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Sloan [31]
3 years ago
6

A new soup recipe contains 33\%33% less sodium per serving than the old soup recipe. The old soup recipe contained xx milligrams

of sodium per serving. Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
Mathematics
2 answers:
Eddi Din [679]3 years ago
6 0

Answer: x(1-0.33) or 0.67 x

Step-by-step explanation:

The old soup recipe contained sodium per serving = x mg

According to the question,

The new soup recipe contains 33% less sodium per serving than the old soup recipe.

That is, the Sodium per serving in the new soup = the Sodium per serving in the new soup - 33% of the Sodium per serving in the new soup

= x - 33% of x

= x - 0.33 x      ( since 1% = 0.01 ⇒ 33 % = 0.33 )

= x(1-0.33)

= x(0.67)

hichkok12 [17]3 years ago
6 0

Answer:

(1-33/100)x

0.67x

Step-by-step explanation:

I did it and got it right

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2 years ago
Find an equation for the inverse of the relation y=6x-3. Show how you found the inverse equation.
Elis [28]
Hi there! The answer is y = 1/6x + 1/2

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y = 6x - 3 \\ x = 6y - 3

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x = 6y - 3

Add 3.
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Divide both sides by 6.
y =  \frac{1}{6}  x+  \frac{3}{6}  \\ y =  \frac{1}{6} x +  \frac{1}{2}

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4 0
2 years ago
I need help, 15 points!
Ira Lisetskai [31]

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3(a + 5b + 7c) and 2x(2 + 5y + 11z)

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7 0
2 years ago
(i) Represent these two sets of data by a back-to-back stem-and-leaf diagram.
alexgriva [62]
<h3>Answer: </h3>

{\begin{tabular}{lll}\begin{array}{r|c|l}\text{Leaf (Ali)} & \text{Stem} & \text{Leaf (Kumar)}\\\cline{1-3} 7 & 4 & 1\ 2\ 3\ 6\ 6\ 9\ 9 \\  9\ 8 & 5 & 2\ 2\ 3\\  5\ 5 & 6 & \\  7\ 2\ 0 & 7 & 8\ 8\ 9\\  9\ 9\ 8\ 4\ 3\ 3\ 3\ 1\ 1 & 8 & 2\ 2\ 4\ 5\\  9\ 8\ 1 & 9 & 0\ 2\ 5\\  \end{array} \\\\ \fbox{\text{Key: 7} \big| \text{4} \big| \text{1 means 4.7 for Ali and 4.1 for Kumar}} \end{tabular}}

=========================================================

Explanation:

The data set for Ali is

8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8,

8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9

which when on a single line looks like this

8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8, 8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9

Let's sort the values from smallest to largest

4.7, 5.8, 5.9, 6.5, 6.5, 7.0, 7.2, 7.7, 8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9, 9.1, 9.8, 9.9

Now lets break the data up into separate rows such that each time we get to a new units value, we move to another row

4.7

5.8, 5.9

6.5, 6.5

7.0, 7.2, 7.7

8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9

9.1, 9.8, 9.9

We have these stems: 4, 5, 6, 7, 8, 9 which represent the units digit of the values. The leaf values are the tenths decimal place.

For example, a number like 4.7 has a stem of 4 and leaf of 7 (as indicated by the key below)

This is what the stem-and-leaf plot looks like for Ali's data only

\ \ \ \ \ \ \ \ \text{Ali's data set}\\\\{\begin{tabular}{ll}\begin{array}{r|l}\text{Stem} & \text{Leaf}\\ \cline{1-2}4 & 7 \\ 5 & 8\ 9 \\ 6 & 5\ 5 \\ 7 & 0\ 2\ 7 \\ 8 & 1\ 1\ 3\ 3\ 3\ 4\ 8\ 9\ 9 \\ 9 & 1\ 8\ 9\\ \end{array} \\\\ \fbox{\text{Key: 4} \big| \text{7 means 4.7}} \\ \end{tabular}}

The stem-and-leaf plot condenses things by tossing out repeated elements. Instead of writing 8.1, 8.1, 8.3 for instance, we can just write a stem of 8 and then list the individual leaves 1, 1 and 3. We save ourselves from having to write two more copies of '8'

Through similar steps, this is what the stem-and-leaf plot looks like for Kumar's data set only

\ \ \ \ \ \ \ \ \text{Kumar's data set}\\\\{\begin{tabular}{ll}\begin{array}{r|l}\text{Stem} & \text{Leaf}\\ \cline{1-2}4 & 1\ 2\ 3\ 6\ 6\ 9\ 9 \\ 5 & \ 2\ 2\ 3\  \  \  \   \\ 6 & \\ 7 & 8\ 8\ 9 \\ 8 & 2\ 2\ 4\ 5\\ 9 & 0\ 2\ 5\\ \end{array} \\\\ \fbox{\text{Key: 4} \big| \text{1 means 4.1}} \\ \end{tabular}}

Kumar doesn't have any leaves for the stem 6, so we will have that section blank. It's important to have this stem so it aligns with Ali's stem plot.

Notice that both stem plots involve the same exact set of stems (4 through 9 inclusive).

What we can do is combine those two plots into one single diagram like this

{\begin{tabular}{lll}\begin{array}{r|c|l}\text{Leaf (Ali)} & \text{Stem} & \text{Leaf (Kumar)}\\\cline{1-3} 7 & 4 & 1\ 2\ 3\ 6\ 6\ 9\ 9 \\  8\ 9 & 5 & 2\ 2\ 3\\  5\ 5 & 6 & \\  0\ 2\ 7 & 7 & 8\ 8\ 9\\  1\ 1\ 3\ 3\ 3\ 4\ 8\ 9\ 9 & 8 & 2\ 2\ 4\ 5\\  1\ 8\ 9 & 9 & 0\ 2\ 5\\  \end{array} \\  \end{tabular}}

Then the last thing to do is reverse each set of leaves for Ali (handle each row separately). The reason for this is so that each row of leaf values increases as you further move away from the stem. This is simply a style choice. This is somewhat similar to a number line, except negative values aren't involved here.

This is what the final answer would look like

{\begin{tabular}{lll}\begin{array}{r|c|l}\text{Leaf (Ali)} & \text{Stem} & \text{Leaf (Kumar)}\\\cline{1-3} 7 & 4 & 1\ 2\ 3\ 6\ 6\ 9\ 9 \\  9\ 8 & 5 & 2\ 2\ 3\\  5\ 5 & 6 & \\  7\ 2\ 0 & 7 & 8\ 8\ 9\\  9\ 9\ 8\ 4\ 3\ 3\ 3\ 1\ 1 & 8 & 2\ 2\ 4\ 5\\  9\ 8\ 1 & 9 & 0\ 2\ 5\\  \end{array} \\\\ \fbox{\text{Key: 7} \big| \text{4} \big| \text{1 means 4.7 for Ali and 4.1 for Kumar}} \end{tabular}}

The fact that Ali is on the left side vs Kumar on the right, doesn't really matter. We could swap the two positions and end up with the same basic table. I placed Ali on the left because her data set is on the top row of the original table given.

The thing you need to watch out for is that joining the stem and leaf for Ali means you'll have to read from right to left (as opposed to left to right). Always start with the stem. That's one potential drawback to a back-to-back stem-and-leaf plot. The advantage is that it helps us compare the two data sets fairly quickly.

6 0
2 years ago
Please Help! Struggling to understand the question ive tried everything
allsm [11]

Answer:

4,16

Step-by-step explanation:

36 buttons = 12×12 square inches

1 button = 12×12÷36=4 square inches

4 buttons=4×4=16square inches

4 0
2 years ago
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