The domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
The domain of a function f(x) is the set of all real values of x, for which real f(x) exists.
In the question, we are asked to find the domain of the function f(x) = 3/x + 2 - √(x - 3).
To find the domain of f(x), we need to check the real values of x, for which real f(x) exists.
We check each part of f(x):
For 3/x, every x gives a real value except x = 0.
For 2, every x gives a real value as it is not dependent on x.
For √(x - 3), real values exist when x - 3 ≥ 0, as negative square roots are not real.
Therefore, after assessing each term, we can say that the domain for f(x) is x - 3 ≥ 0, or x ≥ 3.
Therefore, the domain of f(x) is all real numbers > than it equal to 3, for f(x) = 3/x + 2 - √(x - 3).
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Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
Which of the following histograms is the best representation of the data?
a.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
b.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
c.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
d.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
Please select the best answer from the choices provided
A
B
C
D
A histogram with frequency on the x-axis and ages on the y-axis is shown below. Then the correct option is A.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
A large construction company wants to review the ages of its sales representatives.
A sampling of the ages of 25 sales reps are given:
50, 42, 32, 35, 41, 44, 24, 46, 31, 47, 36, 32, 30, 44, 22, 47, 31, 56, 28, 37, 49, 28, 42, 38, 45.
Then the histogram with frequency table is given as
Range Frequency
20 to 24 2
25 to 29 2
30 to 34 5
35 to 39 4
40 to 44 5
45 to 49 5
50 to 54 1
55 to 59 1
Then the correct option is A.
The histogram is given below.
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Solve the following systems of equations
y= 3x^2 + 6x + 4
Y= -3x^2 + 4
show all work and solutions
Answer:
[tex](-1;1)[/tex] and [tex](0;4)[/tex]
Step-by-step explanation:
First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.
The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.
[tex]3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0[/tex]
which tells us that either [tex]x=0[/tex] or [tex]x=-1[/tex]
Now we can replace these value of x in one of the two to finish our work: [tex]x=0\rightarrow y= 4[/tex]
[tex]x=-1 \rightarrow y= -3+4=1[/tex]
What is 10 1/2 divded by 2 1/4?
Answer:
4.66666666667
Step-by-step explanation:
Answer:
Step-by-step explanation:10 1/2÷ 2 1/4
solution:
=20/2 ÷ 8/4
= 10 ÷
=5
which line has the same slope as the line passing through (-4, -1) and (-1, 5)
A line which has the same slope as the line passing through the given points is: C. y = 2x + 8.
Given the following data:
Points on x-axis = (-4, -1).Points on y-axis = (-1, 5).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;
[tex]Slope = \frac{5\;-\;(-1)}{-1\;-\;(-4)}\\\\Slope = \frac{6}{3}[/tex]
Slope = 2.
Therefore, y = 2x + 8 is a line which has the same slope as the line passing through the given points.
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Complete Question:
Which line has the same slope as the line passing through (-4, -1) and (-1, 5)?
A. y = 3
B. 9x - 3y = 5
C. y = 2x + 8
D. the line passing through (1, 4) and (1, 7)
Solve for x in the diagram below.
Answer:
35 degrees
Step-by-step explanation:
Given all 3 angles add up 180(Sum of angles in a straight line)
[tex]2x + 30 + 40 + 40 = 180 \\ 2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ x = 35deg[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Solve for x in the diagram below.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Notice that all 3 of those angles together make a linear pair, or a [tex]\bf{180^\circ}[/tex] angle.
This is the key to solving this problem, because the sum of these angles is 180 degrees.
[tex]\bf{2x+30+40+40=180}[/tex] | arrange the like terms
[tex]\bf{2x+30=180-40-40}[/tex] | arrange the like terms
[tex]\bf{2x+30=100}[/tex] | subtract 30
[tex]\bf{2x=70}[/tex] | divide by 2
[tex]\bf{x=35}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=m\angle x=35^\circ}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
A. √113
B. √65
C. √50
D. √17
Answer:
Step-by-step explanation:
Givens
x2 = 4
x1 = 3
y2 = 2
y1 = 6
Formula
distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2) )
Solution
distance = sqrt( (4 - 3)^2 + (2 - 6)^2 )
distance = sqrt( 1^2 + 4^2)
distance = sqrt (17)
Answer
D
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
Answer is: ∅ D. √17
Formula:
Distance (d) Square roots (sqrt) ( x 2 - x 1 )² + ( y2 - y1 )²
d = sqrt ( 4 - 3 )² + ( 2 - 6 )²
d = sqrt ( 1² + 4² )
d = sqrt ( 17 ) 1^2 + 4^2 = 17
CarryOnLearning <(￣︶￣)>
The linear function has the domain (-2, -1, 0, 1, 2). Find the range or output of. h(x) = 2x + 3
If the linear function has the domain (-2, -1, 0, 1, 2). Then the range of the function h(x) = 2x + 3 will be (-1, 1, 3, 5, 7).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given as
h(x) = 2x + 3
The linear function has the domain (-2, -1, 0, 1, 2).
For x = -2
h(-2) = 2 (-2) + 3
h(-2) = -1
For x = -1
h(-1) = 2 (-1) + 3
h(-1) = 1
For x = 0
h(0) = 2 (0) + 3
h(0) = 3
For x = 1
h(1) = 2 (1) + 3
h(1) = 5
For x = 2
h(2) = 2 (2) + 3
h(2) = 7
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Question Write an equation of the line that passes through (1, −2) and is parallel to the line y=7x+7. An equation of the parallel line is y= .
Answer:
Step-by-step explanation:
7 = (y+2)/(x-1)
Parallel lines have equal slopes.
You can "massage" the form into any form you need.
factor: 128 + 2d^3
cubes lol
The factorization if the given expression 128 + 2d³ is 2(64 + d³).
Factorization128 + 2d³
There are two parameters in the expression;
128 2d³The common factors between 128 and 2d³ is 2
So,
128 + 2d³
= 2(64 + d³)
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the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?
The margin of error is ±2%
What is Margin error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
Let x be margin of error and y be the percentages of the population.
So,
y-x =33%
y +x = 37%
Solving above equations
2y= 70
y= 35%
and x= 2%
Hence, the margin of error is ±2%.
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Pls help! Geometry
What is the area of the new rectangle?
Answer:
Step-by-step explanation:
Since the ladybug is [tex]3.3cm[/tex] far from each edge of the rectangle, it follows that the length of the new rectangle is [tex]3.3cm+9.5cm + 3.3cm = 16.1cm[/tex] and the width is [tex]3.3cm+7.5cm + 3.3cm = 14.1cm[/tex].
Recall a formula for the area of a rectangle: [tex]A = l \cdot w[/tex], where [tex]l[/tex] is a length and [tex]w[/tex] is a width of the rectangle.
Substitute [tex]l=16.1cm[/tex] and [tex]w=14.1cm[/tex] into the formula:
[tex]A=16.1cm\cdot 14.1cm[/tex]
Multiply the numbers:
[tex]A=[/tex] [tex]227.01cm^{2}[/tex]
Therefore, the required area is equal to [tex]227.01cm^{2}[/tex].
2 factored expressions equivalent to -20x-30
The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression
What are Expressions ?Expressions are the mathematical statement consisting of variables , constants and mathematical operators .
The expression given is
-20x -30
-2(10x +15)
-20x -30
-5x ( x+6)
Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.
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1. Given
G(n) = 4n-5
H(n) = 2n + 1
Find G(H(8))
Answer:
first H(8)= 2×8+1=16+1=17
and G(17)= 4×17-5=68-5=63
find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x2-y2 and 2xy
The expression for hypotenuse is √4x^4 + y^4.
What is Pythagoras theorem?A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
Given:
one leg = 2x²- y²
another leg = 2xy
H² = (2x²- y²)² + (2xy)²
H² = 4x^4 + y^4 - 4x²y² + 4x²y²
H²= 4x^4 + y^4
H= √4x^4 + y^4
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came across this question on my home work can some one please show how to sketch it correctly?
Answer:
Step-by-step explanation:
2. Graph the inverse of the function, then determine if the inverse is a function.
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of
the inverse of F(x). (2 points)
Part II: Is the inverse a function? Explain your answer. (3 points)
The inverse of the function f(x)= x^2 is a function.
The graph of the inverseThe equation of the function is
f(x)= x^2
Rewrite as:
y = x^2
Swap x and y
x = y^2
Make y the subject
[tex]y = \sqrt x[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt x[/tex]
So, the inverse of f(x)= x^2 is [tex]f^{-1}(x) = \sqrt x[/tex]
See attachment for the graph
Is the inverse a function?The inverse is a function.
This is so because it passes the vertical line test
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Most of Mauna Kea, a volcano on Hawaii, lies below sea level. If this volcano begins at 5998 meters below sea level and then rises 10,203 meters, find the height of the volcano above sea level.
Final answer:
Height of volcano above sea level is 4205m.
Step-by-step explanation:
Step 1
Height of volcano below sea level: 5998m
Step 2
Total height of volcano below and above sea level:
10203m
Step 3
Subtract height of volcano below sea level from total height of volcano to get height of volcano above sea level:
10203 - 5998
Step 4
Subtract the terms:
10203 - 5998 = 4205
The mean on a Advanced Algebra test was 86 with a standard deviation of 4.5. If the test scores are normal distributed, find the interval about the mean that contains 68% of the scores. Use the empirical rule.
Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:
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If it cost $6 to fill a gas tank in 1970, how much would it have cost to fill the same tank in 2010?
Step-by-step explanation:
Well since it cost 6$ and the price was 0.36 you can calculate how many gallons you needed to fill up your tank which is calculated by dividing the price to fill the gas tank by the price per gallon
6/0.36 = 16.667 gallons
Now multiply the amount of gallons you need to fill your gas tank by the price in 2010
16.667 * 2.84 = 47.36
You could also just look at the price as a percentage relative to 1970 prices and see that the price increased by 788.9% and the find what 788.9% is of 6$. Which can be done by dividing 788.9 by 100 to convert it into decimal form which gives you 7.889 and then multiply that by the original price of 6$ to fill your gallon to get 47.33 which is slightly different although this is likely due to rounding.
For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8. What is the fourth term?
Answer:
a₄=8n+1= -39.
Step-by-step explanation:
1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then
2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.
3) if n=-5, then the 4th term is:
[tex]a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;[/tex]
or a₄=-39.
Graph the set x-6≤ x < -2} on the number line.
Then, write the set using interval notation.
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
Interval Notation: [ -6, -2 ]
What is the interval notation form of the set of inequality?An inequality has an infinitely number of solution, the solution set is easily described using interval notation.
Given the set of inequality { x| -6 ≤ x < - 2}
This can easily be written in the form of interval notation as;
[ -6, -2 ]
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
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Find the equation of the line through the points (3,-4) and (0,2) answer in slope intercept form
Answer:
y= -2x+2.
Step-by-step explanation:
1) according to the condition interception is '2' (point (0;2));
2) slope is: (2+4)/(0-3)= -2;
3) finally the required equation is: y=-2x+2.
P.S. the suggested option is not the only one.
I need help ASAP! I need this within an hour from now!
Answer:
Definition of circle
Explanation:
1st - Given2nd - Definition of radius3rd - Distance formula4th - Definition of circle5th - Distance formula6th - Definition of circleAll the points that lies on the circle must be same distance from the center.
This is given by the definition of a circle.
AdditionalRadius is the length from the center to the points lying on the circle.
Distance formula: [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Diameter of circle is from one end point to another end point lying on circle.
Two people are packing equal numbers of small boxes into large boxes.
One person has 3 large boxes that are full of smaller boxes and 24 small
boxes that are not yet packed. The other person has 5 large boxes that are
full of smaller boxes and 10 small boxes that are not yet packed. Each large
box holds the same number of small boxes. How many small boxes can
each large box hold? What is the total number of small boxes each person
will pack? How many large boxes will each person need in order to pack all of his or her small boxes?
Please answer as quickly as possible and as detailed as possible!!! Thanks!!!!!!
Answer:
29 small boxes
Step-by-step explanation:
What is an equation of the line that passes
through the point (5,
-2) and is parallel
to the line 2x
- 5y = 35?
Which transformation is not an isometry
From the shapes given, the third transformation is not an isometry.
What is an isometry?An isometry is a mathematical function used to describe the process of moving a geometric object without a changing its size or shape from one point to another.
Thus, from the shapes given, the third transformation is not an isometry.
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A garden table and a bench cost 735 combined. The garden table costs 35 more than the bench. What is the cost of the bench?
Answer:
350
Step-by-step explanation:
Let,
x = bench
x + 35 = garden table
EQUATION:
(x) + (x + 35) = 735
2x = 735 - 35
2x = 700
x = 350
SUBSTITUTE:
bench costs 350 and garden table costs 385
Hello!
Based on the info we have we can form 2 equations :
(Keep in mind x is the cost of the garden table and y is that of the bench)
x + y = 735x = y + 35Now substitute x in the first equation.
⇒ y + 35 + y = 735
⇒ 2y = 700
⇒ y = 350
∴ The cost of the bench is [tex]\fbox {350}[/tex]
Maria is going to purchase celery and onions for a new black bean soup recipe. The recipe calls for 1.5 times as many pounds of onions as celery. If she has $8.10, what is the most pounds of celery she can buy if celery costs $1.80 per pound and onions cost $1.50 per pound?
The maximum pounds of celery she can buy is 3.25 pounds.
What are the linear equations that represent the question?1.5c = o equation 1
1.50o + 1.80c = 8.10 equation 2
Where:
o = pounds of onions
c = pounds of celery
How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1
1.50(1.50) + 1.80c = 8.10
2.25 + 1.80c = 8.10
1.80 = 8.10 - 2.25
1.80c = 5.85
c = 5.85 / 1.80
c = 3.25 pounds
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In an olimpiad , each of the 25 questions is worth 3 marks. So every correct answer is awarded 3 marks. But for every incorrect answer 1 mark is subtracted. lesley scored 55 marks out of a possible 75. how many problems did leley get correct.
An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.
The total number of questions can be written as,
x + y = 25
Solving the equation for y,
y = 25 - x
The total marks can be written as,
3x - 1y = 55
Substitute the value of y,
3x - 25 + x = 55
4x = 80
x = 20
Hence, the number of questions that Lesley answered correctly is 20.
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