Question

1. convert to a decimal.

\\( \frac { 17 } { 25 } \\)

1. write the equivalent

measurement.
\\( 2 \mathrm { c. } = \\) \\( \mathrm { fl oz. } \\)

1. i am making sundaes. i

have \\( 1 / 2 \\) cup of hot fudge to
share between three
sundaes. how much should
i put on each?

1. what is the volume to the

nearest tenth?

1. a marble is randomly

selected from a bag of 32
red and yellow marbles.
what is the probability that
the selected marble is red,
if there are 20 yellow
marbles in the bag?

Explanation:

Step1: Convert fraction to decimal

To convert \(\frac{17}{25}\) to a decimal, we can use the formula \(a\div b\). Here \(a = 17\) and \(b=25\).

$$17\div25=\frac{17\times4}{25\times4}=\frac{68}{100}$$

Step2: Simplify the fraction

Since \(\frac{68}{100}\) is in the form of a fraction with denominator \(100\), it can be directly written as a decimal.
\(\frac{68}{100}=0.68\)

Step3: Unit conversion (for \(2\) c. to fl oz)

We know that \(1\) cup (\(c\)) is equal to \(8\) fluid ounces (\(fl\ oz\)).
Using the formula \(y = kx\) (where \(k = 8\) and \(x = 2\))

$$y=8\times2$$

$$y = 16$$

Step4: Share hot - fudge

We have \(\frac{1}{2}\) cup of hot - fudge to be shared among \(3\) sundaes. Using the formula \(a\div n\) (where \(a=\frac{1}{2}\) and \(n = 3\))
\(\frac{1}{2}\div3=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\approx0.167\)

Step5: Volume of a rectangular prism

The volume formula for a rectangular prism is \(V=l\times w\times h\). Here \(l = 4.6\) ft, \(w=2.1\) ft, \(h = 5.2\) ft

$$V=4.6\times2.1\times5.2$$

First, \(4.6\times2.1=(4 + 0.6)\times(2+0.1)=4\times2+4\times0.1+0.6\times2+0.6\times0.1=8 + 0.4+1.2 + 0.06=9.66\)
Then \(9.66\times5.2=(9+0.66)\times(5 + 0.2)=9\times5+9\times0.2+0.66\times5+0.66\times0.2\)
\(=45+1.8 + 3.3+0.132=50.232\approx50.2\) (to the nearest tenth)

Step6: Probability calculation

The total number of marbles \(n = 32\). The number of yellow marbles \(y = 20\), so the number of red marbles \(r=32 - 20=12\)
The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)

$$P=\frac{12}{32}=\frac{3}{8}=0.375$$

Answer:

1. \(0.68\)
2. \(16\)
3. \(\frac{1}{6}\approx0.167\)
4. \(50.2\)
5. \(0.375\)