y = 80 cm





5 0
3 years ago
Read 2 more answers
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