Step 1
Write down the first coefficient without changes:
−3223−10−3
−3
2
3 −10 −3
2
Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223(−3)⋅2=−63+(−6)=−3−10−3
−
3
2
3
−10 −3
(
−
3
)
⋅
2
=
−
6
2
3
+
(
−
6
)
=
−
3
Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−10(−3)⋅(−3)=9(−10)+9=−1−3
−
3
2 3
−
10
−3 −6
(
−
3
)
⋅
(
−
3
)
=
9
2
−
3
(
−
10
)
+
9
=
−
1
Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−109−1−3(−3)⋅(−1)=3(−3)+3=0
−
3
2 3 −10
−
3
−6 9
(
−
3
)
⋅
(
−
1
)
=
3
2 −3
−
1
(
−
3
)
+
3
=
0
We have completed the table and have obtained the following resulting coefficients: 2,−3,−1,0
2
,
−
3
,
−
1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2−3x−1
2
x
2
−
3
x
−
1
, and the remainder is 0
0
.
Therefore, 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
2
x
3
+
3
x
2
−
10
x
−
3
x
+
3
=
2
x
2
−
3
x
−
1
+
0
x
+
3
=
2
x
2
−
3
x
−
1
Answer: 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
Answer:
Sequence A
Step-by-step explanation:
Answer:
B. ![\frac{b}{2a^{2}c^3}\sqrt[3]{15b}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B2a%5E%7B2%7Dc%5E3%7D%5Csqrt%5B3%5D%7B15b%7D)
Step-by-step explanation:
Given:
The expression to simplify is given as:
![\sqrt[3]{\frac{75a^7b^4}{40a^{13}c^9}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B75a%5E7b%5E4%7D%7B40a%5E%7B13%7Dc%5E9%7D%7D)
Use the exponent property 
Use the exponent property 
Reducing 
to simplest form, we get:
Therefore, expression becomes:
![\sqrt[3]{\frac{15(a^{-2})^3\times b\times b^3}{2^3(c^3)^3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B15%28a%5E%7B-2%7D%29%5E3%5Ctimes%20b%5Ctimes%20b%5E3%7D%7B2%5E3%28c%5E3%29%5E3%7D%7D)
Use the cubic root property:
![\sqrt[3]{x^3} =x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E3%7D%20%3Dx)
. Thus, the expression becomes:
![\frac{a^{-2}b}{2c^3}\sqrt[3]{15b}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B-2%7Db%7D%7B2c%5E3%7D%5Csqrt%5B3%5D%7B15b%7D)
Using the exponent property 
So, the final expression is:
Therefore, the correct option is option B.
Answer:
Line S
Step-by-step explanation:
Complete question :
Standardized tests: In a particular year, the mean score on the ACT test was 19.3 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 532 and the standard deviation was 128. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places. Part: 0/4 Part 1 of 4 (a) Find the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is
Answer:
1.26
Step-by-step explanation:
Given that:
For ACT:
Mean score, m = 19.3
Standard deviation, s = 5.3
Zscore for ACT score of 26;
Using the Zscore formula :
(x - mean) / standard deviation
x = 26
Zscore :
(26 - 19.3) / 5.3
= 6.7 / 5.3
= 1.2641509
= 1.26
