# Math homework help

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Many newspapers, when reporting results of political polls, say that “with 95% confidence, the results are in error by no more than +/- 3 percentage points.” The typical sample size is about 1,500. This allowance for error is intended to cover both sampling variability and the effect of small biases. 1 Assume that the poll (sample) indicates that just about 50% of likely voters favor a particular candidate. How large a +/- term is required for a 95% confidence interval for the population proportion?

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1. Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gas station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of the station and a number of marketing factors related to oil industry and demand for gasoline. After careful analysis, Susan developed the following table:

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1. Solve the expression: 5(B – 4) = 10

2. Solve the following equation for the variable L : p = 2L + 2w

3. Complete the following table for the equation y = x – 3

4. Find the slope-intercept equation of the line passing through (1,2) with a slope of m = 3?

5. Draw the graph of the following linear function and give the domain and range: f(x) = - ½x+5

6. Solve the following equation: | x | = 3

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1) Find the simple interest on the loan. $1400 at 8% for 10 years.

2) Find the total amount due for the simple interest loan. $1300 at 8% for 10 years.

3) Find the interest rate on a loan charging $528 simple interest on a principal of $2750 after 6 years.

4) Find the term of a loan of $500 at 3.5% if the simple interest is $35. .

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*Answer the questions below. Make sure to show your work and justify all of your answers*

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A typical two-stage spray drier is shown in the figure to the right. The drying chamber is a classic bin…cylinder + cone. The product to be dried contains 45% solids. At this moisture level, the spray drier can produce 820 kg/hr of dry powder that is about 3.5% moisture. The finished powdered product has a density of 0.45 kg/1L. Spray dried product is packaged in a cylindrical canister with the following dimensions: Height: 4.5”; Diameter: 3.875”. Five percent headspace is required for the packaging process.

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2. The graphs of the functions *f*(*x*) = *x*^{3} and *g*(*x*) = *x* meet at two places. Revolve the region enclosed by these two graphs around the *y*-axis. What is the volume of the volume of revolution?