There will be n linear factors of a polynomial function f of degree n
We derive the above answer based on the following explanation,
The Linear Factorization Theorem states that . . . if f(x) is a polynomial of degree n, where n > 0, then f has precisely n linear factors f(x) = an(x – c1)( x – c2) . . . (x – cn) where c1, c2, . . . , cn are complex numbers.
Let us assume f to be a polynomial function with real coefficients and suppose a+bi, b≠0, is a zero of f(x). Then, by the Factor Theorem, x−(a+bi) is a factor of f(x). For f to have real coefficients, x-(a−bi) must also be a factor of f(x). This is true because any factor other than x−(a−bi) when multiplied by x−(a+bi), will leave imaginary components in the product. Only conjugate pair multiplication will get rid of the imaginary components and produce real coefficients.
Read more about Polynomial functions from:
https://brainly.com/question/30070005
#SPJ4
The medical assistant weighs patients each month. Mrs. Smith weighed 120 pounds last month.
Over the last 2 months she gained 1½ and - pounds. What is Mrs. Smith's current weight?
13) 120 + 1.5 + 0.25 = 121.75 pounds
14) 4 - 1.5 = 2.5 pints
15) (2.25)(32)= $72
13. Mrs. Smith's current weight is 121.75 pounds.
14. The students should consume an additional 2.5 pints of water.
15. The nurse's overtime earnings amount to $72.00.
Given are words problems based on mixed numbers:
13. To find Mrs. Smith's current weight, we need to add the weight gained over the last two months to her weight last month.
Weight gained in the first month: 1 1/2 pounds
Weight gained in the second month: 1/4 pounds
Total weight gained over the last two months: 1 1/2 + 1/4 = 1 3/4 pounds
Now, to find Mrs. Smith's current weight, we add the total weight gained to her weight last month:
Current weight = Weight last month + Total weight gained
Current weight = 120 pounds + 1 3/4 pounds
Hence, Mrs. Smith's current weight is 121.75 pounds.
14. To calculate the additional water the students should consume to meet the school nurse's recommendation of at least 4 pints daily, we need to find the difference between the recommended amount and the average amount the students currently drink.
The recommended amount is 4 pints, and the average amount the students currently drink is 1 1/2 pints, which can be written as 1.5 pints.
Additional water needed = Recommended amount - Current average amount
Additional water needed = 4 pints - 1.5 pints
Additional water needed = 2.5 pints
Therefore, the students should consume an additional 2.5 pints of water daily to meet the school nurse's recommendation.
15. To calculate the nurse's overtime earnings, you can use the formula:
Overtime Earnings = Overtime Hours × Overtime Pay Rate
First, let's convert the mixed number of overtime hours into an improper fraction:
2 1/4 hours = 2 + 1/4 = 9/4 hours
Now, we can calculate her overtime earnings:
Overtime Hours = 9/4 hours
Overtime Pay Rate = $32.00/hour
Overtime Earnings = (9/4) hours × $32.00/hour
To simplify the calculation, you can convert the fraction to a decimal:
Overtime Earnings = (9/4) hours × $32.00/hour
Overtime Earnings = 2.25 hours × $32.00/hour
Overtime Earnings = $72.00
So, the nurse's overtime earnings amount to $72.00.
Learn more about Mixed numbers click;
https://brainly.com/question/24137171
#SPJ4
Suppose f(x)=2^x. What is of g(x)=f(3x)?
Answer:
All you need to do is suppose x = 3x :
[tex] \tt \: g(x) = \boxed{ \tt{2^{3x} }} [/tex]
------ Happy LearninG <3 ----
) Consider the following probability density function of the random variable X. f(x) = k(2x + 3x2 ), 0 ≤ x ≤ 2. (i) Determine the value of the constant k.
I assume [tex]f(x)=0[/tex] otherwise. If [tex]f(x)[/tex] is indeed a proper PDF, then its integral over the support of [tex]X[/tex] is 1.
[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = k \int_0^2 (2x + 3x^2) \, dx = 1[/tex]
Compute the integral.
[tex]\displaystyle \int_0^2 (2x + 3x^2) \, dx = (x^2 + x^3)\bigg|_{x=0}^{x=2} = (2^2 + 2^3) - (0^2 + 0^3) = 12[/tex]
Then
[tex]12k = 1 \implies \boxed{k=\dfrac1{12}}[/tex]
A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $5, 0.3 for $25, 0.2 for $50, and 0.004 for $75. What
are the odds that the ticket is worth at least $25?
Answer:
0.7
Step-by-step explanation:
Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7
In the figure above, if l is a line, a+b=120 and b+c=100, then what is the value of b?
Based on the angles of a + b and b + c, the value of b can be calculated to be 40°.
How many degrees is B?As this is a triangle, all the internal angles must add up to 180°.
This means that:
a + b + c = 180°
As we have the value of b + c, this becomes:
a + 100 = 180
a = 80°
b is therefore:
a + b = 120
80 + b = 120
b = 120 - 80
= 40 °
Full question is:
If in triangle abc, angle a + angle b= 120° and angle b + angle c = 100°, then find angle b.
Find out more on the internal degrees of a triangle at https://brainly.com/question/7888180.
#SPJ1
what is the answer to 20÷ 1683 pls
Suppose that X is a random variable that has a binomial uncertainty distribution with parameters n = 10 and π = 0.4. Calculate the numerical value of the probability that X = 6. What are the numerical values of the mean and standard deviation of the uncertainty distribution?
The numerical values of the mean and standard deviation are 4 and 1.55, respectively
The numerical value of the probability that x = 6.The given parameters are:
n = 10
π = 0.4
The probability is then calculated as:
[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]
So, we have:
[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]
Apply the combination formula
[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]
So, we have:
[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]
Evaluate
P(6) = 0.1115
Hence, the numerical value of the probability that x = 6 is 0.1115
The numerical values of the mean and standard deviationThe mean value is:
[tex]\bar x = n\pi[/tex]
This gives
[tex]\bar x = 10 * 0.4[/tex]
[tex]\bar x = 4[/tex]
The standard deviation value is:
[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]
This gives
[tex]\sigma = \sqrt{4(1-0.4)[/tex]
[tex]\sigma = 1.55[/tex]
Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively
Read more about mean and standard deviation at:
https://brainly.com/question/16030790
#SPJ1
The city has an average of 13 days of rainfall for April.
What is the probability of having exactly 10 days of precipitation in the month of April?
What is the probability of having less than three days of precipitation in the month of April?
What is the probability of having more than 15 days of precipitation in the month of April?
Using the Poisson distribution, we have that:
There is a 0.0859 = 8.59% probability of having exactly 10 days of precipitation in the month of April.There is a 0.00022 = 0.022% probability of having less than three days of precipitation in the month of April.There is a 0.2364 = 23.64% probability of having more than 15 days of precipitation in the month of April.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.For this problem, the mean is given as follows:
[tex]\mu = 13[/tex]
The probability of having exactly 10 days of precipitation in the month of April is P(X = 10), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 10) = \frac{e^{-13}13^{10}}{(10)!} = 0.0859[/tex]
There is a 0.0859 = 8.59% probability of having exactly 10 days of precipitation in the month of April.
The probability of having less than three days of precipitation in the month of April is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-13}13^{0}}{(0)!} \ approx 0[/tex]
[tex]P(X = 1) = \frac{e^{-13}13^{1}}{(1)!} = 0.00003[/tex]
[tex]P(X = 2) = \frac{e^{-13}13^{2}}{(2)!} = 0.00019[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.00003 + 0.00019 = 0.00022
There is a 0.00022 = 0.022% probability of having less than three days of precipitation in the month of April.
For more than 15 days, the probability is:
P(X > 15) = P(X = 16) + P(X = 17) + ... + P(X = 20)
Applying the formula for each of these values and adding them, we have that P(X > 15) = 0.2364, hence:
There is a 0.2364 = 23.64% probability of having more than 15 days of precipitation in the month of April.
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
#SPJ1
10-A biased die is thrown thirty times and the number of sixes seen is eight. ( The probability of face six is 8 = 4 ) If the die is thrown a further twelve times find:
30 15
(a) the probability that a six will occur exactly twice; (b) the expected number of sixes: () = ;
(c) the variance of the number of sixes.
Using the binomial distribution, we have that:
a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.
b) The expected number of sixes is of 3.2.
c) The variance of the number of sixes is of 2.35.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are given by:
p = 8/30 = 0.2667, n = 12.
Item a:
The probability is P(X = 2), hence;
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111[/tex]
Item b:
The expected number of the binomial distribution is:
E(X) = np.
Hence:
E(X) = 12 x 8/30 = 3.2.
Item c:
The variance of the binomial distribution is:
V(X) = np(1-p).
Hence:
E(X) = 12 x 8/30 x 22/30 = 2.35.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
Use two formulas for volume to find the volume of the figure. Express the volume in terms of 3.14 and than round to the nearest whole number. Note that the figure may not be drawn to scale
The volume of the figure to the nearest whole number = 756π m³.
How to estimate the volume of the given figure?The figure shown exists composed of a cone and a cylinder.
The volume of the figure = volume of cone + volume of the cylinder
Height of cone = 12 - 8 = 4
Radius (r) of cone = 18/2 = 9 m
The volume of the cone V = 1/3hπr²
= 1/3 [tex]*[/tex] 4π [tex]*[/tex] 9² = 108π
The volume of the Cylinder = πr²h
radius (r) = 18/2 = 9 m
height (h) = 8 m
Volume of cylinder = π [tex]*[/tex] 9² [tex]*[/tex] 8 = 648π m³
Volume of the figure = 108π + 648π = 756π
The volume of the figure to the nearest whole number = 756π m³.
To learn more about volume refer to:
https://brainly.com/question/18959925
#SPJ9
(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = -3x2 + 4
Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]
Step-by-step explanation:
[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]
The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given quadratic equations are given as below:-
y = 3x² + 6x + 4
y = -3x² + 4
Equate the equations and solve for the value of x.
3x² + 6x + 4 = -3x² + 4
6x² + 6x = 0
x² + x = 0
x ( x + 1 ) = 0
x = 0 and x = -1
At x=0 and x=-1 the values of y are calculated as below:-
y = -3x² + 4
y = 0+ 4 = 4
y = -3 + 4 = 1
Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ5
pls helpppp a gurllll outtttt : )))))))))
Answer:
2
Step-by-step explanation:
[tex]\frac{3[2(-2)-6] + (-2)^{2} +4[2(-2)+1]}{3[(-2)-5]+2}[/tex]
[tex]\frac{3(-10) - 4 + 4(-3)}{-16}[/tex]
[tex]\frac{-30-4-12}{-16}[/tex]
[tex]\frac{-46}{-16}[/tex]
okay you know what i dont know what im doing but i know the answer is for sure 2..
prove that: 1-sin^2x cos*2x/cos^2x = tan^2x + cos^2x
LHS = (1-sin² cos²)/(cos²)
= (sin² + cos² - sin² cos²)/(cos²)
= (sin/cos)² + 1 - sin²
= tan² + cos²
= RHS
find x and y
pls help
Answer:
Step-by-step explanation:
no idea tbh
x is 40 degrees
y is 40 degrees
Hope this helps!
Accounts Receivable has a balance of $645,000; Allowance for Doubtful Accounts has a credit balance of $6,000; and sales for the year total $2,900,000. Bad debt expense is estimated at 1/4 of 1% of sales.
1. The amount of the adjusting entry for Uncollectible Accounts is $1,250.
2. The adjusted balances of Accounts Receivable Allowance for Doubtful Accounts Bad Debt Expense are:
Accounts Receivable = $3,545,000
Allowance for Doubtful = $7,250
Accounts Bad Debt Expense = $1,250
3. The net realizable value of the accounts receivable is $3,537.750 ($3,545,000 - $7,250).
Data and Calculations:Accounts Receivable Allowance for Doubtful Accounts
Beginning balance $645,000 DR $6,000 CR
Sales 2,900,000
Bad Debt Estimate = $7,250 ($2,900,000 x 0.0025)
Ending balance $3,545,000 $7,250 CR
Bad Debts Expense = $1,250 ($7,250 - $6,000)
Thus, the net realizable value of the accounts receivable shows the amount that the company expects to recover from customers after allowing for doubtful accounts.
Learn more about determining the net realizable value of accounts receivable at https://brainly.com/question/13767014
#SPJ1
Question Completion:1. Determine the amount of the adjusting entry for uncollectible accounts.
2. Determine the adjusted balances of Accounts Receivable, Allowance for Doubtful Accounts, and Bad Debt Expenses.
3. Determine the net realizable value of accounts receivable
If x=y= 2z and x*y*z = 500, then x equals?
Answer:
x is equal to 5
Step-by-step explanation:
Write in standard form: x² - 10x + y² - 4y = -28
Answer:
(x - 5) ^2 + (y -2)^2 = 1
Step-by-step explanation:
This is for a circle.
We need to complete the square
(x^2 -10x ) + ( y^2 -4y ) = -28
(x^2 - 10x +25) + (y^2 - 4y 2y) = -28 + 25 + 4
(x-5)^2 + (y-2)^2 = 1
The center of this circle would be (5,2) with a radius of 1.
Need an detailed step by step answer and solution again
Answer:
12u²
Step-by-step explanation:
area of a regular quadrilateral is always base x vertical height.
the base here is clearly 4 (just count the squares)
draw an imaginary line connecting the bottom right corner to the line before the top right corner (the line should be vertical)
count the squares here too and you get 3.
so the area = 3 x 4,
the area is 12u²
Question 15 of 15
Convert 1,056 yards into miles. Round your answer to the nearest tenth.
Hint. There are 1,760 yards in a mile.
A. 150 miles
O B. 1.6 miles
O C. 0.6 miles
SUBMIT
Answer:
0.6
Step-by-step explanation:
Given what we know, we can set up a proportion to convert 1,056 yards into miles
[tex]\frac{1760 yd}{1mi} =\frac{1056 yd}{x mi} \\\\1760x=1056\\\\x=0.6[/tex]
In the trapezoid below, AP = 6, PB = x + 3, CD = 2x + 6, AC = 10 and the area is 174. Find the value of x to the nearest tenth.
The value of x in the trapezoid given, to the nearest tenth, is: 10.5.
What is a Trapezoid?A trapezoid is a quadrilateral that has two sides only that are parallel to each other.
What is the Area of a Trapezoid?To find the area of a trapezoid, the formula used is expressed as: 1/2(a + b) × h, where:
a and b are length of the two base sides that are parallel.h is the height of altitude of the trapezoid.Given the following:
Area of trapezoid = 174 units²
AP = 6
PB = x + 3
CD = 2x + 6
AC = 10
Using the formula, we variables in the formula are:
a = AP + PB = 6 + x + 3 = x + 9
b = CD = 2x + 3
h = PC = √(AC² - AP²)
h = √(10² - 6²) = 8
Plug in the values into 1/2(a + b) × h:
174 = 1/2(x + 9 + 2x + 3) × 8
174 = 1/2(3x + 12) × 8
174 = (3x + 12) × 4
174 = 12x + 48
174 - 48 = 12x
126 = 12x
126/12 = x
10.5 = x
x = 10.5
Learn more about the trapezoid on:
https://brainly.com/question/1463152
#SPJ1
Find the inverse function of
f(x)=20x-4
Domain of f(x)
Domain of f^-1(x)
Range of f(x)
Range of f^-1(x)
help can you show work for question please
Answer:
[tex]f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = \frac{1}{20} x + \frac{1}{5} \\ substitute \: f {}^{ - 1} (x) \: for \: y \\ f {}^{ - 1} (x) = \frac{1}{20} x + \frac{1}{5} [/tex]
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
Thus, domain of f(x): x∈R = range of f¯¹(x)
and range of f(x): x∈R =domain of f¯¹(x)
Which is the graph of the function f(x)= - squared x
Answer:
top left graph
Step-by-step explanation:
The function is not defined for negative x.
Eliminate top middle and top rightAlso, the range should not include positive numbers.
Eliminate bottom left.So, the answer is the top left graph.
i dont know answer please im in summer school
The centre and the radius of the circle is (-7, -1) and 6 units
Equation of a circleThe equation of the circle in standard from is expressed as:
x^2+y^2+2gx+2fy+C = 0
where;
(-g, -f) is the centre
r= √g²+f²-C
Given the equation below
x^2+y^2+14x+2y+14 = 0
2g = 14
g = 7
2f = 2
f =1
Hence the centre of the circle is (-7, -1)
Radius = √49+1-14
Radius = √36 = 6 units
Hence the centre and the radius of the circle is (-7, -1) and 6 units
Learn more on equation of a circle here: https://brainly.com/question/1506955
#SPJ1
Trail A is 6 3/4 miles long. Trail B is 8 1/2 miles long. How many miles longer is Trail B than Trail A
Given the length of both trail, Trail B is 7/4 miles longer than Trail B.
How many miles longer is Trail B than Trail A?
Given that;
Length of Trail A = 6 3/4 = [ (6×4 + 3 )/4 = 27/4 miles Length of Trail B = 8 1/2 = [ (8×2 + 1 )/4 = 17/2 milesTo determine how many miles longer is Trail B more than Trail A, we subtract the length of tail A from Tail B.
Trail B - Trail A
17/2 - 27/4
17/2 is the same as; 34/4
34/4 - 27/4
We combine the numerators over common denominator
(34 - 27 )/4
7/4 miles
Given the length of both trail, Trail B is 7/4 miles longer than Trail B.
Learn more about fractions here: brainly.com/question/28039882
#SPJ1
Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.
x = 1/12y^2
y = 1/9x^2
y = 1/12x^2
y = -1/12x^22
The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]
None of the given options is correct
Given:
Focus: (0, 3)
Directrix: y = -3
Note that:
f - k = k - (-3)
f - 3 = 3 + 3
f = 6 + 3
f = 9
The equation of the parabola is of the form:
[tex]y=\frac{1}{4(f-k)} (x-h)^2+k[/tex]
Substitute f = 9, k = 3, h = 0 into the equation
[tex]y=\frac{1}{24} (x-0)^2+3\\\\y=\frac{1}{24}x^2+3[/tex]
The equation of the parabola is [tex]y=\frac{1}{24} x^2+3[/tex]
Learn more on equation of a parabola here: https://brainly.com/question/4061870
#SPJ1
Part A Your presentation should make a convincing argument that human activity is the major cause of climate change. Your presentation should answer some of these questions: What is climate? How is Earth’s climate changing? What are the natural and human factors that affect climate? How do scientists know that human activity is the major force behind climate change? What evidence do scientists have that climate is changing? Write down two additional questions you have about climate change that will help you make this argument in your presentation. 12pt
Climate is the long-term weather pattern that can be seen in an area over a period of years.
How to explain the climate?Earth’s climate changing as the Earth's atmosphere heats up, it collects, retains, and drops more water, thereby changing weather patterns and making wet areas wetter and dry areas drier.
The factors that affect climate includ deforestation, desertification, urbanization, etc.
Scientists know that recent climate change is largely caused by human activities from an understanding of basic physics by comparing observations with models, and then fingerprinting the detailed patterns of climate change caused by different human and natural influences
Learn more about climate on:
https://brainly.com/question/17922964
#SPJ1
please help I've been trying to figure it out but I can't
answer : 2 1/2
divide y by x
divide 2 1/2 by 1
its 2 1/2
10 divided by 4 is also
2 1/2
17 1/2 divided by 7 is also
2 1/2
What do l do??? Need help
Answer:
you have to put the formula of perimeter
Answer:
12a. L+8m + 14m
12b. 10m+8m +14m
12c. 66
12d.420m
12e.252m
quick questions
volume= 288cm cubed
Asap I need a answer please
Answer:
-4
Step-by-step explanation:
in order to get from -6 to 24, you need to multiply x by -4 since -6* -4 is 24
A two-digit locker combination is made up of non-zero digits and no digit is repeated in any combination. Event A = the first digit is 4 Event B = the second digit is odd If a combination is chosen at random with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A.5/8
B.4/81
C.1/18
D.5/72
Answer:
D. 5/72
Step-by-step explanation:
The non-zero digits are 1 through 9.
There are 9 different non-zero digits.
p(A) = 1/9
There are 5 odd digits.
p(B) = 5/8
p(A and B) = p(A) × p(B) = 1/9 × 5/8 = 5/72
I think the answer is
A: 1/18