The horizontal asymptote of the given function is 0
Given the function y = 19800/x
Vertical asymptote occurs at when f(x) = 0 where;
f(x) is the denominator of the given function.
From the expression given: f(x) = x
Since f(x) => 0, hence x = 0
To get the horizontal asymptote, we will look at the degree of the numerator and denominator.
If the degree of numerator is less than the denominator,
the horizontal asymptote will be zero. From the function, we can see that the degree of the numerator is zero (being a constant) and that of the denominator is 1.
Since 0<1, hence the horizontal asymptote is 0
x = 0, y = 0
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if 3+1=34
2+2=44
2+3=65
5+3=158
7+2=?
Answer:
7 + 2 = 149 here.
7 × 2 = 14, and 7 + 2 = 9.
[tex]1 1/7 - 5/6[/tex]
What is the equation in point-slope form of the line that passes through the points (7,5) and (−4,−1) ? Responses y+1=67(x+4) y plus 1 equals fraction 6 over 7 end fraction left parenthesis x plus 4 right parenthesis y+1=611(x+4) y plus 1 equals fraction 6 over 11 end fraction left parenthesis x plus 4 right parenthesis y+4=116(x+1) y plus 4 equals fraction 11 over 6 end fraction left parenthesis x plus 1 right parenthesis y−1=611(x−4)
The line that goes through the specified points has the equation into point-slope form is [tex]y+1=6/11(x+4)[/tex].
What is a straight line equation?X-axis points equal (7, -4).
Y-axis points are equal to (5, -1).
To determine the equation of the line passing through the specified points in point-slope form:
A straight line equation's direction and steepness are commonly described by its slope, which is also known as a line's gradient.
In mathematics, the following formula yields the slope of a line:
Slope(m) = [tex]y2-y1/x2-x1[/tex]
slope= [tex]\frac{-1-5}{-4-7}[/tex]
slope= 6/11
To find point slope:
[tex]y-y1=m(x-x1)\\y-(-1)=6/11(x-(-4)\\y+1=6/11(x+4)[/tex]
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Based on the information in the table, what
was the approximate value of this item in
1980?
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
Five cards are dealt from a standard deck. What is the probability that at least four of them are hearts?
Step-by-step explanation:
To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.
There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.
Now, there are two possible scenarios that would result in at least four hearts:
Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).
Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.
So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
Plugging in the values and simplifying, we get:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
= (715 * 39 + 1287) / 2,598,960
= 27,885 / 2,598,960
≈ 0.0107566
So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.
Is (9,8) a solution to this system of equations?
6x - 5y = 16
X = 9
yes
no
A 3 scoops ice-cream cone cost 4.80. A single Scoop ice-cream cost $2. Which one cost less for each scoop of ice cream ? How much less?
A single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
To compare the cost of each scoop of ice cream in a 3-scoop cone and a single scoop, we need to calculate the cost per scoop for each option.
In a 3-scoop cone, the cost of each scoop can be found by dividing the total cost by the number of scoops. Therefore, the cost of each scoop in a 3-scoop cone is:
4.80 ÷ 3 = 1.60
On the other hand, a single scoop of ice cream costs $2. Therefore, the cost of each scoop in a single scoop is:
2 ÷ 1 = 2
Comparing the two options, we can see that a single scoop of ice cream costs less per scoop than a 3-scoop cone. Specifically, a single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.
Therefore, choosing a single scoop of ice cream over a 3-scoop cone will result in a cost savings of $0.40 per scoop.
In conclusion, when comparing the cost per scoop of ice cream, a single scoop is cheaper than a scoop in a 3-scoop cone. The cost savings per scoop is $0.40.
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Is this quadrilateral a parallelogram?
I believe this quadrilateral is a parallelogram.
What is a parallelogram?There are a few ways to choose within the occasion that a quadrilateral may be a parallelogram: Opposite sides are parallel: Within the occasion that inverse sides of a quadrilateral are parallel, at that point it may be a parallelogram.
Inverse sides are said to be consistent: On the off chance that inverse sides of a quadrilateral are consistent, at that point it may be a parallelogram. From the image attached , you can see the both side red are marked equal hence it is a parallelogram
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. Keisha's employer deducts 0.2 times
her wages in payroll taxes. How much is
deducted when Keisha earns $132?
You have to find what 0.2 of 132 is
132 x 0.2 = 26.40
The answer [tex]\boxed{\bold{\$26.40}}[/tex]
PLEASE HELP!!! MIDDLE SCHOOL MATH
Based on the scatter plot below, which is a better prediction for y when x = 74?
PLEASE LOOK AT THE PICTURE!!!!!!!!!!!!!!
The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.
How to find the better prediction ?Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.
From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.
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Kelly’s bill at a restaurant came to $21.52. If she decides to leave a 18% tip, how much of a tip did she leave
Answer:
$3.87 for the 18% tip.
Find the number of different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together (i.e. maximum two Es next to each other).
The eight letters in the word DECEIVED may be arranged in 4200 distinct ways, with two Ds grouped together and three Es not all together.
The following approach may be used to determine how many different ways there are for the eight letters in the word DECEIVED to be arranged such that two Ds are together and three Es are not altogether:
Treat the two Ds as a single object, which we can call DD. Now we have 7 objects to arrange: DD, E, E, C, V, I, and E.First, we count the total number of arrangements of these 7 objects, without considering any restrictions. This is simply the number of permutations of 7 objects, which is 7! = 5040.Next, we count the number of arrangements in which the three Es are all together. We can treat the three Es as a single object, which we can call EEE. Now we have 6 objects to arrange: DD, EEE, C, V, I, and an extra E. The number of arrangements of these objects is 6!, since we can treat the EEE as a single object.However, we have overcounted the arrangements in which the two Es are together with the EEE object. To correct for this, we can treat the two Es as a single object, which we can call EE. Now we have 5 objects to arrange: DD, EEE, EE, C, V, and I. The number of arrangements of these objects is 5!, since we can treat the EEE and EE as single objects.Therefore, the number of arrangements in which the three Es are not all together is the difference between the total number of arrangements and the number of arrangements in which the three Es are all together, minus the number of arrangements in which the two Es are together with the EEE object:7! - 6! - 5! = 5040 - 720 - 120 = 4200
Therefore, there are 4200 different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together.
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Apples $1.20 per pound how much would it cost for 2.5 pounds of apples?
Answer: $3.00
Step-by-step explanation:
To figure this out, we can use the following formula:
[tex]\textsf{Cost per pound x number of pounds we want to buy}[/tex]
In this case, we want to buy 2.5 pounds of apples, so we can multiply 2.5 by $1.20 to get the total cost:
[tex] \textsf{2.5 x 1.20 = 3} [/tex]
So, 2.5 pounds of apples will cost $3.00
I REALLY NEED THIS DONE PLS ITS VERY IMPORTANT!!!
Answer: The answer is D
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer:
A
Step-by-step explanation:
Help me Help me Help me
Answer:
F
Step-by-step explanation:
First, find the answer to (180 /5 + 4 x 12 - 10) which is 74.
Next, start with solving the possible answers.
Lastly, once you have solves determine which answer is the same, which is F.
if you multiplied a number by 1/2 , the result would be Responses
Answer:
half the number you started with
Step-by-step explanation:
8 times 1/2 would be 4....6 times 1/2 would be 3!
Find the area
Round to nearest tenth
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
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a rectangular prism is 12 units high and 5 units wide an 10 units long
Answer:
To find the surface area of a rectangular prism, we can use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Given that the rectangular prism is 12 units high, 5 units wide, and 10 units long, we can substitute these values into the formula:
Surface Area = 2(10)(5) + 2(10)(12) + 2(5)(12)
Surface Area = 100 + 240 + 120
Surface Area = 460 square units
Therefore, the surface area of the rectangular prism is 460 square units
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
a. What was the book value of the equipment at December 31 the end of the fifth year?
b. Assume that the equipment was sold on April 1 of the sixth year for $105,800.
1. Journalize the entry to record depreciation for the three months until the sale date.
2. Journalize the entry to record the sale of the equipment.
The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
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Which of the points below correctly plots the point (2,7π/4)?
Points are plotted on a polar graph.
Answer: E is correct
Step-by-step explanation:
Remember that the coordinates (2,7π4) tell us the radius r=2 and the angle θ=7π4. So the point should be on the circle labeled 2 and form an angle of 7π4 with the positive x-axis. Point E is the correct point.
rationalize the denominator [tex]\frac{6}{\sqrt{x} 2\\}[/tex]
The rationalized form of the expression 6/√x is 6√x/x.
Rationalizing the denominatorFrom the question, we have the following parameters that can be used in our computation:
6/√x
To rationalize the denominator of 6/√x, we can multiply both the numerator and denominator by √x.
This gives:
6/√x * √x/√x = 6√x/x
So the rationalized form of 6/√x is 6√x/x.
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I need help with this Regression question!
A quadratic model for the data is y = -0.0076x² + 0.6915x + 14.711.
The fuel economy at 80 mph is 21.39.
How to determine the linear regression equation and correlation coefficient?In this scenario, the speed (x) would be plotted on the x-axis of the scatter plot while the fuel economy (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the speed (x) and fuel economy (y), a quadratic model for the line of best fit is given by:
y = -0.0076x² + 0.6915x + 14.711
When the speed (x) = 80 mph, the fuel economy (y) is given by;
y = -0.0076(80)² + 0.6915(80) + 14.711
y = 21.39
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643 N
5
2
T
-5-4-3-2-1₁-
-2
-3
-4
-5
y
-
2 3 4 5
X
What is the range of the function on the graph?
O all real numbers
Oall real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
The range of the function is all real numbers.
What is Function?In mathematics, a function is an expression, rule, or law that specifies a relationship between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We know,
The x-values (Input values) on the graph define the domain of the function.
and, The y-values (output values) on the graph determine the range of a function.
From the graph attached,
Here the x value start from +1 to ∞.
Thus, the range of the function is all real numbers.
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A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.
The work done in stretching a spring is given by the formula:
W = (1/2)k[tex]x^{2}[/tex]
where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.
To find the spring constant k, we can use the given information:
F = kx
where F is the force applied to the spring. Rearranging this equation, we get:
k = F/x
Substituting the given values, we get:
k = 350 N / 30 cm = 11.67 N/cm
Now, we can find the work done in stretching the spring from 10 cm to 40 cm:
W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])
where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).
Substituting the values, we get:
W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])
W = (1/2) * 11.67 N/cm * (1600 [tex]cm^{2}[/tex] - 100 [tex]cm^{2}[/tex])
W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]
W = 10,837.5 joules (J)
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A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar. At this rate, how many cups of sugar should be used if 5 cups of flour included?
According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product
According to the given information:If the recipe requires 2 cups of flour for every 2/3 cups of sugar, we can write this relationship as:
2 cups of flour : 2/3 cups of sugar
To find out how many cups of sugar should be used if 5 cups of flour are included, we can set up a proportion:
2 cups of flour / 2/3 cups of sugar = 5 cups of flour / x cups of sugar
where x is the number of cups of sugar we want to find.
To solve for x, we can cross-multiply:
2 cups of flour * x cups of sugar = 2/3 cups of sugar * 5 cups of flour
2x = (2/3) * 5
2x = 10/3
x = 5/3
Therefore, According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
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The concentration C of a drug in a patient's bloodstream t hours after injection is given by C(t) = 100t/2 t^2 + 85.
Use a calculator to approximate the time when the concentration is highest. (Round your answer to two decimal places.)
Approximately 1.18 hours the concentration is highest.
The given function is c(t)=100t/t² +85.
When the concentration is highest, the function becomes
100t/t² +85 =0
100/t +85=0
100+85t=0
85t=100
t=100/85
t=1.18 hours
Therefore, approximately 1.18 hours the concentration is highest.
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I need help w this point to right answer
The angle AOB is approximately 98 degrees.
How to find the central angle of a sector?The measure of the angle AOB of the sector can be found as follows:
AOB is the central angle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅= central angleTherefore,
12 = ∅ / 360 × 2 × 3.14 × 7
12 = 43.96∅ / 360
cross multiply
360 × 12 = 43.96∅
4320 = 43.96∅
divide both sides by 43.96
∅ = 4320 / 43.96
∅ = 98.271155596
Therefore,
∅ = 98 degrees
AOB = 98 degrees
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If the point (1,5) lies on a circle with center (0,0), determine which point in quadrant 2 that also lies on the circle.
Answer:
If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:
r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)
So the equation of the circle is:
x^2 + y^2 = 26
To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.
Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:
For point (a) (-5,1):
x^2 + y^2 = 26
(-5)^2 + 1^2 = 26
25 + 1 = 26
This point does not lie on the circle.
For point (e) (-2,3):
x^2 + y^2 = 26
(-2)^2 + 3^2 = 26
4 + 9 = 26
This point also does not lie on the circle.
Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.
Step-by-step explanation:
since the center of the circle is at the origin, that means that the circle is evenly going through all four quadrants - one quarter arc after the other.
the point (1, 5) is in the first quadrant (upper right one, positive x, positive y).
the circle arc in the second quadrant (upper left one, negative x, positive y) is the mirrored image of the arc in the first quadrant across the y-axis.
so, the point on it gets mirrored too.
that means, it's coordinates are then the same y and the x is converted to its negative value :
(-1, 5)
that is the easily identifiable point in the second quadrant that has to be on the circle.