Cynthia rounds a number, x,to one decimal place. the result is 6.3.
1 answer:
The answer is:
The explanation is shown below:
1. Cynthia rounds the number, which is identified as , to one decimal place and the result is 6.3.
2. Based on this, we know that could have been between 6.25 and 6.35. Therefore, the error interval for
is given by:
Where indicates that the value 6.25 is included and
indicates that the value 6.35 is not included (Because if
had been exactly 6.35, Cynthia would round up to 6.4).
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Answer:
The number of 7th students on the Jackson Middle School basketball teams is 17 and the number of 8th students on the Jackson Middle School basketball teams is 36
Step-by-step explanation:
Let
x ----> the number of 7th students on the Jackson Middle School basketball teams
y ----> the number of 8th students on the Jackson Middle School basketball teams
we know that
There are 53 students on the Jackson Middle School basketball teams
so
-----> equation A
The number of 8th graders is 15 fewer than three times the number of 7th graders
so
----> equation B
substitute equation B in equation A
solve for x
Find the value of y
therefore
The number of 7th students on the Jackson Middle School basketball teams is 17 and the number of 8th students on the Jackson Middle School basketball teams is 36
Distance traveled in clear weather = 50 miles
Distance traveled in thunderstorm = 15 miles
Let speed in clear weather = x
⇒ Speed in thunderstorm = x-20
Total time taken for trip = 1.5 hours
We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).
Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm
⇒ Total time taken for trip = +
⇒ 1.5 = +
⇒ 1.5 =
⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]
⇒ 15x² - 300x = 500x - 10,000 + 150x
⇒ 15x² - 300x = 650x - 10,000
⇒ 15x² - 950x + 10,000 = 0
⇒ 3x² - 190x + 2,000 = 0
The above equation is in the format of ax² + bx + c = 0
To determine the roots of the equation, we will first determine 'D'
D = b² - 4ac
⇒ D = (-190)² - 4*3*2,000
⇒ D = 36,100 - 24,000
⇒ D = 12,100
Now using the D to determine the two roots of the equation
Roots are: x₁ = ; x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = and x₂ =
⇒ x₁ = 50 and x₂ = 13.33
So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.
If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.
Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.