Factorizing the denominator gives
[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}[/tex]
Then the partial fraction decomposition would take the form
[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}[/tex]
The probability distribution for a
random variable x is given in the table.
X
-5 -3 -2 0 2
Probability .17 .13
3
133 16 .11 .10
Find the probability that -2 ≤x≤2
Considering the distribution given in the table, the desired probability is:
[tex]P(-2 \leq X \leq 2) = 0.6[/tex]
What is the probability distribution given in the table?The distribution is:
P(X = -5) = 0.17.P(X = -3) = 0.13.P(X = -2) = 0.33.P(X = 0) = 0.16.P(X = 2) = 0.11.P(X = 3) = 0.10.The values between -2 and 2(inclusive) are -2, 0 and 2, hence the desired probability is:
[tex]P(-2 \leq X \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.6[/tex]
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(1 point)
If A and B are 7 x 2 matrices, and C is a 4 x 7 matrix, which of the following are defined?
OA. CA
B. B - A
C. B-C
D. ABT
E. AC
OF. CT
The statements A, B, D, and E are defined.
When we multiply matrices, the number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.
What is the subtraction of the matrix?
When we add or subtract matrices, the number of rows and columns must be the same.
A) If C is 7x3 and A is 3x2, that means C has 3 columns and A has 3 rows. So C * A is defined.
B) When you transpose a matrix, the number of rows and columns are switched. So C^T has 3 rows and 7 columns. So C^T is defined.
C) B has 2 columns and C has 7 rows, so B * C is not defined.
D) Because A and B have the same number of rows and columns, we can add them. So A + B is defined.
E) B^T has 2 rows and 3 columns, and C^T has 3 rows and 7 columns. So B^T has the same number of columns as the number of rows as C^T. So B^T * C^T is defined.
F) C and A have different numbers of rows and columns, so C-A is not defined.
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A mother gives birth to a 9 pound baby. Every 2 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds.
Answer:
write three methods of writing set. Give one example of each method.
A single die is rolled twice. Find the probability of getting a 1 the first time and a 4 the second time.
Answer:
1/36
Step-by-step explanation:
Rolling a 1 the first time has an 1/6 chance and rolling a 4 has an 1/6 chance the 2nd time.
1/6 * 1/6 = 1/36 chance.
The one-to-one functions g and h are defined as follows.
The value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
g = {(-4, 1), (0, 5), (5, -3), (8, -8)}
As we know,
If f(x) has an ordered pair (x, y) then its inverse of a function has (y, x).
g⁻¹ = {(1, -4), (5, 0), (-3, 5), (-8, 8)}
g⁻¹(5) = 0
h(x) = 3x - 10
h⁻¹(x) = (x+10)/3
h⁻¹(5) = 15/3 = 5
h(h⁻¹(5)) = 3(5) - 10
h(h⁻¹(5)) = 5
Thus, the value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10
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Need help with this one can anyone help me?
What was the full commission rate if Sarah was paid $3,152.50 on the sale of a $97,000 property? Sarah's agreement with her broker is half of the full commission.
Answer:
6.5 %
Step-by-step explanation:
Full commission would then be 2 * 3152.50 = 6305
Full commission percentage of sale is then:
6305 / 97000 * 100 % = 6.5 %
I have 28 students in my MAT121 class who recently took a test. Their results are graphed below.
a. What percent received a score less than 60?
b. How many students received a score greater than 85?
Considering the box-and-whisker plot, it is found that:
a) 25% of the students scored less than 60.
b) 25% of the students received a score greater than 85.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median.The 75th percentile, which is the median of the upper 50%.From the plot given in the graph, we have that:
The 25th percentile is of 60, hence 25% of the students scored less than 60.The 75th percentile is of 85, hence 25% of the students received a score greater than 85.More can be learned about a box-and-whisker plot at https://brainly.com/question/27608957
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The diagram shows a square.
(7x + 3) cm
Find the length of the side of the square.
(5x + 8) cm
Answer:
28
Step-by-step explanation:
The diagram shows a square, and it is known that all side lengths for a square are equal. We can use these information on hand and write the following equation to find the side length:
7x + 3 = 5x + 8 transfer like terms to the same side of the equation
7x - 5x = 8 - 3 add/subtract
2x = 5 divide both sides by 2
x = 2.5 to find a side length simply replace x with 2.5
5x + 8 = 5*(2.5) + 8
5*(2.5) + 8 = 28
2₂
5
●x<0
X>0
●x< 1
3
2
A
-3
2 3
3
What is the domain of the function?
all real numbers
a
Answer:
x>0
Step-by-step explanation:
The domain of a function is the set of x-values.
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0. Which is a y-intercept of the continuous function in the table? (0, –6) (–2, 0) (–6, 0) (0, –2)
The y-intercept of the continuous function in the table is (0, –6)
Data obtained from the questionColumn 1 (x): -4, -3, -2, -1, 0, 1Column 2 [f(x)]: 10, 0, 0, -4, -6, 0y-intercept coordinate =?How to determine the y-intercept coordinateTo determine the y-intercept coordinate, we must understand the y-intercept is a point on a graph where the line passes through the y-axis at x = 0.
With the above information in mind, we can easily obtain the y-intercept coordinate as follow:
From the the two columns given in the question, the value of y when x = 0 is -6.
Thus, the y-intercept coordinate is (0, -6)
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Suppose your weekly paycheck is $300.
Because of losses by your employer, you agree to a temporary 10% pay
cut.
Your employer promises to give you a 10% pay raise after six months.
Will the pay raise restore your original salary?
For full credit, you must explain why or why not in the space provided
below.
Answer:
No
Step-by-step explanation:
[tex]300 \times .9 \times 1.1 = 297[/tex]
If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P (more than 9) with n=12 and p= 0.3 by using the normal distribution as an approximation to the binomial distribution, if np<5 or nq<5, then state that the normal approximation is not suitable
The normal approximation is not suitable as np<5.
Given,
mean = np
It turns out that if np and nq are both at least 5, the normal distribution can be used to approximate the binomial distribution. Additionally, keep in mind that a binomial distribution has a mean of np and variance of npq.
Hence apply the mean formula and get the value for np
n= 12 and p=0.
therefore mean = np
np = n×p
np = 12×0.3×
np = 3.6
np is less than 5.
nq=?
q=1-p
q=1-0.3
q=0.7
∴nq = 12 × 0.7
nq = 8.4
nq is not less than 5
It's remarkable that the normal distribution may accurately represent the binomial distribition when n, np and nq are large.
since here only nq is greater than five and np is less than five, therefore we conclude that normal approximation is not suitable.
Hence np<5 so normal approximation is not suitable.
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NO LINKS!!! What is the transformation f(x)= x^3:
PART 2:
THIS IS NOT MULTIPLE CHOICE!!!
4. f(x)= (5x)^3
5. f(x)= (x+5)^3 + 5
6. f(x)= (x-5)^3-5
Answer:
4. Horizontal shrink by a factor of ¹/₅
5. Left 5, Up 5
6. Right 5, Down 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 4
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(5x)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by 5.
Therefore, the transformation is:
[tex]y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}[/tex]
As a > 1, the transformation visually is a compression in the x-direction, so we can also say: Horizontal shrink by a factor of ¹/₅
Question 5
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x+5)^3+5[/tex]
Comparing the parent function with the given function, we can see that there are a series of transformations:
Step 1
5 has been added to the x-value of the parent function.
[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]
Step 2
5 has then been added to function.
[tex]f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}[/tex]
Transformation: Left 5, Up 5
Question 6
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x-5)^3-5[/tex]
Comparing the parent function with the given function, we can see that there are a series of transformations:
Step 1
5 has been subtracted from the x-value of the parent function.
[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]
Step 2
5 has then been subtracted from function.
[tex]f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}[/tex]
Transformation: Right 5, Down 5
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Answer:
4) Horizontal shrink by a factor of 1/5
5) Left 5, Up 5
6) Right 5, Down 5
Explanation:
Main parent function: f(x) = x^3
4.) f(x) = (5x)^3
Comparing it with f(ax) which gives horizontal compression when a > 1 or horizontal stretch when 0 < |a| < 1 by a factor of 1/a
The function has been compressed horizontally by a factor of 1/5.
5.) f(x) = (x+5)^3 + 5
Comparing with f(x + c) + d, gives function moved c units left, d units up.
The function has moved 5 units left and 5 units up.
6.) f(x) = (x-5)^3 - 5
Comparing with f(x - c) - d, gives function moved c units right, d units down.
The function has moved 5 units right, 5 units down.
Help please with discussion
The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)
How to determine if a given relationship represents an exponential function
Exponential functions are trascendent expressions, these are, expressions that cannot be described algebraically, that are defined by the following expressions:
[tex]f(x) = a \cdot \left(1+ \frac {r}{100}\right)^{x}[/tex] (1)
Where:
a - Initial valuex - Independent variablef(x) - Dependent variabler - Increase rateExponential functions are used to represent constant continuous increases or decreases in terms of the independent variable. The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)
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Write each of the following as a trigonometry ratio of positive acute angles. (a) sin(-194°) (b) cos 481° (c) tan 185° (d) sin 331° Write each of the following as a trigonometry ratio of positive acute angles . ( a ) sin ( -194 ° ) ( b ) cos 481 ° ( c ) tan 185 ° ( d ) sin 331 °
(a) [tex]\sin(-194^{\circ})=-\sin 194^{\circ}=-(-\sin 14^{\circ})=\sin 14^{\circ}[/tex]
(b) [tex]\cos 481^{\circ}=\cos 121^{\circ}=-\cos 59^{\circ}[/tex]
(c) [tex]\tan 185^{\circ}=\tan 5^{\circ}[/tex]
(d) [tex]\sin 331^{\circ}=\sin(-29^{\circ})=-\sin 29^{\circ}[/tex]
What are the solution points for the system graph?
Question 14 options:
A)
(–2,–4) and (4,8)
B)
(–2,8) and (–4,4)
C)
(8,–2) and (4,–4)
D)
(–2,4) and (–4,8)
Answer:
btyivh
Step-by-step explanation:he was so much for your support of school and I have a great day of school and I have a great day of school and I have a great day of school
The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.
We need to find the solution to the given function.
How to find the solution to the function from the graph?The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be at the point where the two lines intersect.
From the given graph we can see that the two functions are intersecting at (–2,–4) and (4,8).
The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.
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Please help!! Getting timed for this! Consider the following system of two linear equations:
3y + 2x = 15
x – y = 0
Select the graph that correctly displays this system of equations and point of intersection.
Answer: plug in the coordinates for x and y
Step-by-step explanation:
take a look at my work if you still need some help
what are the values Of p and q ?
The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
x - 3 (i.e. x = 3) and x + 9 (i.e. x = -9) are factors of f(x) = 2x³ + 17x² - 3px - 5q
Hence:
f(3) = 0
2(3)³ + 17(3)² - 3p(3) - 5q = 0 (1)
Also:
2(-9)³ + 17(-9)² - 3p(-9) - 5q = 0 (2)
Hence, p = 8, q = 27
The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27
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In a survey of 4096 adults, 733 oppose allowing transgender students to use the bathrooms of the opposite biological sex Construct a 99% confidence interval for the population proportionInterpret the results A 99% confidence interval for the population proportion is (Round to three decimal places as needed)
A 99% confidence interval for the population proportion is; CI = (0.164, 0.194)
How to construct the confidence Interval?We are given;
Sample size; n = 4096
Number that opposed transgender students; x = 733
Thus;
Proportion; p^ = x/n = 733/4096 = 0.179
Formula for confidence interval of proportions is;
CI = p^ ± z√[p^(1 - p^)/n]
The z-value for confidence level of 99% is z = 2.576
Thus;
CI = 0.179 ± 2.576√[0.179(1 - 0.179)/4096]
CI = 0.179 ± 0.015
CI = (0.164, 0.194)
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mer School)
Applying the Addition Rule of Mutually Exclusive Even
A day of the week is randomly chosen. What is the probability of choosing Monday or a day that starts with t
S?
Try It
P(Monday) =
P(starts with S) =
P(Monday or starts with S) =
Step-by-step explanation:
a probability is always the number of desired cases over the number of total possible cases.
in this situation the number of total cases is 7 : days of the week.
the 3 probabilities just differ based on the number of desired cases.
P(Monday) : there is only one desired case out of the 7 possible ones. so, the probability is
1/7 = 0.142857143...
P(starts with S) : 2 desired cases (Saturday and Sunday).
so the probability is
2/7 = 0.285714286...
P(Monday or starts with S) : 3 desired cases (Monday, Saturday, Sunday).
so the probability is
3/7 = 0.428571429...
Select the correct answer. Consider these functions: f(x)=x+1 g(x)=2/x.Which polynomial is equivalent to (f ◦ g)(x)?
The polynomial which is equivalent to fog(x) is 2/x + 1.
What is Polynomial?A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).
Here,
given functions are;
f(x) = x + 1 ; g(x) = 2/x
Now, we need to compose fog(x) from the given function;
fog(x) = f ( g(x) )
= f( 2/x)
= 2/x + 1
Thus, the polynomial which is equivalent to fog(x) is 2/x + 1.
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Find the sin T. Round to the nearest hundredth.
Answer:
.38
Step-by-step explanation:
sin is the opposite side from angle T over the hypotenuse.
5/13
I’m having some problems understanding. I get it but don’t at the same time.
Answer:
C is the correct answer.
Step-by-step explanation:
-Angle 1 is not equal to Angle 5.
-Angle 3 + Angle 5 will not equal 180 degrees, since they are corresponding angles, not supplementary angles.
Though, Angle 8 is equal to Angle 6, likewise that 7 is equal to 9. Therefore, these angles will create a 180 degrees angle. This is because if 8 and 9 are supplementary, and 7 is a corresponding angle of 9, this will make Angle 8 + Angle 7 = 180 degrees.
2=3√4x-12 x=? Please help with this question
Answer: 49/9
Step-by-step explanation:
[tex]2=3\sqrt{4x}-12\\\\14=3\sqrt{4x}\\\\\frac{14}{3}=\sqrt{4x}\\\\4x=\frac{196}{9}\\\\x=\frac{196}{36}\\\\x=\frac{49}{9}[/tex]
Quick PLEASE! Fred wants to have $25 000 saved in ten years to help pay for a down payment on a house. How much would he have to invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly. Make sure to show all your work.
The amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79
Compound interestThe formula for calculating the compound interest is given as:
A = P(1+r/n)^nt
Given the following parameters
25000 = P(1+0.06/12)^12(10)
25000 = P(1+0.005)^120
25000 = P (1.005)^120
25000 = 1.8194P
P = 25000/1.8194
P = $13740.79
Hence the amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79
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Select the correct answer. Function f is an exponential function that is negative on the interval (-∞, 1) and positive on the interval (1, ∞). Which could be the graph of function f? A. An exponential function passes through (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3) B. An exponential function passes through (minus 1, minus 2), (minus 0.5, 0), (0, 1), and (4, 3) C. An exponential function passes through (minus 5, 3), (minus 2, 2), (minus 1, 0), and (0, minus 6) D. An exponential function passes through (minus 4, 3), (minus 1, 3.8), and (0, 5)
The exponential function which passes through (0,-2),(1,0),(2,2) (5,3) is negative on the interval (-∞,1) and positive on the interval (1,∞).
Given Function f is negative on the interval (-∞,1) and positive on the interval (1,∞)
We have to find the statement for which the exponential function' s values are given.
First option is having the statement which says that exponential
function passes through points (0,-6)(0.5,-2),(1,0),(2,2) (5,3). These points are showing the domain and value of the function which is codomain.
for x=0 it has -6,
for x=1 it has 0,
for x=2 it has 2,
for x=5 it has 3.
for x=0.5 it has -2
The description says that value of function is negative in interval (-∞,1) and positive in (1,∞) which is true for option A as it has negative values of -2 for x=0 and for x=2,5 it has value of 2 and 3.
Hence the function f is an exponential function passes through (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3).
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1. The cost of three dozen eggs and two dozen oranges is ¢6.96. The cost of two dozen eggs and one dozen
oranges is $4.08. What is the cost per dozen of each item
Answer:
$1.20 per dozen eggs, $1.68 per dozen oranges
Step-by-step explanation:
Let x=cost of one dozen eggs and y=cost of one dozen oranges.
3x + 2y = 6.96------>3x + 2y = 6.96
2x + y = 4.08-------->4x + 2y = 8.16
---------------------
x = 1.20
4(1.20) + 2y = 8.16
4.80 + 2y = 8.16
2y = 3.36
y = 1.68
Answer:
The cost of one dozen of egg is 1.2
The cost of one dozen of orange is 1.68
Step-by-step explanation:
The solution is in the image
For an output level below Qg, the value of a unit to a buyer is
Suppose a firm that produces for this market is able to influence the market price, which leads to an outcome that differs from the free market
equilibrium shown in the previous graph. Such a situation is characterized by
, which is an example of
the cost of a unit to a seller.
Step-by-step explanation:
გჰჰბფჯ არ არის დაწერეთ პირველი კომენტარი არ არის დაწერეთ პირველი კომენტარი არ არის დაწერეთ პირველი
explain in words with mathematical representations how you would dividie this polynomial in each of the three ways:
The division of a polynomial is illustrated below.
What is a polynomial?It should be noted that a polynomial simply means an expression that consist of variables which involves the operation of addition, subtraction, etc.
The way to divide the polynomial will be:
Set up the division problem.
Determine the first term of the quotient.
Multiply the answer by the divisor.
Write it below the like terms of the dividend.
Subtract the bottom binomial from the term above it.
Bring it down and repeat the steps until you reach the last term.
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