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3 years ago

Complementary angles If G= (6x-15)° and H= (3x+6)° find the x value and H

Mathematics

1 answer:

Liula [17]3 years ago

5 0

Answer:

x = 11 and H = 39°

Step-by-step explanation:

Complementary angles add up to 90 degrees, so angles G and H will add up to 90 degrees.

Create an equation by adding the expressions together and setting it equal to 90.

(6x - 15) + (3x + 6) = 90

Solve for x by adding like terms first:

9x - 9 = 90

Isolate x and solve:

9x = 99

x = 11

Then, find H by plugging in 11 as x into the expression:

3x + 6

3(11) + 6

33 + 6

= 39

So, x = 11 and H = 39°

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The sum of two numbers is -14 one number is 20 less than the other find the numbers

Lisa [10]

Answer:

x=-17,y=3

Step-by-step explanation:

x+y=-14

x=x

y=x+20

x+(x+20)=-14

2x+20=-14

2x=-14-20

2x=-34

x=-34/2

x=-17

y=-17+20

y=3

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3 years ago

10 gallons of gasoline costs $130. The cost of gasoline per gallon is

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13 dollars per gallon

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2 years ago

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3 years ago

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.

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