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aniked [119]
3 years ago
11

Colby worked three more hours on tuesday than he did on monday. on wednesday, he worked one hour more than twice the number of h

ours that he worked on monday. if the total number of hours is two more than five times the number of hours worked on monday, how many hours did he work on monday>
Mathematics
1 answer:
bulgar [2K]3 years ago
6 0
Monday = X
Tuesday = X + 3 (Problem says three more hours than he worked on Monday)
Wednesday = 2x + 1
(Problem says he worked 1 hour more than two times the number of hours on monday) 
This side of the equation would be - 
X + (X +3) + (2X + 1) 
That's monday plus tuesday plus wednesday. 
Then you would set up the other side of the equation. 
This would be the total number of hours so it would be equal to monday, tuesday and wednesday combined. 
2 + (5x) 
Two hours more than five times the amount of Monday (X) 

Now we put this together to have an equation 
X + (X + 3) + (2x+ 1) = 2 + 5x 
Now we need to collect like terms
4x + 4 = 2 + 5x 
I just simplified the left side of the equation
Now I will subtract 4x from the left side to get all the variables on one side 
4 = 2 + x 
Now I subtract 2 to get the numbers both on one side
2 = x 
So, Colby worked 2 hours on Monday.
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Strike441 [17]

Answer:

a) Standard error = 2

b) Range = (76.08, 83.92)

c) P=0.69

d) Smaller

e) Greater

Step-by-step explanation:

a) When we have a sample taken out of the population, the standard error of the mean is calculated as:

\sigma_m=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{25}}=\dfrac{10}{5}=2

where n is te sample size (n=25) and σ is the population standard deviation (σ=10).

Then, the standard error of the classroom average score is 2.

b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.

The population standard deviation is know and is σ=10.

The population mean is M=80.

The sample size is N=25.

The standard error of the mean is σM=2.

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_M=1.96 \cdot 2=3.92

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 80-3.92=76.08\\\\UL=M+t \cdot s_M = 80+3.92=83.92

The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).

c) We can calculate this by calculating the z-score of X=79.

z=\dfrac{X-\mu}{\sigma}=\dfrac{79-80}{2}=\dfrac{-1}{2}=-0.5

Then, the probability of getting a average score of 79 or higher is:

P(X>79)=P(z>-0.5)=0.69146

The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.

d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.

e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.

6 0
3 years ago
What value(s) of x will make each equation below true
Dahasolnce [82]

We need to solve for x. Let's try problem b:

2x-6=3x+1-x-7

Let us first combine line terms. 3x and -x as well as 1 and -7 can be combined. Let's do that:

2x-6=2x-6

Since this is true, your answer would be:

All real numbers

------------------------------------------------------------------

Let's solve for problem c:

3x+1=43

Let's isolate x, so subtract 1 from both sides:

3x=42

Since x can't have a coefficient, divide both sides by 3:

\frac{3x}{3}=\frac{42}{3}

x=14

So, only the value of 14 would make this equation true.

------------------------------------------------------------------

Let's try problem d:

4x-1=4x+7

Let's get our whole numbers on the right side. Add 1 to both sides:

4x=4x+8

Subtract 4x from the right side on both sides:

0=8

Since this is not true, your answer would be:

No solution

7 0
3 years ago
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