2 years ago

Solve the following system of equations by using the substitution method.

1 answer:

3 0

X = y + 3
2x + y = 9

Solution..
---------------

Substitute for x=y+3 in the second equation...

2x+y = 9

2(y+3)+y=9

2y+6+y=9
3y+6=9
3y=9-6
3y=3
y=3/3
y=1....

Substitute for y=1 in the first equation...

x=y+3

x = 1+3
x=4..

Am sure the answer is quite evident now...

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Two towns are 1300 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet af

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240(v+2.5)=1300-240v

240v+600=1300-240v

480v=1900

v=95/24

v-2.5=v-5/2

95/24-60/24=35/24

So the faster group travels at 95/24 mph (≈3.96 mph) and the slower group travels at 35/24 mph (≈1.46mph)

check...

240(95/24)=950 miles from the origin...

1300-240(35/24)=950 miles from the origin...

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Suppose that 4% of a population has a virus. You test 1064 people. You wish to find the probability that 45 of the people in the

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In a triangle the first angle is 10 degrees more than the second angle. The third angle is equal to the sum of first 2 angles .

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First angle= x+10
Second angle = x
Third angle = x+x+10 or 2x+10

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2 years ago

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Scores from an exam are normally distributed with a mean of 85 and a standard deviation of 5. Suppose 188 students take the exam

charle [14.2K]

The mean is $\mu=85$ and standard deviation is $\sigma=5$ . Then the variable $X\sim N(85,5)$ .

Use substitution $Z=\dfrac{X-\mu}{\sigma}=\dfrac{X-85}{5}$ , then the variable $Z\sim N(0,1)$ .

The probability $Pr(X>80)$ can be calculated in the following way:

for X=80, $Z=\dfrac{80-85}{5} =-1$ and $Pr(X>80)=Pr(Z>-1)$ . From the diagram $Pr(Z>-1)=0.34+0.34+0.135+0.025=0.84$ .

Conclusion: if 188 students take the exam, then 188·0.84=157.92 (157) would receive a score above 80

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