Answer:
the initial value is 15 and it represents the y-intersect in the context of this problem
Step-by-step explanation:
Answer:
The margin of error is 30.22
Step-by-step explanation:
Sample size 19(lesser than 30), and we only have the sample standard deviation. So we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 19 - 1 = 18
Now, we have to find a value of T, which is found looking at the t table, with 18 degrees of freedom(y-axis) and a confidence level of 0.995(
). So we have T = 2.878
The margin of error is:
M = T*s = 10.5*2.878 = 30.22
2/5, 1/10, and 1/20 are all less than 1/2
<span><span><span><span>2x</span>+<span>3y</span></span>=1</span>;<span><span>x+<span>4y</span></span>=<span>−2
</span></span></span>Steps:
<span>Multiply the second equation by -2, then add the equations together.
</span><span>(<span><span><span>2x</span>+<span>3y</span></span>=1</span>)
</span><span><span>−2</span><span>(<span><span>x+<span>4y</span></span>=<span>−2</span></span>)
</span></span>Becomes:
<span><span><span>2x</span>+<span>3y</span></span>=1
</span><span><span><span>−<span>2x</span></span>−<span>8y</span></span>=4
</span>Add these equations to eliminate x:
<span><span>−<span>5y</span></span>=5
</span>Then solve<span><span>−<span>5y</span></span>=5</span>for y:
<span><span><span>−<span>5y</span></span><span>−5</span></span>=<span>5<span>−5</span></span></span>(Divide both sides by -5)
<span>y=<span>−1
</span></span>Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
<span><span><span>2x</span>+<span>3y</span></span>=1
</span>Substitute<span>−1</span>foryin<span><span><span><span>2x</span>+<span>3y</span></span>=1</span>:
</span><span><span><span>2x</span>+<span><span>(3)</span><span>(<span>−1</span>)</span></span></span>=1
</span><span><span><span>2x</span>−3</span>=1</span>(Simplify both sides of the equation)
<span><span><span><span>2x</span>−3</span>+3</span>=<span>1+3</span></span>(Add 3 to both sides)
<span><span>2x</span>=4
</span><span><span><span>2x</span>2</span>=<span>42</span></span>(Divide both sides by 2)
<span>x=2
</span>Answer:
<span><span>x=<span><span>2<span> and </span></span>y</span></span>=<span>−<span>1
</span></span></span>
Given:
Machine dispenser
Average = 600 mL soda to every glass
Volumes recorded in one day (random sampling)
600.15
599.92
599.85
599.92
599.81
600.14
600.04
599.98
Average = (sum of the volumes)/(number of readings)
= 4799.81/8
Average = 599.976 mL
Therefore there is sufficient evidence to conclude that the average volume of soda dispenser is different from 600 mL.
