<h3>Answers:</h3><h3>x = 1 or x = 16</h3>
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Work Shown:
Draw out a rectangle that is 32 units wide horizontally and 8 units tall vertically.
Then draw out another rectangle that is 4 meters wide horizontally and x meters tall vertically.
The horizontal and vertical sides pair up to form these fractions: 32/4 and 8/x
Set the fractions equal to one another. Solve for x
32/4 = 8/x
32x = 8*4 ... cross multiply
32x = 32
x = 32/32 ... divide both sides by 32
x = 1
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Somewhere else on your paper, draw the same 32 by 8 rectangle to make 32 the horizontal component
Next to this rectangle, draw a rectangle that has x as the horizontal part and 4 as the vertical. Note the swap here.
We now have this equation to solve for
32/x = 8/4
once again, note the swap
Let's solve for x
32/x = 8/4
32*4 = 8*x
128 = 8x
8x = 128
x = 128/8
x = 16
Answer:
14
Step-by-step explanation:
Since we're given the conversion 24 cm for every 3 presents wrapped, we can divide our total amount of tape by this conversion, assuming a constant proportion.
Evren has 112 cm of tape. We can write the following proportion:
, where
is the number of presents he can wrap with 112 cm.
Cross-multiplying, we have:
![24x=336,\\x=\frac{336}{24}=\boxed{14\text{ presents}}](https://tex.z-dn.net/?f=24x%3D336%2C%5C%5Cx%3D%5Cfrac%7B336%7D%7B24%7D%3D%5Cboxed%7B14%5Ctext%7B%20presents%7D%7D)
The 90% confidence interval is given by mean - 1.645(s.d. / sqrt(n)) < μ < mean + 1.645(s.d. / sqrt(n))
mean - 1.645(s.d. / sqrt(n)) + mean + 1.645(s.d. / sqrt(n)) = 2<span>μ = 5.22 + 5.98 = 11.2
</span><span>μ = 11.2 / 2 = 5.6
Thus, </span><span>mean - 1.645(s.d. / sqrt(n)) = 5.6</span><span> - 1.645(s.d. / sqrt(n)) = 5.22
5.6 - 5.22 = </span><span>1.645(s.d. / sqrt(n)) = 0.38
</span><span><span>s.d. / sqrt(n) = 0.38 / 1.645 = 0.231
</span>The 95% confidence interval is given by </span>mean - 1.96(s.d. / sqrt(n)) < μ < mean + 1.96(s.d. / sqrt(n)) = 5.6 - 1.96(0.231) < <span>μ < 5.6 + 1.96(0.231) = 5.6 - 0.4528 < </span><span>μ < 5.6 + 0.4528 = 5.15 < </span><span>μ < 6.05
The 95% confidence interval provides more information because it has a larger interval.</span>
Answer:
a
Step-by-step explanation: