Answers
The value of the function f/g is (x - 1) / (x + 8)
Let's start by writing out the functions we are given:
f(x) = 4 / (x + 8)
g(x) = x / (x - 1)
To find f/g, we need to divide f(x) by g(x). We can do this by multiplying f(x) by the reciprocal of g(x), which is (x - 1) / x. Multiplying f(x) by this reciprocal gives us:
f(x) * (x - 1) / x = 4 / (x + 8) * (x - 1) / x
To simplify this expression, we can first find a common denominator for the two fractions on the right-hand side:
4 / (x + 8) * (x - 1) / x = 4(x - 1) / x(x + 8)
Now we can simplify this expression by canceling out any common factors in the numerator and denominator. In this case, we can cancel out a factor of 4 and a factor of (x - 1):
4(x - 1) / x(x + 8) = (x - 1) / (x + 8)
Therefore, the quotient of f(x) and g(x), or f/g, is:
f/g = (x - 1) / (x + 8)
We can interpret this expression as a new function, h(x), where h(x) = f(x) / g(x) = (x - 1) / (x + 8). This new function takes a value of x and returns the ratio of f(x) to g(x) at that value.
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Related Questions
Geometry
All I need is the letter that is correct. Don’t mind the ones I already circled
Answers
The translation of ABC by (Rx + Ry) is UVW and the rigid composition of XYZ to X'Y'Z' cannot be determined
Translation image of the triangleThe rule (Rx + Ry) represents a translation image of a shape, where R is a vector representing the direction and distance of the translation, and (x, y) are the coordinates of the original shape.
To apply this rule to a shape, we simply add the vector R to each point of the shape, which moves the shape in the direction and distance specified by R.
Using the above as a guide, we have the following the translation of ABC by (Rx + Ry) to be UVW
The rigid composition of XYZ to X'Y'Z'The triangle X'Y'Z' is not given in the figure
So, the rigid composition of XYZ to X'Y'Z' cannot be determined
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Find each angle measure.
Answers
Answer:
The answer for <M is 28°
Step-by-step Explanation:
<P=180-48
<P=132°
base angles in an isosceles are equal
<M+<N+<P=180
3y+1+2y+2+132=180
3y+2y+3+132=180
5y+135=180
5y=180-135
5y=45
divide both sides by 5
5y/5=45/5
y=9
<M=3(9)+1=27+1=28°
A printer is printing photos. For every 6 photos, the printer takes 3 minutes.
Complete the table below showing the number of photos and the time it takes to print them.
Answers
We can start by finding the rate at which the printer is printing photos. Since it takes 3 minutes to print 6 photos, we can calculate the rate as 6 photos / 3 minutes = 2 photos/minute. This means that for every minute that passes, the printer prints 2 photos.
Now that we know the rate, we can use it to find out how long it will take to print 16 photos. Since the rate is 2 photos/minute, we can set up an equation to solve for y (time) when x (photos) is 16: 2 = 16/y. Solving for y, we get y = 16/2 = 8.
Therefore, when x (photos) is 16, y (time) is 8 minutes. This means that it will take the printer 8 minutes to print 16 photos.
If y (time) is 5 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 5 minutes = 10 photos.
Therefore, if y (time) is 5 minutes, the printer will print 10 photos.
If y (time) is 7 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 7 minutes = 14 photos.
Therefore, if y (time) is 7 minutes, the printer will print 14 photos.
A bag contains 19 blue, 28 purple, 21
red, and 29 orange balls. You pick
one ball at random. Find the
probability that it is not blue.
P(not blue) =
Simplify your answer completely.
Answers
Answer:
78/97
Step-by-step explanation:
First, add up all the balls to find the total amount of balls in the bag (19+28+21+29). Then determine how many balls are not blue (you could either take the total and subtract 19 or add up all the colors that are not blue). There are 97 balls total and 78 of them are not blue which is shown as 78/97. 78/97 cannot simplify further.
In how many distinct ways can the digits in the number 2,563,183,083 be arranged?
(If there are any zero digits then assume they can be placed in any position)
Answers
However, we need to account for the fact that three of the digits are 3s and two of the digits are 8s. To do this, we need to divide out the number of arrangements of those duplicates.
There are 3! = 6 ways to arrange the three 3s among themselves, and 2! = 2 ways to arrange the two 8s among themselves. So, we divide the total number of arrangements by these permutations of the duplicates:
10! / (3! * 2!) = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 604,800
Therefore, there are 604,800 distinct ways to arrange the digits in the number 2,563,183,083, assuming that any zero digits can be placed in any position.
Someone help i really need help with this
Answers
Step-by-step explanation:
we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.
please help me
What degree of rotation about the origin will cause the triangle below to map
onto itself?
Answers
I NEED HELP ASAP I have to tern this packet in tomorrow and i do not know how to solve scales in geometry
Answers
Answer:
The anser is letter C)
Step-by-step explanation:
because it multiplies x3
0,5×3=1,5
1,5×10=15
10×3=30
Answer:
1cm=30m
use compass and ruler to contruct bisector of the angle
Answers
Bisector of the angle is the line that divides the angle into two angles with the same measure. In the image attached, the bisector of the angle is represented by the green line.
Here, we have,
The next steps show you how to construct the bisector of the angle from a ruler and a compass.
Draw an arc using the vertex of the angle (O) as the center;
Mark the points A and B;
Draw an arc using the point (A) as the center;
Draw an arc, with the same radius, using the point (B) as the center. This arc should intersect the arc that you draw in the previous step.
Draw a line connecting the point C to the vertex O.
Finally, you have the bisector of the angle that is represented by the green line.
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What is the length of the side labeled x cm?
10.8
13.7
9.9
20.8
Answers
Answer:
B
Step-by-step explanation:
the answer is B because I know it
Draw and describe the plane section that results from the following cut: a cylinder cut parallel to the base.
Answers
When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.
Write the following Babylonian numeral as a Hindu-Arabic numeral.
<|| <<||||
Answers
Answer:
The Babylonian numeral <|| <<|||| represents the number 51 in the Babylonian numeral system.
To convert it to the Hindu-Arabic numeral system, we first need to determine the place values of the symbols. The symbol <|| represents 50 and <<|||| represents 1.
So, we can write the number as:
50 + 1 = 51
Therefore, the Hindu-Arabic numeral equivalent of the Babylonian numeral <|| <<|||| is 51.
With Bonds, banks pay you back with
O free banking
O a fixed amount
O interest
O stocks
Answers
Select all that apply. By making the financially irresponsible decision of maxing out your credit card limit, you might...
A) not have money for an emergency situation.
B) get a very low interest rate when you want to buy a house.
C) not be able to buy the things you need.
D) have enough saved up for retirement.
Answers
By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.
As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.
When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.
Now, maxing out credit card leads to negative results.
So, either not have money for an emergency situation or not be able to buy the things you need.
But we can still spend after maxing out the limit.
Thus, not have money for an emergency situation is correct option.
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what is the volume of this triangular prism?
Answers
The volume of the triangular prism is 36 in³.
What is a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
To calculate the volume of the triangular prism, we use the formula below
Formula:
V = bhH/2.................... Equation 1Where:
b = Base of the triangleh = Height of the triangleH = Height of the prismFrom the question,
Given:
b = 3 inh = 4 inH = 6 inSubstitute these values into equation 1
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Of the 22 students in a classroom, 10 are transfer students, 7 are nursing students, 4 are AAS students and 1 student is undecided. If 5 students are chosen randomly, with replacement, find the probability that at least one student is a transfer student.
Answers
The probability that a randomly chosen student is not a transfer student is 12/22, since there are 12 students who are not transfer students out of a total of 22 students. Therefore, the probability that none of the 5 students chosen are transfer students is:
(12/22)^5 = 0.068
To find the probability that at least one student is a transfer student, we can subtract this from 1:
1 - 0.068 = 0.932
Therefore, the probability that at least one student is a transfer student is 0.932.
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answers
Answer: X = 25
Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25
Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.
A culture started with 3,000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after 10 hours.
Round your answer to the nearest whole number.
P = Aekt
Answers
Answer:
Step-by-step explanation:
To predict the number of bacteria after 10 hours using the formula P = Aekt, where P is the final population, A is the initial population, k is the growth rate, and t is the time elapsed, we need to first find the value of k.
dw
We know that after 4 hours, the population grew from 3,000 bacteria to 3,600 bacteria. So we can set up an equation:
3,600 = 3,000e^(4k)
Dividing both sides by 3,000 gives:
1.2 = e^(4k)
Taking the natural logarithm of both sides gives:
ln(1.2) = 4k
Solving for k, we get:
k = ln(1.2)/4
k ≈ 0.051
Now that we have the value of k, we can use the formula to predict the number of bacteria after 10 hours:
P = 3,000e^(0.051*10)
P ≈ 5,426
Therefore, we predict that after 10 hours, there will be approximately 5,426 bacteria present in the culture.
find the statement that is incorrect. Then, correct and rewrite the statement in the space provided. Show any necessary work.
Answers
The incorrect statement is b. When an aeroplane takes off, the work done by its weight is negative.
The inaccurate assertion is:
b) When a plane removes, the work done by its weight is positive.
The right assertion is:
b) When a plane removes, the work done by its weight is negative.
Clarification:
At the point when a plane removes, the work done by the heaviness of the plane is negative in light of the fact that the weight acts the other way to the dislodging of the plane. As indicated by the work-energy hypothesis, work done by the heaviness of the plane will diminish its motor energy, and that implies that the work done is negative. Hence, articulation (b) is inaccurate.
a) Work and energy have various units.
This assertion is right. Work has units of Joules (J) and energy additionally has units of Joules (J), however they are not exactly the same thing.
c) The possible energy of spring increments when it is broadened and diminishes when it is packed.
This assertion is right. The potential energy put away in a spring is straightforwardly corresponding to its expansion or pressure. While a spring is broadened, its potential energy increments, and when it is packed, its potential energy diminishes.
d) On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.
This assertion is right. On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.
The work-energy hypothesis expresses that the net work done on a framework is equivalent to the adjustment of its motor energy, and in the event that the net work is negative, the dynamic energy diminishes, and that implies that the energy of the framework diminishes.
e) When a body is falling unreservedly from a level, its dynamic energy stays consistent.
This assertion is erroneous. At the point when a body is falling unreservedly from a level, its potential energy is changed over into dynamic energy as it falls. Hence, its motor energy increments as it falls, and its potential energy diminishes.
f) The unit of force is watt.
This assertion is right. The unit of force is watt (W), which is characterized as the pace of taking care of business or the pace of move of energy.
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The complete question is:
Identify the wrong statement among the following. Rewrite them by making necessary corrections.
a) Work and energy have different units.
b) When an aeroplane takes off, the work done by its weight is positive.
c) The potential energy of spring increases when it is extended and decreases when it is compressed.
d) If the work done by external forces on a system is negative then the energy of the system decreases.
e) When a body is falling freely from a height, its kinetic energy remains constant.
f) The unit of power is watt.
I need help pleaseee
Answers
The matrix row operation on the matrix A gives us: 0x + 10y - 25z = 4
How to solve matrix row operations?There are 3 primary basic operations that are utilized on the rows of a matrix when we utilize the matrix to solve a particular system of linear equations . The aim is usually to get the left region of the matrix to resemble the identity matrix .
The three primary operations are:
Switching Rows
Multiplying a Row by a Number
Adding Rows
Now, from the given matrix, the equations are:
x - y + 5z = -1
x - y - 4z = 5
5x + y + 0z = -1
We are told to add -5 times row 1 to row 3 and this gives:
-5x + 5x + 5y + 5y - 25z + 0z = 5 - 1
0x + 10y - 25z = 4
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cos(0) = 2 ar
sin(8) = ?
- 2
**
2
√√2
2
√√2
DONE
,and
3
<
< 0 < 21, evaluate sin(0) and tan(0)
tan(8)=L
DONE
Answers
Using trigonometric identities when cosθ = √2/2 and 3π/2 < θ < 2π
sinθ = -√2/2 tanθ = - 1What are trigonometric identities?Trigonometric identities are mathematical equations that contain tigonometric ratios
Since cosθ = √2/2 and 3π/2 < θ < 2π, we desire to find sinθ and tanθ. We proceed as follows
a. To find sinθ, using the trigonometric identity
sin²θ = 1 - cos²θ
⇒ sinθ = ±√(1 - cos²θ)
So, substituting the value of cosθ into the equation, we have that
sinθ = ±√(1 - cos²θ)
sinθ = ±√(1 - (√2/2)²)
= ±√(1 - 2/4)
= ±√[(4 - 2)/4]
= ±√[2/4]
= ±√2/2
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, sinθ = -√2/2
b. To find tannθ, using the trigonometric identity
tan²θ = sec²θ - 1
⇒ tanθ = ±√(sec²θ - 1)
= ±√(1/cos²θ - 1)
So, substituting the value of cosθ into the equation, we have that
tanθ = ±√(1/cos²θ - 1)
tannθ = ±√(1/(√2/2)² - 1)
= ±√(1/2/4 - 1)
= ±√(4/2 - 1)
= ±√[2 - 1]
= ±√1
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, tanθ = -1
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Just by looking at the equation x+6+2x=2x+6+4x+6+2x=2x+6+4 , find the value of x .
Answers
Step-by-step explanation:
How do you have two equal to signs omg?
Anyway,
x+6+2x=2x+6+4x+6+2x=2x+6+4
3x+6=8x+12=2x+10
0=5x+6=2x+10
0=3x-4=0
3x-4=0
3x=4
x = 4/3 = 1 ⅓
12 A quality control inspector at a plant has found the probability of randomly selecting a defective
battery from a batch of batteries being produced is 0.02. The probability of rain that day has been
projected to be 0.75. If these two events are independent, what is the probability that on that particular
day, it rains, and the inspector chooses a defective battery from the batch being produced?
(1) 0.77
(3) 0.015
(2) 0.5
(4) 0.95
Answers
Answer:
The answer is (3) 0.015.
Step-by-step explanation:
This is because to find the probability of finding both independent events happening at the same time, we must multiply them.
The independent events are:
- Randomly selecting a defective battery: 0.02
- Raining tomorrow: 0.75
0.02 x 0.75 = 0.015
Therefore, the answer is (3) 0.015.
A local store was offering a discount of 25% on original parice on older model laptops. Gina bought an older model laptop for $963 that includes a 7% tax on the discounted price
Answers
Answer:
Step-by-step explanation:To solve this problem, we need to work backwards from the final price that Gina paid and determine the discounted price before tax was added.
Let x be the original price of the laptop. After a 25% discount, the discounted price is:
Discounted price = x - 0.25x = 0.75x
Next, we add 7% tax to the discounted price:
Final price = (0.75x) + 0.07(0.75x) = 0.8025x
We know that the final price that Gina paid was $963, so we can set up an equation:
0.8025x = 963
Solving for x, we get:
x = 1200
Therefore, the original price of the laptop was $1200, and the discounted price before tax was:
Discounted price = 0.75x = 0.75(1200) = $900
To check, we can add the 7% tax to the discounted price:
Final price = $900 + 0.07($900) = $963
This matches the price that Gina paid, so we can be confident in our answer.
The terminal point of 0 is (0,1). What is tan 0?
Answers
Help me please How would you informally prove that you are taking courses online?
A) You could show a registrar’s receipt with the current date.
B) You could show your course notes with the current date.
C) You could repeat all the material you learned.
D) You could ask for an enrollment verification notice from the school.
Answers
Answer: b is correct
Step-by-step explanation:
What is the area of this figure?
8 m
6 m
5 m
2 m
13 m
8 m
Answers
Answer:
It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?
Step-by-step explanation:
Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Answers
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Select all that is TRUE
Question 11 options:
Adding a constant to all the data points does NOT change the correlation
Interchanging X and Y changes the correlation
Correlation has no units
Outliers do NOT effect the correlation
If r is close to 1 then it is a strong positive correlation
Correlation could be positive or negative
Correlation and y-intercept have the same sign
Answers
The True statements about the correlation are: (1), (2), (3), (5), (6) and (7)
1) We know that the adding, subtracting, multiplying or dividing a constant to all of the data points in one or both variables does not change the correlation coefficient.
So, the first statement is True.
2) We know that the correlation measures the strength of the pattern around a line of regression as well as the direction of the line. So, interchanging the variables would not change the correlation. The correlation between x and y is the same as the correlation between y and x.
Thus the second statement is True.
3) We know that the correlation coefficient does not have any units.
It is just a number between -1 to +1.
Thus the third statement is True.
4) We know that the outlier may weaken the correlation. It makes the data more scattered. So the correlation coefficient r gets closer to 0.
Thus the fourth statement is False.
5) We know that if the correlation coefficient r is close to 1 then it is a strong positive correlation and if r is close to -1 then it is a strong negative correlation.
Thus the fifth statement is True.
6) We know that the corrletaion coefficient values can range from -1 to 1.
Thus the sixth statement is True.
7) We know that the y-intercept is nothing but the point at which the regression line intercepts the y-axis. The y-intercept of the regression line and the correlation coefficient have the same sign.
Thus the seventh statement is True.
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If the ratio of a circle's circumference to the circle's area is 2/9, then find the circles area.
Answers
The area of the circle is 81π. Option A.
What is area of a circle?The area of a given circle is the amount of space that the circle will cover when considered in a 2 dimensional plane. It can be determined by;
area of a circle = πr^2
where r is the radius.
The circumference of a circle is the curved boundary of a circle. It can be determined by;
circumference of a circle = 2πr
where r is its radius.
From the given information in the question, we have a circle's circumference to the circle's area;
circumference/ area = 2/ 9
But,
circumference/ area = 2πr/ πr^2
= 2/ r
Then;
2/ r = 2/ 9
2r = 2*9
= 19
r = 18/ 2
r = 9
Thus,
area of the circle = πr^2
= π(9)^2
= 81π
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