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ValentinkaMS [17]
3 years ago
9

What are consecutive integers?

Mathematics
1 answer:
saul85 [17]3 years ago
8 0
Consecutive integers<span> are </span>integers<span> that follow each other in order. They have a difference of 1 between every two numbers. In a set of </span>consecutive integers<span>, the mean and the median are equal. If n is an </span>integer, then n, n+1, and n+2 would be consecutive integers<span>. Examples.</span>
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A line is perpendicular to y=2/3x +2/3 and intersects the point (-2,4). what is the equation of this perpendicular line?
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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel
Alexeev081 [22]
Use Law of Cooling:
T(t) = (T_0 - T_A)e^{-kt} +T_A
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
42 = (80-20)e^{-3k} +20 \\  \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\  \\ k = -\frac{1}{3} ln (\frac{11}{30})

Substituting k back into cooling equation gives:
T(t) = 60(\frac{11}{30})^{t/3} + 20

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\  \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80
Solve for x:
x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80
Sub back into original cooling equation, x = T(t)
-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20
Solve for t:
60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3}  = 60 \\  \\  (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\  \\  \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\  \\ \\  t = 4.959

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM
8 0
3 years ago
What is the answer to 5.09x15
Lady bird [3.3K]

5.09 times 15 equals 76.35

4 0
3 years ago
What is the greatest common factor of 180 and 240
maria [59]
The GCF of 180 and 240 is 60
4 0
4 years ago
Read 2 more answers
The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 year
puteri [66]

Answer:

z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29  

Step-by-step explanation:

information given

\bar X=10.6 represent the sample mean  

\sigma=4.1 represent the population standard deviation

n=45 sample size  

\mu_o =12 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.  

z would represent the statistic

p_v represent the p value for the test

Hypothesis to test

We want to test if the true mean is less than 12, the system of hypothesis would be:  

Null hypothesis:\mu \geq 10  

Alternative hypothesis:\mu < 10  

The statistic is given by:

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

Replacing the info given we got:

We can replace in formula (1) the info given like this:  

z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29  

8 0
4 years ago
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