The hole of f(x) is x = -3.
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x + 3) / (x - 4)(x + 3)
Now,
We see that there is a common factor both in the numerator and the denominator.
This means,
There is a hole in f(x).
i.e
x + 3 = 0
x = -3 is the hole.
Thus,
x = -3 is the hole of f(x).
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Answer: x = -3
Step-by-step explanation:
correct on edge :)
Carmony Computer Consultants charges a $255 fee plus $85 per hour for its work. Holliday Computer Work charges a flat rate of $115 per hour. For how many hours of work is it cheaper to hire Carmony?
Answer: Let's call the number of hours worked h.
The cost of hiring Carmony is $255 + $85h.
The cost of hiring Holliday is $115h.
We want to find the number of hours h such that $255 + $85h is less than $115h.
We can write this as:
$255 + $85h < $115h
Subtracting $115h from both sides:
$255 < $115h - $85h
Combining like terms:
$255 < $30h
Dividing both sides by $30:
8.5 < h
So, it is cheaper to hire Carmony for more than 8.5 hours. For 8.5 hours or less, it is cheaper to hire Holliday.
Step-by-step explanation:
An expression to determine the growth rate of a cell is written as 3(1. 25)/5. What would be an approximate form of this expression for all values of t?
3(0. 25)
O 3(1. 05)'
O 3. 05
O 3. 14
Option A is the correct option
So, the approximate form of the expression for all values of t is 0.75.
The expression 3(1.25)/5 can be simplified to
3/5 * 1.25
= 0.75.
=3(0.25)
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided. Algebra Expression Example: 3x + 9, 5x + 10
To simplify simply is to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
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please help ill give brain list after 2 people have answered
Step-by-step explanation:
If the slope is -1 then every time it moves 1 down it moves 1 right
It is going down because the slope is negative.
It touches the y-axis at -1.
(Download pdf to see graph)
Hope this helps! Please mark me as brainliest!
Answer:
Step-by-step explanation:
y=-1x+1/6
very urgent 50 points 1) In your own words, write a definition for sales tax.
2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes?
- Explain in detail, the steps you would take to solve this sales tax question. 3 paragraphs please
He has to pay $1.05 in taxes for the meal.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Sales tax
A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.
Now it costs $15.00 and the tax is 7%
Treating the taxable amount as $15 and now to find 7% equivalent we get
Now 7%×15=$1.05
Thus he has to pay $1.05 in taxes
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Which fee pays for services such as a credit score check, an attorney, and a notary?
Typically, these services are covered by closing costs associated with a real estate transaction. Closing costs are fees charged by various parties involved in the home-buying process and can include the cost of a credit score check, attorney fees, and notary fees.
A credit score check is often required by a lender as part of the mortgage approval process, and the fee for this service can be included in the closing costs. The fee for an attorney can also be included in closing costs, especially if the attorney is hired to review and explain the closing documents. An attorney can also represent the buyer or the seller during the closing process and advise them of their rights and obligations.
A notary is typically required to witness the signing of legal documents, such as the mortgage or deed, and a notary fee can also be included in the closing costs. The exact amount of each of these fees can vary, and it's common for buyers to receive an estimate of their total closing costs from their lender prior to closing.
It's important to note that closing costs are separate from the down payment and can add several thousands of dollars to the overall cost of buying a home, so it's a good idea for buyers to carefully review their closing cost estimate and understand what each fee covers.
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What is the mean and standard deviation of the random variable Y (the number of females out of 40 who are color blind)? Answers may be rounded.
mean= 40, standard deviation=.01
mean =.01, standard deviation = 40
mean =0.4, standard deviation = .629
mean = 0.4, standard deviation = .396
We cannot find the mean and standard deviation since the probability distribution table is not given.
Mean = μ = 0.40
Standard deviation = σ = 0.015
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Female colorblindness proportion = 1%
Male colorblindness proportion = 8%
Female sample size = 40
Male sample size = 20
Hence, We get;
Let us check if the condition np ≥ 10 is satisfied or not,
⇒ np
⇒ 40 × 0.01
⇒ 0.4 < 10
Since, the condition np ≥ 10 is not satisfied the binomial random variable cannot be well approximated by a normal random variable. A larger sample size would be required to satisfy the condition np ≥ 10.
Hence, The mean is,
μ = np
μ = 40*0.01
μ = 0.40
And, The standard deviation is,
σ = √p(1 - p)/n
σ = √0.01(1 - 0.01)/40
σ = 0.015
Thus, We get;
Mean = μ = 0.40
Standard deviation = σ = 0.015
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The sum of two integers is -45. If one of them is 90 find the other.
Answer: -135
Step-by-step explanation:
90 + 45 = 135
90 - 135 = -45
I hope this helps
What is the relationship of each linear equation below to y=[tex]\frac{1}{2}x + 1?
(Select ONE option for each equation)
Relations of the line with the given equation of line are:
No relationParallelPerpendicularParallelWhat is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given an equation of line y = 1/5x +1
Comparing with the slope-intercept general formula of line
the slope of the given line = 1/5
And the slope of the line that is perpendicular to this will be = -1/slope
the slope of the line that is perpendicular to this will be = -5
For A) y = 5x +1
Slope = 5
this line has no relation with the equation of the line given
For B) y = 1/5x -2
Slope = 1/5
thus, this line is parallel to the given line.
For c)
10x + 2y = 10
In slope intercept
y = -5x +5
Slope = -5
Thus this line is perpendicular to the line given
For D)
x - 5y = 20
In slope intercept
y = 1/5x -4
Slope = 1/5
thus, this line is parallel to the given line.
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the table shows three unique, discrete functions. which statements can be used to compare the characteristics of the functions? select three option
The statements can be used to compare the characteristics of the functions is:
f(x) has the greatest maximumAll three functions share the same domainAll three functions share the same y-interceptIf the values in a set of data are distinct and separate, the set is said to be discrete (unconnected values).
"All the values" that are input into a function are referred to as the domain of a function. A function's domain is the set of all potential inputs. Consider this box to represent the f(x) = 2x function. When the input values are x = 1,2,3,4,..., the domain is merely the collection of natural numbers, and the values that are returned are referred to as the range.
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Complete question:
The table shows three unique, discrete functions. Which statements can be used to compare the characteristics of the functions? Select three options.
has the greatest maximum. f(x)
has the greatest x-intercept. h(x)
has the smallest minimum value. g(x)
All three functions share the same domain.
All three functions share the same y-intercept.
You roll a 6-sided die.
What is P(divisor of 45)?
Write your answer as a percentage.
Answer:
50%
Step-by-step explanation:
You want the probability of rolling a divisor of 45 on a 6-sided die.
ProbabilityThe probability is the ratio of outcomes of interest to the total number of possible outcomes, assuming they are equally likely.
The numbers on a die that are divisors of 45 are 1, 3, 5, which are 3 of the 6 possible outcomes.
P(divisor of 45) = 3/6 = 1/2 = 0.50 = 50%
The probability of rolling a divisor of 45 is 50%.
__
Additional comment
This problem statement asks for the answer as a percentage. It can also be written as a fraction (1/2) or a decimal (0.50).
The divisors of 45 are 1, 3, 5, 9, 15, 45.
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naruto practices his harmonica 1/4 hour, spends 2/3 hour working on homework and takes another 1/2 hour to do chores everyday. how much longer does naruto spend practicing his harmonica and doing his chores than working on homework?
(1/4 + 1/2) - 2/3
Help ASAP ! Please!!!
In part (a), the y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3. In part (b), the y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0. In part (c), the y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.
What do you mean by transformation?A transformation of a function is a process that changes the position or shape of the function on a coordinate plane. There are several types of transformations, including:
Translation: A translation moves the graph of a function horizontally or vertically, but does not change its shape. This can be accomplished by adding or subtracting a constant to the input or output of a function.
Scaling: A scaling changes the size of a function's graph, but not its shape. This can be accomplished by multiplying the input or output of a function by a constant.
Reflection: A reflection flips the graph of a function over a line. This can be accomplished by negating either the input or the output of a function.
Stretching or Compression: A stretching or compression changes the height or width of a function's graph, but not its shape. This can be accomplished by multiplying the output of a function by a constant greater than 1 for stretching, or by a constant between 0 and 1 for compression.
These transformations can be used to shift, scale, reflect or distort the graph of a function, allowing for greater understanding and analysis of its properties.
a. f(x) = [tex]3(2)^{x}[/tex] + 3 is an exponential function that has been vertically shifted up by 3 units. The y-intercept is (0,3), which means that when x = 0, the value of f(x) is 3.
b. f(x) = [tex]6(4)^{x}[/tex] * 0.5 is an exponential function that has been vertically stretched by a factor of 0.5 and horizontally stretched by a factor of 6. The y-intercept is (0,0), which means that when x = 0, the value of f(x) is 0.
c. f(x) = [tex]4(0.5)^{x}[/tex] - 6 is an exponential function that has been vertically shifted down by 6 units. The y-intercept is (0,-6), which means that when x = 0, the value of f(x) is -6.
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the sum of 4.5 and one-third a number is equal to at most 38.9. what are all the possible values of the number? how would you write an inequality that could be used to solve this problem?(1 point)
The possible values of the number x are any real number that is less than or equal to 103.2. This can be written as: x <= 103.2
Let's call the number "x".
The sum of 4.5 and one-third of x can be written as:
4.5 + (1/3)x
The inequality to represent the statement "the sum is equal to at most 38.9" would be:
4.5 + (1/3)x <= 38.9
To solve for x, we can isolate x by subtracting 4.5 from both sides:
(1/3)x <= 34.4
And finally, multiplying both sides by 3:
x <= 103.2
So, all the possible values of the number x are any real number that is less than or equal to 103.2. This can be written as:
x <= 103.2
or
-∞ < x <= 103.2
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Emily gets paid to recruit people to join an email list at work. If she signs up 5 friends and they all sign up 5 more friends, the function y = 5^x represents the number of new people on the email list after so many cycles. Select all the key features that apply to y = 5^x
A) The domain is all real numbers. The relevant domain is all nonnegative integers.
B) The domain and relevant domain are both {x >= 0}.
C) The range is all real numbers.
D) the y-intercept is 1.
E) The y-intercept is 5.
F) As x increases, y increases; and, as x decreases, y approaches 0.
Solve :) please this is hard.
Refer to the attached image.
In the coordinate plane A CDE is translated 3 units right and 2 units down.
Answer: (3, 1)
Step-by-step explanation:
point D is at (0,3) if it is translated 3 units to the right and 2 units down that means the x value will be added by 3 and the y value will be subtracted by 2
0+3 = 3; 3-2 = 1
D' is at (3,1)
If the distance between the points (a, 3) and (8, 3) is 7 units, find the value of a?
Answer:
a =
Step-by-step explanation:
Line is straight across so you just
8 - a =
a =
Challenge Dona paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. She uses one bottle of paint to paint 155 cm2. How many bottles of paint does she need in order to paint 70 ornaments? Use 3.14 for π. The surface area of one ornament is about ? cm2.
Number of bottles of paint needed to paint 70 ornaments is 112.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object
Each ornament is made up of two identical cones.
A cone has a circular base and a lateral surface
Surface area of base = πr², where r is the radius
Lateral surface area of the cone = πrl, where r is radius and l is slant height.
Total surface area of a cone = πr² + πrl = πr (r + l)
There are 2 identical cones for an ornament.
Surface area of an ornament = 2πr (r + l)
= 2π × 3.3 (3.3 + 8.6)
= 246.6156 cm²
Surface area of 70 ornaments = 70 × 246.6156 cm²
= 17263.092 cm²
Bottle of paint for 155 cm² = 1
Bottle of paint for 17263.092 cm² = 17263.092 / 155
= 111.374
≈ 112
Hence Dona needs approximately 112 bottles of paint.
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In the diagram shown, BC, EF, DK, and AK intersect at point K. Determine the values
of x and y
Answer:
x=65
y=25
Step by step explanation:
90+90+25+x+x+y= 360
2x+y=155 (1)
90+25+x= 180
x= 65 (2)
sub (2) into (1):
2(65)+y=155
y= 25
What is the unit rate for meters per second if a car travels 209 meters in 11 seconds?
Answer:
19 meters
Step-by-step explanation:
209/11 = 19 meters per second
Answer: 19
209 divided by 11 is 19, which means that car moves 19 meters per second.
Hope this helped <3 !!
complete the equivalent fractions
please help
brainly i have 19 mins left
100 points
Answer:
4. 175
5. 2
6. 72
7. 48
8. 45
9. 5
10. 18
11. 3
12. 10
13. 30
14. 12
15. 1
16. 2
17. 2
18. 8
Al’s family ate dinner at a local restaurant. The cost of the food and drinks (before tax and tip) was $128.95. If the sales tax is 7.5% and Al tips the waiter 18%, what will be the total bill for the dinner? Be sure to round your answer to the nearest cent.
The total cost of the dinner is given by the equation A = $ 161.19
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of the dinner be represented as A
Now , the equation will be
The cost of the dinner without tax and tip = $ 128.95
The sales tax percentage = 7.5 %
So , the sales tax amount = ( 7.5 % ) x cost of the dinner without tax and tip
Substituting the values in the equation , we get
The sales tax amount = ( 7.5/100 ) x 128.95
The sales tax amount = $ 9.0265
Now , the percentage of tip = 18 %
So , the tip amount = ( 18 % ) x 128.95
The tip amount = $ 23.211
And , the total cost of the dinner A = cost of the dinner without tax and tip + sales tax amount + tip amount
On simplifying the equation , we get
The total cost of the dinner A = $ 128.95 + $ 9.0265 + $ 23.211
The total cost of the dinner A = $ 161.1875
Hence , the total amount of dinner is $ 161.19
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The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty?
a) The probability of selecting a jury of all students is 792 / 245, 157.
b) The probability of selecting a jury of all faculty us 330/ 245157
c) The probability of selecting a jury of of students and faculty is 0.0000043
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
Given:
Out of 12 students and 11 faculty, a jury of six individuals can be select C(23, 7).
A) The probability of selecting a jury of all students
= C( 12, 7) / C(23, 7).
= 792 / 245, 157
B) The probability of selecting a jury of all faculty
= C( 11, 7) / C(23, 7).
= 330/ 245, 157
C) The probability of selecting a jury of students and faculty
= 792 / 245, 157 x 330/ 245, 157
= 0.0000043
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50 POINTS. The function f(x)=x+4−−−−−√3 is transformed to f(x)=x−1−−−−−√3+3.
What transformations are performed from function f to function g?
Choose each correct answer.
Responses
Function f is translated to the right 3 units.
Function , f , is translated to the right 3 units.
Function f is translated down 1 unit.
Function , f, is translated down 1 unit.
Function f is translated up 3 units.
Function , f , is translated up 3 units.
Function f is translated to the right 5 units.
Function f(x) is translated to the right 5 units.
What is dilation?resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
The function f(x)=∛x+4 is transformed to f(x)=∛(x−1) +3.
Putting the values in the graph we see that mid points of both the graphs are:
[tex]\left(-4,\ 0\right)[/tex] original function
[tex]\left(1,\ 3\right)[/tex] transformed function
x₁ ⇒ x₂ and y₁ ⇒ y₂ is the transformation
here,
-4 ⇒ 1
= +5 (positive symbol means to the right)
and
0 ⇒ 3
= +3 (positive symbol means to upward direction)
Thus, Function F translated to up 3 units and translated right 5 units
Hence, Function f is translated to the right 5 units.
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A building cast a
140 ft shadow
while a 18 ft pole
cast a 4 ft shadow.
How tall is the
building?
Answer:
630 ft
Step-by-step explanation:
[tex]\frac{x}{140}=\frac{18}{4}\\ \\4x=2520\\\\x=630[/tex]
Hence, the height of the building is 630 feet.
what is the most precise name for quadrilateral abcd with vertices a(-2, -1), b(2, 2), c(1, -2), and d(-3, -3)?
Note that the most precise name for quadrilateral ABCD with vertices a(-2, -1), b(2, 2), c(1, -2), and d(-3, -3) is an Irregular Quadilateral. See the image attached.
What is an Irregular Quadilateral?An irregular quadrilateral is a polygon with four sides, but all four (opposite) sides and angles are incongruent.
Rectangles, parallelograms, kites, and isosceles trapezoids are examples of irregular quadrilaterals. There are several formulas for calculating the area of these quadrilaterals. Set formulae may be used to compute the area of rectangles, parallelograms, kites, and isosceles trapezoids.
There is just one angle attribute for an irregular quadrilateral: the sum of the angles equals 360° 360° 360°. Add all internal angles that are known.
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suppose x and y are randomly chosen real numbers such that 0
The probability of X and Y being randomly chosen real numbers such that 0 is 1.
Let X and Y be two random variables such that X is uniformly distributed on the interval [0,1] and Y is uniformly distributed on the interval [0,2]. The probability density function (pdf) of X and Y is given by:
[tex]f_X(x) = 1 and f_Y(y) = 1[/tex]
The probability of X and Y being in the interval [0,1] and [0,2] respectively is given by the integral of their pdfs over the given intervals:
[tex]P(0 < X < 1) = ∫_0^1 1dx = 1\\P(0 < Y < 2) = ∫_0^2 1/2dy = 1[/tex]
Therefore, the probability of X and Y being randomly chosen real numbers such that 0 is 1.
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complete question:
What is the probability of x and y being randomly chosen real numbers such that 0?
Find the probability of being dealt six clubs and three cards with one card of each other remaining suit in 9-card poker
0.00426 is the probability of being dealt six clubs and three cards with one card .
Describe probability using an example?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
We will get 9 cards out of 52 cards
Probability of getting 6 clubs is
total we have 13 clubs
no of chances = 13C6
chances of getting 3 cards from 3 other suits
= 39C3
Now, the total probability
= 13C6 * 39C3 / 52C9
= 1716 * 9139 / 3679075400
= 0.00426
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any probability statement involving a normal random variable can be converted to an equivalent statement involving a standard normal random variable through the process of
Any probability statement involving a normal random variable can be converted to an equivalent statement involving a standard normal random variable through the process of standardization.
Standardization is converting a normal random variable, X, to a standard normal random variable, Z, by subtracting its mean, μ, and dividing by its standard deviation, σ. The formula for standardization is given:
Z = (X - μ) / σ
Once a normal random variable has been standardized, it is easier to find probabilities because the standard normal distribution is well-known and widely used in statistical analysis. For example, if X is normally distributed with mean μ and standard deviation σ, the probability of X being between two values a and b can be found using the cumulative distribution function (CDF) of the standard normal distribution.
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suppose the session table is set up as follows. is this design correct? if not, in which normal form would you correct it?
As per normalization, the session table uses the third normal form
Normalization is an important step in designing a database, as it helps to eliminate issues such as data integrity and redundancy. This is achieved through a series of steps, known as normalization.
The Sports Physical Therapy Center database has a table named Session that keeps track of all therapy appointments at the center. The table contains various pieces of information such as the session number, date, patient number, length of session, therapist ID, therapist's last and first name, and the therapy code.
The Session table is used to check if there are any design issues and to apply the necessary normalization steps to fix these issues and ensure data is stored in an organized manner.
Thorough this we have identified that the 3rd normal for is used here.
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