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krok68 [10]
2 years ago
11

Solve the system: 4x – 3y = -21 X=-y-14

Mathematics
2 answers:
Reika [66]2 years ago
7 0

Answer:X=−4x/3−21

                 y=4x/3+7

Step-by-step explanation:

Liula [17]2 years ago
4 0

Answer:

The solution for the system of equations is

x=2,y=−2

Explanation:

4x−3y=14.....equation (1)

y=−3x+4.....equation (2)

Solving by substitution

Substituting equation 2 in equation 1

4x−3⋅(−3x+4)=14

4x+9x−12=14

13x=14+12

13x=26

x=2

Finding y by substituting x in equation 1

4x−3y=14

4⋅2−3y=14

8−3y=14

8−14=3y

3y=−6

y=−2

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A sample of blood pressure measurements is taken from a data set and those values​ (mm Hg) are listed below. The values are matc
swat32

Answer:

Step-by-step explanation:

Systolic. Calculate the mean

118+128+158+96+156+122+116+136+126+120+

=1276÷10 = 127.6.

To calculate the median arrange the values from the lowest to the highest.

96,116,118,120,122,126,128,136,156,158.

122+126+2=124.

Disastolic

80+76+74+52+90+88+58+64+72+82= 736÷10=73.6

To calculate the median arrange the values from the lowest to the highest.

52,58,64,72,74,76,80,82,88,90

Median= 74+76=150÷2=75.

Comparison

The Systolic and diastolic blood pressure measures different things, so comparing them is of no use.

It will be good if the relationship between the blood pressure can be investigated because the data are in pairs.

8 0
3 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
52 plus what equals 180
Pavlova-9 [17]

Answer:

128

Step-by-step explanation:

180-52= 128

7 0
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Can someone please help me
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Answer:

B

Step-by-step explanation:

minimum = 1

first quartile = 12

median = 6

third quartile = 16

maximum = 19

6 0
2 years ago
SOMEONE PLZ HELP?????
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(43)3 multiplied by x=y
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