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maria [59]
3 years ago
15

At the end of last week, a baseball player’s average was .256. One week later, after getting 12 hits in 35 at-bats, the player’s

average is now .275. How many hits and how many at-bats does the player now have for the season?
Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

Let the player has x hits in y at-bats.

Since players initial average is 0.256, therefore, we can set up an equation:

\frac{x}{y} =0.256

Further, we are given that player hits 12 in 35 at-bats. Therefore, the total hits are now (x+12) and total at-bats are now (y+35).

Since the new average becomes 0.275, therefore, we can set up:

\frac{x+12}{y+35} =0.275

Our next step is to solve these two equations and get values of x and y.

\frac{x}{y}=0.256\Rightarrow x=0.256y\\
\frac{x+12}{y+35}=0.275\Rightarrow x+12=0.275y+9.625\\

Upon using substitution method, we get:

0.256y+12=0.275y+9.625\\
0.275y-0.256y=12-9.625\\
0.019y=2.375\\
y=\frac{2.375}{0.019}=125

We can find the value of x by substituting this value of y in the first equation.

x=0.256(125)\Rightarrow x=32

Therefore, player made 32 hits in 125 at bats.

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\begin{equation}
\sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6
\end{equation}

Explanation:

Given the irrational numbers:

$3 \sqrt{2}, \sqrt{3}-1, \sqrt{19}+1,6$, $2 \sqrt{10} \div 5,\sqrt{14}$

In order to arrange the numbers from the least to the greatest, we convert each number into its decimal equivalent.

\begin{gathered} 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{3}-1\approx1.732-1=0.732 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \end{gathered}

Finally, sort these numbers in ascending order..

\begin{gathered} \sqrt{3}-1\approx1.732-1=0.732 \\ 2\sqrt{10}\div5=2(3.1623)\div5=1.2649 \\ \sqrt{14}=3.7147 \\ 3\sqrt{2}=3\times1.414\approx4.242 \\ \sqrt{19}+1\approx4.3589+1=5.3589 \\ 6=6 \end{gathered}

The given numbers in ascending order is:

\begin{equation}
\sqrt{3}-1,2 \sqrt{10} \div 5, \sqrt{14}, 3 \sqrt{2}, \sqrt{19}+1,6
\end{equation}

Note: In your solution, you can make the conversion of each irrational begin on a new line.

8 0
1 year ago
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