The complete question is;
The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____
Answer:
A) degree = 6
B) -9 is also a zero of the polynomial
C) 0 has multiplicity of 2
1 has multiplicity of 3
Step-by-step explanation:
A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.
The terms are;
5x², (x - 1)³, (x + 9)
The exponents are, 2, 3 and 1 respectively.
Thus, degree = 2 + 3 + 1 = 6
B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.
Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².
Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³
Thus,we are left with the term (x + 9)
So for the polynomial to be zero, (x + 9) = 0
Thus,x = -9
So -9 is a zero of the polynomial
C) The zero 0 is from the term 5x².
Thus,the multiplicity is the highest power of x which is 2.
The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3
Write the equation in slope-intercept form. y=2(x−8)+4x
Answer:
y=6x-8
Step-by-step explanation:
y=2(x-8)+4x
y=2x+4x-8, y=6x-8
whats the scale factor of this one please?????
Answer:
0.5
Step-by-step explanation:
E to E'
(0, 3) to (0, 1.5) each term of E' is ½ of the corresponding term of E
N to N'
(-1, 1) to (-0.5, 0.5) each term of N' is ½ of the corresponding term of N
U to U'
(2, -2) to (1, -1) each term of U' is ½ of the corresponding term of U
V to V'
(1, -3) to (0.5, -1.5) each term of V' is ½ of the corresponding term of V
How do I Simplify
-72 divide by 3
Answer:
by doing the problem and you should get -24
Step-by-step explanation:
please help
Question: 6b = 18
Answer: ?
Answer:
6b=18
b=18/6
b=3
.
.
.
.
.
.
Answer:
6b=18
b=18/6
b=3
.
Step-by-step explanation:
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Playing the game of roulette, where the wheel consists of slots numbered 00, 0, 1, 2, ..., To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.a. The sample space is (00, 0}. b. The sample space is (00, 0, 1,2,., 33). c. The sample space is (00). d. The sample space is (1, 2,..., 33).
Answer:
The correct option is (B).
Step-by-step explanation:
It is provided that, in a game of roulette the wheel consists of slots numbered 00, 0, 1, 2, ..., 33.
The sample space of an experiment, is the set of all the possible outcomes of the random trials.
There are a total of 35 slots on the roulette wheel where the ball can land.
So, there are a total of 35 outcomes for one rotation of the wheel.
Then the sample space consists of all the 35 outcomes, i.e.
S = {00, 0, 1, 2, 3, ..., 33}
Thus, the correct option is (B).
Complete the table for the function
Answer:
C
Step-by-step explanation:
y(x) = x^(1/3)+7
y(-8)=(-8)^(1/3)+7=5
y(-1)=(-1)^(1/3)+7=6
y(1)=(1)^(1/3)+7=8
y(8)=(8)^(1/3)+7=9
A right cylinder has a radius of 3 and a height of 12. What is its surface area?
O A. 9077 units2
B. 72 units2
O C. 10877 units
D. 457 units2
Answer:
Option A, [tex]90\pi[/tex] [tex]units^{2}[/tex], is correct.
Step-by-step explanation:
The formula for the surface area of a cylinder is as follows:
A= [tex]2\pi rh+2\pi r^{2}[/tex]
We know that the radius, r, is 3, and the height, h, is 12.
r=3
h=12
Pi will be rounded to 3.14.
Thus, applying the known values to the formula:
A=[tex]2(3.14)(3)(12)+2(3.14)(3)^{2}[/tex]
A=226.08+56.52
A=282.6 [tex]units^{2}[/tex]
In accord with the given options, we must determine which one has a product of around 282.6:
A. [tex]90\pi =282.7433388[/tex]
B.[tex]72\pi =226.1946711[/tex]
C.[tex]108\pi =339.2920066[/tex]
D.[tex]45\pi =141.3716694[/tex]
Therefore, option A, [tex]90\pi units^{2}[/tex], is correct.
PLZ HELPPPPPPPPPPPPPPPPPPP
 evaluate the expression for k=6 -18+2k=
Answer:
-6
Step-by-step explanation:
-18 + 2k wherre k = 6
=> -18 + 2(6)
=> -18 + 12
=> -6
Milo receives a commission of 4% on all sales. If his commission on a sale was $51.00 , find the cost of the item he sold.
Answer:
1275
Step-by-step explanation:
51.00 = x*.04
51/.04 = 1275
Answer:
Step-by-step explanation:
4% x = 51
4/100 * x = 51 Multiply both sides by 100
100 * 4/100 * x = 5100
4x = 5100 Divide by 4
x = 5100/4
x = 1275
I didn't believe it was that large. Give the other answerer the Brainlest.
Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. 12-8x=5
Answer:
x = 0.88Step-by-step explanation:
[tex]12-8x=5\\\\Collect\:like\:terms\\\\-8x =5-12\\\\-8x = -7\\\\Divide\:both\:sides\:by -8\\\frac{-8x}{-8} \\=\frac{-7}{-8} \\\\x = 0.875\\\\x = 0.88[/tex]
1/9, -0.1, -2/12 in order
Answer:
-2/12, -0.1, 1/9
Step-by-step explanation:
Answer:
Least to greatest: -2/12 , -0.1 , 1/9
Greatest to least: 1/9, -0.1, -2/12
Step-by-step explanation:
Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.
Divide:
1/9 = ~0.111 (rounded)
-0.1 = -0.1
-2/12 = - ~0.167 (rounded)
Put the numbers in number order:
-~0.167 , -0.1 , ~0.111
-2/12 , -0.1 , 1/9
~
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
Temp. 174 176 177 178 178 179 180 181
Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74
Temp. 184 184 184 184 184 185 185 186
Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94
Temp. 186 186 186 188 188 189 190 192
Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16
(a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.)
y =
(b) Calculate a point estimate for true average efficiency ratio when tank temperature is 186. (Round your answer to four decimal places.)
(c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 186. (Round your answers to four decimal places.)
(186, 0.94)
(186, 1.85)
(186, 2.02)
(186, 2.64)
(d) What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? (Round your answer to four decimal places.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temp. 174 176 177 178 178 179 180 181
Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74
Temp. 184 184 184 184 184 185 185 186
Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94
Temp. 186 186 186 188 188 189 190 192
Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16
A)
Using the online linear regression calculator, the lie of best fit which models the data above is :
ŷ = 0.09386X - 15.55523
Where ;
X = independent variable
ŷ = predicted or dependent variable
- 15.55523 = intercept
0.09386 = gradient / slope
B)
Point estimate when tank temperature is 186
ŷ = 0.09386(186) - 15.55523
ŷ = 17.45796 - 15.55523
ŷ = 1.90273
C)
Residual error (y - ŷ), ŷ = 1.90273 when x = 186
(0.94 - 1.90273) = −0.96273
(1.85 - 1.90273) = −0.05273
(2.02 - 1.90273) = 0.11727
(2.64 - 1.90273) = 0.73727
D)
To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.
To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement?
A. The sample size is 50 and the population proportion under null hypothesis is 25%.
B. The sample size is 70 and the population proportion under null hypothesis is 90%.
C. The sample size is 50 and the population proportion under null hypothesis is 15%.
D. The sample size is 200 and the population proportion under null hypothesis is 4%.
Answer:
The sample size is 50 and population proportion under null hypothesis is 25% ( A ) meets the requirement
Step-by-step explanation:
when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and n( 1-p ) > 10
A) sample size ( n ) = 50
population proportion = 25%
np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )
n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )
B ) sample size (n) = 70
population proportion = 90%
np = 70*0.9 = 63 which is > 10 ( 1st condition met )
n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )
C) sample size ( n ) = 50
population proportion = 15% = 0.15
np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )
D) sample size ( n ) = 200
population proportion = 4% = 0.04
np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )
hence : The sample size of 50 with population proportion under null hypothesis of 25% meets the requirement
√10 Multiple √15 is equal to
(a) 5√6
(b) 6√5
(c) √30
(d) √25
step by step
Solve :-
Answer:
(a). 5√6
Step-by-step explanation:
[tex] \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = 5 \sqrt{6} [/tex]
Which expression gives the area of the triangle shown below?
A.
(r)(x)
B.
px
C.
(p)(x)
D.
rx
base = r
height = x
area of triangle = (1/2)*(base*height)
area of triangle = (1/2)*(r*x)
area of triangle = (1/2)rx
Answer: Choice DHow do we solve this? Please help?
Answer:
f'(1) = 7/2
Step-by-step explanation:
We are given the function: [tex]f'(x)=\frac{7}{2\sqrt{x} }[/tex]
To find f'(1), substitute the value for x and evaluate it.
[tex]f'(1)=\frac{7}{2\sqrt{1} }\\\\f'(1)=\frac{7}{2(1)}\\\\f'(1)=\frac{7}{2}[/tex]
Therefore, f'(1) = 7/2.
Assume that f(x)=ln(1+x) is the given function and that Pn represents the nth Taylor Polynomial centered at x=0. Find the least integer n for which Pn(0.2) approximates ln(1.2) to within 0.01.
Answer:
the least integer for n is 2
Step-by-step explanation:
We are given;
f(x) = ln(1+x)
centered at x=0
Pn(0.2)
Error < 0.01
We will use the format;
[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01
So;
f(x) = ln(1+x)
First derivative: f'(x) = 1/(x + 1) < 0! = 1
2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1
3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2
4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6
This follows that;
Max|f^(n+1) (c)| < n!
Thus, error is;
(n!/(n + 1)!) × 0.2^(n + 1) < 0.01
This gives;
(1/(n + 1)) × 0.2^(n + 1) < 0.01
Let's try n = 1
(1/(1 + 1)) × 0.2^(1 + 1) = 0.02
This is greater than 0.01 and so it will not work.
Let's try n = 2
(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267
This is less than 0.01.
So,the least integer for n is 2
In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;
the least integer for n is 2
The function given in this exercise corresponds to:
[tex]f(x) = ln(1+x)[/tex]
knowing that the x point will be centered on:
[tex]x=0\\Pn(0,2)\\Error < 0.01[/tex]
By rewriting the equation we have to:
[tex][[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01[/tex]
So doing the derivatives related to the first function given in the exercise we have to:
[tex]f(x) = ln(1+x)[/tex]
First derivative: [tex]f'(x) = 1/(x + 1) < 0! = 1[/tex] 2nd derivative: [tex]f"(x) = -1/(x + 1)^2 < 1! = 1[/tex] 3rd derivative: [tex]f"'(x) = 2/(x + 1)^3 < 2! = 2[/tex] 4th derivative: [tex]f""(x) = -6/(x + 1)^4 < 3! = 6[/tex]Following this we have to:
[tex]Max|f^{(n+1)} (c)| < n![/tex]
Thus, error is;
[tex](n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01[/tex]
[tex](1/(n + 1))* 0.2^{(n + 1)} < 0.01[/tex]
Let's try n = 1
[tex](1/(1 + 1)) *0.2^{(1 + 1)} = 0.02[/tex]
This is greater than 0.01 and so it will not work. Let's try n = 2
[tex](1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267[/tex]
This is less than 0.01. So,the least integer for n is 2.
See more about Taylor polynomial at brainly.com/question/23842376
Determine if the process appears to be within statistical control. If not, state the reason why not.
a. It does not appear to be within statistical control because there is an upward shift.
b. It appears to be within statistical control.
c. It does not appear to be within statistical control because there is an upward trend.
d. It does not appear to be within statistical control because there is increasing variation.
Answer:
c. It does not appear to be within statistical control because there is an upward trend.
Step-by-step explanation:
Statistical process control is a method for quality control which employs statistical method to monitor and control process. It ensures operation efficiency and ensuring required specification to reduce wastes in production lines. Here the process variation is out of control because the statistical control has an upward trend.
A new coffee shop is being built. Its location is the reflection of the arcade's coordinates across
the y-axis. Which procedure will find the correct distance between the arcade and the new coffee shop?( there is more than one answer)
Step-by-step explanation:
mark me brainlist
please mark mep
A table has five bowls. None of the quantities in the bowls are prime, though the last two bowls are empty. Two of the quantities are squares, and when added to the remaining number, the sum is 21. What are the amounts in the first three bowls?
Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16
Let's consider each possibility
1 and 4
21-1-4=16, but 16 is also square and there can be only two square so NO
1 and 9
21-1-9=11, but 11 is prime, so NO
1 and 16
21-1-16=4... 4 is a square ,so NO
4 and 9
21-4-9=8 , 8 is not prime and not a square, so YES
4 and 16
21-4-16=1, but 1 is a square ,so NO
9 and 16
9+16=25>21 so.. NO
Therefore, the amounts in the first three bowls are 4,8,9.
For each of the indicates values given for x and y, determine which expression has a greater value (x+y)^2 or (x-y)^2
y=mx+6 , solve for m
Answer:
m = [tex]\frac{y-6}{x}[/tex]
Step-by-step explanation:
Given
y = mx + 6 ( subtract 6 from both sides )
y - 6 = mx ( divide both sides by x )
[tex]\frac{y-6}{x}[/tex] = m
Justin is married with one child. He works 40 hours each week at a rate of $16 per hour. His wife began working part time
after their daughter was born, but still contributes about $350 to the cash inflow each month. Their monthly cash outflow
is generally about $3,000. They have a balance of $2,000 in their savings account. Justin has retirement contributions
taken out of his paycheck at work. They have renter's, car and life insurance coverage.
Based on this information, what part of their financial plan should Justin and his wife work on?
managing income
b. managing liquidity
c. protecting assets
d. retirement
a.
Please select the best answer from the choices provided
Answer:
THe answer is A
Step-by-step explanation:
vector v has a horizontal vector component with magnitude 19 and a vertical vector component with magnitude 35. what is the acute angle theta formed by v and positive x-axis?
9514 1404 393
Answer:
61.5°
Step-by-step explanation:
The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.
Tan = Opposite/Adjacent
tan(α) = 35/19
α = arctan(35/19) ≈ 61.5°
The angle made by v and the positive x-axis is 61.5°.
Need the answer please, soon as possible
9514 1404 393
Answer:
(d) 27.4%
Step-by-step explanation:
The desired percentage is ...
(juniors for Kato)/(total juniors) × 100%
= 129/(129 +194 +147) × 100%
= (129/470) × 100% ≈ 27.4%
About 27.4% of juniors voted for Kato.
How many dimensions does an angle have?
Answer:
the length has dimension 1, the area has the dimension 2, the volume has dimension 3, etc. And the angle has dimension 0.
Step-by-step explanation:
State the value of the expression (4.1x10^2)(2.4x10^3) over (1.5x10^7) in scientific notation?
Answer:
[tex]6.56 * 10^{-2}[/tex]
Step-by-step explanation:
:| I would just start bashing this one.
[tex]((4.1 * 10^2 ) (2.4 * 10^3))/(1/5 * 10^7) =[/tex]
[tex]((410)(2400))/(15000000) =[/tex]
[tex]984000/15000000 =[/tex]
[tex]984/15000 =[/tex]
[tex]123/1875 =[/tex]
[tex]0.0656 =[/tex]
[tex]6.56 * 10^{-2}[/tex]
Help please
I don’t know what it is and I need to find the value of x please HELP
Answer:
[tex]\large \boxed{x\° = 130}[/tex]
Step-by-step explanation:
The triangle is an isosceles triangle. The base angles are equal.
Angles in a triangle add to 180 degrees.
[tex]y+65+65=180\\y+130=180\\y=50[/tex]
Angles on a straight line add up to 180 degrees.
[tex]x+50=180\\x=130[/tex]
Answer:
[tex]\huge\boxed{\sf x = 130\ degrees}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of non-adjacent interior angles.
So,
x = 65 + 65
x = 130 degrees
Question 2 of 10
What is the slope of the line x = 3?
Answer:
[tex]\boxed{\mathrm{U n d e f i n e d \ slope }}[/tex]
Step-by-step explanation:
x = 3 is a vertical line.
The slope of a vertical line is undefined.