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Jlenok [28]
3 years ago
8

Explain the graphing directions for the rules given below (x, y) = (x + 6, y – 3)

Mathematics
1 answer:
zaharov [31]3 years ago
6 0
Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
a
3
-
b
3
=
(
a
-
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
2
a
=
x
2
and
b
=
y
b
=
y
.
(
x
2
−
y
)
(
(
x
2
)
2
+
x
2
y
+
y
2
)
(
x
2
-
y
)
(
(
x
2
)
2
+
x
2
y
+
y
2
)
Multiply the exponents in
(
x
2
)
2
(
x
2
)
2
.
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2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati
Ket [755]

Answer:

\sigma = 11.28 --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

<u>Start by calculating the mean</u>

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

\bar x = \frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}

\bar x = \frac{7531}{91}

\bar x = 82.76

Next, calculate the variance using the following formula:

\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}

\sigma^2 = \frac{11580.6816}{91}

\sigma^2 = 127.26

Lastly, take the square root of the variance to get the standard deviation

\sigma = \sqrt{\sigma^2}

\sigma = \sqrt{127.26}

\sigma = 11.28 --- approximated

<em>Hence, the standard deviation is approximately 11.28</em>

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0
2 years ago
Find the values of X and Y.
Natasha_Volkova [10]

Answer:

x = 90°

y = 43°

Step-by-step explanation:

We know that one angle equals 47°.

The two triangles are right triangles, so that makes x = 90°.

To find y, we add 90 + 47.

That would give us 137°.

All triangles add up to 180°.

180 - 137 = 43.

43° is the answer.

3 0
3 years ago
Read 2 more answers
Help me fast literally fast!!!!
lions [1.4K]
The correct answer is 12. Hope this helps.
8 0
3 years ago
Read 2 more answers
What is the least common multiple of 9, 17, and 51? A. 51 B. 102 C. 153 D. 867
Luden [163]

Answer:

<h2>C. 153</h2>

<em>Hope</em><em> this</em><em> helps</em>

<em>shshsgshsh</em>

3 0
3 years ago
I am very not smart so can ya'll help me out on this one?
laila [671]

Answer:

H is not a solution

Step-by-step explanation:

plug each point into the equation and see which one does not work.

F(-3,6): 4(-3) + 3(6) = 6, -12 + 18 = 6, 6=6

G(0,2): 4(0) + 3(2) = 6, 6=6

H(1,-2): 4(1) + 3(-2) = 6, 4 - 6 =6, -2=6

J(3,-2): 4(3) + 3(-2) = 6, 12 -6 = 6, 6=6

H is not a solution

5 0
3 years ago
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