Emu123

It is 237/40 as a fraction with integer numerators and denominators.

Here is the full \(\LaTeX\) according to the order of operations:

1. Let \(f(x)= 3x+\frac{3}{x}+1\). Find the domain of \(f\)

2. Let \(q(x)=\frac{2}{\sqrt{x}}\). Find the domain of \(q\)

3.Let \(g(x)=3(x-6)^2+1\). Find the range of \(g\)

4.let \(f(a,b)= 2a-3b^2+7\). If \(f(k,3)=90\), then what is k?

5.Define the operation\( \heartsuit\) so that, \(a \heartsuit b=a+b/2\)

Find the value of \((5 \heartsuit 7) \heartsuit 11-5 \heartsuit (7 \heartsuit 11)\)

So we start by thinking. Since 44 students take ONLY spanish, 97 - 44 = 53 students take chinese (ONLY and both languages). Since there are 8 more students in chinese than spanish, there are 53 - 8 = 45 students take spanish (ONLY and both languages). 45 - 44 = 1 student not taking ONLY spanish but still takes spanish so there are only 1 student taking both languages. (How lonely...)

(Please upvote!)

On Monday, James ate a total of 15 + 15 + 10 = 30 + 10 = 40 grams of protein. On Wednesday, James ate a total of 8 + 10 = 18 grams of protein. On Friday, James ate a total of 6 + 10 + 12 = 6 + 22 = 28 grams of protein. The only day given that had james eat meet or exceeded the Recommended Daily Allowance for protein was Wednesday. 

35 - 26 = 9 grams of protein left to eat. Since each slice of pizza at Sally's has 9 protein, he will need to buy at least \(\frac{9}{9} = \boxed{1}\) slice of pizza at Sally's

 if he wants to try to eat enough protein for the day.

(Upvotes please!)

We start by assigning the variable \(s\) to the silver balloons and \(g\) to the gold balloons. The first thing they said was that \(g + 156 = s\). The second was that \((s-\frac{5s}{6})+ (g - \frac{3g}{4}) = \frac{s}{6} + \frac{g}{4} = 106\). Subsituting the first equation into the second gives us \(\frac{g+156}{6} + \frac{g}{4} = 106\)

=> \(\frac{g}{6} + \frac{156}{6} + \frac{g}{4} = \frac{g}{6} + \frac{g}{4} + 26 = 106\)

=> \(\frac{g}{6} + \frac{g}{4} = 80\)

=> \(2g + 3g = 5g = 80 * 12 = 960\)

=> \(g = \frac{960}{5} = 192\)

and having g = 192 in the first equation gives us \(s = 192 + 156 = 348\) so the total number of balloons in the start is \(348 + 192 = 540\).

(Please upvote!)

We let Aaron's share be \(a\), Bill's share be \(b\), and Cavin's share be \(c\). From the problem, we get the equations \(\frac{a}{2} = \frac{b}{3}\), \(\frac{b}{4} = \frac{c}{5}\). To answer the first problem, we multiply both sides of the first equation by \(\frac{3}{4}\) to get \(\frac{3a}{4(2)} = \frac{b}{4}= \frac{3a}{8}\). Now, we have \(\frac{3a}{8} = \frac{b}{4} = \frac{c}{5}\). We want to find someting to multiply all of them to cancel out the fractions. The number we need is LCM(4, 8, 5) = 40 so we multiply them all by 40 to get \(\frac{120a}{8} = \frac{40b}{4} = \frac{40c}{5} = 15a = 10b = 8c\) so the answer to the first question is 15 : 10 : 8. 

For the second problem, we return to the equation \(\frac{3a}{8} = \frac{b}{4} = \frac{c}{5}\). We start from the equation \(\frac{a}{2} = \frac{b}{3}\). Multiplying all sides by 2 gives us \(a = \frac{2b}{3}\). Then, from the equation \(\frac{b}{4} = \frac{c}{5}\), we multiply both sides by 5 to get \(\frac{5b}{4} = c\). Suubsituting them all into the first thng they told us: \(a+b+c = 2345\) gives us \(\frac{2b}{3} + b + \frac{5b}{4} = \frac{2}{3}b + 1b + \frac{5}{4}b = (\frac{2}{3} + 1 +\frac{5}{4})b = (\frac{8}{12} + \frac{12}{12} + \frac{15}{12})b = \frac{8+12+15}{12}b = \frac{35}{12}b = 2345\). Multiplying by \(\frac{12}{35}\) gives us \(b = \frac{12 * 2345}{35} = \frac{28140}{35} = 804\) so Bill got $804.

Please edit your LaTex to have:

"Suppose that \(f(x)\) and \(g(x)\) are polynomials of degree 4 and 5 respectively. What is the degree of \(f(x^3) \cdot g(x^2)\)?"

Since \(3.141*15^2 * \frac{18}{3} = 3.141 * 225 * 6 \) (1)

\(= 3.141*5 * 45 * 2 * 3 \)(2)

\(= 3.141 * 45 * 3 * 10\)(3)

\(= 31.41 * 135\)(4)

\(= 4240.35\)(5)

Note that from step 3 or 4, we found that we don't need to round it to the nearest hundredth because that is what the answer is in and step 5 tels us the answer.