The domain for the rational function is the set of all real numbers except for 8, this is written as:
{x | x ∈ R, x≠8}
How to find the domain of the given function?
For any function f(x), the domain is the set of the possible inputs.
In this case, we have the rational function:
f(x) = (x - 3)/(x - 8)
Now, we start by assuming that the domain is the set of all real numbers, and then we remove all the problematic values.
Now, we can't divide by zero, so the value of x that makes the denominator zero needs to be removed, that is such:
x - 8 = 0
x = 8
So the domain is the set of all real numbers except for 8, this is written as:
{x | x ∈ R, x≠8}
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
For each of the professions in the left column, calculate the annual pay based on full-time, year-round employment consisting of 2,000 hours a year (40 hours per week for 50 weeks per year). Record your calculations under "Annual income" in the table. Then, find the difference between each annual wage figure and a) the poverty threshold and b) the median household income. If the difference is a negative number, record it as such.
The difference between each annual wage figure and the poverty threshold is as shown in the attached completed table.
How to calculate Annual Income?
Annual Income is a term in economics that is calculated by multiplying the Hourly wage by 4,000 hours.
Now, the Difference between annual wage and the federal poverty line is calculated by subtracting the 2019 Poverty threshold of $13,011 from the Annual Income.
The Difference between annual wage and median household income is calculated by deducting the 2019 Median household income of $68,703 from the Annual income. Negative balances are highlighted.
The attached table shows us the completed annual income table
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Elena buys 8 tokens for $4.40.
At this rate, how many tokens could she buy with $6.05?
Answer: 11
Step-by-step explanation: 8/4.40 = x/6.05
8 times 6.05
Divide by 4.40 is 11
equation of the line that passes through the point (1, -1) & is parallel to the graph of y = 3/5x + 2?
Equation is 5y = 3x + 8.
What is slope?Slope is the inclination of a line with respect to the horizontal is measured numerically. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Given Data
line that passes through the point (1, -1) &
is parallel to the graph of y = 3/5x + 2
y = mx + c
y = [tex]\frac{3}{5}[/tex]x + 2
m = [tex]\frac{3}{5}[/tex]
Equating points,
-1 = [tex]\frac{3}{5}[/tex](1) + c
-1 = [tex]\frac{3}{5}[/tex] + c
-1 - [tex]\frac{3}{5}[/tex] = c
[tex]\frac{-5-3}{5}[/tex] = c
[tex]\frac{-8}{5}[/tex]
Equation-
y = [tex]\frac{3}{5}[/tex]x + [tex]\frac{8}{5}[/tex]
5y = 3x + 8
Equation is 5y = 3x + 8.
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after school, a group of students decides to have a snowball fight. with 2 students on a team, they can make 6 snowballs per minute. with 10 students on a team, they can make 30 snowballs per minute. what is the slope in this situation?
Based on the calculations using the given points, the slope in this situation is equal to 5.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (30 - 10)/6 - 2)
Slope = 20/4
Slope = 5.
In conclusion, the slope of the line that passes through the given points is equal to 5.
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Find the length of side x in simplest radical form with a rational denominator
Length of the side, x = 11/2
radical form, x = √5.5
Define Hypotenuse.The longest side of a right-angled triangle which is the side opposite to the right angle is called hypotenuse. The hypotenuse can be easily found using the Pythagorean theorem. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
As given in question, ∅ = 60°,
Using, Cos ∅ = adjacent/hypotenuse :
Cos 60°= x/11
As we know cos 60° = 1/2
1/2 = x/11
x, length of the side = 11/2= 5.5
radical form = 5.5
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Question 6
Solve. Write it on paper to solve it.
5y + 4 = 4y + 5
Answer: y=1
Step-by-step explanation:
1. Subtract 4y from both sides to get y + 4 = 5.
2. Then subtract 4 from both sides to get y = 1.
Therefore, you get your answer, y = 1. Hope this helps!
59 + 43.6 estimate the sum or difference
Answer:
Step-by-step explanation:
59+ 43.6
43.6=44.0
59+44
59+43.6
=103.0
how do i do this problem.
ANSWER
[tex]g(5x)=75x^2\text{ + 5}[/tex]STEP-BY-STEP EXPLANATION:
Given information
[tex]g(x)=3x^2\text{ + 5}[/tex]Find g(5x)?
Step 1: make x = 5x
[tex]\begin{gathered} g(x)=3x^2\text{ + 5} \\ g(5x)=3(5x)^2\text{ + 5} \\ g(5x)=3(25x^2)+5^{} \\ g(5x)=75x^2\text{ + 5} \end{gathered}[/tex](-a^4b³)^-4x(a^-3b^4)^5
Answer:
5
Step-by-step explanation:
use math-way
Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may
apply.)
square root of -9
Select all descriptions that may apply.
A. Nonreal complex
B. Real
C. Pure imaginary
D. Complex
Answer:
acxdddhdhxhhh sax skskskkkkkddffffffrrkel sssddjeeeeerrjrrjtjjj
Find the first four terms of the binomial series for the function (1+2x)^1/2
The first four terms of the binomial series are 1, x, - x²/2 and - 1/32x³ respectively.
The binomial provided to us is [tex](1+2x)^{1/2}[/tex]
To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.
(1+x)^n = 1 + nx + [n(n - 1)/2!] x² + [n(n - 1)(n - 2)/3!] x³ +...
As we can see here,
The value of x = 2x,
The value of n = 1/2.
We get,
(1+2x)^1/2 = 1 + 1/2(2x) + [1/2(1/2-1)/2!]x² + [1/2(1/2-1)(1/2-2)/3!]x³ +
(1+2x)^1/2 = 1 + x - x²/2 - 9/4x³ + .....
From the expansion, we can see,
First term = 1
Second term = x
Third term = -x²/2
Fourth term = -1/32x³.
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I need help with this question on my assignment please and thank you
Given:
The expression is,
[tex]45x^2y^2+18x^3[/tex]Simplify the expression,
[tex]\begin{gathered} 45x^2y^2+18x^3=9\times5x^2y^2+9\times2x^3 \\ =(9\times5\times x^2\times y^2)+(9\times2\times x^2\times x) \\ \text{Take 9x}^2\text{ common from both the brackets,} \\ =9\times x^2\lbrack5\times y^2\rbrack+9\times x^2\lbrack2x\rbrack \\ =9x^2(5y^2+2x) \end{gathered}[/tex]Answer:
[tex]9x^2(5y^2+2x)[/tex]Need to find 2 successes and 4. Successes probablity first 2
• Given:
[tex]\begin{gathered} n=15 \\ p=0.4 \end{gathered}[/tex]You need to find this probability:
[tex]P(x=4)[/tex]The Binomial Distribution Formula is:
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number of trials, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case you know that:
[tex]x=4[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=(\frac{15!}{(15-4)!4!})(0.4)^4(1-0.4)^{15-4}[/tex][tex]P(x=4)=(\frac{15!}{(11)!4!})(0.4)^4(0.6)^{11}[/tex][tex]P(x=4)\approx0.1268[/tex]• Given that:
[tex]\begin{gathered} n=12 \\ p=0.2 \end{gathered}[/tex]You need to find:
[tex]P(x=2)[/tex]In this case:
[tex]x=2[/tex]Therefore, using the same formula, you get:
[tex]P(x=2)=(\frac{12!}{(12-2)!2!})(0.2)^2(1-0.2)^{12-2}[/tex][tex]P(x=2)=(\frac{12!}{(10)!2!})(0.2)^2(0.8)^{10}[/tex][tex]P(x=2)\approx0.2835[/tex]• Given:
[tex]\begin{gathered} n=20 \\ p=0.05 \end{gathered}[/tex]You need to find:
[tex]P(x\leq3)[/tex]This is:
[tex]P(x\leq3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)[/tex]Therefore, using the formula, set up:
[tex]P(x\leq3)=(\frac{20!}{(20-0)!0!})(0.05)^0(1-0.05)^{20}(\frac{20!}{(20-1)!1!})(0.05)^1(1-0.05)^{20-1}+(\frac{20!}{(20-2)!2!})(0.05)^2(1-0.05)^{20-2}+(\frac{20!}{(20-3)!3!})(0.05)^3(1-0.05)^{20-3}[/tex]Then, you get:
[tex]P(x\leq3)\approx0.9841[/tex]Hence, the answers are:
[tex]P(x=4)\approx0.1268[/tex][tex]P(x=2)\approx0.2835[/tex][tex]P(x\leq3)\approx0.9841[/tex]
Jeremy invests $8,500 into an account with a 2.4% interest rate that is compounded quarterly. How much money will be in this account after 6 years?
Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.
Answer:
9812.29
Step-by-step explanation:
Using the compound interest formula,
[tex]8500 \left(1+\frac{0.024}{4} \right)^{(6)(4)} \approx 9812.29[/tex]
A committee has fourteen members. There are two members that currently serve as the board's chairman
and ranking member. Each member is equally likely to serve in any of the positions. Two members are
randomly selected and assigned to be the new chairman and ranking member. What is the probability of
randomly selecting the two members who currently hold the positions of chairman and ranking member and
reassigning them to their current positions?
...
Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
As given,
Total members in the committee=14
Number of members serve as chairman and ranking member=2
Total number of ways to assigned new position
=¹⁴P₂
=(14!) / (14-2)!
=(14 × 13 × 12!) / 12!
=14 ×13
=182
Each member is equally likely to serve in any of positions.
Each position there is only one way to reassign position.
Probability of randomly selecting two members = 1 /182
Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).
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A restaurant serves an "all you can eat" buffet. At the beginning of serve, the value of the inventory is determined to be $1,200, and at the end of the meal period, it is
$800. That meal period the restaurant served 275 customers. The average food cost per customer for that meal period would be
O $3.64.
O $1.45
O $7.27.
O $5.82.
Answer:
1.45
Step-by-step explanation:
1200-800=400
400/275=1.4545454545...
the answer $1.45
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Solve the inequality and graph the solution.
−0.4b + 2.4 < 5.6
number line with an open circle plotted at negative eight and arrow pointing right
number line with a closed circle plotted at negative eight and arrow pointing right
number line with an open circle plotted at negative eight and arrow pointing left
number line with a closed circle plotted at negative eight and arrow pointing left
The graph of the solution to this inequality is: C. number line with an open circle plotted at negative eight and arrow pointing left.
What is a number line?A number line simply refers to a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
Next, we would solve the given inequality as follows:
−0.4b + 2.4 < 5.6
Subtracting 2.4 from both sides, we have:
−0.4b + 2.4 - 2.4 < 5.6 - 2.4
−0.4b < 5.6 - 2.4
−0.4b < 3.2
Dividing both sides by -0.4, we have:
b < -3.2/0.4
b < -8
In conclusion, the circle on a number line should be open and would point to the left when the inequality symbol is <.
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a gear reduction drive has three separate stages with ratio of 3:1,2.38:1 and 4.2:1. the total ratio of the drive is?
The total ratio of the drive is 9.58:1.
What are ratios?A relationship between two quantities that are typically stated as the product of their respective quotients is known as a ratio.The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.Given ratios of the three separate stages of a gear reduction drive are 3:1,2.38:1 and 4.2:1.
To find the total ratio of the drive we have to add the respective ratios.
When the denominator of the ratios are same, as in this case we just have to add the numerators to obtain the result.
Total ratio of the drive = 3:1 + 2.38:1 + 4.2:1 = 9.58:1
So, the total ratio of the drive is 9.58:1.
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What is the value of x9+(12−y), when x = 2 and y = –5?
Answer: 35
Step-by-step explanation:
1) Substitute the x's and y's
(2)9+(12−(-5))
2) Simplify the numbers inside the equation
18+(12-(-5)
= 18+(17)
= 35
3) Solved.
35
Translate this sentence into an equation.
Carlos's height decreased by 7 is 62
Use the variable c to represent Carlos's height
The Pythagorean Identity is sin^2x+cos^2x=1. Write this equation two other ways.
[tex]\sin^2 x=1-\cos^2 x \\ \\ \cos^2 x=1-\sin^2 x[/tex]
T 4 Account 1 point Which trig function should Sharlot use to find the measure of angle A ? C Pashboard 5 Courses 1 1 A B 12 Calendar 2 O sine 49 cosine Inbox 3 tangent O History 4 pythagorean theorem o
In the given triangle we have :
Base line with angle A, and the Hypotenuse of angle A
Since the ratio of Base to the hypotenuse is the Cosine trignometric ratio:
[tex]\text{Cos}\theta=\frac{Base}{Hypotenuse}[/tex]Answer : Cosine
The functions f and g are defined as follows.
f (x) = 4x - 3 g (x) = -3x^2 - 2
Find f (-4) and g (3)/
Simplify your answers as much as possible.
Answer: [tex]f(-4)=-19, g(3)=-29[/tex]
Step-by-step explanation:
[tex]f(-4)=4(-4)-3=-19\\\\g(3)=-3(3)^2 -2=-29[/tex]
You have a combination lock
with 3 secret digits. Find the 3
correct digits using the
following clues and enter your
answer below.
127 One digit is right and in its place
138 One digit is right, but in the wrong place
791
Two digits are right but both are in the
wrong place
452 All digits are wrong
8
529 One digit is right, but in the wrong place
Answer:
987
Step-by-step explanation:
You want to determine a three-digit combination based on clues about which digits are right and/or correctly placed.
Clue 1This tells you one of digits 1, 2, or 7 is correct and correctly placed.
Clue 2 tells you that digit is not 1. Clue 4 tells you that digit is not 2.
7 is correctly placed as the 3rd digit
Clue 2We already know that 1 is not the correct digit. This means 3 must be the first digit, or 8 must be the first or second digit.
Clue 3We already know that 7 is a correct digit, properly placed as the 3rd digit. Since 1 is not a correct digit, 9 must be a correct digit, properly placed as the 1st digit.
9 is correctly placed as the 1st digit
Combining this fact with Clue 2 means ...
8 is correctly placed as the 2nd digit
The combination is 987.
__
Check
Clues 4 and 5 are consistent with this combination.
Write an expression that is equivalent to 8 using each of the following numbers and symbols once in the expression.
optionsWe want to obtain an expression equivalent to 8 using these symbols and numbers.
The option that exactly matches this is,
[tex](7\text{ }\frac{.}{.}7)^2+7[/tex]That is because,
7 divided by 7 is 1.
1 squared is still one, and;
1 added to 7 is 8.
So one answer is option D.
We also have another answer.
Which is;
[tex](7+7^2)\frac{.}{.}7[/tex]That's because 7 squared is 49, and 7 + 49 is 56.
56 divided by 7 is 8.
So our answers are option C and option D
Somebody, please help me ASAP! I have 2 questions
1. Write, then simplify, an expression for the perimeter of the rectangle below.
3x | 6x +5
2. Write, then simplify, an expression for the perimeter of the figure below.
3x + 2 | x | 2x + 5 | 6x - 17
Please help!!!
Answer: for the first one, there is no picture i need a picture to solve it that's also for the second one.
Step-by-step explanation:
hope that helps
A man spends 1/4 of his monthly income on children's school fees and 3/5 and- on home affairs. What fraction of his income is left?
The fraction of the man's income left is 3/20.
What are fractions?In mathematics, a fraction is represented by a numerical value that represents a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object.Let's assume the monthly income of the man is x.
Income spend on children's school fees = [tex]\frac{1}{4} x[/tex]
Income spend on home affairs = [tex]\frac{3}{5} x[/tex]
The fraction of his income left with the man is,
Total income - Total expenditure
= [tex]x-(\frac{1}{4} x + \frac{3}{5} x)[/tex]
= [tex]x-(\frac{5x+12x}{20})[/tex]
= [tex]x - \frac{17x}{20}[/tex]
= [tex]\frac{3}{20}x[/tex]
So the man has 3/20 of his income left with him.
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Pls help with this !!!
The given graph shown in the image is a function, Option b is correct.
Given that,
A graph is shown, and we have to determine whether the graph shown is a function or not.
The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
here,
The graph shows of a curve representing an exponential function,
There is why the graph shown is a function, and also the graph is continuous and as well as differentiable.
Thus, the given graph shown in the image is a function, Option b is correct.
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Determine a bank account balance if the account starts with $300 has a annual rate of %4 what is the money in the account after 10 years
Answer:420
Step-by-step explanation: multiply 300 times 4% =12. Then multiply 12 times 10=120. Then add 300 and 120=420